The biomedical engineering handbook [Fourth edition] 9781439863114, 1439863113

Table of contents :
Content: [v. 1]. Biomedical engineering fundamentals --
[v. 2]. Medical Devices and Human Engineering --
[v. 3]. Biomedical Signals, Imaging, and Informatics --
[v. 4]. Molecular, Cellular, and Tissue Engineering.

Citation preview

THE BIOMEDICAL ENGINEERING HANDBOOK FOURTH EDITION

Biomedical Engineering Fundamentals

Edited by

Joseph D. Bronzino Donald R. Peterson

THE BIOMEDICAL ENGINEERING HANDBOOK FOURTH EDITION

Biomedical Engineering Fundamentals

THE BIOMEDICAL ENGINEERING HANDBOOK FOURTH EDITION

Biomedical Engineering Fundamentals Edited by

Joseph D. Bronzino

Founder and President Biomedical Engineering Alliance and Consortium (BEACON) Hartford, Connecticut, U.S.A.

Donald R. Peterson

Professor of Engineering Dean of the College of Science, Technology, Engineering, Mathematics, and Nursing Texas A&M University – Texarkana Texarkana, Texas, U.S.A.

MATLAB® is a trademark of The MathWorks, Inc. and is used with permission. The MathWorks does not warrant the accuracy of the text or exercises in this book. This book’s use or discussion of MATLAB® software or related products does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular use of the MATLAB® software.

CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2015 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Version Date: 20141009 International Standard Book Number-13: 978-1-4398-2519-8 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright.com (http:// www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com

Contents Preface���������������������������������������������������������������������������������������������������������������������� ix Editors���������������������������������������������������������������������������������������������������������������������� xv Contributors����������������������������������������������������������������������������������������������������������xvii MATLAB Statement���������������������������������������������������������������������������������������������� xxv

Section I  Physiologic Systems Herbert F. Voigt

1 An Outline of Cardiovascular Structure and Function..................................... 1-1 Daniel J. Schneck

2 Kidney Structure and Physiology ............................................................................. 2-1 Joel M. Henderson and Mostafa Belghasem

3 Nervous System.............................................................................................................. 3-1 Evangelia Micheli-Tzanakou

4 Vision System................................................................................................................. 4-1 Aaron P. Batista and George D. Stetten

5 Auditory System............................................................................................................ 5-1 Ben M. Clopton and Herbert F. Voigt

6 Gastrointestinal System............................................................................................... 6-1 Berj L. Bardakjian

7 Respiratory System........................................................................................................ 7-1 Arthur T. Johnson, Christopher G. Lausted, and Joseph D. Bronzino

Section II Biomechanics Donald R. Peterson

8 Mechanics of Hard Tissue........................................................................................... 8-1 J. Lawrence Katz, Anil Misra, Orestes Marangos, Qiang Ye, and Paulette Spencer

9 Musculoskeletal Soft-Tissue Mechanics.................................................................. 9-1 Richard L. Lieber, Samuel R. Ward, and Thomas J. Burkholder

v

vi

Contents

10

Joint-Articulating Surface Motion ......................................................................... 10-1

11

Joint Lubrication .......................................................................................................... 11-1

12

Analysis of Gait ............................................................................................................ 12-1

13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

Kenton R. Kaufman and Kai-Nan An Michael J. Furey

Roy B. Davis III, Sylvia Õunpuu, and Peter A. DeLuca

Mechanics of Head/Neck .......................................................................................... 13-1 Albert I. King and David C. Viano

Biomechanics of Chest and Abdomen Impact .................................................... 14-1 David C. Viano and Albert I. King

Cardiac Biomechanics ................................................................................................ 15-1 Andrew D. McCulloch and Roy C. P. Kerckhoffs

Heart Valve Dynamics ............................................................................................... 16-1 Choon Hwai Yap, Erin Spinner, Muralidhar Padala, and Ajit P. Yoganathan

Arterial Macrocirculatory Hemodynamics .......................................................... 17-1 Baruch B. Lieber

Mechanics of Blood Vessels ...................................................................................... 18-1 Thomas R. Canfield and Philip B. Dobrin

The Venous System ..................................................................................................... 19-1 Artin A. Shoukas and Carl F. Rothe

The Microcirculation Physiome .............................................................................. 20-1 Aleksander S. Popel and Roland N. Pittman

Mechanics and Deformability of Hematocytes ................................................... 21-1 Richard E. Waugh and Robert M. Hochmuth

Mechanics of Tissue/Lymphatic Transport .......................................................... 22-1 Geert W. Schmid-Schönbein and Alan R. Hargens

Modeling in Cellular Biomechanics ....................................................................... 23-1 Alexander A. Spector and Roger Tran-Son-Tay

Cochlear Mechanics ................................................................................................... 24-1 Charles R. Steele and Sunil Puria

Inner Ear Hair Cell Bundle Mechanics ................................................................. 25-1 Jong-Hoon Nam and Wally Grant

Exercise Physiology ..................................................................................................... 26-1 Cathryn R. Dooly and Arthur T. Johnson

Factors Affecting Mechanical Work in Humans ................................................ 27-1 Ben F. Hurley and Arthur T. Johnson

Section III Biomaterials Joyce Y. Wong

28

Metallic Biomaterials ................................................................................................. 28-1 Joon B. Park and Young Kon Kim

Contents

vii

29

Ceramic Biomaterials ................................................................................................. 29-1

30

Polymeric Biomaterials .............................................................................................. 30-1

31

Composite Biomaterials ............................................................................................. 31-1

32 33

W. G. Billotte

Hai Bang Lee, Gilson Khang, and Jin Ho Lee Roderic S. Lakes

Biodegradable Polymeric Biomaterials: An Updated Overview ..................... 32-1 C. C. Chu

Biologic Biomaterials: Tissue-Derived Biomaterials (Collagen) .................... 33-1 Shu-Tung Li

34

Biologic Biomaterials: Silk ........................................................................................ 34-1

35

Biofunctional Hydrogels ........................................................................................... 35-1

36

Soft Tissue Replacements .......................................................................................... 36-1

37

Biman Mandal and David L. Kaplan

Melissa K. McHale and Jennifer L. West

K. B. Chandran, K. J. L. Burg, and S. W. Shalaby

Hard Tissue Replacements ........................................................................................ 37-1 Sang-Hyun Park, Adolfo Llinás, and Vijay K. Goel

Section IV  Bioelectric Phenomena Roger C. Barr

38

Basic Electrophysiology ............................................................................................. 38-1

39

Volume Conductor Theory ....................................................................................... 39-1

40 41 42

Roger C. Barr

Robert Plonsey

Electrical Conductivity of Tissues .......................................................................... 40-1 Bradley J. Roth

Cardiac Microimpedances ........................................................................................ 41-1 Andrew E. Pollard

Membrane Models ....................................................................................................... 42-1 Anthony Varghese

43 Computational Methods and Software for Bioelectric Field Problems .............................................................................................................. 43-1 44

Christopher R. Johnson

The Potential Fields of Triangular Boundary Elements ................................... 44-1 A. van Oosterom

45

Principles of Electrocardiography .......................................................................... 45-1

46

Electrodiagnostic Studies .......................................................................................... 46-1

Edward J. Berbari

Sanjeev D. Nandedkar

viii

Contents

47

Principles of Electroencephalography ................................................................... 47-1

48

Biomagnetism ............................................................................................................... 48-1

49

Electrical Stimulation of Excitable Tissue ............................................................ 49-1

Joseph D. Bronzino Jaakko Malmivuo

Dominique M. Durand

Section V Neuroengineering Daniel J. DiLorenzo

50

History and Overview of Neural Engineering .................................................... 50-1

51

Theory and Physiology of Electrical Stimulation of the Central Nervous System ............................................................................................................ 51-1

Daniel J. DiLorenzo and Robert E. Gross

Warren M. Grill

52

Transcutaneous FES for Ambulation: The Parastep System ........................... 52-1

53

Comparing Electrodes for Use as Cortical Control Signals: Tines, Wires, or Cones on Wires—Which Is Best? ......................................................... 53-1

Daniel Graupe

Philip R. Kennedy

54

Development of a Multifunctional 22-Channel Functional Electrical Stimulator for Paraplegia .......................................................................................... 54-1 Ross Davis, T. Johnston, B. Smith, R. Betz, T. Houdayer, and A. Barriskill

55

An Implantable Bionic Network of Injectable Neural Prosthetic Devices: The Future Platform for Functional Electrical Stimulation and Sensing to Restore Movement and Sensation .............................................. 55-1 J. Schulman, P. Mobley, J. Wolfe, Ross Davis, and I. Arcos

56

Visual Prostheses ........................................................................................................ 56-1

57

Interfering with the Genesis and Propagation of Epileptic Seizures by Neuromodulation .................................................................................................. 57-1

Robert J. Greenberg

Ana Luisa Velasco, Francisco Velasco, Marcos Velasco, Bernardo Boleaga, Mauricio Kuri, Fiacro Jiménez, and José María Núñez

58

Transcranial Magnetic Stimulation of Deep Brain Regions ........................... 58-1 Yiftach Roth and Abraham Zangen

Preface During the past eight years since the publication of the third edition—a three-volume set—of The Biomedical Engineering Handbook, the field of biomedical engineering has continued to evolve and expand. As a result, the fourth edition has been significantly modified to reflect state-of-the-field knowledge and applications in this important discipline and has been enlarged to a four-volume set: • • • •

Volume I: Biomedical Engineering Fundamentals Volume II: Medical Devices and Human Engineering Volume III: Biomedical Signals, Imaging, and Informatics Volume IV: Molecular, Cellular, and Tissue Engineering

More specifically, this fourth edition has been considerably updated and contains completely new ­sections, including • Stem Cell Engineering • Drug Design, Delivery Systems, and Devices • Personalized Medicine as well as a number of substantially updated sections, including • • • • • •

Tissue Engineering (which has been completely restructured) Transport Phenomena and Biomimetic Systems Artificial Organs Medical Imaging Infrared Imaging Medical Informatics

In addition, Volume IV contains a chapter on ethics because of its ever-increasing role in the biomedical engineering arts. Nearly all the sections that have appeared in the first three editions have been significantly revised. Therefore, this fourth edition presents an excellent summary of the status of knowledge and activities of biomedical engineers in the first decades of the twenty-first century. As such, it can serve as an excellent reference for individuals interested not only in a review of fundamental physiology but also in quickly being brought up to speed in certain areas of biomedical engineering research. It can serve as an excellent textbook for students in areas where traditional textbooks have not yet been developed and as an excellent review of the major areas of activity in each biomedical engineering sub-discipline, such as biomechanics, biomaterials, bioinstrumentation, medical imaging, and so on. Finally, it can serve as the “bible” for practicing biomedical engineering professionals by covering such topics as historical perspective of medical technology, the role of professional societies, the ethical issues associated with medical technology, and the FDA process.

ix

x

Preface

Biomedical engineering is now an important and vital interdisciplinary field. Biomedical engineers are involved in virtually all aspects of developing new medical technology. They are involved in the design, development, and utilization of materials, devices (such as pacemakers, lithotripsy, etc.), and techniques (such as signal processing, artificial intelligence, etc.) for clinical research and use, and they serve as members of the healthcare delivery team (clinical engineering, medical informatics, rehabilitation engineering, etc.) seeking new solutions for the difficult healthcare problems confronting our society. To meet the needs of this diverse body of biomedical engineers, this handbook provides a central core of knowledge in those fields encompassed by the discipline. However, before presenting this detailed information, it is important to provide a sense of the evolution of the modern healthcare system and identify the diverse activities biomedical engineers perform to assist in the diagnosis and treatment of patients.

Evolution of the Modern Healthcare System Before 1900, medicine had little to offer average citizens, since its resources consisted mainly of physicians, their education, and their “little black bag.” In general, physicians seemed to be in short supply, but the shortage had rather different causes than the current crisis in the availability of healthcare professionals. Although the costs of obtaining medical training were relatively low, the demand for doctors’ services also was very small, since many of the services provided by physicians also could be obtained from experienced amateurs in the community. The home was typically the site for treatment and recuperation, and relatives and neighbors constituted an able and willing nursing staff. Babies were delivered by midwives, and those illnesses not cured by home remedies were left to run their natural, albeit frequently fatal, course. The contrast with contemporary healthcare practices in which specialized physicians and nurses located within hospitals provide critical diagnostic and treatment services is dramatic. The changes that have occurred within medical science originated in the rapid developments that took place in the applied sciences (i.e., chemistry, physics, engineering, microbiology, physiology, pharmacology, etc.) at the turn of the twentieth century. This process of development was characterized by intense interdisciplinary cross-fertilization, which provided an environment in which medical research was able to take giant strides in developing techniques for the diagnosis and treatment of diseases. For example, in 1903, Willem Einthoven, a Dutch physiologist, devised the first electrocardiograph to measure the electrical activity of the heart. In applying discoveries in the physical sciences to the analysis of the biological process, he initiated a new age in both cardiovascular medicine and electrical measurement techniques. New discoveries in medical sciences followed one another like intermediates in a chain reaction. However, the most significant innovation for clinical medicine was the development of x-rays. These “new kinds of rays,” as W. K. Roentgen described them in 1895, opened the “inner man” to medical inspection. Initially, x-rays were used to diagnose bone fractures and dislocations, and in the process, x-ray machines became commonplace in most urban hospitals. Separate departments of radiology were established, and their influence spread to other departments throughout the hospital. By the 1930s, x-ray visualization of practically all organ systems of the body had been made possible through the use of barium salts and a wide variety of radiopaque materials. X-ray technology gave physicians a powerful tool that, for the first time, permitted accurate diagnosis of a wide variety of diseases and injuries. Moreover, since x-ray machines were too cumbersome and expensive for local doctors and clinics, they had to be placed in healthcare centers or hospitals. Once there, x-ray technology essentially triggered the transformation of the hospital from a passive receptacle for the sick to an active curative institution for all members of society. For economic reasons, the centralization of healthcare services became essential because of many other important technological innovations appearing on the medical scene. However, hospitals remained institutions to dread, and it was not until the introduction of sulfanilamide in the mid-1930s and penicillin in the early 1940s that the main danger of hospitalization, that is, cross-infection among

Preface

xi

patients, was significantly reduced. With these new drugs in their arsenals, surgeons were able to perform their operations without prohibitive morbidity and mortality due to infection. Furthermore, even though the different blood groups and their incompatibility were discovered in 1900 and sodium citrate was used in 1913 to prevent clotting, full development of blood banks was not practical until the 1930s, when technology provided adequate refrigeration. Until that time, “fresh” donors were bled and the blood transfused while it was still warm. Once these surgical suites were established, the employment of specifically designed pieces of medical technology assisted in further advancing the development of complex surgical procedures. For example, the Drinker respirator was introduced in 1927 and the first heart–lung bypass in 1939. By the 1940s, medical procedures heavily dependent on medical technology, such as cardiac catheterization and angio­ graphy (the use of a cannula threaded through an arm vein and into the heart with the injection of radiopaque dye) for the x-ray visualization of congenital and acquired heart disease (mainly valve disorders due to rheumatic fever) became possible, and a new era of cardiac and vascular surgery was established. In the decades following World War II, technological advances were spurred on by efforts to develop superior weapon systems and to establish habitats in space and on the ocean floor. As a by-product of these efforts, the development of medical devices accelerated and the medical profession benefited greatly from this rapid surge of technological finds. Consider the following examples:



1. Advances in solid-state electronics made it possible to map the subtle behavior of the fundamental unit of the central nervous system—the neuron—as well as to monitor the various physiological parameters, such as the electrocardiogram, of patients in intensive care units. 2. New prosthetic devices became a goal of engineers involved in providing the disabled with tools to improve their quality of life. 3. Nuclear medicine—an outgrowth of the atomic age—emerged as a powerful and effective approach in detecting and treating specific physiological abnormalities. 4. Diagnostic ultrasound based on sonar technology became so widely accepted that ultrasonic studies are now part of the routine diagnostic workup in many medical specialties. 5. “Spare parts” surgery also became commonplace. Technologists were encouraged to provide cardiac assist devices, such as artificial heart valves and artificial blood vessels, and the artificial heart program was launched to develop a replacement for a defective or diseased human heart. 6. Advances in materials have made the development of disposable medical devices, such as needles and thermometers, a reality. 7. Advancements in molecular engineering have allowed for the discovery of countless pharmacological agents and to the design of their delivery, including implantable delivery systems. 8. Computers similar to those developed to control the flight plans of the Apollo capsule were used to store, process, and cross-check medical records, to monitor patient status in intensive care units, and to provide sophisticated statistical diagnoses of potential diseases correlated with specific sets of patient symptoms. 9. Development of the first computer-based medical instrument, the computerized axial tomography scanner, revolutionized clinical approaches to noninvasive diagnostic imaging procedures, which now include magnetic resonance imaging and positron emission tomography as well. 10. A wide variety of new cardiovascular technologies including implantable defibrillators and chemically treated stents were developed. 11. Neuronal pacing systems were used to detect and prevent epileptic seizures. 12. Artificial organs and tissue have been created. 13. The completion of the genome project has stimulated the search for new biological markers and personalized medicine. 14. The further understanding of cellular and biomolecular processes has led to the engineering of stem cells into therapeutically valuable lineages and to the regeneration of organs and tissue structures.

xii

Preface

15. Developments in nanotechnology have yielded nanomaterials for use in tissue engineering and facilitated the creation and study of nanoparticles and molecular machine systems that will assist in the detection and treatment of disease and injury. The impact of these discoveries and many others has been profound. The healthcare system of today consists of technologically sophisticated clinical staff operating primarily in modern hospitals designed to accommodate the new medical technology. This evolutionary process continues, with advances in the physical sciences such as materials and nanotechnology and in the life sciences such as molecular biology, genomics, stem cell biology, and artificial and regenerated tissue and organs. These advances have altered and will continue to alter the very nature of the healthcare delivery system itself.

Biomedical Engineering: A Definition Bioengineering is usually defined as a basic research-oriented activity closely related to biotechnology and genetic engineering, that is, the modification of animal or plant cells or parts of cells to improve plants or animals or to develop new microorganisms for beneficial ends. In the food industry, for example, this has meant the improvement of strains of yeast for fermentation. In agriculture, bioengineers may be concerned with the improvement of crop yields by treatment of plants with organisms to reduce frost damage. It is clear that future bioengineers will have a tremendous impact on the quality of human life. The potential of this specialty is difficult to imagine. Consider the following activities of bioengineers: • • • • • • • •

Development of improved species of plants and animals for food production Invention of new medical diagnostic tests for diseases Production of synthetic vaccines from clone cells Bioenvironmental engineering to protect human, animal, and plant life from toxicants and pollutants Study of protein–surface interactions Modeling of the growth kinetics of yeast and hybridoma cells Research in immobilized enzyme technology Development of therapeutic proteins and monoclonal antibodies

Biomedical engineers, on the other hand, apply electrical, mechanical, chemical, optical, and other engineering principles to understand, modify, or control biological (i.e., human and animal) systems as well as design and manufacture products that can monitor physiological functions and assist in the diagnosis and treatment of patients. When biomedical engineers work in a hospital or clinic, they are more aptly called clinical engineers.

Activities of Biomedical Engineers The breadth of activity of biomedical engineers is now significant. The field has moved from being concerned primarily with the development of medical instruments in the 1950s and 1960s to include a more wide-ranging set of activities. As illustrated below, the field of biomedical engineering now includes many new career areas (see Figure P.1), each of which is presented in this handbook. These areas include • Application of engineering system analysis (physiological modeling, simulation, and control) to biological problems • Detection, measurement, and monitoring of physiological signals (i.e., biosensors and biomedical instrumentation) • Diagnostic interpretation via signal-processing techniques of bioelectric data • Therapeutic and rehabilitation procedures and devices (rehabilitation engineering) • Devices for replacement or augmentation of bodily functions (artificial organs)

xiii

Preface

Biomaterials Molecular, cell, and tissue engineering

Biomechanics

Human performance engineering Rehabilitation engineering

Drug design and delivery systems

Bioelectric and physiologic systems modeling

Regenerative medicine and cell therapies

Biosignals and biosensors Biomedical instrumentation and devices

Personalized medicine, genomics, and proteomics Biomimetics

Neural engineering

Micro and nanotechnology and bioMEMs

Medical and infrared imaging

Prosthetic devices and artificial organs

Medical robotics Medical and biological analysis

Telemedicine and E-health Clinical engineering

Biotechnology Medical and bioinformatics

FIGURE P.1  The world of biomedical engineering.

• Computer analysis of patient-related data and clinical decision making (i.e., medical informatics and artificial intelligence) • Medical imaging, that is, the graphic display of anatomic detail or physiological function • The creation of new biological products (e.g., biotechnology and tissue engineering) • The development of new materials to be used within the body (biomaterials) Typical pursuits of biomedical engineers, therefore, include • • • • • • • • • • • • • • • • •

Research in new materials for implanted artificial organs Development of new diagnostic instruments for blood analysis Computer modeling of the function of the human heart Writing software for analysis of medical research data Analysis of medical device hazards for safety and efficacy Development of new diagnostic imaging systems Design of telemetry systems for patient monitoring Design of biomedical sensors for measurement of human physiological systems variables Development of expert systems for diagnosis of disease Design of closed-loop control systems for drug administration Modeling of the physiological systems of the human body Design of instrumentation for sports medicine Development of new dental materials Design of communication aids for the handicapped Study of pulmonary fluid dynamics Study of the biomechanics of the human body Development of material to be used as a replacement for human skin

Biomedical engineering, then, is an interdisciplinary branch of engineering that ranges from theoretical, nonexperimental undertakings to state-of-the-art applications. It can encompass research, development, implementation, and operation. Accordingly, like medical practice itself, it is unlikely that any single person can acquire expertise that encompasses the entire field. Yet, because of the

xiv

Preface

interdisciplinary nature of this activity, there is considerable interplay and overlapping of interest and effort between them. For example, biomedical engineers engaged in the development of biosensors may interact with those interested in prosthetic devices to develop a means to detect and use the same bioelectric signal to power a prosthetic device. Those engaged in automating clinical chemistry laboratories may collaborate with those developing expert systems to assist clinicians in making decisions based on specific laboratory data. The possibilities are endless. Perhaps, a greater potential benefit occurring from the use of biomedical engineering is identification of the problems and needs of our present healthcare system that can be solved using existing engineering technology and systems methodology. Consequently, the field of biomedical engineering offers hope in the continuing battle to provide high-quality care at a reasonable cost. If properly directed toward solving problems related to preventive medical approaches, ambulatory care services, and the like, biomedical engineers can provide the tools and techniques to make our healthcare system more effective and efficient and, in the process, improve the quality of life for all. Joseph D. Bronzino Donald R. Peterson Editors-in-Chief

Editors Joseph D. Bronzino is currently the president of the Biomedical Engineering Alliance and Consortium (BEACON; www.beaconalliance.org), which is a nonprofit organization dedicated to the promotion of collaborative research, translation, and partnership among academic, medical, and industry people in the field of biomedical engineering to develop new medical technologies and devices. To accomplish this goal, Dr. Bronzino and BEACON facilitate collaborative research, industrial partnering, and the development of emerging companies. Dr. Bronzino earned a BSEE from Worcester Polytechnic Institute, Worcester, Massachusetts, in 1959, an MSEE from the Naval Postgraduate School, Monterey, California, in 1961, and a PhD in electrical engineering from Worcester Polytechnic Institute in 1968. He was recently the Vernon Roosa Professor of Applied Science and endowed chair at Trinity College, Hartford, Connecticut. Dr. Bronzino is the author of over 200 journal articles and 15 books, including Technology for Patient Care (C.V. Mosby, 1977), Computer Applications for Patient Care (Addison-Wesley, 1982), Biomedical Engineering: Basic Concepts and Instrumentation (PWS Publishing Co., 1986), Expert Systems: Basic Concepts (Research Foundation of State University of New York, 1989), Medical Technology and Society: An Interdisciplinary Perspective (MIT Press and McGraw-Hill, 1990), Management of Medical Technology (Butterworth/Heinemann, 1992), The Biomedical Engineering Handbook (CRC Press, 1st Edition, 1995; 2nd Edition, 2000; 3rd Edition, 2006), Introduction to Biomedical Engineering (Academic Press, 1st Edition, 1999; 2nd Edition, 2005; 3rd Edition, 2011), Biomechanics: Principles and Applications (CRC Press, 2002), Biomaterials: Principles and Applications (CRC Press, 2002), Tissue Engineering (CRC Press, 2002), and Biomedical Imaging (CRC Press, 2002). Dr. Bronzino is a fellow of IEEE and the American Institute of Medical and Biological Engineering (AIMBE), an honorary member of the Italian Society of Experimental Biology, past chairman of the Biomedical Engineering Division of the American Society for Engineering Education (ASEE), a charter member of the Connecticut Academy of Science and Engineering (CASE), a charter member of the American College of Clinical Engineering (ACCE), a member of the Association for the Advancement of Medical Instrumentation (AAMI), past president of the IEEE-Engineering in Medicine and Biology Society (EMBS), past chairman of the IEEE Health Care Engineering Policy Committee (HCEPC), and past chairman of the IEEE Technical Policy Council in Washington, DC. He is a member of Eta Kappa Nu, Sigma Xi, and Tau Beta Pi. He is also a recipient of the IEEE Millennium Medal for “his contributions to biomedical engineering research and education” and the Goddard Award from WPI for Outstanding Professional Achievement in 2005. He is presently editor-in-chief of the Academic Press/ Elsevier BME Book Series. Donald R. Peterson is a professor of engineering and the dean of the College of Science, Technology, Engineering, Mathematics, and Nursing at Texas A&M University in Texarkana, Texas, and holds a joint appointment in the Department of Biomedical Engineering (BME) at Texas A&M University in College Station, Texas. He was recently an associate professor of medicine and the director of the xv

xvi

Editors

Biodynamics Laboratory in the School of Medicine at the University of Connecticut (UConn) and served as chair of the BME Program in the School of Engineering at UConn as well as the director of the BME Graduate and Undergraduate Programs. Dr. Peterson earned a BS in aerospace engineering and a BS in biomechanical engineering from Worcester Polytechnic Institute, in Worcester, Massachusetts, in 1992, an MS in mechanical engineering from the UConn, in Storrs, Connecticut, in 1995, and a PhD in biomedical engineering from UConn in 1999. He has 17 years of experience in BME education and has offered graduate-level and undergraduate-level courses in the areas of biomechanics, biodynamics, biofluid mechanics, BME communication, BME senior design, and ergonomics, and has taught subjects such as gross anatomy, occupational biomechanics, and occupational exposure and response in the School of Medicine. Dr. Peterson was also recently the co-executive director of the Biomedical Engineering Alliance and Consortium (BEACON), which is a nonprofit organization dedicated to the promotion of collaborative research, translation, and partnership among academic, medical, and industry people in the field of biomedical engineering to develop new medical technologies and devices. Dr. Peterson has over 21 years of experience in devices and systems and in engineering and medical research, and his work on human–device interaction has led to applications on the design and development of several medical devices and tools. Other recent translations of his research include the development of devices such as robotic assist devices and prosthetics, long-duration biosensor monitoring systems, surgical and dental instruments, patient care medical devices, spacesuits and space tools for NASA, powered and non-powered hand tools, musical instruments, sports equipment, computer input devices, and so on. Other overlapping research initiatives focus on the development of computational models and simulations of biofluid dynamics and biomechanical performance, cell mechanics and cellular responses to fluid shear stress, human exposure and response to vibration, and the acoustics of hearing protection and communication. He has also been involved clinically with the Occupational and Environmental Medicine group at the UConn Health Center, where his work has been directed toward the objective engineering analysis of the anatomic and physiological processes involved in the onset of musculoskeletal and neuromuscular diseases, including strategies of disease mitigation. Dr. Peterson’s scholarly activities include over 50 published journal articles, 2 textbook chapters, 2 textbook sections, and 12 textbooks, including his new appointment as co-editor-in-chief for The Biomedical Engineering Handbook by CRC Press.

Contributors Kai-Nan An Mayo Clinic Rochester, Minnesota

Edward J. Berbari Indiana University–Purdue University, Indianapolis Indianapolis, Indiana

I. Arcos Alfred Mann Foundation for Scientific Research Valencia, California

R. Betz Shriners Hospital for Children Philadelphia, Pennsylvania

Berj L. Bardakjian University of Toronto Toronto, Ontario, Canada

W. G. Billotte Department of Biology University of Dayton Dayton, Ohio

Roger C. Barr Department of Biomedical Engineering and Department of Pediatrics Duke University Durham, North Carolina

Bernardo Boleaga CTScanner de México Mexico City, Mexico

A. Barriskill Neopraxis Pty. Ltd. North South Wales, Australia

K. J. L. Burg Department of Bioengineering Clemson University Clemson, South Carolina

Aaron P. Batista Department of Bioengineering Swanson School of Engineering University of Pittsburgh and Carnegie Mellon University Pittsburgh, Pennsylvania Mostafa Belghasem Department of Pathology and Laboratory Medicine Boston University School of Medicine Boston, Massachusetts

Joseph D. Bronzino Trinity College Hartford, Connecticut

Thomas J. Burkholder School of Applied Physiology Georgia Institute of Technology Atlanta, Georgia Thomas R. Canfield Argonne National Laboratory Argonne, Illinois K. B. Chandran Department of Biomedical Engineering University of Iowa Iowa City, Iowa xvii

xviii

C. C. Chu Department of Fiber Science and Apparel Design Cornell University Ithaca, New York Ben M. Clopton Advanced Cochlear Systems Snoqualmie, Washington Ross Davis Florida Institute of Technology Melbourne, Florida Roy B. Davis III Motion Analysis Laboratory Shriners Hospitals for Children Greenville, South Carolina Peter A. DeLuca Center for Motion Analysis Connecticut Children’s Medical Center Farmington, Connecticut Daniel J. DiLorenzo Neurosurgery Department University of Texas Medical Branch Galveston, Texas and NeuroVista Corporation and DiLorenzo Biomedical, LLC Seattle, Washington Philip B. Dobrin Hines VA Hospital Hines, Illinois and Loyola University Medical Center Maywood, Illinois Cathryn R. Dooly Department of Physical Education Lander University Greenwood, South Carolina

Contributors

Dominique M. Durand Department of Biomedical Engineering Case Western Reserve University Cleveland, Ohio Michael J. Furey Department of Mechanical Engineering Virginia Polytechnic Institute and State University Blacksburg, Virginia Vijay K. Goel Department of Bioengineering University of Toledo Toledo, Ohio Wally Grant Department of Biomedical Engineering and Department of Engineering Science and Mechanics College of Engineering Virginia Polytechnic Institute and State University Blacksburg, Virginia Daniel Graupe University of Illinois at Chicago Urbana, Illinois Robert J. Greenberg Second Sight Inc. Sylmar, California Warren M. Grill Department of Biomedical Engineering Duke University Durham, North Carolina Robert E. Gross Emory University Atlanta, Georgia Alan R. Hargens Department of Orthopaedic Surgery UCSD Medical Center University of California, San Diego San Diego, California

xix

Contributors

Joel M. Henderson Department of Pathology and Laboratory Medicine Boston University School of Medicine Boston Medical Center and Department of Biomedical Engineering Boston University College of Engineering Boston, Massachusetts Robert M. Hochmuth Department of Mechanical Engineering and Materials Science Duke University Durham, North Carolina T. Houdayer Neural Engineering Clinic Augusta, Maine Ben F. Hurley University of Maryland Baltimore, Maryland Fiacro Jiménez Mexico City General Hospital Stereotaxic and Functional Neurosurgery Unit Mexico City, Mexico Arthur T. Johnson University of Maryland Baltimore, Maryland Christopher R. Johnson Scientific Computing and Imaging Institute University of Utah Salt Lake City, Utah T. Johnston Shriners Hospital for Children Philadelphia, Pennsylvania David L. Kaplan Department of Biomedical Engineering Tufts University Medford, Massachusetts

J. Lawrence Katz (deceased) Department of Biomedical Engineering Case School of Engineering and School of Medicine and Department of Oral and Maxillofacial Surgery School of Dental Medicine Case Western Reserve University Cleveland, Ohio and Department of Mechanical Engineering and Surgery, Orthopedics Schools of Engineering and Medicine University of Kansas Lawrence, Kansas Kenton R. Kaufman Mayo Clinic Rochester, Minnesota Philip R. Kennedy Neural Signals Inc Duluth, Georgia Roy C. P. Kerckhoffs School of Bioengineering Institute of Engineering in Medicine University of California, San Diego La Jolla, California Gilson Khang Department of BIN Fusion Technology Chonbuk National University Jeonju, South Korea Young Kon Kim Inje University Gimhae, South Korea Albert I. King Wayne State University Detroit, Michigan Mauricio Kuri CTScanner de México Mexico City, Mexico

xx

Roderic S. Lakes Departments of Engineering Physics, Materials Science, and Biomedical Engineering University of Wisconsin Madison, Wisconsin Christopher G. Lausted Institute for Systems Biology Seattle, Washington Hai Bang Lee Biomaterials Laboratory Korea Research Institute of Chemical Technology Daejeon, South Korea Jin Ho Lee Department of Advanced Materials Hannam University Daejeon, South Korea Shu-Tung Li Collagen Matrix Inc. Oakland, New Jersey Baruch B. Lieber Department of Neurosurgery State University of New York at Stony Brook Stony Brook, New York Richard L. Lieber Departments of Orthopaedics, Radiology and Bioengineering Biomedical Sciences Graduate Group University of California, San Diego and Veterans Administration Medical Centers La Jolla, California

Contributors

Biman Mandal Department of Biomedical Engineering Tufts University Medford, Massachusetts Orestes Marangos Bioengineering Research Center School of Engineering University of Kansas Lawrence, Kansas Andrew D. McCulloch School of Bioengineering Institute of Engineering in Medicine University of California, San Diego La Jolla, California Melissa K. McHale Department of Bioengineering Rice University Houston, Texas Evangelia Micheli-Tzanakou (deceased) Department of Biomedical Engineering Rutgers University Piscataway, New Jersey Anil Misra Department of Civil Engineering School of Engineering University of Kansas Lawrence, Kansas P. Mobley Alfred Mann Foundation for Scientific Research Valencia, California

Adolfo Llinás Department of Orthopaedics and Traumatology Fundacion Santafe de Bogota University Hospital Fundacion Cosme and Damian and Universidad de los Andes Bogota, Colombia

Jong-Hoon Nam Department of Biomedical Engineering and Department of Mechanical Engineering Hajim School of Engineering and Applied Sciences University of Rochester Rochester, New York

Jaakko Malmivuo Aalto University Helsinki, Finland

Sanjeev D. Nandedkar Natus Medical Inc. New York

xxi

Contributors

José María Núñez Mexico City General Hospital Stereotaxic and Functional Neurosurgery Unit Mexico City, Mexico Sylvia Õunpuu Center for Motion Analysis Connecticut Children’s Medical Center Farmington, Connecticut Muralidhar Padala Division of Cardiothoracic Surgery Emory University School of Medicine Atlanta, Georgia Joon B. Park Department of Biomedical Engineering University of Iowa Iowa City, Iowa Sang-Hyun Park Tissue Healing Laboratory Orthopedic Hospital and Department of Orthopaedics University of California, Los Angeles Los Angeles, California

Sunil Puria Department of Mechanical Engineering and Department of Otolaryngology-HNS Stanford University Stanford, California Bradley J. Roth Department of Physics Oakland University Rochester, Michigan Yiftach Roth New Advanced Technology Center Sheba Medical Center Tel-Hashomer, Israel Carl F. Rothe Department of Cellular and Integrative Physiology School of Medicine Indiana University Indianapolis, Indiana Geert W. Schmid-Schönbein Department of Bioengineering University of California, San Diego La Jolla, California

Roland N. Pittman Department of Physiology and Biophysics Medical College of Virginia Campus Virginia Commonwealth University Richmond, Virginia

Daniel J. Schneck Virginia Polytechnic Institute and State University Blacksburg, Virginia

Robert Plonsey Department of Biomedical Engineering Duke University Durham, North Carolina

J. Schulman Alfred Mann Foundation for Scientific Research Valencia, California

Andrew E. Pollard Department of Biomedical Engineering University of Alabama at Birmingham Birmingham, Alabama

S. W. Shalaby (deceased) Poly-Med, Inc. Anderson, South Carolina

Aleksander S. Popel Department of Biomedical Engineering School of Medicine Johns Hopkins University Baltimore, Maryland

Artin A. Shoukas Department of Biomedical Engineering School of Medicine Johns Hopkins University Baltimore, Maryland

xxii

B. Smith Shriners Hospital for Children Philadelphia, Pennsylvania Alexander A. Spector Department of Biomedical Engineering School of Medicine Johns Hopkins University Baltimore, Maryland Paulette Spencer Department of Mechanical Engineering Bioengineering Research Center School of Engineering University of Kansas Lawrence, Kansas Erin Spinner School of Biomedical Engineering Georgia Institute of Technology Atlanta, Georgia Charles R. Steele Department of Mechanical Engineering Stanford University Stanford, California George D. Stetten University of Pittsburgh and Carnegie Mellon University Pittsburgh, Pennsylvania Roger Tran-Son-Tay University of Florida Gainesville, Florida

Contributors

Ana Luisa Velasco Mexico City General Hospital Stereotaxic and Functional Neurosurgery Unit Mexico City, Mexico Francisco Velasco Mexico City General Hospital Stereotaxic and Functional Neurosurgery Unit Mexico City, Mexico Marcos Velasco Mexico City General Hospital Stereotaxic and Functional Neurosurgery Unit Mexico City, Mexico David C. Viano Wayne State University Detroit, Michigan Herbert F. Voigt Boston University Boston, Massachusetts Samuel R. Ward Departments of Orthopaedics, Radiology and Bioengineering Biomedical Sciences Graduate Group University of California, San Diego and Veterans Administration Medical Centers La Jolla, California Richard E. Waugh Department of Biomedical Engineering University of Rochester Rochester, New York

A. van Oosterom Radboud University Nijmegen Nijmegen, The Netherlands

Jennifer L. West Department of Bioengineering Rice University Houston, Texas

Anthony Varghese Department of Computer Science University of Wisconsin, River Falls River Falls, Wisconsin

J. Wolfe Alfred Mann Foundation for Scientific Research Valencia, California

xxiii

Contributors

Choon Hwai Yap School of Biomedical Engineering Georgia Institute of Technology Atlanta, Georgia

Ajit P. Yoganathan School of Biomedical Engineering Georgia Institute of Technology Atlanta, Georgia

Qiang Ye Bioengineering Research Center School of Engineering University of Kansas Lawrence, Kansas

Abraham Zangen Department of Neurobiology Weizmann Institute of Science Rehovot, Israel

MATLAB Statement MATLAB ® and Simulink® are registered trademarks of The MathWorks, Inc. For product information, please contact: The MathWorks, Inc. 3 Apple Hill Drive Natick, MA 01760-2098 USA Tel: 508 647 7000 Fax: 508-647-7001 E-mail: [email protected] Web: www.mathworks.com

xxv

Physiologic Systems

I

Herbert F. Voigt Boston University



1 An Outline of Cardiovascular Structure and Function  Daniel J. Schneck....................1-1 Working Fluid: Blood • Pumping Station: The Heart • Piping Network: Blood Vessels • Cardiovascular Control • Defining Terms • Acknowledgments • References



2 Kidney Structure and Physiology  Joel M. Henderson and Mostafa Belghasem............. 2-1 Introduction • Kidney Anatomy • Vasculature of the Kidney • Architecture of the Nephron • Structure of the Glomerulus and the Glomerular Filtration Barrier • Mechanical Properties of the Glomerulus • Glomerular Filtration • Factors Governing Glomerular Filtration • Permselectivity of the Glomerular Barrier • Tubulo-Interstitial Structure and Organization • Solute Recovery from the Ultrafiltrate • Water Reabsorption and Its Regulation • Endocrine Function of Kidney • Assessment of Kidney Function • References



3 Nervous System  Evangelia Micheli-Tzanakou.................................................................... 3-1 Definitions • Functions of the Nervous System • Representation of Information in the Nervous System • Lateral Inhibition • Higher Functions of the Nervous System • Abnormalities of the Nervous System • References



4 Vision System  Aaron P. Batista and George D. Stetten...................................................... 4-1 Fundamentals of Vision Research • A Modular View of the Vision System • Eye Movements • Defining Terms • References • Further Reading



5 Auditory System  Ben M. Clopton and Herbert F. Voigt.................................................... 5-1 Overview • Peripheral Auditory System • Central Auditory System • Pathologies • Further Topics • References



6 Gastrointestinal System  Berj L. Bardakjian...................................................................... 6-1 Introduction • GI Electrical Oscillations • A Historical Perspective • The Stomach • The Small Intestine • The Colon • Epilogue • Acknowledgments • References



7 Respiratory System  Arthur T. Johnson, Christopher G. Lausted, and Joseph D. Bronzino............................................................................................................7-1 Respiration Anatomy • Lung Volumes and Gas Exchange • Perfusion of the Lung • Gas Partial Pressure • Pulmonary Mechanics • Respiratory Control • Pulmonary Function Laboratory • Defining Terms • References • Further Reading I-1

1 An Outline of Cardiovascular Structure and Function

Daniel J. Schneck Virginia Polytechnic Institute and State University

1.1 Working Fluid: Blood........................................................................ 1-1 1.2 Pumping Station: The Heart............................................................ 1-3 1.3 Piping Network: Blood Vessels........................................................ 1-7 1.4 Cardiovascular Control...................................................................1-11 Defining Terms............................................................................................ 1-12 Acknowledgments....................................................................................... 1-13 References..................................................................................................... 1-13

Since not every cell in the human body is near enough to the environment to easily exchange its mass (including nutrients, oxygen, carbon dioxide, and the waste products of metabolism), energy (including heat), and momentum, the physiologic system is endowed with a major highway network—organized to make available thousands of miles of access tubing for the transport to and from a different neighborhood (on the order of 10 μm or less) of any given cell whatever it needs to sustain life. This highway network, called the cardiovascular system (Schneck, 1990; Tortora and Grabowski, 1993), includes a pumping station, the heart; a working fluid, blood; a complex branching configuration of distributing and collecting pipes and channels, blood vessels; and a sophisticated means for both intrinsic (inherent) and extrinsic (autonomic and endocrine) control.

1.1  Working Fluid: Blood Accounting for about 8 ± 1% of the total body weight, averaging 5200 mL, blood is a complex, heterogeneous suspension of formed elements—the blood cells, or hematocytes—suspended in a continuous, straw-colored fluid called plasma. Nominally, the composite fluid has a mass density of 1.057 ± 0.007 g/cm3, and it is 3–6 times as viscous as water. The hematocytes (Table 1.1) include three basic types of cells: red blood cells (erythrocytes, totaling nearly 95% of the formed elements), white blood cells (leukocytes, averaging C∙C< double bond in the diamide segment could also conjugate with the two carbonyl groups and resulted in a higher rigidity of the polymer backbone, while the >C∙C< double bond in the diester segment is isolated by the adjacent methylene group, the lack of conjugation. Contrary to the unsaturated AA-UPEAs having double bonds in the backbone, those unsaturated AA-UPEAs having pendant >C∙C< double bonds (Pang et al., 2010; Pang and Chu, 2010a,b) actually lowers their Tg when compared with the corresponding saturated AA-PEAs. For example, 2-Phe-4 and 8-Phe-4 had Tg of 55°C and 40°C, respectively, while the Phe-based UPEA copolymers with pendant >C∙C< double bonds (from 2-allyl glycine) had Tg values ranging from 20°C to 38°C, depending on methylene chain length in diacid, diols, as well as the feed ratio of regular amino acid to 2-allyl glycine. This suggested that the presence of 2-allyl glycine unit in the AA-UPEA backbone could impart additional chain flexibility due to the increasing free volume from pendant double bonds which could act as internal plasticizers, lowered the intermolecular interaction between copolymer chains. Therefore, more allylglycine contents could result in higher chain flexibility and hence lower Tg values as reported (Pang et al., 2010; Pang and Chu, 2010a,b). These >C∙C< double bonds in unsaturated AA-UPEAs also provide potential reactive sites for either synthesizing additional derivatives or attaching biologically active agents to render biological activity to AA-UPEAs. An example of synthesizing additional derivatives from AA-UPEAs is the reported studies of AA-UPEA-based hydrogels via photocrosslinking with PEG diacrylate precursor (Guo and Chu, 2005; Pang and Chu, 2010b). Figure 32.5 illustrates the scanning electron microscopic images of a AA-UPEA-based hydrogel. Figure 32.5a is from AA-UPEAs with pendant >C∙C< double bonds, whereas Figure 32.5b is from AA-UPEAs with >C∙C< located in the AA-UPEAs backbone. These pendant or backbone >C∙C< groups have also been converted into other functional groups like thiol-based –COOH by using 3-mercaptopropionic acid, –NH3Cl by using 2-aminoethanethiol hydrochloride, and –SO3Na by using sodium-3-mercapto-1-propanesulfonate (Guo and Chu, 2010; Pang and Chu, 2010a). Figure 32.6 shows the chemical scheme to synthesize these functional AA-PEAs via the unsaturated >C∙C< bonds in the AA-UPEAs backbone (Guo and Chu, 2010). As a result, additional functional AA-PEAs could be designed and synthesized from AA-UPEAs. Beside the unsaturated AA-UPEA approach to provide additional functionality to AA-PEAs via their unsaturated >C∙C< bonds, other efforts could also provide chemical functionality to AA-SPEAs, the

32-15

Biodegradable Polymeric Biomaterials: An Updated Overview (a)

10 µm (b)

10 µm Keck SEM Mag = 2.00 K X

2 µm WD = 8 mm File name =106.tif

EHT = 2.00 KV

Aperture size = 30.00 µm Signal A = SE2

Date : 24 Mar 2009 Time : 21 : 27 : 47

FIGURE 32.5  Scanning electron microscopic images of two representative hybrid hydrogel fabricated from (a) Phe-based unsaturated AA-UPEAs, and poly(ethylene glycol) diacrylate (PEGDA) and (b) Arg-based unsaturated AA-UPEAs and pluronic acid diacrylate.

copolymer approach. Chu et al. recently reported two different copolymer means to provide pendant functional groups via either l-lysine or other amino acid co-monomer (Jokhadze et al., 2007; Deng et al., 2009, 2011). The first copolymer approach led to the AA-PEA copolymers having pendant-free carboxylic acid (located in the Lys block) over a wide range of desirable concentrations (Jokhadze et al., 2007). These free carboxylic acids provide the reactive sites for the attachment of biologically active agents, such as nitric oxide derivative, and the resulting AA-PEA copolymers would have biological activity and intelligence similar to that of nitric oxide (Lee and Chu, 1996, 1998). The second copolymer approach used a new monomer of ε-(benzyloxycarbonyl)-amino acid-N-­ carboxyanhydride (Z-amino acid-NCA) and its ring-opening reaction with the regular AA-PEA O

CH2Ph

O NH O

O

R1

O

N H

O

CH2Ph

+

R2

HS

n

FPB or F3EG DMA 70°C, 24 h

O

O NH S

O

O CH2Ph

R1

CH2Ph

O O

N H

n

FIGURE 32.6  Chemical scheme to illustrate the synthesis of pendant functional AA-PEAs from the unsaturated >C∙C< bonds in the AA-UPEA backbone. (Adapted from Guo, K. and Chu, C.C., 2010. J. Appl. Polym. Sci. 117(6): 3386–3394.)

32-16

Biomaterials

O NH

CH2

O

O

2

CH2

O

O NH

NH O

4

O

O m

NH

CH2

O

O

2

CH2

O

NH

4

O

O

n-m

NH2

FIGURE 32.7  Chemical structure of the repeating unit of functional AA-PEAs synthesized via ε-(benzyloxycarbonyl)-amino acid-N-carboxyanhydride (Z-amino acid-NCA) route (the second copolymer approach as described above) (Deng et al., 2010).

monomers (di-p-toluenesulfonic acid salts of bis-(α-amino acid) α,ω-alkylene diesters and di-p-nitrophenyl esters of diacids). The resulting functional AA-PEAs could have either free pendant –NH2, –OH or –COOH, depending on the type of the new Z-amino acid-NCA monomer (Deng et al., 2009, 2011). For example, if Lys is used (Z-Lys-NCA), the resulting AA-PEA copolymer would have pendant –NH2 functionality. Note the difference in pendant functional group between the first and second copolymer approaches even though the same Lys was used. The chemical structure of the functional AA-PEA copolymers from the second copolymer approach (Figure 32.7) is quite different from the chemical structure of the functional AA-PEAs from the first copolymer approach. In the first copolymer approach (Jokhadze et al., 2007), each of the two amino acids is distinctively located at two different blocks, for example, Phe in one block and Lys in another block. In the second copolymer approach (Deng et al., 2009, 2011), two amino acids are located in the same block and directly connected by a peptide bond, and one of these two amino acids is also located in a separate block. Deng et al. (2009) reported that the pendant –NH2 group can be attached by a NHS-fluorescein, and the resulting dye-tagged AA-PEAs exhibit fluorescence characteristic. Glilies et al. also recently reported another method of synthesizing functional AA-PEAs with free pendant amino groups (De Wit et al., 2008). They incorporated bis(l-lysine) R,ω-alkylene diester monomer into the PEA, and the pendant amine group can be recovered after deprotection reaction. However, the chemical structure of Glilies et al.’s functional AA-PEAs differs from that of Deng et al.’s in that the two amino acids within the same block in the Glilies et al.’s study are separated by diacid spacer on the AA-PEA backbone, while the two amino acids in the same block in the Deng et al.’s study are directly connected via a peptide bond. An effort to integrate saturated AA-SPEAs with unsaturated AA-UPEAs into one single entity was recently reported and an example is shown in Figure 32.8 (Guo and Chu, 2007a), and the major advantage of such an integration is to combine the merits of both saturated and unsaturated AA-PEAs into one single entity via chemical linkages so that a wide range of physical, chemical, thermal, and biological properties could be obtained by simply changing the composition ratio of saturated to unsaturated AA-PEAs. Beside ester and amide linkages in AA-PEAs, Guo and Chu (2007b, 2008, 2010) reported the addition of ether linkage into AA-PEAs as shown in Figure 32.9. The resulting poly(ether ester amide) O

O NH O

O

CH2Ph O

CH2Ph

O

NH O

m

O x O

NH

O CH2Ph

CH2Ph

O

NH O

n

FIGURE 32.8  The chemical structure of the repeating unit of saturated and unsaturated amino acid-based poly(ester amide)s. (Adapted from Guo, K. and Chu, C.C., 2007a. J. Polym. Sci. Polym. Chem. Ed., 45: 1595–1606.)

32-17

Biodegradable Polymeric Biomaterials: An Updated Overview

O

O NH O

O CH2Ph

O

O O

2O

C

NH CH2Ph

O NH

x m

O

O O

CH2Ph

O

2O

C

NH CH2Ph

n

FIGURE 32.9  The chemical structure of the repeating unit of the copolymer of saturated and unsaturated poly(ester ether amide)s. (Adapted from Guo, K. and Chu, C.C., 2007b. Biomacromolecules, 8(9): 2851–2861.)

(AA-PEEA) would have three types of linkages: ether, ester, and amide. The ether linkage was introduced by the use of oligo(ethylene glycol). The AA-PEEAs had Tg values lower than that of the AA-PEAs of similar structures due to the incorporation of ether bonds in the backbones. An increase in the number of ether bonds in PEEA resulted in a lower Tg value. The solubility of the PEEA polymers in a wide range of common organic solvents was significantly improved when compared with the corresponding AA-PEAs. Guo et al. (2008) stated that by adjusting monomers feed ratio between saturated AA-SPEEAs and unsaturated AA-UPEEAs, AA-USPEEA copolymers could have controlled chemical, physical, and biodegradation properties. Both saturated AA-SPEAs and AA-UPEAs were easily biodegraded by enzymes such as lipase or α-chymotrypsin; however, their biodegradability in pure saline buffer is slow as shown in Figure 32.10. The Phe-based AA-PEA fibers were completely biodegraded after 2 days exposure to α-chymotrypsin at 0.1 mg/mL concentration (far right), while these AA-PEA fibers remained intact in phosphate-buffered saline (PBS) at the same duration. It appears that an increase in the hydrophobicity of AA-PEAs (via longer methylene groups in diols and dicarboxylic acid segments) leads to a faster enzyme-catalyzed biodegradation (Tsitlanadze et al., 2004a,b). In addition to the hydrophobicity factor to interpret this relationship between the length of methylene groups and enzyme-catalyzed biodegradation rate, the lack of intermolecular hydrogen bonds resulting from misalignment of the adjacent AA-PEA macromolecules was also suggested as a possible cause behind such a relationship. The presence of ether linkage in AA-PEEAs accelerates the enzymatic hydrolysis rates (in terms of weight loss) and was found to be much faster than those of AA-PEAs. The zero-order-like biodegradation kinetics and molecular weight data of AA-PEAs and AA-PEEAs also suggested surface erosion biodegradation mechanisms like peeling onions which is very different from the well-known bulk hydrolytic degradation of aliphatic polyesters, that is, degrading throughout the whole biomaterials.

FIGURE 32.10  Enzyme effect on the biodegradation of Phe-based AA-PEA fibers. α-Chymotrypsin concentration at 0.1 mg/mL. The two bottles on the left were treated by PBS, whereas the two bottles on the right were treated by α-chymotrypsin in PBS. The duration of immersion were 24 (inner bottles) and 48 h (outer bottles).

32-18

Biomaterials

FIGURE 32.11  Variety of physical forms of AA-PEAs engineered. (a) 3D microporous hydrogel; (b) micro/nanospheres; (c) electrospun fibrous membrane.

32-19

Biodegradable Polymeric Biomaterials: An Updated Overview

A variety of physical forms of AA-PEAs, such as fibers, films, electrospun 3D microporous fibrous membranes, hydrogels, hollow gel tube, and micro/nanospheres have been successfully engineered to meet specific clinical needs and they are shown in Figure 32.11 (Guo and Chu, 2005, 2009; Song, 2007; Chu and Sun, 2008; Li and Chu, 2009; Horwitz et al., 2010; Pang and Chu, 2010; Wu, 2010; Song and Chu, 2012). These physical forms of AA-PEAs have been used to deliver drugs and proteins (e.g., bFGF, IL-12, pactlitaxel, albumin, nitric oxide derivatives, gallium nitrate, antibiotics, biotin) via preloading, postloading, or chemical conjugation modes. The most unique biological property of these biodegradable amino acid-based poly(ester amide)s is the very low foreign-body inflammatory response that the AA-PEAs can induce as well as their support of more natural wound healing (Lee et al., 2002; Schwartz et al., 2008; DeFife et al., 2009; Horwitz et al., 2010; Wu, 2010). As shown in Figure 32.12, DeFife et al. (2009) reported that human peripheral blood monocytes cultured on AA-PEA films secreted over fivefold less IL-6 proinflammatory cytokine release over 24 h than the classical absorbable aliphatic polyesters like polyglycolide and lactide copolymers (50/50 molar ratio), poly-n-butylmethacrylate (PBMA), and tissue culture-treated polystyrene (TCPS) as IL-6 is known to increase macrophage cytotoxic activity. The very low inflammatory response toward AA-PEA-based biomaterials is further confirmed by examining the IL-1β receptor antagonist secreted by monocytes, and a similar pattern of release of IL-1β, a potent proinflammatory cytokine, on monocyte cultured AA-PEA biomaterials. The amounts of IL-1β released on AA-PEAs were one-quarter to one-half of the FDA-approved absorbable PLGA and nonabsorbable PBMA biomaterials. The low inflammatory characteristic of AA-PEAs was further confirmed in an in vivo porcine coronary artery model of AA-PEA-coated stent (Lee et al., 2002) as well as in vivo study of the wound healing performance of Phe-based PEA fibrous membrane for treating second-degree burns in a porcine model (Schwartz et al., 2008). In the porcine coronary artery model, 28 days postimplantation, the AA-PEA copolymer-coated 316L stainless-steel stent (Genic stent) exhibited statistically similar inflammatory score as the bare stent control (1.18 ± 0.38 of AA-PEA-coated stent versus 1.11 ± 0.32 of bare stent control). There was no statistical difference inb% area of stenosis and neointimal hyperplasia between the AA-PEA-coated and bare stents either. These biocompatibility data in an in vivo porcine arterial model also suggest that these new biodegradable AA-PEA copolymers induce very low level of inflammatory response. Interleukin-6

4000

IL-6 (pg/mL)

3500 3000 2500 2000 1500 1000 500 S TC P

A M PB

K 73 A G PL

PL

G

A

PO EM

z PE

A

.A c.T

AAc .B PE

34 K

0

FIGURE 32.12  In vitro inflammatory response of Leu−Lys-based AA-PEA copolymers in terms of cytokine IL-6 secretion upon seeding monocytes onto AA-PEA films. PEA-Ac.Bz is a protected AA-PEA copolymer (i.e., the –COOH pendant group in the Lys segment is protected by a benzyl ester). PEA.Ac.TEMPO is a deprotected AA-PEA and its –COOH group was conjugated with a nitroxyl radical, 4-amino-2,2,6,6-tetramethylpiperidine-1-oxy (or 4-amino TEMPO. PLGA is a poly(lactic-co-glycolic acid) copolymer with a molecular weight of 36,000 (Resomer RG 502) and 73,000 Da (Resomer RG 504). PBMA is n-poly(butyl methacrylate). TCPS is a tissue culture polystyrene plate.

32-20

Biomaterials

FIGURE 32.13  Drug-eluting AA-PEA fibrous membranes for treating partial thickness wound in a porcine model after 3 days postoperation. Gallium nitrate drug was physically impregnated within AA-PEA fibrous membranes (far right). DuoDerm as the commercial control (far left and third from left). Pure AA-PEA fibrous membrane (second from left) also served as a control.

The in vivo porcine burn model study showed that the AA-PEA-based fibrous membranes with or without impregnated drug (gallium nitrate) showed accelerated wound healing with a healing rate of 4–5 days faster than the commercial DuoDerm® control as shown in Figure 32.13 (Schwartz et al., 2008). Therefore, this new family of AA-PEAs appear to support a more natural wound healing process by promoting reendothelialization and lowering foreign-body-induced inflammatory response.

32.4.4  Poly(carbonate-acetal)s from Dihydroxyacetone The building blocks of all existing synthetic absorbable or biodegradable polymeric biomaterials have largely from the human body metabolic products like PGA, PLA, and PCL. The newly reported poly(carbonate-acetal)s (PCA) are synthesized from dihydroxyacetone (DHA), an intermediate of glucose metabolism (Zelikin and Putnam, 2005; Zawaneha et al., 2005; Henderson et al., 2010). Figure 32.14 O OH OH I

O O

HO O O

HO OH

IIIa

HO O

O OH

ii

O O

HO

OH II

iii O

IIIb

iii

O O O O

OH

O O

O

O O

C

n IVa

O O O O

O O

C

n IVb

FIGURE 32.14  The chemical scheme to illustrate the synthesis of poly(carbonate-acetal)s from the dimer of dihydroxyacetone. I—Dihydroxyacetone; II—dimer of dihydroxyacetone; IIIa—2,5-diethoxy-1,4-dioxane-2,5dimethanol; IIIb—2,5-diisopropoxy-1,4-dioxane-2,5-dimethanol; IVa—poly(carbonate-acetal) from IIIa; IVb— poly(carbonate-acetal) from IIIb. (Adapted from Zelikin, A.N. and Putnam, D., 2005. Macromolecules, 38: 5532–5537.)

Biodegradable Polymeric Biomaterials: An Updated Overview

32-21

shows the synthesis scheme of poly(carbonate-acetal)s from the dimer form of DHA with the help of ­triphosgene. The resulting PCA has yields from 56% to 93% with weight-average molecular weight from 28 × 103 to 48 × 103, and Tg ranging from 42°C to 61°C. The wettability (in terms of water contact angle) of these PCA ranges from 76° to 88o, and is similar to those Phe-based poly(ester amide) s (Horwitz et al., 2010). A preliminary MTT assay and cell proliferation study (NIH/3T3 cell line) indicate that poly(carbonate-acetal)s are not cytotoxic and support cell growth. A PCA derivative from PEGylated DHA diblock copolymer has shown good hemostatic property (Henderson et  al., 2010), while this PEGylated DHA physically cross-linked hydrogel can act as a space filler and has been tested for prevention of seroma following ablative and reconstructive surgeries (Zawaneha et al., 2005).

32.5 Biodegradation Properties of Synthetic Biodegradable Polymers The reported biodegradation studies of a variety of biodegradable polymeric biomaterials have mainly focused on their tissue biocompatibility, the rate of drug release, or loss of strength and mass. Recently, the degradation mechanisms and the effects of intrinsic and extrinsic factors, such as pH (Chu, 1981, 1982), enzymes (Williams and Mort, 1977; Williams and Chu, 1984; Williams, 1979; Chu and Williams, 1983), γ-irradiation (Campbell et al., 1981; Chu and Campbell, 1982; Chu and Williams, 1983; Williams and Chu, 1984; Zhang et al., 1993), electrolytes (Pratt et al., 1993), cell medium (Chu et  al., 1992), superoxide (Lee et al., 1999, 2000), annealing treatment (Chu and Browning, 1988), plasma surface treatment (Loh et al., 1992), external stress (Miller and Williams, 1984; Chu, 1985a), and polymer morphology (Chu and Kizil, 1989), and on a chemical means to examine the degradation of PGA fibers (Chu and Louie, 1985) have been systemically examined and the subject has been recently reviewed (Chu, 1985b, 1991, 1995a,b; Hollinger, 1995; Chu et al., 1997). Table 32.5 is an illustration of structural factors of polymers that could control their degradation. Besides these series of experimental studies of a variety of factors that could affect the degradation of biodegradable polymeric biomaterials, there are two new areas that broaden the above traditional study of biodegradation properties of biodegradable polymers into the frontier of science. They are theoretical modeling and the role of free radicals.

32.5.1 Theoretical Modeling of Degradation Properties The most systematic theoretical modeling study of degradation properties of biodegradable biomaterials was reported by Pratt and Chu who used computational chemistry to theoretically model the effects of a variety of substituents which could exert either steric effect and/or inductive effect on the degradation properties of glycolide/lactide-based biodegradable polymers (Pratt and Chu, 1993, 1994a,b). This TABLE 32.5  Structural Factors to Control the Polymer Degradability Factors Chemical structure of main chain and side groups Aggregation state Crystalline state Hydrophilic/hydrophobic balance Surface area Shape and morphology

Methods of Control Chemical linkages and functional groups Processing, copolymerization Polymer blend, copolymerization feed ratio, processing temperature Copolymerization, chemical linkages, introduction of functional groups Micropores, nanotechnology Fiber, film, hydrogels, composite

Source: Adapted from Kimura, Y., 1993. Biomedical Applications of Polymeric Materials, pp. 164–190. CRC Press, Boca Raton, FL.

32-22

Biomaterials

new approach could provide scientists with a better understanding of the relationship between the chemical structure of biodegradable polymers and their degradation behavior at a molecular level. It also could help the future research and development of this class of polymers through the intelligent prediction of structure–property relationships. In those studies, Pratt and Chu examined the affect of various derivatives of linear aliphatic polyester (PGA) and a naturally occurring linear polysaccharide (hyaluronic acid) on their hydrolytic degradation phenomena and mechanisms. The data showed a decrease in the rate of hydrolysis by about a factor of 106 with isopropyl ct-substituents, but nearly a sixfold increase with t-butyl α-substituents (Pratt and Chu, 1993). The role of electron-donating and electron-withdrawing groups on the rate of hydrolytic degradation of linear aliphatic polyesters was also theoretically modeled by Pratt and Chu (Pratt and Chu, 1994a). Electron-withdrawing substituents to the carbonyl group would be expected to stabilize the tetrahedral intermediate resulting from hydroxide attack, that is, favoring hydroxide attack but disfavoring alkoxide elimination. Electronreleasing groups would be expected to show the opposite effect. Similarly, electronegative substituents on the alkyl portion of the ester would stabilize the forming alkoxide ion and favor the elimination step. Pratt and Chu found that the rate of ester hydrolysis is greatly affected by halogen substituents due primarily to charge delocalization. The data suggest that the magnitude of the inductive effect on the hydrolysis of glycolic esters decreases significantly as the location of the substituent is moved further away from the α-carbon because the inductive effect is very distance-sensitive. In all three locations of substitutions (α and γ), Cl and Br substituents exhibited the largest inductive effect compared to other halogen elements. Therefore, Pratt and Chu concluded that the rate of ester hydrolysis is greatly affected by both alkyl and halogen substituents due primarily to either steric hindrance or charge delocalization. In the steric effect, alkyl substituents on the glycolic esters cause an increase in activation enthalpies and a corresponding decrease in reaction rate, up to about three carbon sizes, while bulkier alkyl substituents other than isopropyl make the rate-determining elimination step more facile. It appears that aliphatic polyesters containing isopropyl groups, or slightly larger linear alkyl groups, such as n-butyl, n-pentyl, and so on, would be expected to show a longer strength retention, given the same fiber morphology. In the inductive effect, ct-substituents on the acyl portion of the ester favor the formation of the tetrahedral intermediate through charge delocalization, with the largest effect seen with Cl substitution, but retard the rate-determining alkoxide elimination step by stabilizing the tetrahedral intermediate. The largest degree of stabilization is caused by the very electronegative F substituent.

32.5.2 The Role of Free Radicals in Degradation Properties Salthouse et al. had demonstrated that the biodegradation of synthetic absorbable sutures is closely related to macrophage activity through the close adhesion of macrophage onto the surface of the absorbable sutures (Matlaga and Salthouse, 1980). It is also known that inflammatory cells, particularly leukocytes and macrophages, are able to produce highly reactive oxygen species such as superoxide (•O2−) and hydrogen peroxide during inflammatory reactions toward foreign materials (Badwey and Kamovsky, 1980; Devereux et al., 1991). These highly reactive oxygen species participate in the biochemical reaction, frequently referred to as a respiratory burst, which is characterized by the one electron reduction of O2 into superoxide via either NADPH or NADH oxidase as shown below. The reduction of O2 results in an increase in O2 uptake and the consumption of glucose.

oxidase) 2O2 + NADPH ⎯(NADPH ⎯⎯⎯⎯⎯ → 2iO2− + NADP + + H +



(32.1)

The resulting superoxide radicals are then neutralized to H2O2 via cytoplasmic enzyme superoxide dismutase (SOD).

2iO2 − + 2H + ⎯(SOD) ⎯⎯ → H 2O2 + O2



(32.2)

32-23

Biodegradable Polymeric Biomaterials: An Updated Overview

Williams et al. suggested that these reactive oxygen species may be harmful to polymeric implant surfaces through their production of highly reactive, potent, and harmful hydroxyl radicals •OH in the presence of metals like iron as shown in the following series of redox reactions (Williams and Zhong, 1991; Ali et al., 1993; Zhong et al., 1994). i



O2 + Mn + → O2 + M(n −1)+

(32.3)

H2O2 + M(n −1)+ → iOH + HO− + Mn +





(32.4)

The net reaction will be

i

O2 − + H2O2 → iOH + HO− + O2



(32.5)

and is often referred to as the metal-catalyzed Haber–Weiss reaction (Haber and Weiss, 1934). Although the role of free radicals in the hydrolytic degradation of synthetic biodegradable polymers is largely unknown, a very recent study using absorbable sutures like Vicryl in the presence of an aqueous free radical solution prepared from H 2O2 and ferrous sulfate, FeSO4, raised the possibility of the role of free radicals in the biodegradation of synthetic absorbable sutures (Williams and Zhong, 1991; Zhong et al., 1994). As shown below, both •OH radicals and OH− are formed in the process of oxidation of Fe2+ by H2O2 and could exert some influence on the subsequent hydrolytic degradation of Vicryl sutures.

Fe2 + + H2O2 → Fe3 + + iOH + OH −

SEM results indicated that Vicryl sutures in the presence of free radical solutions exhibited many irregular surface cracks at both 7 and 14 days in vitro, while the same sutures in the two controls (H2O2 or FeSO4 solutions) did not have these surface cracks. Surprisingly, the presence of surface cracks of Vicryl sutures treated in the free radical solutions did not accelerate the tensile-breaking strengthloss as would be expected. Thermal properties of Vicryl sutures under the free radical and 3% H2O2 media showed the classical well-known maximum pattern of the change of the level of crystallinity with hydrolysis time. The level of crystallinity of Vicryl sutures peaked at 7 days in both media (free radical and 3% H2O2). The time for peak appearance in these two media was considerably earlier than Vicryl sutures in conventional physiological buffer media. Based on Chu’s suggestion of using the time of the appearance of the crystallinity peak as an indicator of degradation rate, it appears that these two media accelerated the degradation of Vicryl sutures when compared with regular physiological buffer solution. Based on their findings, Williams et al. proposed the possible routes of the role of •OH radicals in the hydrolytic degradation of Vicryl sutures (Zhong et al., 1994). Unfortunately, the possible role of OH−, one of the byproducts of Fenton reagents (H2O2/FeSO4), was not considered in the interpretation of their findings. OH− species could be more potent than OH toward hydrolytic degradation of synthetic absorbable sutures. This is because hydroxyl anions are the sole species which attack carbonyl carbon of the ester linkages during alkaline hydrolysis. Since an equal amount of •OH and OH− are generated in Fenton reagents, the observed changes in morphological, mechanical, and thermal properties could be partially attributed to OH− ions as well as •OH radicals. Besides hydroxyl radicals, the production of superoxide ions and singlet oxygen during phagocytosis has been well documented (Babior et al., 1973). Although the role of superoxide in simple organic ester hydrolysis has been known since the 1970s (Johnson, 1976; Mango and Bontempeli, 1976; San Fillipo et al., 1976; Forrester and Purushotham, 1984, 1987), its role in the hydrolytic degradation of synthetic biodegradable polyester-based biomaterials has remained largely unknown. Such an understanding of the superoxide ion role during the biodegradation of foreign materials has become increasingly desirable

32-24

Biomaterials

because of the advanced understanding of how the human immune system reacts to foreign materials and the increasing use of synthetic biomaterials for human body repair. Lee and Chu examined the reactivity of the superoxide ion toward biodegradable biomaterials having an aliphatic polyester structure at different reaction conditions such as temperature, time, and superoxide ion concentration (Lee et al., 1999; Lee and Chu, 2000). Due to the extreme reactivity of the superoxide ion, it has been observed that the effect of superoxide ion-induced hydrolytic degradation of PDLLA and PLLA was significant in terms of changes in molecular weights and thermal properties (Lee et al., 1999). The superoxide ion-induced fragmentation of PDLLA would result in a mixture of various species with different chain lengths. A combined GPC method with a chemical tagging method revealed that the structure of oligomer species formed during the superoxide-induced degradation of PDLLA and PLLA was linear. The significant reduction in molecular weight of PDLLA by superoxide ion was also evident in the change of thermal properties like Tg. The linear low-molecular species (oligomer, trimers, and dimers) in the reaction mixture could act as an internal plasticizer to provide the synergetic effects of lowering Tg by increasing free volume. The effect of the superoxide ion-induced hydrolytic degradation on molecular weight of PLLA was similar to PDLLA but with a much smaller magnitude. The mechanism of simple hydrolysis of ester by superoxide ion proposed by Forrester et al. was subsequently modified to interpret the data obtained from the synthetic biodegradable polymers. In addition to PDLLA and PLLA, superoxide ions also have a significant adverse effect on the hydrolytic degradation of synthetic absorbable sutures (Lee and Chu, 2000). A significant reduction in molecular weight has been found along with mechanical and thermal properties of these sutures over a wide range of superoxide ion concentrations, particularly during the first few hours of contact with superoxide ions. For example, the PGA suture lost almost all of its mass at the end of 24 h contact with superoxide ions at 25°C, while the same suture would take at least 50 days in an in vitro buffer for a complete mass loss. The surface morphology of these sutures was also altered drastically. The exact mechanism, however, is not fully known yet; Lee et al. suggested the possibility of simultaneous occurrence of several main-chain scissions by three different nucleophilic species. Lee and Chu also reported that the addition of Fenton agent or hydrogen peroxide to the degradation medium would retard the well-known adverse effect of the conventional γ-irradiation sterilization of synthetic absorbable sutures (Lee and Chu, 1996). They found that these γ-irradiated sutures retained better tensile-breaking strength in the Fenton medium than in the regular buffer media. Chu et al. postulated that the γ-irradiation-induced α-carbon radicals in these sutures react with the hydroxyl radicals from the Fenton agent medium and hence neutralize the adverse effect of α-carbon radicals on the backbone chain scission. This mechanism is supported by the observed gradual loss of ESR signal of the sutures in the presence of the Fenton agent in the medium. Instead of the adverse effect of free radicals on the degradation properties of synthetic biodegradable polyesters, Lee and Chu described an innovative approach of covalent bonding nitroxyl radicals onto these biodegradable polymers so that the nitroxyl radical attached polymers would have biological functions similar to nitric oxide (Lee and Chu, 1996, 1998). The same approach was also used to chemically attach nitroxyl radicals onto the amino acid-based biodegradable poly(ester amide) copolymers (Chu and Katsarava, 2003). A preliminary in vitro cell culture study of these new biologically active absorbable aliphatic polyesters indicated that they could retard the proliferation of human smooth muscle cells as native nitric oxides do. The full potential of this new biologically active biodegradable polymers is currently under investigation by Chu for a variety of therapeutic applications like drug-eluting stents and vascular grafts.

32.6 Role of Linear Aliphatic Biodegradable Polyesters in Tissue Engineering and Regeneration The use of biodegradable polymers as the temporary scaffolds either to grow cells/tissues in vitro for tissue engineering applications or to regenerate tissues in vivo has very recently become a highly important

Biodegradable Polymeric Biomaterials: An Updated Overview

32-25

aspect of research and development that broadens this class of biodegradable polymers beyond their traditional use in wound closure and drug control/release biomaterials. The scaffolds used in either tissue engineering or regeneration are to provide support for cellular attachment and subsequent controlled proliferation into a predefined shape or form. Obviously, a biodegradable scaffold would be preferred because of the elimination of chronic foreign body reaction and the generation of additional volume for regenerated tissues. Although many other biodegradable polymers of natural origin such as alginate (Atala et al., 1994), hyaluronate (Benedetti et al., 1993; Larsen et al., 1993), collagen (Hirai and Matsuda, 1995), and laminin (Dixit, 1994) have been experimented with for such a purpose, synthetic biodegradable polymers of linear aliphatic polyesters such as PGA, PLA, and their copolymers (Bowald et al., 1979, 1980; Greisler, 1982; Greisler et al., 1985, 1987a,b, 1988a,b,c; Greisler, 1991; Freed et al., 1993; Mikos et al., 1993; Yu and Chu, 1993; Yu et al., 1994; Mooney et al., 1994, 1995, 1996a,b,c; Kim et al., 1998; Kim and Mooney, 1998; Yu et al., 2010) have received more attention because of their consistent sources, reproducible properties, means to tailor their properties, and versatility in manufacturing processes. Biodegradable polymers must be fabricated into stable textile structures before they can be used as the scaffold for tissue engineering or regeneration. The stability of the scaffold structure is important during tissue engineering and regeneration in order to maintain its proper size, shape, or form upon the shear force imposed by the circulating culture media in a bioreactor, the contractile force imposed by the growing cells on the scaffold surface, and other forces like the compression from surrounding tissues. Kim et al. reported that, although ordinary nonwoven PGA matrices have very good porosity (to facilitate diffusion of nutrients) with a high surface-to-volume ratio (to promote cell attachment and proliferation) and have been used to engineer dental pulp and smooth muscle tissues having comparable biological contents as the native tissues (Mooney et al., 1996c; Kim et al., 1998), these nonwoven PGA matrices could not maintain their original structure during tissue engineering due to the relatively weak nonwoven textile structure and stronger contractile force exerted by the attached and proliferated cells/ tissues (Kim and Mooney, 1998). This led to deformed engineered tissues that may have undesirable properties; for example, the smooth muscle engineered on collagen gels exhibited significant contraction over time (Ziegler and Nerem, 1994; Hirai and Matsuda, 1995). Because of this shortcoming of the existing nonwoven PGA matrices, Kim and Mooney (1998) very recently reported the use of PLLA to stabilize the PGA matrices. A 5% (w/v) PLLA solution in chloroform was sprayed onto PGA nonwoven matrices (made of 12 µm diameter PGA fibers) of 97% porosity and either 3 or 0.5 mm thickness. The PLLA-impregnated PGA nonwovens could be subjected to additional heat treatment at 195°C to enhance their structural stability further. Figure 32.15 shows the morphology of such a heat-annealed PLLA-impregnated PGA nonwoven matrix (Kim and Mooney, 1998). The PLLA was deposited mainly on the crosspoints of PGA fibers and hence interlocked the possible sliding of PGA fibers upon external force. Depending on the amount of PLLA used and subsequent heat treatment, the resulting PLLA-impregnated PGA nonwoven matrices had an increase in compressive modulus of 10–35-fold when compared with the original PGA non-woven. The PLLA-impregnated PGA nonwoven matrices also retained their initial volume (101 ± 4%) and about same shape as the original during the seven weeks in culture, while the untreated PGA nonwoven exhibited severe distortion in shape and contracted about 5% of its original volume. Since PLLA is well known to degrade at a much slower rate than PGA, its presence on the PGA fiber surface would be expected to make the treated PGA nonwoven matrices degrade at a much slower rate than the untreated PGA nonwoven. For example, the PLLA-treated PGA nonwoven retained about 80% of its initial mass, while the untreated PGA control had only 10% at the end of the 7-week culture. Linear aliphatic polyesters such as PGA, its lactide copolymer, and PDS have also been fabricated into both woven and knitted forms for the in vivo regeneration of blood vessels in animals (Bowald et al., 1979, 1980; Greisler, 1982; Greisler et al., 1985, 1987a, 1988c, 1991; Yu and Chu, 1993; Yu et al., 1994). The published results from a variety of animals like dogs and rabbits indicate that full-wall healing with

32-26

Biomaterials

FIGURE 32.15  Scanning electron micrograph of the exterior of PLLA-impregnated and annealed PGA matrix. (From Kim, B.S. and Mooney, D.J., 1998. J. Biomed. Mater. Res., 41: 322–332. With permission.)

pseudo-endothelial lining was observed. This class of synthetic biodegradable polymers are promising candidates for the regeneration of vascular tissue. These encouraging findings were believed to be associated with the intense macrophage/biomaterial interactions (Greisler, 1988a; Greisler et al., 1989). This interaction leads to a differential activation of the macrophage which, in turn, yields different macrophage products being released into the microenvironment (Greisler et al., 1991). Greisler et al. (1988b) have documented active stimulatory or inhibitory effects of various bioresorbable and nonresorbable materials on myofibroblast, vascular smooth muscle cell, and endothelial cell regeneration, and has shown a transinterstitial migration to be their source when lactide/glycolide copolymeric prostheses are used. The rate of tissue ingrowth parallels the kinetics of macrophage-mediated prosthetic resorption in all lactide/glycolides studied (Greisler, 1982; Greisler et al., 1985, 1987a, 1988a). Macrophage phagocytosis of the prosthetic material is observed histologically as early as 1 week following implantation of a rapidly resorbed material, such as PGA or polyglactin 910 (PG910), and is followed by an extensive increase in the myofibroblast population and neovascularization of the inner capsules (Greisler, 1982; Greisler et al., 1985, 1986). Autoradiographic analyses using tritiated thymidine demonstrated a significantly increased mitotic index within these inner capsular cells, that mitotic index paralleling the course of prosthetic resorption (Greisler, 1991). Polyglactin 910, for example, resulted in a mitotic index of 20.1 ± 16.6% three weeks following implantation, progressively decreasing to 1.2 ± 1.3% after 12 weeks. The more slowly resorbed poly-p-dioxanone prostheses demonstrated a persistently elevated mitotic index, 7.1 ± 3.8%, 12 weeks after implantation, a time in which the prosthetic material was still being resorbed. By contrast, Dacron never yielded greater than a 1.2 ± 1.3% mitotic index (Greisler, 1991). These mitotic indices correlated closely with the slopes of the inner capsule thickening curves, suggesting that myofibroblast proliferation contributed heavily to this tissue deposition. Therefore, the degradation property of synthetic biodegradable polymers somehow relates to macrophage activation which subsequently leads to the macrophage production of the required growth factors that initiate tissue regeneration. Different degradation properties of synthetic biodegradable polymers would thus be expected to result in different levels of macrophage activation, that is, different degrees of tissue regeneration.

Biodegradable Polymeric Biomaterials: An Updated Overview

32-27

One major obstacle of using those commercially available absorbable polymers like aliphatic polyester-based as scaffolds for tissue engineering is the inherent foreign-body-induced inflammatory response that these FDA-approved biomaterials can induce. This obstacle may be able to be solved by the very recent development of amino acid-based biodegradable poly(ester amide)s (AA-PEAs). Two very recent studies (Horwitz et al., 2010; Jun, 2010) suggest that not only the AA-PEAs themselves exhibit much lower foreign-body inflammatory response than those FDA-approved absorbable polymeric biomaterials, but also can tame the inflammatory response of these FDA biomaterials when coupled with AA-PEAs. The details can be found in Section 32.4.3.

32.7  Supercritical Carbon Dioxide Sterilization There has been relatively little innovation in the area of medical device sterilization over the past many decades. Ethylene oxide (ETO) and gamma irradiation (γ-irradiation) are the only technologies currently available for medical devices. In particular, medical devices made from absorbable or biodegradable polymers such as absorbable sutures, surgical meshes, bone screws, and plates are sterilized almost exclusively by ETO due to undesirable chemical/thermal degradation from γ-irradiation or autoclave (Shalaby and Jamiolkowski, 1984; Shalaby and Linden, 1996). Although variations on γ-irradiation (namely, radiochemical sterilization pioneered by Shalaby et al., 2003) have been discovered and show promise in reducing absorbable biomaterial degradation, cobalt-60 γ-irradiation is still required and these facilities are generally housed in large industrial or research institutions that contribute to high operating costs associated with this technology. Thus, ETO sterilization is a standard method used for all absorbable polymer sterilization due to its effectiveness and lack of acceptable alternative means. In addition to the need of a prolonging period of degassing (e.g., 8–48 h depending on the material), the EPA and other government agencies have started to monitor ETO in response to personal and environmental issues because of the concern of both the short- and long-term adverse effects of residual ETO in sterilized products (e.g., cytotoxicity, delayed healing, etc.), and the fact that ETO is a recognized carcinogen and the precautionary measures needed to operate around the toxic and explosive nature of ETO. In an OSHA published web site (http://www.osha.gov/SLTC/ethyleneoxide/), it states: “EtO possesses several physical and health hazards that merit special attention. EtO is both flammable and highly reactive. Acute exposures to EtO gas may result in respiratory irritation and lung injury, headache, nausea, vomiting, diarrhea, shortness of breath, and cyanosis. Chronic exposure has been associated with the occurrence of cancer, reproductive effects, mutagenic changes, neurotoxicity, and sensitization.” The need of a viable alternative can also be illustrated from a practical standpoint. Due to safety concerns and barriers related to high upfront capital investment, medical device manufacturers do not normally have in house ETO or γ-irradiation facilities. The sterilization is done offsite, resulting in loss of product control, increased production time, and significant elevation of costs. Thus, the development of alternative sterilization processes that are capable of achieving validated sterility assurance levels of 10-6 (SAL6)—the benchmark for medical devices—without the use of dangerous ETO or damaging γ-irradiation is of great importance. NovaSterilis has developed a viable sterilization technology based on supercritical carbon dioxide technology (US patent 7,108,832). This alternative sterilization protocol uses supercritical carbon dioxide (scCO2) to sterilize absorbable biomaterials to a sterility assurance level of 10-6 (SAL6) while maintaining the mechanical properties of the biomaterials. The NovaSterilis scCO2 sterilization process involves the use of low temperature, low pressure, and a proprietary peracetic acid-based, nontoxic sterilization additive called Novakill. CO2 has a unique critical point, defined by a pressure (Pc = 1099 psi) and a temperature (Tc = 31.1°C) at which the liquid and vapor phases become indistinguishable. scCO2 has the density of a liquid, with increased solvating power but no surface tension. The inherent properties of scCO2 such as density, solvency, gas-like viscosity, diffusivity, compressibility, and very low surface tension facilitate penetration to the interior

32-28

Biomaterials

Percent of original stress left (%)

(a)

Normalized Dexon tensile stress comparisons between control and sterilized groups 120 100 80 60 40

Dexon control group

20

Dexon sterilized group

0

0 days

6–7 days

14 days

19–21 days 26–27 days

Number of days immersed (b) Percent of original strain left (%)

120

Normalized Dexon tensile strain comparisons between control and sterilized groups

100 80 60

Dexon control group

40

Dexon sterilized group

20 0

0 days

6–7 days

14 days

19–21 days 26–27 days

Number of days immersed

Percent of weight left (%)

(c)

105

Normalized Dexon weight loss comparisons between control and sterilized groups

100 95 90 Dexon control group

85

Dexon sterilized group

80 75

6–7 days

14 days

19–21 days

25–26 days

Number of days immersed

FIGURE 32.16  (a) Comparison of the tensile stresses of the sterilized and control groups of Dexon sutures upon in vitro degradation in pH 7.4 buffer over a period of 27 days. (b) Comparison of the tensile strains of sterilized and control groups of Dexon sutures upon in vitro degradation in pH 7.4 buffer over a period of 27 days. (c) Comparison of the modulus values of the sterilized and control groups of Dexon sutures upon in vitro degradation in pH 7.4 buffer over a period of 27 days.

Biodegradable Polymeric Biomaterials: An Updated Overview

32-29

of bone or soft tissue, thereby allowing inactivation of embedded pathogens. scCO2 retains the diffusive properties of CO2 gas and thus can rapidly penetrate substrates. The supercritical form of CO2 is a more potent biocide than argon, nitrogen, and nitrous oxide used under similar conditions, suggesting that its potency as a sterilant is derived from its chemical nature as well as transformation to the supercritical state. In fact, scCO2 on its own has been used to achieve high levels of disinfection (Dillow et al., 1999), but to attain the sterility assurance level required for medical devices (SAL6), a treatment must reduce the probability of contamination to 1 in one million, when the initial bioburden of an item is ≥106 colony forming units (CFUs) of a bioindicator organism. NovaSterilis developed NovaKill additive, a peracetic acid-based (PAA) entrainer (White et al., 2006). Addition of NovaKill to a sterilization cycle using scCO2 results in a SAL6 reduction in B. atrophaeus (standard biological indicator), which meets the definition for sterility. Furthermore, NovaSterilis has shown that scCO2 in the presence of Novakill additive can be used to inactive viruses and a host of organisms including bacteria, molds, and other fungi. In a recent collaborative preliminary study, Chu et al. have demonstrated that PGA sutures (Dexon) can be sterilized by scCO2 without any adverse effect on their tensile and hydrolytic degradation properties. In addition to achieving SAL6 sterilization on these sutures, we showed that the various tensile properties (e.g., tensile strain, tensile stress, and Young’s modulus) were unchanged between experimental (sterilized) and control groups (Figure 32.16). Furthermore, the data in Figure 32.16 also show that the scCO2 sterilization process led to a better retention of Dexon suture mechanical properties than the standard gas sterilization method (as control in Figure 32.16) upon in vitro degradation over a period of 27 days. Whether the NovaSterilis scCO2 sterilization technology could be applied to other absorbable polymers, further in-depth study would be required.

Defining Terms Biodegradation: Materials that could be broken down by nature either through hydrolytic mechanisms without the help of enzymes and/or enzymatic mechanism. It is loosely associated with absorbable, erodable, resorbable. Tissue Engineering: The ability to regenerate tissue through the help of artificial materials and devices.

References Ali, S.A.M., Zhong, S.P., Doherty, P.J., and Williams, D.F., 1993. Mechanisms of polymer degradation in implantable devices. I. Poly(caprolactone). Biomaterials, 14: 648. Atala, A., Kim, W., Paige, K.T., Vancanti, C.A., and Retil, A., 1994. Endoscopic treatment of vesicoureterall reflux with a chondrocye-alginate suspension. J. Urol., 152: 641–643. Babior, B.M., Kipnes R.S., and Cumutte, J.T., 1973. Biological defense mechanisms. The production by leukocytes of superoxide, a potential bactercidal agent. J. Clin. Invest., 52: 741. Badwey, J.A. and Kamovsky, M.L., 1980. Active oxygen species and the functions of phagocytic leucocytes. Ann. Rev. Biochem., 49: 695. Barrows, T.H., 1986. Degradable implant materials: A review of synthetic absorbable polymers and their applications. Clin. Mater., 1: 233–257. Barrows, T.H., 1994. Bioabsorbable poly(ester-amides). In: Biomedical Polymers: Designed-to-Degrade Systems, S.W. Shalaby, Ed., New York, Hanser, Chap. 4. Benedetti, L., Cortivo, R., Berti, T., Berti, A., and Pea, F., 1993. Biocompatibility and biodegradation of different hyaluronan derivatives (Hyaff) implanted in rats. Biomaterials, 14: 1154–1160. Bezwada, R.S., Jamiolkowski, D.D., Lee, I.Y., Agarwal, V., Persivale, J., Trenka-Benthin, S., Erneta, M., Suryadevara, J., Yang, A., and Liu, S., 1995. Monocryl suture: A new ultra-pliable absorbable monofilament suture. Biomaterials, 16: 1141–1148.

32-30

Biomaterials

Bezwada, R.S., Shalaby, S.W., Newman, H.D. Jr., and Kafrawy, A., 1990. Bioabsorbable copolymers of p-dioxanone and lactide for surgical devices. Trans. Soc. for Biomater., XIII: 194. Bostman, O.M., 1991. Absorbable implants for the fixation of fractures. J. Bone Joint Surg. Am., 73: 148. Bostman, O.M., Hirvensalo, E., Vainionpaa, S. et al., 1990. Degradable polyglycolide rods for the internal fixation of displaced bimalleolar fractures. Intern. Orthop. (Germany), 14: 1–8. Bowald, S., Busch, C., and Eriksson, I., 1979. Arterial regeneration following polyglactin 910 suture mesh grafting. Surgery, 86: 722–729. Bowald, S., Busch, C., and Eriksson, I., 1980. Absorbable material in vascular prosthesis. Acta Chir. Scand., 146: 391–395. Brandrup, J. and Immergut, E.H., 1975. Polymer Handbook, 2nd ed., New York, Wiley. Breitenbach, A. and Kissel, T. 1998. Biodegradable comb polyesters: Part I. Synthesis, characterisation and structural analysis of poly(lactide) and poly(lactic-co-glycolide) grafted onto water soluble poly(vinyl alcohol) as backbone. Polymer 39: 3261–3271. Breitenbach, A., Pistel, K.F., and Kissel, T. 2000. Biodegradable comb polyesters: Part II. Erosion and release properties of poly(vinyl alcohol)-graft-poly(lactic-co-glycolic acid). Polymer 41: 4781–4792. Campbell, N.D. and Chu, C.C., 1981. The effect of γ-irradiation on the biodegradation of polyglycolic acid synthetic sutures, the Tensile Strength Study. 27th International Symposium on Macromolecules, Abstracts of Communications, Vol. II, pp. 1348–1352, Strasbourg, France, July 6–9, 1981. Casey, D.J. and Roby, M.S., 1984. Synthetic copolymer surgical articles and method of manufacturing the same. US Patent 4,429,080, American Cyanamid. Cawthon, A.G., Defife, K.M., Vitiello, A., Charles, C.H., Landis, G., Mendy, J., Parcher, B., Bigger, J.E., and Turnell, W.G., 2007, Novel polymer vaccine protects ferrets against lethal challenge with highly pathogenic avian influenza virus, In: World Vaccine Congress, Washington, D.C., Four Seasons Hotel, March 19–22, 2007. Chatani, Y., Suehiro, K., Okita, Y., Tadokoro, H., and Chujo, K., 1968. Structural studies of polyesters, I. Crystal structure of polyglycolide. Die Makromol. Chem., 113: 215–229. Chen, S., Pieper, R., Webster, D.C., and Singh, J. 2005. Triblock copolymers: Synthesis, characterization, and delivery of a model protein. Int. J. Pharm., 288: 207–218. Chkhaidze, E., Tugushi, D., Kharadze1, D., Gomurashvili, Z., Chu, C.C., and Katsarava, R. 2011. New unsaturated biodegradable poly(ester amide)s composed of fumaric acid, leucine and α,ω-alkylene diols. J. Macromol. Sci. Part A—Pure & Appl. Chem. 48(7): 544–555. Choi, S., Kwon, Y.M., and Kim, S.W. 2004. Control of blood glucose by novel GLP-1 delivery using biodegradable triblock copolymer PLGA–PEG–PLGA in type 2 diabetic rats. Pharm Res., 21: 827–831. Chu, C.C., 1981. The In-vitro degradation of poly(glycolic acid) sutures: Effect of pH. J. Biomed. Mater. Res., 15: 795–804. Chu, C.C., 1982. The effect of pH on the in vitro degradation of poly(glycolide lactide) copolymer absorbable sutures. J. Biomed. Mater. Res., 16: 117–124. Chu, C.C., 1985a. Strain-accelerated hydrolytic degradation of synthetic absorbable sutures. In: Surgical Research Recent Development, ed. C.W. Hall, Pergamon Press, San Antonio, TX. Chu, C.C., 1985b. The Degradation and biocompatibility of suture materials. In: CRC Critical Reviews in Biocompatibility, ed. D.F. Williams, Vol. 1(3), CRC Press, Boca Raton, FL, pp. 261–322. Chu, C.C., 1991. Recent advancements in suture fibers for wound closure. In: High-Tech Fibrous Materials: Composites, Biomedical Materials, Protective Clothing, and Geotextiles, ed. T.L. Vigo and A.F. Turbak, ACS Symposium Series #457, American Chemical Society, Washington, DC, pp. 167–213. Chu, C.C., 1995a. Biodegradable suture materials: Intrinsic and extrinsic factors affecting biodegradation phenomena. In: Handbook of Biomaterials and Applications, ed. D.L. Wise, D.E. Altobelli, E.R. Schwartz, M. Yszemski, J.D. Gresser, and D.J. Trantolo, Marcel Dekker, New York. Chu, C.C. 1995b. Biodegradable suture materials: Intrinsic and extrinsic factors affecting biodegradation. In: Encyclopedic Handbook of Biomaterials and Applications, Part A: Materials, Vol. 1, ed. D.L. Wise, Marcel Dekker, New York, Chap. 17, pp. 543–688.

Biodegradable Polymeric Biomaterials: An Updated Overview

32-31

Chu, C.C., An overview of surgical suture materials, In: Biotextiles as Medical Implants, ed. M.W. King and B.S. Gupta, Chap. 16, Woodhead Publisher (In Press). Chu, C.C. and Browning, A., 1988. The study of thermal and gross morphologic properties of polyglycolic acid upon annealing and degradation treatments. J. Biomed. Mater. Res., 22: 699–712. Chu, C.C. and Campbell, N.D., 1982. Scanning electron microscope study of the hydrolytic degradation of poly(glycolic acid) suture. J. Biomed. Mater. Res., 16: 417–430. Chu, C.C., Hsu, A., Appel, M., and Beth, M. 1992. The effect of macrophage cell media on the in vitro hydrolytic degradation of synthetic absorbable sutures. 4th World Biomaterials Congress, April 27– May 1, 1992, Berlin, Germany. Chu, C.C. and Katsarava, R., 2003. Elastomeric Functional Biodegradable Copolyester Amides and Copolyester Urethanes. US Patent 6,503,538, January 7, 2003. Chu, C.C. and Kizil, Z., 1989. The effect of polymer morphology on the hydrolytic degradation of synthetic absorbable sutures. 3rd International ITV Conference on Biomaterials—Medical Textiles, Stuttgart, Germany, June 14–16, 1989. Chu, C.C. and Louie, M., 1985. A chemical means to study the degradation phenomena of polyglycolic acid absorbable polymer. J. Appl. Polym. Sci., 30: 3133–3141. Chu, C. C. and Sun, D., 2008. New electrospun synthetic biodegradable poly(ester amide) drug-eluting fibrous membranes for potential wound treatment, AATCC Symposium Proceeding Medical, Nonwovens, and Technical Textiles, Oct. 6–7, 2008, Durham, NC, pp. 60–76. Chu, C.C., von Fraunhofer, J.A., and Greisler, H.P., 1997. Wound Closure Biomaterials and Devices, CRC Press, Boca Raton, FL. Chu, C.C. and Williams, D.F., 1983. The effect of γ-irradiation on the enzymatic degradation of polyglycolic acid absorbable sutures. J. Biomed. Mater. Res., 17: 1029. Chu, C.C., Zhang, L., and Coyne, L., 1995. Effect of irradiation temperature on hydrolytic degradation properties of synthetic absorbable sutures and polymers. J. Appl. Polym. Sci. 56: 1275–1294. Chujo, K., Kobayashi, H., Suzuki, J., Tokuhara, S., and Tanabe, M., 1967a. Ring-opening polymerization of glycolide. Die Makromol. Chem., 100: 262–266. Chujo, K., Kobayashi, H., Suzuki, J., and Tokuhara, S., 1967b. Physical and chemical characteristics of polyglycolide. Die Makromol. Chem., 100: 267–270. Daniels, A.U., Taylor, M.S., Andriano, K.P., and Heller, J., 1992. Toxicity of absorbable polymers proposed for fracture fixation devices. Trans. 38th Ann. Mtg. Orthop. Res. Soc., 17: 88. DeFife, K.M., Grako, K., Cruz-Aranda, G., Price, S., Chantung, R., Macpherson, K., Khoshabeh, R., Gopalan, S., and Turnell, W., 2009. Poly(ester amide) co-polymers promote blood and tissue compatibility. J. Biomaterials Sci., Polym. Ed. 20(11): 1495–1511. Deng, M.X., Wu, J., Reinhart-King, C., and Chu, C.C., 2009. Synthesis and characterization of biodegradable poly(ester amide)s with pendant amine functional groups and in vitro cellular response. Biomacromolecules, 10(1): 14–20. Deng, M.X., Wu, J., Reinhart-King, C.A., and Chu, C.C., 2011. Biodegradable functional poly(ester amide) s with pendant hydroxyl functional groups: Synthesis, characterization, fabrication and in vitro cellular response. Acta Biomater., 7: 1504–1515. Devereux, D.F., O’Connell, S.M., Liesch, J.B., Weinstein, M., and Robertson, F.M., 1991. Induction of leukocyte activation by meshes surgically implanted in the peritoneal cavity. Am. J. Surg., 162: 243. De Wit, M.A., Wang, Z., Atkins, K.M., Mequanint, K., and Gillies, E.R., 2008. Syntheses, characterization, and functionalization of poly(ester amide)s with pendant amine functional groups. J. Polym. Sci., Part A: Polym. Chem., 46: 6376–6392. Dillow, A.K., Dehghani, F., Hrkach, J.S., Foster, N.R., and Langer, R., 1999. Bacterial inactivation by using near- and supercritical carbon dioxide. Proc. Natl Acad. Sci. USA, 96(18): 10344–10348. Dixit, V., 1994. Development of a bioartificial liver using isolated hepatocytes. Artif. Organs, 18: 371–384. Eitenmuller, J., David, A. et al. 1989a, ‘Die Versorgung von Sprunggelenksfrakturen unter ….’ Read at Jahrestagung der Deutschen Gesellschaft fur Unfalheikunde, Berlin, Nov. 22, 1989a.

32-32

Biomaterials

Eitenmüller, K.L., Schmickal, G.T., and Muhr, G., 1989b. Die versorgung von sprunggelenksfrakturen unter verwendung von platten und schrauben aus resorbierbarem polymer material. Presented at Jahrestagung der Deutschen Gesellschaft für Unfallheilkunde, Berlin, November 1989. Farnsworth. B.N. 2002. Posterior intravaginal slingplasty (infracoccygeal sacropexy) for severe posthysterectomy vaginal vault prolapse: A preliminary report on efficacy and safety. Int. Urogynecol. J., 13: 4–8. FDA, 2007. ‘FDA clears first of its kind suture made using DNA technology’, US Food and Drug Administration, February 12, 2007, US Department of Health and Human Services, http://www. fda.gov/bbs/topics/NEWS/2007/NEW01560.html. Forrester, A.R. and Purushotham, V., 1984. Mechanism of hydrolysis of esters by superoxide. J. Chem. Soc., Chem. Commun., 1505. Forrester, A.R. and Purushotham, V., 1987. Reactions of carboxylic acid derivatives with superoxide. J. Chem. Soc. Perkin Trans. 1: 945. Fredericks, R.J., Melveger, A.J., and Dolegiewitz, L.J., 1984. Morphological and structural changes in a copolymer of glycolide and lactide occurring as a result of hydrolysis. J. Polym. Sci. Phys. Ed. 22: 57–66. Freed, L.E., Marquis, J.C., Nohia, A., Emmanual, J., Mikos, A.G. and Langer, R., 1993. Neocartilage formation in vitro and in vivo using cells cultured on synthetic biodegradable polymers. J. Biomed. Mater. Res., 27: 11–23. Fukuzaki, H., Yoshida, M., Asano, M., Aiba, Y., and Kumakura, M., 1989. Direct copolymerization of glycolic acid with lactones in the absence of catalysts. Eur. Polym. J., 26: 457–461. Fukuzaki, H., Yoshida, M., Asano, M., Kumakura, M., Mashimo, T., Yuasa, H., Imai, K., Yamandka, H., Kawaharada, U., and Suzuki, K., 1991. A new biodegradable copolymer of glycolic acid and lactones with relatively low molecular weight prepared by direct copolycondensation in the absence of catalysts. J. Biomed. Mater. Res., 25: 315–328. Ganaha, F., Kao, E.Y., Wong, H., Elkins, C.J., Lee, J., Modanlou, S., Rhee, C. et al. 2004. Stent-based controlled release of intravascular angiostatin to limit plaque progression and in-stent restenosis. J Vasc Interv Radiol 15: 601–608. Gogolewski, S. and Pennings, A.J., 1983. Resorbable materials of poly(l-lactide). II. Fibres spun from solutions of poly(l-lactide) in good solvents. J. Appl. Polym. Sci., 28: 1045–1061. Goldstein, H.B., Vakili, B., Franco, N., Echols, K.T., and Chesson, R.R., 2007. The effect of suture material on outcomes of surgery for pelvic organ prolapse. Pelviperineology, 26: 174–177. Greisler, H.P., 1982. Arterial regeneration over absorbable prostheses. Arch. Surg., 117: 1425–1431. Greisler, H.P., 1988. Macrophage–biomaterial interactions with bioresorbable vascular prostheses. Trans. ASAIO, 34: 1051–1059. Greisler, H.P., 1991. Macrophage activation in bioresorbable vascular grafts. In: Vascular Endothelium: Physiological Basis of Clinical Problems. eds. J.D. Catravas, A.D. Callow, C.N. Gillis, and U. Ryan, Plenum Press, New York, NATO Advanced Study Institute, pp. 253–254. Greisler, H.P., Dennis, J.W., Endean, E.D., Ellinger, J., Friesel, R., and Burgess, W., 1989. Macrophage/ biomaterial interactions: The stimulation of endothelialization. J. Vasc. Surg., 9: 588–593. Greisler, H.P., Dennis, J.W., Endean, E.D., and Kim, D.U., 1988b. Derivation of neointima of vascular grafts. Circ. Suppl. I, 78: I6–I12. Greisler, H.P., Ellinger, J., Schwarcz, T.H., Golan, J., Raymond, R.M., and Kim, D.U., 1987a. Arterial regeneration over polydioxanone prostheses in the rabbit. Arch. Surg., 122: 715–721. Greisler, H.P., Endean, E.D., Klosak, J.J., Ellinger, J., Dennis, J.W., Buttle, K., and Kim, D.U., 1988c. Polyglactin 910/polydioxanone bicomponent totally resorbable vascular prostheses. J. Vasc. Surg., 7: 697–705. Greisler, H.P., Kim, D.U., Dennis, J.W., Klosak, J.J., Widerborg, K.A., Endean, E.D., Raymond, R.M., and Ellinger, J., 1987b. Compound polyglactin 910/polypropylene small vessel prostheses. J. Vasc. Surg., 5: 572–583. Greisler, H.P., Kim, D.U., Price, J.B., and Voorhees, A.B., 1985. Arterial regenerative activity after prosthetic implantation. Arch. Surg., 120: 315–323.

Biodegradable Polymeric Biomaterials: An Updated Overview

32-33

Greisler, H.P., Schwarcz, T.H., Ellinger, J., and Kim, D.U., 1986. Dacron inhibition of arterial regenerative activity. J. Vasc. Surg., 747–756. Greisler, H.P., Tattersall, C.W., Kloask, J.J. et al., 1991. Partially bioresorbable vascular grafts in dogs. Surgery, 110: 645–655. Gross, R.A., 1994. Bacterial polyesters: Structural variability in microbial synthesis. In: Biomedical Polymers: Designed-to-Degrade Systems, ed. S.W. Shalaby, Chap. 7, Hanser, New York. Gunatillake, P., Mayadunne, R., and Adhikari, R., 2006. Recent developments in biodegradable synthetic polymers. Biotechnol. Annu. Rev. 12: 301–347. Guo, K. and Chu, C.C., 2005. Synthesis, characterization and swelling behaviors of novel biodegradable unsaturated poly(ester-amide)s/poly(ethylene glycol) diacrylate hydrogels. J. Polym. Sci. Polym. Chem. Ed., 43: 3932–3944. Guo, K. and Chu, C.C., 2007a. Synthesis, characterization and biodegradation of copolymers of unsaturated and saturated poly(ester amide)s. J. Polym. Sci. Polym. Chem. Ed., 45: 1595–1606. Guo, K. and Chu, C.C., 2007b. Synthesis, characterization and biodegradation of novel poly(ether ester amide)s based on l-phenylalanine and oligoethylene glycol. Biomacromolecules, 8(9): 2851–2861. Guo, K. and Chu, C.C., 2008. Copolymers of unsaturated and saturated poly(ether ester amide)s: Synthesis, characterization and biodegradation. J. Appl. Polym. Sci., 110(3): 1858–1869. Guo, K. and Chu, C.C., 2009. Biodegradable and injectable Paclitaxel-loaded poly(ester amide)s microspheres: Fabrication and characterization, J. Biomed. Mater. Res. Part B. Appl. Biomater., 89 (2): 491–500. Guo, K. and Chu, C.C., 2010. Synthesis of biodegradable amino acid-based poly(ester amide) and poly(ether ester amide) with pendant functional groups, J. Appl. Polym. Sci. 117(6): 3386–3394. Guo, K., Chu, C.C., Chkhaidze, E., and Katsarava, R., 2005. Synthesis and characterization of novel biodegradable unsaturated poly(ester-amide)s. J. Polym. Sci. Polym. Chem. Ed., 43: 1463–1477. Haber, F. and Weiss, J., 1934. The catalytic decomposition of hydrogen peroxide by iron salts. Proc. R. Soc. Lond., A, 147: 332. Helder, J., Feijen, J., Lee, S.J., and Kim, W., 1986. Copolyemrs of d,l-lactic acid and glycine. Makromol. Chem. Rapid. Commun., 7: 193. Henderson, P.W., Kadouch, D.J.M., Singh, S.P., Zawaneh, P.N., Weiser, J., Yazdi, S., Weinstein, A., Krotscheck, U., Wechsler, B., Putnam, D., and Spector, J.A., 2010. A rapidly resorbable hemostatic biomaterial based on dihydroxyacetone, J. Biomed. Mater. Res., 93A: 776–782. Hirai, J. and Matsuda, T., 1995. Self-organized, tubular hybrid vascular tissue composed of vascular cells and collagen for low pressure-loaded venous system, Cell Transpl., 4: 597–608. Hofmann, G.O., 1992. Biodegradable implants in orthopaedic surgery—A review of the state of the art. Clin. Mater., 10: 75. Hollinger, J.O., 1995. Biomedical Applications of Synthetic Biodegradable Polymers, CRC Press, Boca Raton, FL. Horwitz, J.A., Shum, K.M., Bodle, J.C., Deng, M.X., Chu, C.C., and Reinhart-King, C.A., 2010. Biological performance of biodegradable amino acid-based poly(ester amide)s: Endothelial cell adhesion and inflammation in vitro. J. Biomed. Mater. Res. Part A, 95: 371–380. Huh, K.M., Cho, Y.W., and Park, K., 2003. PLGA–PEG block copolymers for drug formulations. Drug Deliv. Technol., 3(5): 42, 44–49. Ikada, Y. and Tsuji, H., 2000. Stereocomplex formation between enantiomeric poly(lactic acid)s. 12. Spherulite growth of low-molecular-weight poly(lactic acid)s from the melt. Macromol. Rapid Commun., 21: 117–132. Jamiokowski, D.D. and Shalaby, S.W., 1991. A polymeric radiostabilizer for absorbable polyesters. In: Radiation Effect of Polymers, ed. R.L. Clough and S.W. Shalaby, Chap. 18, pp. 300–309. ACS Symposium Series # 475, ACS, Washington, DC. Jeong, J.H., Kim, S.W., and Park, T.G., 2004. Biodegradable triblock copolymer of PLGA–PEG–PLGA enhances gene transfection efficiency. Pharm. Res., 21: 50–54. Johnson, R.A., 1976. Bis(3-methylbenzoyl)peroxide B-0-031 35 Di-m-ioluoyl peroxide. Tetrahedron Lett., 331.

32-34

Biomaterials

Jokhadze, G., Machaidze, M., Panosyan, H., Chu, C.C., and Katsarava, R., 2007. Synthesis and characterization of functional elastomeric biodegradable poly(ester amide)s copolymers. J. Biomater. Sci. Polym. Ed. 18(4): 411–438. Jung, T., Breitenbach, A., and Kissel, T., 2000. Sulfobutylated poly(vinyl alcohol)-graft-poly(lactideco-­glycolide)s facilitate the preparation of small negatively charged biodegradable nanospheres. J. Control Rel., 67: 157–169. Katsarava, R., Beridze, V., Arabuli, N., Kharadze, D., Chu, C.C., and Won, C.Y., 1999. Amino acid based bioanalogous polymers. Synthesis and study of regular poly(ester amide)s based on bis(α-amino acid) α, ω-alkylene diesters and aliphatic dicarboxylic acids. J. Polym. Sci. Part A: Polym Chem., 37: 391–407. Katsarava, R.D., Kharadze, D.P., Japaridze, N., Avalishvili, L.M., Omiadze, T.N., and Zaalishvili, M.M. 1985. Hetero-chain polymers based on natural amino-acids. Synthesis of polyamides from N-alpha, N-epsilon-bis(trimethylsilyl) lysine alkyl esters. Makromol. Chem., 186: 939–954. Katz, A., Mukherjee, D.P., Kaganov, A.L., and Gordon, S., 1985. A new synthetic monofilament absorbable suture made from polytrimethylene carbonate. Surg. Gynecol. Obstet., 161: 213–222. Kim, B.S. and Mooney, D.J., 1998. Engineering smooth muscle tissue with a predefined structure. J. Biomed. Mater. Res., 41: 322–332. Kim, B.S., Putman, A.J., Kulik, T.J., and Mooney, D.J., 1998. Optimizing seeding and culture methods to engineer smooth muscle tissue on biodegradable polymer matrices. Biotechnol. Bioeng., 57: 64–54. Kimura, Y., 1993. Biodegradable polymers. In: Biomedical Applications of Polymeric Materials, eds. T. Tsuruta, T. Hayashi, K. Kataoka, K. Ishihara, and Y. Kimura, pp. 164–190. CRC Press, Boca Raton, FL. Koelmel, D.F., Jamiokowski, D.D., Shalaby, S.W., and Bezwada, R.S., 1991. Low modulus radiation sterilizable monofilament sutures. Polym. Prepr., 32: 235–236. Kumar, N., Ravikumar, M.N.V., and Domb, A.J. 2001. Biodegradable block copolymers. Adv. Drug Deliv. Rev., 53:23–44. Kwon, Y.M. and Kim, S.W., 2004. Biodegradable triblock copolymer microspheres based on thermosensitive sol–gel transition. Pharm. Res., 21: 339–343. Larsen, N.E., Pollak, C.T., Reiner, K., Leshchiner, E., and Balazs, E.A., 1993. Hylan gel biomaterial: Dermal and immunologic compatibility. J. Biomed. Meter. Res., 27: 1129–1134. Lee, K.H. and Chu, C.C., 1996. The role of free radicals in hydrolytic degradation of absorable polymeric biomaterials. 5th World Biomaterials Congress, Toronto, Canada, May 29–June 2. Lee, K.H. and Chu, C.C., 1998. Molecular design of biologically active biodegradable polymers for biomedical applications. Macromol. Symp., 130: 71. Lee, K.H. and Chu, C.C., 2000. The effect of superoxide ions in the degradation of five synthetic absorbable suture materials. J. Biomed. Mater. Res., 49(1): 25–35. Lee, K.H., Chu, C.C., and Fred, J., 1996. Aminoxyl-containing radical spin in polymers and copolymers. U.S. Patent 5,516,881, May 16, 1996. Lee, K.H., Won, C.Y., and Chu, C.C., 1999. Hydrolysis of biodegradable polymers by superoxide ions. J. Polym. Sci. Part A, Polym. Chem. Ed., 37 (18): 3558–3567. Lee, P.Y., Li, Z., and Huang, L. 2003. Thermosensitive hydrogel as a TGF-beta gene delivery vehicle enhances diabetic would healing. Pharm. Res., 20: 1995–2000. Lee, S.H., Szinai, I., Carpenter, K., Katsarava, R., Jokhadze, G., Chu, C.C., Scheerder, I.D., and Hong, M.K., 2002. In vivo biocompatibility evaluation of stents coated by a new biodegradable elastomeric and functional polymer. Coron. Artery Dis., 13(4): 237–241. Leenslag, J.W. and Pennings, A.J., 1984. Synthesis of high-molecular weight poly(l-lactide) initiated with tin 2-ethylhexanoate. Makromol. Chem., 188: 1809–1814. Li, L. and Chu, C.C., 2009. Nitroxyl radical incorporated lectrospun biodegradable poly(ester amide) nanofibrous membranes. J. Biomater. Sci. Polym. Ed., 20: 341–361. Li, S., Anjard, S., Tashkov, I., and Vert, M., 1998. Hydrolytic degradation of PLA/PEO/PLA triblock copolymers prepared in the presence of Zn metal or CaH2. Polymer, 39: 5421–5430.

Biodegradable Polymeric Biomaterials: An Updated Overview

32-35

Li, Y. and Kissel, T., 1998. Synthesis, characteristics and in vitro degradation of star-block copolymers consisting of l-lactide, glycolide and branched multi-arm poly(ethylene oxide). Polymer, 39: 4421–4427. Loh, I.H., Chu, C.C., and Lin, H.L., 1992. Plasma surface modification of synthetic absorbable fibers for wound closure. J. Appl. Biomater. 3: 131–146. Magno, F. and Bontempelli, G., 1976. On the reaction kinetics of electrogenerated superoxide ion with aryl benzoates. J. Electroanal. Chem., 68: 337. Martin, D.P. and Williams, S.F. 2003. Medical applications of poly-4-hydroxybutyrate: A strong flexible absorbable biomaterial. Biochem. Eng. J., 16: 97–105. Matlaga, V.F. and Salthouse, T.N., 1980. Electron microscopic observations of polyglactin 910 suture sites, In First World Biomaterials Congress, Abstr., Baden, Austria, April 8–12, p. 2. Mikos, A.G., Sarakinos, G., Leite, S.M., Vacanti, J.P., and Langer, R., 1993. Laminated three-dimensional biodegradable forms for use in tissue engineering. Biomaterials, 14: 323–330. Miller, N.D. and Williams, D.F., 1984. The in vivo and in vitro degradation of poly(glycolic acid) suture material as a function of applied strain. Biomaterials, 5: 365–368. Miller, R.A., Brady, J.M., and Cutright, D.E., 1977. J. Biomed. Mater. Res., 11: 711. Mooney, D.J., Baldwin, D.F., Vacanti, J.P. and Langer, R., 1996a. Novel approach to fabricate porous sponges of poly(d,l-lactic-co-glycolic acid) without the use of organic solvents. Biomaterials, 17: 1417–1422. Mooney, D.J., Breuer, C., McNamara, K., Vacanti, J.P., and Langer, R., 1995. Fabricating tubular devices from polymers of lactic and glycolic acid for tissue engineering. Tissue Eng., 1: 107–118. Mooney, D.J., Mazzoni, C.L., Breuer, K., McNamara, J.P., Vacanti, J.P., and Langer, R., 1996b. Stabilized polyglycolic acid fibre-based tubes for tissue engineering. Biomaterials, 17: 115–124. Mooney, D.J., Organ, G., Vacanti, J.P., and Langer, R., 1994. Design and fabrication of biodegradable polymer devices to engineer tubular tissue. Cell Transplant, 3: 203–210. Mooney, D.J., Powell, C., Piana, J., and Rutherford, B., 1996c. Engineering dental pulp-like tissue in vitro. Biotechnol. Prog., 12: 865–868. Nair, L.S. and Laurencin, C.T., 2007. Biodegradable polymers as biomaterials. Prog. Polym. Sci. 32: 762–798. Nathan, A. and Kohn, J., 1994. Amino acid derived polymers. In: Biomedical Polymers: Designed-to-Degrade Systems, ed. S.W. Shalaby, Chap. 5. Hanser Publishers, New York. Pang, X. and Chu, C.C., 2010a. Synthesis, characterization and biodegradation of novel poly(ester amide)s and their functionalization. Biomaterials, 31(14): 3745–3754. Pang, X., Wu, J., Reinhart-King, C.A., and Chu, C.C., 2010. Synthesis and characterization of functionalized water soluble cationic poly(ester amide)s. J. Polym. Sci. Part A: Polym. Chem., 48: 3758–3766. Pang, X. and Chu, C.C., 2010b. Synthesis, characterization and biodegradation of poly(ester amide)s based hydrogels. Polymer, 51: 4200–4210. Paredes, N., Rodriguez-Gala, A., and Puiggali, N.J., 1998. Synthesis and characterization of a family of biodegradable poly(ester amide)s derived from glycine. J. Polym. Sci. Part A: Polym. Chem., 36: 1271–1282. Park, K., Shalaby, W.S.W., and Park. H., 1993. Biodegradable Hydrogels for Drug Delivery, Technomic Publishing, Lancaster, PA. Pistel, K.F., Breitenbach, A., Zange-Volland, R., and Kissel, T. 2001. Brush-like branched biodegradable polyesters: Part III. Protein release from microspheres of poly(vinyl alcohol)-graft-poly(lactic-coglycolic acid). J. Control Rel., 73: 7–20. Pratt, L. and Chu, C.C., 1993. Hydrolytic degradation of α-substituted polyglycolic acid: A semi-empirical computational study. J. Comput. Chem., 14: 809–817. Pratt, L. and Chu, C.C., 1994. The effect of electron donating and electron withdrawing substituents on the degradation rate of bioabsorbable polymers: A semi-empirical computational study. J. Mol. Struct., 304: 213–226. Pratt, L. and Chu, C.C., 1994b. A computational study of the hydrolysis of degradable polysaccharide biomaterials: Substituent effects on the hydrolytic mechanism. J. Comput. Chem., 15: 241–248.

32-36

Biomaterials

Pratt, L., Chu, A., Kim, J., Hsu, A., and Chu, C.C., 1993. The effect of electrolytes on the in vitro hydrolytic degradation of synthetic biodegradable polymers: Mechanical properties, thermodynamics and molecular modeling. J. Polym. Sci. Polym. Chem. Ed., 31: 1759–1769. Puelacher, W.C., Mooney, D., Langer, R., Upton, J., Vacanti, J.P., and Vananti, C.A., 1994. Design of nasoseptal cartilage replacements sunthesized from biodegradable polymers and chondrocytes. Biomaterials, 15: 774–778. San Fillipo, Jr., J., Romano, L.J., Chem, C.I., and Valentine, J.S., 1976. Cleavage of esters by superoxide. J. Org. Chem., 4: 586. Schwartz, S., Demars, S., Chu, C.C., White, J., Cooper, A, Rothrock, M., Adelman, M., and Yurt, R., 2008. Efficacy of poly(ester amide) dressings on partial thickness wound healing. Paper presented at the 3rd World Union of Wound Healing Societies, June 4–8, Toronto, Canada. Shalaby, S.W. and Jamiolkowski, D.D., 1984. Monomer process patent, US Patent, 1984, Ethicon, Inc. Shalaby, S.W., 1994. Biomedical Polymers: Designed-to-Degrade Systems, Hanser Publishers, New York. Shalaby, S.W. and Linden, C.L.J., 1996, Irradiation of Polmers, In Irradiation of Poymers, ed. R.L. Clough and S.W. Shalaby, American Chemical Society, Washington, DC, p. 246. Shalaby, S.W., Doyle, Y., Anneauxa, B.L., Carpentera, K.A., and Schiretz, F.R., 2003. Radiochemical sterilization and its use for sutures. Nucl. Instrum. Methods Phys. Res. B, 208: 110–114. Shieh, S.J., Zimmerman, M.C., and Parsons, J.R., 1990. Preliminary characterization of bioresorbable and nonresorbable synthetic fibers for the repair of soft tissue injuries. J. Biomed. Mater. Res., 24: 789–808. Song, H., 2007. l-Arginine-based Biodegradable Poly(ester amide)s, their Synthesis, Characterization, Fabrication, and Application as Drug and Gene Carriers, PhD thesis, Cornell University, May 2007. Song, H. and Chu, C.C., 2012. Synthesis and characterization of a new family of cationic poly (ester amide) s and their biological properties. J. Appl. Polym. Sci. 124(5): 3840–3853. Sugnuma, J., Alexander, H., Traub, J., and Ricci, J.L., 1992. Biological response of intramedullary bone to poly-l-lactic acid. In: Tissue-Inducing Biomater, ed. L.G. Cima and E.S. Ron, Mater. Res. Soc. Symp. Proc., Boston, MA, Material Research Society, 252: 339–343. Tsitlanadze, G., Machaidze, M., Kviria, T., Djavakhishvili, N., Chu, C.C., and Katsarava, R., 2004b. Biodegradation of amino acid based poly(ester amide)s: in vitro weight loss and preliminary in vivo study. J. Biomater. Sci. Polym. Ed. 15(1): 1–24. Tsitlanadze, G., Machaidze, M., Kviria, T., Katsarava, R., and Chu, C.C., 2004a. In vitro enzymatic biodegradation of amino acid based poly(ester amide)s biomaterials. J. Mater. Sci.: Mater. Med., 15: 185–190. Tunc, D.C., 1983. A high strength absorbable polymer for internal bone fixation. Trans. Soc. Biomater., 6: 47. Vert, M., Feijen, J., Albertsson, A., Scott, G., and Chiellini, E., 1992. Biodegradable Polymers and Plastics, Royal Society of Chemistry, Cambridge, England, UK. Villa, M.T., White, L.E., Alam, M., Yoo, S.S., and Walton, R.L. 2008. Barbed sutures: A review of the literature. Plast. Reconstr. Surg., 121(3): 102e–108e. White, A., Burns, D., and Christiansen, T.W., 2006. Effective terminal sterilization using supercritical carbon dioxide. J. Biotechnol., 123(4): 504–515. Williams, D.F., 1979. Some observations on the role of cellular enzymes in the in vivo degradation of polymers. ASTM Spec. Tech. Publ., 684: 61–75. Williams, D.F., 1990. Biodegradation of medical polymers. In: Concise Encyclopedia of Medical and Dental Materials, ed. D.F. Williams, pp. 69–74. Pergamon Press, New York. Williams, D.F. and Mort, E., 1977. Enzyme-accelerated hydrolysis of polyglycolic acid. J. Bioeng., 1: 231–238. Williams, D.F. and Chu, C.C., 1984. The effects of enzymes and gamma irradiation on the tensile strength and morphology of poly(p-dioxanone) fibers. J. Appl. Polym. Sci., 29: 1865–1877. Williams, D.F. and Zhong, S.P., 1991. Are free radicals involved in the biodegradation of implanted polymers. Adv. Mater., 3: 623. Winet, H. and Hollinger, J.O., 1993. Incorporation of polylactide–polyglycolide in a cortical defect: Neoosteogenesis in a bone chamber. J. Biomed. Mater. Res., 27: 667–676.

Biodegradable Polymeric Biomaterials: An Updated Overview

32-37

Wise, D.L., Fellmann, T.D., Sanderson, J.E., and Wentworth, R.L., 1979. Lactic/glycolic acid polymers. In: Drug Carriers in Biology and Medicine, ed. G. Gregoriadis, pp. 237–270. Academic Press, New York. Woodruff, M.A. and Hutmacher, D.W., 2010, The return of a forgotten polymer— Polycaprolactone in the 21st century. Progr. Polym. Sci., 35: 1217–1256. Wu, J., 2010. Arginine and Phenylalanine Based Poly(ester amide)s: Synthesis, Characterization and Applications, PhD thesis, Cornell University, August 2010. Yamanouchi, D., Wu, J., Lazar, A.N., Kent, K.G., Chu, C.C., and Liu, B., 2008. Biodegradable arginine-based poly(ester-amide)s as non-viral gene delivery reagents. Biomaterials, 29(22): 3269–3277. Yu, N.Y.C., Schindeler, A., Little, D.G., and Ruys, A.J., 2010. Biodegradable poly(a-hydroxy acid) polymer scaffolds for bone tissue engineering. J. Biomed. Mater. Res. Part B: Appl. Biomater., 93B: 285–295. Yu, T.J. and Chu, C.C., 1993. Bicomponent vascular grafts consisting of synthetic biodegradable fibers. Part I. In vitro study. J. Biomed. Mater. Res., 27: 1329–1339. Yu, T.J., Ho, D.M., and Chu, C.C., 1994. Bicomponent vascular grafts consisting of synthetic biodegradable fibers. Part II. In vivo healing response. J. Investigative Surg. 7: 195–211. Zawaneha, P.N., Singh, S.P., Paderac, R.F., Henderson, P.W., Spector, J.A., and Putnama, D. 2005. Design of an injectable synthetic and biodegradable surgical biomaterial. Proc. Natl Acad. Sci., USA, 107(24): 11014–11019. Zelikin, A.N. and Putnam, D., 2005. Poly(carbonate-acetal)s from the dimer form of dihydroxyacetone, Macromolecules, 38: 5532–5537. Zhang, L., Loh, I.H., and Chu, C.C., 1993. A combined γ-irradiation and plasma deposition treatment to achieve the ideal degradation properties of synthetic absorbable polymers. J. Biomed. Mater. Res., 27: 1425–1441. Zhong, S.P., Doherty, P.J., and Williams, D.F., 1994. A preliminary study on the free radical degradation of glycolic acid/lactic acid copolymer. Plast., Rubber Composites Process. Appl., 21: 89. Ziegler, T. and Nerem, R.M., 1994. Tissue engineering a blood vessel: Regulation of vascular biology by mechanical stress. J. Cell. Biochem., 56: 204–209.

Further Information Several recent books have very comprehensive descriptions of a variety of biodegradable polymeric  biomaterials, their synthesis, physical, chemical, mechanical, biodegradable, and biological properties. Barrows, T.H., 1986. Degradable implant materials: A review of synthetic absorbable polymers and their applications. Clin. Mater., 1: 233–257. Bastioli, C., 2005. Handbook of Biodegradable Polymers, UK, Smithers Rapra Press. Chu, C.C., 1995. Biodegradable suture materials: Intrinsic and extrinsic factors affecting biodegradation phenomena, In: Handbook of Biomaterials and Applications, eds. D.L. Wise, D.E. Altobelli, E.R. Schwartz, M. Yszemski, J.D. Gresser, and D.J. Trantolo, Marcel Dekker, New York. Chu, C.C., von Fraunhofer, J.A., and Greisler, H.P., 1997. Wound Closure Biomaterials and Devices, CRC Press, Boca Raton, FL. Domb, A. and Kumar, N., 2011. Biodegradable Polymers in Clinical use and Clinical Development, Wiley, New York. Hollinger, J.O., Ed., 1995. Biomedical Applications of Synthetic Biodegradable Polymers, CRC Press, Boca Raton, FL. Kimura, Y., 1993. Biodegradable polymers, In: Biomedical Applications of Polymeric Materials, T. Tsuruta, T. Hayashi, K. Kataoka, K. Ishihara, and Y. Kimura, Eds., pp. 164–190. CRC Press, Boca Raton, FL. Mittal, V., 2011. Nanocomposites with Biodegradable Polymers: Synthesis, Properties, and Future Perspectives, New York, NY, Oxford University Press.

32-38

Biomaterials

Park, K., Shalaby, W.S.W., and Park. H., 1993. Biodegradable Hydrogels for Drug Delivery, Technomic Publishing, Lancaster, PA. Shalaby, S.W., 1994. Biomedical Polymers: Designed-to-Degrade Systems, Hanser Publishers, New York. Shalaby, S.W. and Burg, K.J.L., 2003. Absorbable and Biodegradable Polymers, Boca Raton, CRC Press. Vert, M., Feijen, J., Albertsson, A., Scott, G., and Chiellini, E., 1992. Biodegradable Polymers and Plastics, Royal Society of Chemistry, Cambridge, England, UK.

33 Biologic Biomaterials: Tissue-Derived Biomaterials (Collagen) 33.1 Structure and Properties of Collagen and Collagen-Rich Tissues............................................................................................... 33-1 Structure of Collagen  •  Properties of Collagen-Rich Tissue

33.2 Biotechnology of Collagen........................................................... 33-11 Isolation and Purification of Collagen  •  Matrix Fabrication Technology

33.3 Design of a Resorbable Collagen-Based Medical Implant...... 33-13 Biocompatibility • Physical Dimension • Apparent Density • Pore Structure • Mechanical Property • Hydrophilicity • Permeability

Shu-Tung Li Collagen Matrix Inc.

33.4 Tissue Engineering for Tissue and Organ Regeneration......... 33-17 Defining Terms.......................................................................................... 33-18 References...................................................................................................33-20

33.1 Structure and Properties of Collagen and Collagen-Rich Tissues 33.1.1  Structure of Collagen Collagen is a multifunctional family of proteins of unique structural characteristics. It is the most abundant and ubiquitous protein in the body; its functions ranging from serving crucial biomechanical functions in bone, skin, tendon, and ligament to controlling cellular gene expressions in development (Nimni and Harkness, 1988). Collagen molecules, like all proteins, are formed in vivo by enzymatically regulated step-wise polymerization reaction between amino and carboxyl groups of amino acids, where R is a side group of an amino acid residue:



O H H  | | (−C − N − C −)n | R

(33.1)

The simplest amino acid is glycine (Gly) (R=H), where a hypothetical flat sheet organization of polyglycine molecules can form and be stabilized by intermolecular hydrogen bonds (Figure 33.1a). However, when R is a large group as in most other amino acids, the stereochemical constraints frequently force the 33-1

33-2

Biomaterials (a)

HR N

H

C

N

(b)

HR C

N

H

H

R

O

H

O

HR

H

O

N

C

C H R

O

N

C

H

O

Hydrogen bond

H R Right-handed helix

0.72 nM

FIGURE 33.1  (a) Hypothetical flat sheet structure of a protein. (b) Helical arrangement of a protein chain.

polypeptide chain to adapt a less constraining conformation by rotating the bulky R groups away from the crowded interactions, forming a helix, where the large R groups are directed toward the surface of the helix (Figure 33.1b). The hydrogen bonds are allowed to form within a helix between the hydrogen attached to nitrogen in one amino acid residue and the oxygen attached to a second amino acid residue. Thus, the final conformation of a protein, which is directly related to its function, is governed primarily by the amino acid sequence of the particular protein. Collagen is a protein comprised of three polypeptides (α chains), each having a general amino acid sequence of (–Gly–X–Y–)n, where X is any other amino acid and is frequently proline (Pro) and Y is any other amino acid and is frequently hydroxyproline (Hyp). A typical amino acid composition of collagen is shown in Table 33.1. The application of helical diffraction theory to a high-angle collagen x-ray diffraction pattern (Rich and Crick, 1961) and the stereochemical constraints from the unusual amino acid composition (Eastoe, 1967) led to the initial triple-helical model and subsequent modified triple helix of the collagen molecule. Thus, collagen can be broadly defined as a protein which has a typical triple helix extending over the major part of the molecule. Within the triple helix, glycine must be present as every third amino acid, and proline and hydroxyproline are required to form and stabilize the triple helix. To date, 19 proteins can be classified as collagen (Fukai et al., 1994). Among the various collagens, type I collagen is the most abundant and is the major constituent of bone, skin, ligament, and TABLE 33.1  Amino Acid Content of Collagen Amino Acids Gly Pro Hyp Acid polar (Asp, Glu, Asn) Basic polar (Lys, Arg, His) Other

Content, Residues/1000 Residuesa 334 122 96 124 91 233

Source: From Eastoe, J.E. 1967. Treatise on Collagen, pp. 1–72, Academic Press, New York. With permission. a Reported values are average values of 10 different determinations for tendon tissue.

33-3

Biologic Biomaterials: Tissue-Derived Biomaterials (Collagen)

tendon. Due to the abundance and ready accessibility of these tissues, they have been frequently used as a source for the preparation of collagen. This chapter will not review the details of the structure of the different collagens. The readers are referred to recent reviews for a more in-depth discussion of this subject (Nimni, 1988; van der Rest et  al., 1990; Fukai et  al., 1994; Brodsky and Ramshaw, 1997). It is, however, of particular relevance to review some salient structural features of the type I collagen in order to facilitate the subsequent discussions of properties and its relation to biomedical applications. A type I collagen molecule (also referred to as tropocollagen) isolated from various tissues has a molecular weight of about 283,000 Da. It is comprised of three left-handed helical polypeptide chains (Figure 33.2a) which are intertwined forming a right-handed helix around a central molecular axis (Figure 33.2b). Two of the polypeptide chains are identical (α1) having 1056 amino acid residues, and the third polypeptide chain (α2) has 1029 amino acid residues (Miller, 1984). The triple-helical structure has a rise per residue of 0.286 nm and a unit twist of 108°, with 10 residues in three turns and a helical pitch (repeating distance within a single chain) of 30 residues or 8.68 nm (Fraser et al., 1983). More than 95% of the amino acids have the sequence Gly–X–Y. The remaining 5% of the molecules do not have the sequence Gly–X–Y and are, therefore, not triple helical. These nonhelical portions of the molecules are located at the N- and C-terminal ends and are referred to as telopeptides (9–26 residues) (Miller, 1984). The whole molecule has a length of about 280 nm and a diameter of about 1.5 nm and has a conformation similar to a rigid rod (Figure 33.2c). The triple-helical structure of a collagen molecule is stabilized by several factors (Figure 33.3): (1) a tight fit of the amino acids within the triple helix—this geometrical stabilization factor can be appreciated from a space-filling model constructed from a triple helix with Gly–Pro–Hyp sequence (Figure 33.3); (2) the interchain hydrogen bond formation between the backbone carbonyl and amino hydrogen interactions; and (3) the contribution of water molecules to the interchain hydrogen bond formation. (a)

0.286 nm

2.86 nm

(b) α1 α1 α2

(c)

1.5 nm 280 nm 280 nm

(d)

0.4D

0.6D

4.4D 64 nm

FIGURE 33.2  Formation of collagen, which can be visualized as taking place in several steps: (a) singlechain left-handed helix; (b) three single chains intertwined into a triple stranded helix; (c) a collagen (tropocollagen) molecule; (d) collagen molecules aligned in D staggered fashion in a fibril producing overlap and hole regions.

33-4

Biomaterials

FIGURE 33.3  A space-filling model of the collagen triple helix, showing all the atoms in a 10-residue segment of repeating triplet sequence (Gly–Pro–Hyp)n. The arrow shows an interchain hydrogen bond. The arrowheads identify the hydroxy groups of hydroxyproline in one chain. The circle shows a hydrogen-bonded water molecule. The short white lines identify the ridge of amino acid chains. The short black lines indicate the supercoil of one chain. (Reprinted from Extracellular Matrix Biochemistry, In K.A. Piez and A.H. Reddi (Eds.), New York, Piez, K.A., Molecular and aggregate structures of the collagens. p. 5, Copyright 1984, with permission from Elsevier.)

The telopeptides are regions where intermolecular crosslinks are formed in vivo. A common intermolecular crosslink is formed between an allysine (the ε-amino group of lysine or hydroxy-lysine has been converted to an aldehyde) of one telopeptide of one molecule and an ε-amino group of a lysine or hydroxylysine in the triple helix or a second molecule (Equation 33.2). Thus, the method commonly used to solubilize the collagen molecules from crosslinked fibrils with proteolytic enzymes such as pepsin removes the telopeptides (cleaves the intermolecular crosslinks) from the collagen molecule. The pepsin-solubilized collagen is occasionally referred to as atelocollagen (Stenzl et al., 1974).



OH | Pr − CH2 − CH2 − CH2 − CHO + H2 N − CH2 − CH − CH2 − CH2 − Pr Allysine Hydroxylysine OH | → Pr − CH2 − CH2 − CH2 − CH = N − CH2 − CH − CH2 − CH2 − Pr Dehydrohydroxylysinonorleucine

(33.2)



Since the presence of hydroxyproline is unique in collagen (elastin contains a small amount), the determination of collagen content in a collagen-rich tissue is readily done by assaying the hydroxyproline content. Collagen does not appear to exist as isolated molecules in the extracellular space in the body. Instead, collagen molecules aggregate into fibrils. Depending on the tissue and age, a collagen fibril varies from about 50 to 300 nm in diameter with indeterminate length and can easily be seen under electron microscopy (Figure 33.4). The fibrils are important structural building units for large fibers (Figure 33.5). Collagen molecules are arranged in specific orders both longitudinally and in cross-sectionally, and the

Biologic Biomaterials: Tissue-Derived Biomaterials (Collagen)

33-5

FIGURE 33.4  (a) Scanning electron micrograph of the surface of an adult rabbit bone matrix, showing how the collagen fibrils branch and interconnect in an intricate, woven pattern (×4800). (Adapted from Tiffit, J.T. 1980. Fundamental and Clinical Bone Physiology, p. 51, JB Lippincott Co., Philadelphia, PA.) (b) Transmission electron micrographs of (×24,000) parallel collagen fibrils in tendon. (c) Transmission electron micrographs of (×24,000) mesh work of fibrils in skin. ((b) and (c) With kind permission from Springer Science+Business Media: Biomechanics, Mechanical Properties of Living Tissues, 2nd ed., 1993, p. 255, New York, Fung, Y.C.)

organization of collagen molecules in a fibril is tissue-specific (Katz and Li, 1972, 1973b). The 2-D structure (the projection of a 3-D structure onto a 2-D plane) of a type I collagen fibril has been unequivocally defined both by an analysis of small-angle x-ray diffraction pattern along the meridian of a collagenous tissue (Bear, 1952) and by examination of the transmission electron micrographs of tissues stained with negative or positive stains (Hodge and Petruska, 1963). In this structure (Figure 33.2d), the collagen molecules are staggered with respect to one another by a distance of D (64–67 nm) or multiple of D, where D is the fundamental repeat distance seen in the small-angle x-ray diffraction pattern, or the repeating distance seen in the electron micrographs. Since a collagen molecule has a length of about 4.4D, this staggering of collagen molecules creates overlap regions of about 0.4D and hole or defect regions of about 0.6D. One interesting and important structural aspect of collagen is its approximate equal number of acidic (aspartic and glutamic acids) and basic (lysines and arginines) side groups. Since these groups are charged under physiological conditions, the collagen is essentially electrically neutral (Li and Katz, 1976). The packing of collagen molecules with a D staggering results in clusters of regions where the charged groups are located (Hofmann and Kuhn, 1981). These groups therefore are in close proximity to form intra- and intermolecular hydrogen-bonded salt-linkages of the form

33-6

Biomaterials

Unit fibrils 800–1000 Å

1–4 μ

FIGURE 33.5  Collagen fibers of the connective tissue in general which are composed of unit collagen fibrils.

(Pr–COO −+ H3N–Pr) (Li et al., 1975). In addition, the side groups of many amino acids are nonpolar [alanine (Ala), valine (Val), leucine (Leu), isoleucine (Ile), proline (Pro), and phenolalanine (Phe)] in character and hence hydrophobic; therefore, chains with these amino acids avoid contact with water molecules and seek interactions with the nonpolar chains of amino acids. In fact, the result of molecular packing of collagen in a fibril is such that the nonpolar groups are also clustered, forming hydrophobic regions within collagen fibrils (Hofmann and Kuhn, 1981). Indeed, the packing of the collagen molecules in various tissues is believed to be a result of intermolecular interactions involving both the electrostatic and hydrophobic interactions (Li et al., 1975; Hofmann and Kuhn, 1981; Katz and Li, 1981). The 3-D organization of type I collagen molecules within a fibril has been the subject of extensive research over the last 40 years (Ramachandran, 1967; Katz and Li, 1972, 1973a,b, 1981; Miller, 1976; Fraser et al., 1983; Yamuchi et al., 1986). Many structural models have been proposed based on an analysis of equatorial and off-equatorial x-ray diffraction patterns of rat-tail-tendon collagen (North et al., 1954; Miller, 1976), intrafibrillar volume determination of various collagenous tissues (Katz and Li, 1972, 1973a,b), intermolecular side chain interactions (Hofmann and Kuhn, 1981; Katz and Li, 1981; Li et al., 1981), and intermolecular crosslinking patterns studies (Yamuchi et al., 1986). The general understanding of the 3-D molecular packing in type I collagen fibrils is that the collagen molecules are arranged in hexagonal or near-hexagonal arrays (Katz and Li, 1972, 1981; Miller, 1976). Depending on the tissue, the intermolecular distance varies from about 0.15 nm in rat tail tendon to as large as 0.18 nm in bone and dentin (Katz and Li, 1973b). The axial staggering of the molecules by 1–4D with respect to one another is tissue-specific and has not yet been fully elucidated. There are very few interspecies differences in the structure of type I collagen molecule. The extensive homology of the structure of type I collagen may explain why this collagen obtained from animal species is acceptable as a material for human implantation.

Biologic Biomaterials: Tissue-Derived Biomaterials (Collagen)

33-7

33.1.2  Properties of Collagen-Rich Tissue The function of collagenous tissue is related to its structure and properties. This section reviews some important properties of collagen-rich tissues. 33.1.2.1  Physical and Biomechanical Properties The physical properties of tissues vary according to the amount and structural variations of the collagen fibers. In general, a collagen-rich tissue contains about 75–90% of collagen on a dry weight basis. Table 33.2 is a typical composition of a collagen-rich soft tissue such as skin. Collagen fibers (bundles of collagen fibrils) are arranged in different configurations in different tissues for their respective functions at specific anatomic sites. For example, collagen fibers are arranged in parallel in tendon (Figure 33.4b) and ligament for their high-tensile strength requirements, whereas they are arranged in random arrays in skin (Figure 33.4c) to provide the resiliency of the tissue under stress. Other structure-supporting functions of collagen such as transparency for the lens of the eye and shaping of the ear or tip of the nose can also be provided by the collagen fiber. Thus, an important physical property of collagen is the 3-D organization of the collagen fibers. The collagen-rich tissues can be thought of as a composite polymeric material in which the highly oriented crystalline collagen fibrils are embedded in the amorphous ground substance of noncollagenous polysaccharides, glycoproteins, and elastin. When the tissue is heated, its specific volume increases, exhibiting a glass transition at about 40°C and a melting of the crystalline collagen fibrils at about 56°C. The melting temperature of crystalline collagen fibrils is referred to as the denaturation temperature of collagenous tissues. The stress–strain curves of a collagenous tissue such as tendon exhibit nonlinear behavior (Figure 33.6). This nonlinear behavior of stress–strain of tendon collagen is similar to that observed in synthetic fibers. The initial toe region represents alignment of fibers in the direction of stress. The steep rise in slope represents the majority of fibers stretched along their long axes. The decrease in slope following the steep rise may represent the breaking of individual fibers prior to the final catastrophic failure. Table 33.3 summarizes some mechanical properties of collagen and elastic fibers. The difference in biomechanical properties between collagen and elastin is a good example of the requirements for these proteins to serve their specific functions in the body. Unlike tendon or ligament, skin consists of collagen fibers randomly arranged in layers or lamellae. Thus skin tissues show mechanical anisotropy (Figure 33.7). Another feature of the stress–strain curve of the skin is its extensibility under small load when compared to tendon. At smaller loads, the fibers are straightened and aligned rather than stretched. Upon further stretching, the fibrous lamellae align with respect to each other and resist further extension. When the skin is highly stretched, the modulus of elasticity approaches that of tendon as expected of the aligned collagen fibers. Cartilage is another collagen-rich tissue which has two main physiological functions. One is the maintenance of shape (ear, tip of nose, and rings around the trachea) and the other is to provide bearing surfaces at joints. It contains very large and diffuse proteoglycan (protein-polysaccharide) TABLE 33.2  Composition of Collagen-Rich Soft Tissues Component

Composition (%)

Collagen Proteoglycans and polysaccharides Elastin and glycoproteins Water

75 (dry), 30 (wet) 20 (dry)  0  i = 0, …, N. (43.21) Thus, Δϕi = 0, i = 0,…,N, and by virtue of Equation 43.20, δϕ = 0, such that ϕ1 = ϕ2. The identity contradicts the assumption of two distinct Galerkin solutions. This proves the solution is unique [33].

43.4.2  Finite Difference Method Perhaps the most traditional way to solve Equation 43.1 utilizes the FD approach by discretizing the solution domain Ω using a grid of uniform hexahedral elements. The coordinates of a typical grid point

43-9

Computational Methods and Software for Bioelectric Field Problems

are x = lh, y = mh, z = nh (l,m,n = integers), and the value of Φ(x, y, z) at a grid point is denoted by Φl,m,n. Taylor’s theorem can then be utilized to provide the difference equations. For example ⎛ ⎞ ∂ Φ 1 2 ∂ 2 Φ 1 3 ∂ 3Φ Φ l +1,m,n = ⎜ Φ + h + h + h + ⎟⎠ l ,m,n ⎝ ∂ x 2 ∂ x2 6 ∂ x3



(43.22)

with similar equations for Φl−1,m,n, Φl,m+1,n, Φl,m−1,n,…. The FD representation of Equation 43.1 is Φ l +1,m,n − 2Φ l ,m,n + Φ l −1,m,n Φ l ,m +1,n − 2Φ l ,m,n + Φ l ,m −1,n + h2 h2 Φ l ,m,n +1 − 2Φ l ,m,n + Φ l ,m,n −1 = − I l ,m,n (v ) + h2



(43.23)

or, equivalently

Φl+1,m,n + Φl−1,m,n + Φl,m+1,n + Φl,m−1,n + Φl,m,n+1 + Φl,m,n−1 − 6Φl,m,n = −h2 Il,m,n (v). (43.24)

If we define the vector Φ to be [Φ1,1,1…Φ1,1,N−1;…Φ1,N−1,1…ΦN−1,N−1,N−1]T to designate the (N − 1)3 unknown grid values, and pull out all the known information from Equation 43.24, we can reformulate Equation 43.1 by its FD approximation in the form of the matrix equation AΦ = b, where b is a vector that contains the sources and modifications due to the Dirichlet boundary condition. Unlike the traditional Taylor’s series expansion method, the Galerkin approach utilizes basis functions, such as linear piecewise polynomials, to approximate the true solution. For example, the Galerkin approximation to the sample problem Equation 43.1 would require evaluating Equation 43.13 for the specific grid formation and specific choice of basis function: ⎛



∫ ⎜⎝ σ Ω

x

∂φ ∂ψ i ⎞ ∂φ ∂ψ i ∂φ ∂ψ i dΩ = − I v ψ i dΩ. + σy + σz ∂ z ∂ z ⎟⎠ ∂y ∂y ∂x ∂ x

∫

Ω



(43.25)

Difference quotients are then used to approximate the derivatives in Equation 43.25. We note that if linear basis functions are utilized in Equation 43.25, one obtains a formulation that corresponds exactly with the standard FD operator. Regardless of the difference scheme or order of basis function, the approximation results in a linear system of equations of the form AΦ = b, subject to the appropriate boundary conditions.

43.4.3  Finite Element Method As we have seen above, in the classical numerical treatment for partial differential equations—the FD method—the solution domain is approximated by a grid of uniformly spaced nodes. At each node, the governing differential equation is approximated by an algebraic expression that references adjacent grid points. A system of equations is obtained by evaluating the previous algebraic approximations for each node in the domain. Finally, the system is solved for each value of the dependent variable at each node. In the FE method, the solution domain can be discretized into a number of uniform or nonuniform FEs that are connected via nodes. The change of the dependent variable with regard to location is approximated within each element by an interpolation function. The interpolation function is defined relative to the values of the variable at the nodes associated with each element. The original boundary value problem is then replaced with an equivalent integral formulation (such as Equation 43.13). The interpolation functions are then substituted into the integral equation, integrated, and combined with the results from all other elements in the solution domain. The results of this procedure can be

43-10

Bioelectric Phenomena

reformulated into a matrix equation of the form AΦ = b, which is subsequently solved for the unknown variable [3,36]. The formulation of the FE approximation starts with the Galerkin approximation, (σ∇Φ, ∇Φ) = −(I v , Φ), where Φ is our test function. We now use the FE method to turn the continuous problems into a discrete formulation. First, we discretize the solution domain, Ω = ∪eE=1 Ωe , and define a finite dimensional subspace, Vh ⊂ V = {Φ: Φ is continuous on Ω, ∇Φ is piecewise continuous on Ω} . One usually defines parameters of the function Φ ∈ Vh at node points α i = Φ(xi ), i = 0,1,…,N. If we now define the basis functions, ψi ∈ V h, as linear continuous piecewise functions that take the value 1 at node points and zero at other node points, then we can represent the function Φ ∈ Vh as N

Φ(x ) =



∑ α Ψ (x), i

(43.26)

i

i =0

such that each Φ ∈ Vh can be written in a unique way as a linear combination of the basis functions Ψi ∈ V h. Now, the FE approximation of the original boundary value problem can be stated as

Find Φ h ∈ Vh such that (σ ∇Φ h , ∇Φ) = −(I v , Φ).

(43.27)

Furthermore, if Φh ∈V h satisfies Equation 43.27, then we have (σ∇Φh, ∇Ψi ) = −(Iv, Ψi ) [42,47]. Finally, since Φh itself can be expressed as the linear combination N

Φh =

∑ ξ Ψ (x ) i

i

ξ i = Φ h (xi ),

(43.28)

i =0

we can then write Equation 43.27 as N

∑ ξ (σ ∇Ψ , ∇Ψ ) = −(I , Ψ ) i



ij

i

j

v

j

j = 0,…, N ,

(43.29)

i =0

subject to the Dirichlet boundary condition. Then the FE approximation of Equation 43.1 can equivalently be expressed as a system of N equations with N unknowns ξi,…,ξN (e.g., the electrostatic potentials). In matrix form, the above system can be written as Aξ = b, where A = (aij) is called the global stiffness matrix and has elements (aij) = (σij ∇Ψi, ∇Ψj), while bi = −(Iv, Ψi) and is usually termed the load vector. For volume conductor problems, A contains all the geometry and conductivity information of the model. The matrix A is symmetric and positive definite; thus, it is nonsingular and has a unique solution. Because the basis function differs from zero for only a few intervals, A is sparse (only a few of its entries are nonzero). 43.4.3.1  Application of the FE Method for 3D Domains We now illustrate the concepts of the FE method by considering the solution of Equation 43.1 using linear 3D elements. We start with a 3D domain Ω that represents the geometry of our volume conductor and break it up into discrete elements to form a finite dimensional subspace, Ωh. For 3D domains, we have the choice of representing our function as either tetrahedra

 = α + α x + α y + α z, Φ 1 2 3 4



(43.30)

43-11

Computational Methods and Software for Bioelectric Field Problems

or hexahedra

 = α + α x + α y + α z + α xy + α yz + α xz + α xyz. Φ 1 2 3 4 5 6 7 8



(43.31)

Because of space limitations, we restrict our development to tetrahedra, knowing that it is easy to modify our formulae for hexahedra. We take out a specific tetrahedra from our finite dimensional subspace and apply the previous formulations for the four vertices



 ⎞ ⎛1 ⎛Φ 1 ⎜ ⎟ ⎜ ⎜ Φ2 ⎟ = ⎜1 ⎜Φ  ⎟ ⎜1 ⎜ 3⎟ ⎜  ⎟⎠ ⎝ 1 ⎜⎝ Φ 4

x1 x2 x3 x4

y1 y2 y3 y4

z1 ⎞ ⎛ α1 ⎞ z2 ⎟ ⎜ α 2 ⎟ ⎟⎜ ⎟, z3 ⎟ ⎜ α 3 ⎟ ⎟⎜ ⎟ z4 ⎠ ⎝ α4 ⎠

(43.32)

or  = Cα, Φ i



(43.33)



which define the coordinate vertices, and  , α = C −1Φ i



(43.34)



 at any point within which defines the coefficients. From Equations 43.30 and 43.34, we can express Φ the tetrahedra

 = [1, x , y , z ]α = Sα = SC −1Φ  Φ i



(43.35)

or, most succinctly  = Φ

∑ N Φ . i

(43.36)

i

i



 is the solution value at node i, and N = SC −1 is the local shape function or basis function. This can be Φ i expressed in a variety of ways in the literature (depending, usually, on whether you are reading engineering or mathematical treatments of FE analysis):



Φ j (N i ) = N i ( x , y , z ) = f i ( x , y , z ) ≡

ai + bi x + ci y + di z , 6V

(43.37)

z1 z2 z3 z4

(43.38)

where

defines the volume of the tetrahedra, V.

1 1 6V = 1 1

x1 x2 x3 x3

y1 y2 y3 y3



43-12

Bioelectric Phenomena

Now that we have a suitable set of basis functions, we can find the FE approximation to our 3D problem. Our original problem can be formulated as a(u, v) = (Iv, v) ​ ​ ∀ v ∈ Ω,



(43.39)

where

∫

a(u, v ) = ∇u ⋅ ∇v dΩ

(43.40)



Ω

and (I v , v) =

∫I

v

⋅ v dΩ.

(43.41)



Ω

The FE approximation to the original boundary value problem is a(uh, v) = (Iv, v) ​ ​ ∀ v ∈ Ωh,



(43.42)

which has the equivalent form N

∑ ξ a(Φ , Φ ) = (I , Φ ), i



i

j

v

(43.43)

j

i =1



where a(Φi, Φj) = a(Φi(Nj), Φj(Ni)), (43.44)



which can be expressed by the matrix and vector elements aij =

⎛ ∂Ni ∂N j ∂Ni ∂N j ∂Ni ∂N j ⎞ dΩ + + ∂x ∂y ∂y ∂ z ∂ z ⎟⎠

∫ ⎜⎝ ∂x

ΩE

(43.45)



and Ii =

∫ N I dΩ. i v

ΩE

(43.46)



Fortunately, the above quantities are easy to evaluate for linear tetrahedra. As a matter of fact, there are closed form solutions for the matrix elements (aij):

∫N N N N a 1



b 2

Ωh

c 3

d 4

dΩ = 6V

a !b ! c ! d ! . (a + b + c + d + 3)!

(43.47)



Therefore aij =

∫

ΩE

bib j + cic j + did j bib j + cic j + did j dΩ = , 6V 6V 2

(43.48)

and, for the right-hand side (RHS), we have, assuming constant sources, Ii =

∫

ΩE

ai + bi x + ci y + di z VI I v dΩ = v . 6V 4



(43.49)

43-13

Computational Methods and Software for Bioelectric Field Problems

which have the compact forms aij(n) =



1 (n ) (n ) (b b + ci(n)c (jn) + di(n)d (jn) ) 6V i j

(43.50)

and VI v 4

I i(n) =



for constant sources.

(43.51)



Now, we add up all the contributions from each element into a global matrix and global vector. Nel

∑ (a



(n ) ij

)(ξ i ) = (I i(n) ),

(43.52)

n =1

where Nel is equal to the total number of elements in the discretized solution domain and i represents the node numbers (vertices). This yields a linear system of equations of the form AΦ = b, where Φ is our solution vector of voltages, A represents the geometry and conductivity of our volume conductor, and b represents the contributions from the current sources and boundary conditions. For the FD method, it turns out that the Dirichlet boundary condition is easy to apply while the Neumann condition takes a little extra effort. For the FE method, it is just the opposite. The Neumann boundary condition ∇Φ ⋅ n = 0



(43.53)

is satisfied automatically within the Galerkin and variational formulations. This can be seen by using Green’s divergence theorem

∫ ∇ ⋅ A dx = ∫ A ⋅ n dS,



Ω

Γ

(43.54)

and applying it to the left-hand side of the Galerkin FE formulation: ∂v ∂w ⎤ ⎡ ∂v ∂w dΩ + ∂ x2 ∂ x2 ⎥⎦ 1 ∂ x1

∫ ∇v ⋅ ∇w dΩ ≡ ∫ ⎢⎣ ∂ x Ω

Ω

=

⎡ ∂ 2w ∂ 2w ⎤ ∂w ⎤ ⎡ ∂w ⎢v ∂ x n1 + v ∂ x n2 ⎥ dS − v ⎢ ∂ x 2 + ∂ x 2 ⎥ dΩ 1 2 ⎣ ⎦ 2 ⎦ ⎣ 1 Γ Ω

∫ ∫

= v

Γ

∫

∂w dS − v ∇2w dΩ. ∂n

∫

(43.55)

Ω

If we multiply our original differential equation, ∇2Φ = −Iv, by an arbitrary test function and integrate, we obtain

∫

(I v , v ) = − (∇2Φ)v dΩ = −

Ω

∂Φ

∫ ∂n Γ

∫

(43.56)

v dS + ∇Φ ⋅ ∇v dΩ = a(Φ, v ), Ω



where the boundary integral term, ∂ Φ/∂n vanishes and we obtain the standard Galerkin FE formulation.

43-14

Bioelectric Phenomena

To apply the Dirichlet condition, we have to work a bit harder. To apply the Dirichlet boundary condition directly, one usually modifies the (aij) matrix and bi vector such that one can use standard linear system solvers. This is accomplished by implementing the following steps. Assuming we know the ith value of ui 1. Subtract from the ith member of the RHS the product of aij and the known value of Φi (call it Φi ); this yields the new RHS, bi = bi − aij Φ j . 2. Zero the ith row and column of A: aij = a ji = 0. 3. Assign a ii = 1 . 4. Set the jth member of the RHS equal to Φi . 5. Continue for each Dirichlet condition. 6. Solve the augmented system, A Φ = bv .

43.4.4  Boundary Element Method For bioelectric field problems with isotropic domains (and few inhomogeneities), another technique, called the BE method, may be utilized. This technique utilizes information only upon the boundaries of interest, and thus reduces the dimension of any field problem by one. For differential operators, the response at any given point to sources and boundary conditions depends only on the response at neighboring points. The FD and FE methods approximate differential operators defined on subregions (volume elements) in the domain; hence, direct mutual influence (connectivity) exists only between neighboring elements, and the coefficient matrices generated by these methods have relatively few nonzero coefficients in any given matrix row. As is demonstrated by Maxwell’s laws [39], equations in differential forms can often be replaced by equations in integral forms, for example, the potential distribution in a domain is uniquely defined by the volume sources and the potential and current density on the boundary. The BE method utilizes this fact by transforming the differential operator defined in the domain to integral operators defined on the boundary. In the BE method [6,13,40], only the boundary is discretized; hence, the mesh generation is considerably simpler for this method than for the volume methods. Boundary solutions are obtained directly by solving the set of linear equations; however, potentials and gradients in the domain can be evaluated only after the boundary solutions have been obtained. As this method has a rich history in bioelectric field problems, the reader is referred to some of the classic references for further information regarding the application of the BE method to bioelectric field problems [5,30,67,69].

43.4.5  Solution Methods and Computational Considerations The application of each of the previous approximation methods to Equation 43.1 yields a system of linear equations of the form AΦ = b, which must be solved to obtain the final solution. There are a plethora of available techniques for the solutions of such systems. The solution techniques can be broadly categorized as direct and iterative solvers. Direct solvers include Gaussian elimination and lower-upper (LU) decomposition, while iterative methods include Jacobi, Gauss–Seidel, successive overrelaxation (SOR), and conjugate gradient (CG) methods, among others. The choice of the particular solution method is highly dependent upon the approximation technique employed to obtain the linear system, upon the size of the resulting system, and upon accessible computational resources. For example, the linear system resulting from the application of the FD or FE method will yield a matrix A that is symmetric, positive definite, and sparse. The matrix resulting from the FD method will have a specific band-diagonal structure that is dependent on the order of difference equations one uses to approximate the governing equation. The matrix resulting from the FE method will be exceedingly sparse so that only a few of the off diagonal elements will be nonzero. The application of the BE method, on the other hand, will yield a matrix A that is dense and nonsymmetric and thus requires a different choice of solver.

Computational Methods and Software for Bioelectric Field Problems

43-15

The choice of the optimal solver is further complicated by the size of the system versus access to computational resources. Sequential direct methods are usually confined to single workstations and thus the size of the system should fit in memory for optimal performance. Sequential iterative methods can be employed when the size of the system exceeds the memory of the machine; however, one pays a price in terms of performance as direct methods are usually much faster than iterative methods. In many cases, the size of the system exceeds the computational capability of a single workstation and one must resort to the use of clusters of workstations and/or parallel computers. While new and improved methods continue to appear in the numerical analysis literature, the author’s studies comparing various solution techniques for direct and inverse bioelectric field problems have resulted in the conclusion that the preconditioned CG methods and MG methods are the best overall performers for volume conductor problems computed on single workstations. Specifically, the incomplete Choleski conjugate gradient (ICCG) method works well for the FE method* and the preconditioned biconjugate gradient (BCG) methods are often utilized for BE methods. When clusters of workstations and/or parallel architectures are considered, the choice is less clear. For use with some high-performance architectures that contain large amounts of memory, parallel direct methods such as LU decomposition become attractive; however, preconditioned CG methods still perform well. A discussion of parallel computing methods for the solution of biomedical field problems could fill an entire text. Thus, the reader is directed to the following references on parallel scientific computing [18,23,28].

43.4.6 Comparison of Methods Since we do not have space to provide a detailed, quantitative description of each of the previously mentioned methods, we give an abbreviated summary of the applicability of each method in solving different types of bioelectric field problems. As outlined above, the FD, FE, and BE methods can all be used to approximate the boundary value problems that arise in biomedical research problems. The choice depends on the nature of the problem. The FE and FD methods are similar in that the entire solution domain must be discretized, while with the BE method, only the bounding surfaces must be discretized. For regular domains, the FD method is generally the easiest method to code and implement, but the FD method usually requires special modifications to define irregular boundaries, abrupt changes in material properties, and complex boundary conditions. While typically more difficult to implement, the BE and FE methods are preferred for problems with irregular, inhomogeneous domains and mixed boundary conditions. The FE method is superior to the BE method for representing nonlinearity and true anisotropy, while the BE method is superior to the FE method for problems where only the boundary solution is of interest or where solutions are wanted in a set of highly irregularly spaced points in the domain. Because the computational mesh is simpler for the BE method than for the FE method, the BE program requires less bookkeeping than an FE program. For this reason, BE programs are often considered easier to develop than FE programs; however, the difficulties associated with singular integrals in the BE method are often highly underestimated. In general, the FE method is preferred for problems where the domain is highly heterogeneous, whereas the BE method is preferred for highly homogeneous domains.

43.5  Adaptive Methods Thus far, we have discussed how one formulates the problem, discretizes the geometry, and finds an approximate solution. We are now faced with answering the difficult question pertaining to the accuracy

*

This is specifically for the FE method applied to elliptic problems. Such problems yield a matrix that is symmetric and positive definite. The Choleski decomposition only exists for symmetric, positive-definite matrices.

43-16

Bioelectric Phenomena

of our solution. Without reference to experimental data, how can we judge the validity of our solutions? To give yourself an intuitive feel for the problem (and possible solution), consider the approximation of a two-dimensional region discretized into triangular elements. We will apply the FE method to solve the Laplace equation in the region. First, consider the approximation of the potential field Φ(x, y) by a two-dimensional Taylor’s series expansion about a point (x, y):



∂ Φ( x , y ) ⎤ ⎡ ∂ Φ( x , y ) Φ( x + h , y + k ) = Φ( x , y ) + ⎢ h +k ∂ ∂ y ⎥⎦ x ⎣ 1 ⎡ ∂ 2 Φ( x , y ) ∂ 2 Φ( x , y ) ∂ 2 Φ( x , y ) ⎤ + ⎢h 2 + + 2hk + k2 2 2! ⎣ ∂x ∂y ∂ x ∂ 2 y ⎥⎦



(43.57)

where h and k are the maximum x and y distances within an element. Using the first two terms (up to first-order terms) in the above Taylor’s expansion, we can obtain the standard linear interpolation function for a triangle:



∂ Φ( x i , y i ) 1 = [Φ ( y − ym ) + Φ m ( yi − y j ) + Φ j ( ym − yi )], ∂x 2A i j

(43.58)

where A is the area of the triangle. Likewise, one could calculate the interpolant for the other two nodes and discover that ∂ Φ( x i , y i ) ∂ Φ( x j , y j ) ∂ Φ( x m , y m ) = = ∂x ∂x ∂x



(43.59)

is constant over the triangle (and thus so is the gradient in y as well). Thus, we can derive the standard linear interpolation formulas on a triangle that represent the first two terms of the Taylor’s series expansion. This means that the error due to discretization (from using linear elements) is proportional to the third term of the Taylor’s expansion: ε≈

∂ 2 Φ( x , y ) ∂ 2 Φ( x , y ) ⎤ 1 ⎡ 2 ∂ 2 Φ( x , y ) , h + 2hk + k2 ⎢ 2 2! ⎣ ∂x ∂ y ∂x ∂2 y ⎥⎦



(43.60)

where Φ is the exact solution. We can conjecture, then, that the error due to discretization for firstorder linear elements is proportional to the second derivative. If Φ is a linear function over the element, then the first derivative is a constant and the second derivative is zero and there is no error due to discretization. This implies that the gradient must be constant over each element. If the function is not linear, or the gradient is not constant over an element, the second derivative will not be zero and is proportional to the error incurred due to “improper” discretization. Examining Equation 43.60, we can easily see that one way to decrease the error is to decrease the size of h and k. As h and k go to zero, the error tends to zero as well. Thus, decreasing the mesh size in places of high errors due to high gradients decreases the error. As an aside, we note that if one divides Equation 43.9 by hk, one can also express the error in terms of the elemental aspect ratio h/k, which is a measure of the relative shape of the element. It is easy to see that one must be careful to maintain an aspect ratio as close to unity as possible. The problem with the preceding heuristic argument is that one has to know the exact solution a priori before one can estimate the error. This is certainly a drawback considering we are trying to accurately approximate Φ.

Computational Methods and Software for Bioelectric Field Problems

43-17

43.5.1 Convergence of a Sequence of Approximate Solutions Let us try to quantify our error a bit further. When we consider the preceding example, it seems to make sense that if we increase the number of DOF we used to approximate our function, the accuracy must approach the true solution. That is, we would hope that the sequence of approximate solutions will converge to the exact solution as the number of DOF increases indefinitely:

 (x ) → 0 as N → ∞. Φ( x ) − Φ n



(43.61)

This is a statement of pointwise convergence. It describes the approximate solution as approaching arbitrarily close to the exact solution at each point in the domain as the number of DOF increases. Measures of convergence often depend on how the closeness of measuring the distance between functions is defined. Another common description of measuring convergence is uniform convergence, which  (x ) in the domain vanish as N → ∞. This is stronger requires that the maximum value of Φ(x ) − Φ n than pointwise convergence as it requires a uniform rate of convergence at every point in the domain. Two other commonly used measures are convergence in energy and convergence in mean, which involve measuring an average of a function of the pointwise error over the domain [14]. In general, proving pointwise convergence is very difficult except in the simplest cases, while proving the convergence of an averaged value, such as energy, is often easier. Of course, scientists and engineers are often much more interested in assuring that their answers are accurate in a pointwise sense than in an energy sense because they typically want to know values of the solution Φ(x) and gradients ∇Φ(x) at specific places. One intermediate form of convergence is called the Cauchy convergence. Here, we require the sequences of two different approximate solutions to approach arbitrarily close to each other:

 (x ) → 0 as M , N → ∞. Φ m (x ) − Φ n

(43.62)

While the pointwise convergence expression would imply the previous equation, it is important to note that the Cauchy convergence does not imply pointwise convergence, as the functions could converge to an answer other than the true solution. While we cannot be assured of pointwise convergence of these functions for all but of the simplest cases, there do exist theorems that ensure that a sequence of approximate solutions must converge to the exact solution (assuming no computational errors) if the basis functions satisfy certain conditions. The theorems can only ensure convergence in an average sense over the entire domain but it is usually the case that if the solution converges in an average sense (energy, etc.), then it will converge in the pointwise sense as well.

43.5.2 Energy Norms The error in energy, measured by the energy norm, is defined in general as [88–90]



⎛ T ⎞ e = ⎜ e LedΩ⎟ ⎝Ω ⎠

∫

1/ 2

,

(43.63)

 (x ) and L is the differential operator for the governing differential equation (i.e., it where e = Φ(x ) − Φ n contains the derivatives operating on Φ(x) and any function multiplying Φ(x)). For physical problems, this is often associated with the energy density.

43-18

Bioelectric Phenomena

Another common measure of convergence utilizes the L2 norm. This can be termed the average error and can be associated with errors in any quantity. The L2 norm is defined as



(e)L2

⎛ T ⎞ = ⎜ e edΩ⎟ ⎝ ⎠

∫

1/ 2

Ω

.

(43.64)

While the norms given above are defined on the whole domain, one can note that the square of each can be obtained by summing element contributions M



(e)2 =

∑ (e) , 2 i

(43.65)

i =1

where i represents an element contribution and m the total element number. Often for an optimal FE mesh, one tries to make the contributions to this square of the norm equal for all elements. While the absolute values given by the energy or L2 norms have little value, one can construct a relative percentage error that can be more readily interpreted:

η=

(e) × 100. (Φ)

(43.66)

This quantity, in effect, represents a weighted RMS error. The analysis can be determined for the whole domain or for element subdomains. One can use it in an adaptive algorithm by checking element errors against some predefined tolerance, η0, and increasing the DOF only of those areas above the predefined tolerance. Two other methods, the p and the hp methods, have been found, in most cases, to converge faster than the h method. The p method of refinement requires that one increase the order of the basis function that was used to represent the interpolation (i.e., linear to quadratic to cubic, etc.). The hp method is a combination of the h and p methods and has recently been shown to converge the fastest of the three methods (but, as you might imagine, it is the hardest to implement). To find out more about adaptive refinement methods, see References 2, 14, 22, 43, 47, 71, and 88.

43.6  Software for Bioelectric Field Problems In the past few years, there have been a number of research software systems that have been created for the computational study of biomedical problems, including bioelectric field problems. Below, I have listed several open source software that are useful for computational bioelectric field problems. The list is meant to be representative and not comprehensive and I apologize for inevitable omissions. • SCIRun (software.sci.utah.edu/scirun) is our own example of a general-purpose, problem-solving environment that has found extremely broad application both within biomedicine [34,46,48,77,85] and in areas as diverse as nuclear physics [49,70] and combustion [63]. An overview of SCIRun will be presented below. • CMISS (www.cmiss.org) also has a very broad technical scope and application domain [9] and is the basis of many simulation studies in bioelectric fields and biomechanics of the heart and other organs [24,35,60], respiratory physiology [78], and bioelectric fields in the gastrointestinal system [68]. • Simbios (simbios.stanford.edu) is a newly emerging software system from the NIH-funded “Center for Physics-Based Simulation of Biological Structures” [72]. The biological coverage of Simbios is very broad, with the goal to help biomedical researchers understand biological

Computational Methods and Software for Bioelectric Field Problems

•

• • • • • • •

•

• • • • •

•

•

43-19

form and function as they create novel drugs, synthetic tissues, medical devices, and surgical interventions [8,10,11,20]. 3D Slicer (www.slicer.org) is a multiplatform, open source set of tools for visualization and image computing. It is also from an NIH NCBC Center, the “National Alliance for Medical Image Computing” (NA-MIC) (www.na-mic.org) [65]. Slicer includes a wide variety of image processing and visualization capabilities, including segmentation, registration, and analysis [52,56]. Seg3D (www.seg3d.org) is a lightweight 3D segmentation program, which includes interactive volume visualization capabilities [91]. Brainstorm (neuroimage.usc.edu/brainstorm) is an integrated toolkit dedicated to visualization and processing of data recorded from magnetoencephalography (MEG) and EEG. Brainstorm provides a comprehensive set of tools for researchers interested in MEG/EEG [41,61,74]. SimBio and NeuroFEM (www.simbio.de and www.neurofem.com) is a combination of programs directed at source localization in the brain using patient-specific FE models with multiple conductivities and even anisotropic conductivity [85]. Continuity (www.continuity.ucsd.edu) is a problem-solving environment for multiscale modeling in bioengineering and physiology with special emphasis on cardiac biomechanics, transport, and electrophysiology. PCEnv (www.cellml.org/downloads/pcenv) is the Physiome CellML Environment, an integrated software that provides an interface to the cell simulation models of the CellML project. Virtual Cell (www.nrcam.uchc.edu) is a software system for a wide range of scientists, from experimental cell biologists to theoretical biophysicists, who wish to create models of cellular structure and chemical, electrical, or mechanical function. Neuron (www.neuron.yale.edu/neuron) is a simulation environment for modeling individual neurons and networks of neurons, which is especially well suited to comparisons with experimental data. It has a very user-friendly interface that provides tools for building, managing, and using models in a way that is numerically sound and computationally efficient. Genesis (www.genesis-sim.org) has a very similar application domain as Neuron as a generalpurpose simulation platform to simulate neural systems ranging from subcellular organelles and biochemical reactions to complex models of single neurons, large networks, and systems-level models. TetGen (tetgen.berlios.de) creates tetrahedral volume meshes from volume data made from triangulated surfaces for solving partial differential equations by FE or finite volume methods. BioMesh3D (www.sci.utah.edu/software) is a 3D tetrahedral and hexahedral mesh generator [92]. ITK (www.itk.org), the Insight ToolKit, is a comprehensive set of software functions to perform image processing or analysis. ITK is the basis of many other tools (e.g., SCIRun and Seg3D) as they lack a graphical user interface (UI) and exist only as a C++ class library [37]. VTK (www.vtk.org), the Visualization ToolKit, consists of an extensive library for visualization functions that is a component in many larger systems, for example, 3D slicer [73]. ImageVis3D (www.sci.utah.edu/software) is a volume visualization program that allows for largescale interactive visualization of scalar field datasets using isosurface extraction and volume rendering. ImageVis3D [93] works on multiple platforms, including desktops and laptops, the iPhone and iPad, and large distributed high-performance computers via the VisIT software system. VisIT (www.vacet.org) is a scalable, parallel software system for visualizing results of large-scale computational simulations. VisIT was created as part of the DOE ASCI and SciDAC programs. Research and development of VisIT continues as part of the DOE Visualization and Analytics Center for Enabling Technologies (VACET). ECGSim (www.ecgsim.org) is a program that computes the body surface potentials from the heart and allows the user to make changes in the electrical characteristics of the cells in any region of the heart. Its goal is to provide an educational tool but also a way to study the relationship between

43-20

Bioelectric Phenomena

the electric activity of the ventricular myocardium and the resulting potentials on the thorax under both normal and pathological conditions. • LabHeart (www.labheart.org) is primarily a teaching tool that simulates the cardiac action potential, including the individual ionic currents and the fluctuations in intracellular calcium concentration. • iCell is an Internet-based simulation program that allows the user to generate action potentials from a wide range of cell types [21].

43.6.1 SCIRun This section provides a brief overview of the SCIRun and BioPSE problem-solving environments and presents examples of their use for the solution of bioelectric field problems. The SCIRun* software system is an integrated, extensible, visualization-driven, open source, problem-solving environment that has been developed at the University of Utah’s Scientific Computing and Imaging Institute [38]. For an application developer, SCIRun provides a software platform, upon which other applications can be rapidly constructed. SCIRun provides native support for interprocess communication, resource management (e.g., thread migration, memory management), and parallel computing. These operating system type services enable the dataflow aspects of the system. In addition to these low-level services, SCIRun also provides a number of built-in libraries and data structures that developers can use and can build upon. And at the highest level, SCIRun provides a rich set of algorithms for modeling, simulation, and visualization. All these levels of functionality can be leveraged by the developer when constructing new algorithms or applications in SCIRun [46,64,84]. The application program interface (API) to SCIRun is the visual dataflow environment called the network editor. Within the network editor, programs can be visually assembled from the library of available algorithms. The dataflow network for a sample bioelectric field simulation is shown in Figure 43.4. The boxes in the network are called modules, and the lines connecting them are called datapipes. The point of attachment, where a datapipe attaches to a module, is called a dataport; the dataports on the tops of the modules are input ports, and the ports on the bottoms of the modules are output ports. In SCIRun, the dataports are color-coded to indicate the type of the data. For example, the blue datapipes are for matrices, and the yellow datapipes are for fields. Fields are used to represent 3D geometry as well as the data values that are defined over that geometry. Taken as a whole, the collection of modules and datapipes in a dataflow application is called a network, or net. Each module can have an optional UI button on its module; if the user presses the UI button, a separate window appears, with controls for viewing and modifying the state of the module’s parameters.

43.6.2 BioPSE SCIRun comes with a set of general-purpose modules that are not specific to any particular application. Modules can also be generated for a specific application, or for adding a set of optional functionality (such as raster data processing), in which case they are organized into a package. The package that has been primarily used and extended in this work is called BioPSE [17]. BioPSE stands for biomedical problem-solving environment, and contains all the functionality that is specific to bioelectric field problems. The example network in Figure 43.4 is solving a bioelectric field problem for a dipolar source in a volume conductor model of a head. The domain is discretized with linear tetrahedral FEs, with five

*

SCIRun is pronounced “ski-run” and derives its name from the Scientific Computing and Imaging (SCI) Institute, which is pronounced “ski” as in “Ski Utah.”

Computational Methods and Software for Bioelectric Field Problems

43-21

FIGURE 43.4  BioPSE dataflow network for modeling, simulating, and visualizing the bioelectric field generated in a realistic head model due to a single dipole source.

different conductivity types assigned through the volume. The problem is numerically approximated with a linear system, and is solved using the CG method. A set of virtual electrode points are rendered as pseudocolored spheres, to visualize the potentials at those locations on the scalp, and an isopotential surface and several pseudocolored electric field streamlines are also shown. The BioPSE network implements this simulation and visualization with a collection of interconnected modules. The tetrahedral FE mesh with conductivity values is read in with one of the FieldReaders. That Field is then passed into the SetupFEMatrix module, which produces a stiffness matrix, A, as output. The RHS of the linear system, b, is generated by the ApplyFEMCurrentSource module, which applies

43-22

Bioelectric Phenomena

the dipole source as a boundary condition. The linear system AΦ = b is then solved by the SolveMatrix module to recover the potentials at all the nodes in the domain. This solution is then attached to the geometry with the ManageFieldData module, and the results are visualized. A complete description of this application is available in the tutorial section of the SCIRun User’s Guide, and can be downloaded from the SCI Institute’s website [1]. In addition to the BioPSE modules that appear in the above net, BioPSE also contains modules for generating and using FE lead fields, for constructing separating surfaces from segmented volumes or planar contours, for running boundary element method (BEM) simulations, and for visualizing lead potentials over time.

43.6.3 PowerApps Historically, one of the major hurdles to SCIRun becoming a tool for the scientist as well as the engineer has been SCIRun’s dataflow interface. While visual programming is natural for computer scientists and engineers, who are accustomed to writing software and building algorithmic pipelines, it is overly cumbersome for application scientists. Even when a dataflow network implements a specific application

FIGURE 43.5  BioPSE dataflow interface to the forward bioelectric field application. The underlying dataflow network implements the application with modular interconnected components called modules. Data are passed between the modules as input and output parameters to the algorithms. While this is a useful interface for prototyping, it is nonintuitive for end-users; it is confusing to have a separate user interface window to control the settings for each module. Moreover, the entries in the user interface windows fail to provide a semantic context for their settings. For example, the text-entry field on the SampleField user interface that is labeled “Maximum number of samples” is controlling the number of electric field streamlines that are produced for the visualization.

Computational Methods and Software for Bioelectric Field Problems

43-23

(such as the forward bioelectric field simulation network provided with BioPSE and detailed in the BioPSE tutorial), the UI components of the network are presented to the user in separate UI windows, without any semantic context for their settings. For example, SCIRun provides file browser UIs for reading in data. However, on the dataflow network, all the file browsers have the same generic presentation. Historically, there has not been a way to present the filename entries in their semantic context, for example, to indicate that one entry should identify the electrodes input file and another should identify the FE mesh file. While this interface shortcoming has long been identified, it has only recently been addressed. With the 1.20 release of BioPSE/SCIRun (in October 2003), we introduced PowerApps. A PowerApp is a customized interface built atop a dataflow application network. The dataflow network controls the execution and synchronization of the modules that comprise the application, but the generic UI windows are replaced with entries that are placed in the context of a single application-specific interface window. With the 1.20 release of BioPSE, we released a PowerApp called BioFEM. BioFEM has been built atop the dataflow network shown in Figure 43.4, and provides a useful example for demonstrating the differences between the dataflow and PowerApp views of the same functionality. In Figure 43.5, the dataflow version of the application is shown: the user has separate interface windows for controlling different aspects of the simulation and visualization. In contrast, the PowerApp version is shown in Figure 43.6; here, the application has been wrapped up into a single interface window, with logically arranged and semantically labeled UI elements composed within panels and notetabs.

FIGURE 43.6  The BioFEM custom interface. Though the application is functionality equivalent to the dataflow version shown in Figures 43.4 and 43.5, this PowerApp version provides an easier-to-use custom interface. Everything is contained within a single window; the user is led through the steps of loading and visualizing the data with the tabs on the right; the generic control settings have been replaced with contextually appropriate labels; and application-specific tooltips (not shown) appear when the user places the cursor over any user interface element.

43-24

Bioelectric Phenomena

FIGURE 43.7  The BioTensor PowerApp. Just as with BioFEM, we have wrapped up a complicated dataflow network into a custom application. In the left panel, the user is guided through the stages of loading the data, co-registering the diffusion-weighted images, and constructing diffusion tensors. On the right panel, the user has controls for setting the visualization options. In the rendering window in the middle, the user can render and interact with the dataset.

In addition to bioelectric field problems, the BioPSE system can also be used to investigate other biomedical applications. For example, we have wrapped the tensor and raster data processing functionality of the Teem toolkit into the Teem package of BioPSE, and we have used that increased functionality to develop the BioTensor PowerApp, as seen in Figure 43.7. BioTensor presents a customized interface to a 140-module dataflow network. With BioTensor, the user can visualize diffusion-weighted imaging (DWI) datasets to investigate the anisotropic structure of biological tissues. The application supports the import of DICOM and Analyze datasets, and implements the latest diffusion tensor visualization techniques, including superquadric glyphs [51] and tensorlines [83] (both shown).

Acknowledgments Support for this research comes largely from the NIH Center for Integrative Biomedical Computing (www. sci.utah.edu/cibc), funded by grants from the National Center for Research Resources (5P41RR012553-14) and the National Institute of General Medical Sciences (8 P41 GM103545-14) from the National Institutes of Health. I thank David Weinstein, Jeroen Stinstra, and Rob MacLeod for their contribution to the illustrative examples and the section on software.

References 1. 2010. Scientific Computing and Imaging Institute (SCI), University of Utah, www.sci.utah.edu. 2. A. Ainsworth and J.T. Oden. A Posteriori Error Estimation in Finite Element Analysis. WileyInterscience, New York, 2000. 3. J.E. Akin. Finite Element Analysis for Undergraduates. Academic Press, New York, 1986. 4. Th. Apel, M. Berzins, P.K. Jimack, G. Kunert, A. Plaks, I. Tsukerman, and M. Walkley. Mesh shape and anistropic elements: Theory and practice. The Mathematics of Finite Elements and Applications X, p. 367–376, 2000. 5. R.C. Barr, T.C. Pilkington, J.P. Boineau, and M.S. Spach. Determining surface potentials from current dipoles, with application to electrocardiography. IEEE Trans Biomed Eng, 13:88–92, 1966.

Computational Methods and Software for Bioelectric Field Problems

43-25

6. G. Beer and J.O. Watson. Introduction to Finite and Boundary Element Methods for Engineers. Wiley, New York, 1992. 7. O. Bertrand. 3D finite element method in brain electrical activity studies. In J. Nenonen, H.M. Rajala, and T. Katila, editors, Biomagnetic Localization and 3D Modeling, p. 154–171. Helsinki University of Technology, Helsinki, 1991. 8. T.F. Besier, G.E. Gold, S.L. Delp, M. Fredericson, and G.S. Beaupre. The influence of femoral internal and external rotation on cartilage stresses within the patellofemoral joint. J Orthop Res, 26(12):1627– 1635, 2008. 9. S. Blackett, D. Bullivant, C. Stevens, and P. Hunter. Open source software infrastructure for computational biology and visualization. Conf Proc IEEE Eng Med Biol Soc, 6:6079–6080, 2005. 10. S.S. Blemker, D.S. Asakawa, G.E. Gold, and S.L. Delp. Image-based musculoskeletal modeling: Applications, advances, and future opportunities. J Magn Reson Imaging, 25(2):441–451, 2007. 11. G.R. Bowman, X. Huang, Y. Yao, J. Sun, G. Carlsson, L.J. Guibas, and V.S. Pande. Structural insight into RNA hairpin folding intermediates. J Am Chem Soc, 130(30):9676–9678, 2008. 12. A. Bowyer. Computing Dirichlet tesselations. Comput J, 24:162–166, 1981. 13. C.A. Brebbia and J. Dominguez. Boundary Elements: An Introductory Course. McGraw-Hill, Boston, 1989. 14. D.S. Burnett. Finite Element Method. Addison Wesley, Reading, MA, 1988. 15. M. Callahan, M.J. Cole, J.F. Shepherd, J.G. Stinstra, and C.R. Johnson. A meshing pipeline for biomedical computing. Eng Comput, 25(1):115–130, 2009. 16. C.D. Carbonera and J.F. Shepherd. A constructive approach to constrained hexahedral mesh generation. In Proceedings of the 15th International Meshing Roundtable, September 2006. 17. CIBC, 2009. BioPSE: Problem solving environment for modeling, simulation, image processing, and visualization for biomedical computing applications. Scientific Computing and Imaging Institute (SCI), Download from: http://www.scirun.org. 18. E.F. Van de Velde. Concurrent Scientific Computing. Springer-Verlag, New York, 1994. 19. C. Deitrich, C.E. Scheidegger, J. Schreiner, J. Comba, L.P. Nedel, and C.T. Silva. Edge transformations for improving mesh quality of marching cubes. IEEE Trans Vis Comput Graphics, 15(1):150– 159, 2009. 20. S.L. Delp, F.C. Anderson, A.S. Arnold, P. Loan, A. Habib, C.T. John, E. Guendelman, and D.G. Thelen. Opensim: Open-source software to create and analyze dynamic simulations of movement. IEEE Trans Biomed Eng, 54(11):1940–1950, 2007. 21. S.S. Demir. Interactive cell modeling web-resource, iCell, as a simulation-based teaching and learning tool to supplement electrophysiology education. Ann Biomed Eng, 34:1077–1087, 2006. 22. J.E. Flaherty. Adaptive Methods for Partial Differential Equations. SIAM, Philadelphia, 1989. 23. T.L. Freeman and C. Phillips. Parallel Numerical Algorithms. Prentice Hall, New York, 1992. 24. A. Garny, P. Kohl, P.J. Hunter, M.R. Boyett, and D. Noble. One-dimensional rabbit sinoatrial node models: Benefits and limitations. J Cardiovasc Electrophysiol, 14(10 Suppl):S121–S132, 2003. 25. P.L. George. Automatic Mesh Generation. Wiley, New York, 1991. 26. V.B. Glasko. Inverse Problems of Mathematical Physics. American Institute of Physics, New York, 1984. 27. G.H. Golub and C.F. Van Loan. Matrix Computations. Johns Hopkins, Baltimore, 1989. 28. G.H. Golub and J.M. Ortega. Scientific Computing: An Introduction with Parallel Computing. Academic Press, Boston, 1993. 29. F. Greensite, G. Huiskamp, and A. van Oosterom. New quantitative and qualitative approaches to the inverse problem of electrocardiology: Their theoretical relationship and experimental consistency. Med Phys, 17(3):369–379, 1990. 30. R.M. Gulrajani, F.A. Roberge, and G.E. Mailloux. The forward problem of electrocardiography. In P.W. Macfarlane and T.D. Veitch Lawrie, editors, Comprehensive Electrocardiology, p. 197–236. Pergamon Press, Oxford, England, 1989.

43-26

Bioelectric Phenomena

31. P.C. Hansen. Regularization tools: A MATLAB package for analysis and solution of discrete illposed problems. Technical report, Technical University of Denmark, 1992. Available via netlib in the library numeralgo/no4. 32. P.C. Hansen. Analysis of discrete ill-posed problems by means of the L-curve. SIAM Rev, 34(4):561–580, 1992. 33. C.S. Henriquez, C.R. Johnson, K.A. Henneberg, L.J. Leon, and A.E. Pollard. Large scale biomedical modeling and simulation: From concept to results. In N. Thakor, editor, Frontiers in Biomedical Computing. IEEE Press, Philadelphia, 1995. 34. C.S. Henriquez, J.V. Tranquillo, D.M. Weinstein, E.W. Hsu, and C.R. Johnson. Three-dimensional propagation in mathematic models: Integrative model of the mouse heart. In D.P. Zipes and J. Jalife, editors, Cardiac Electrophysiology: From Cell to Bedside, Chapter 30, p. 273–281. Saunders, Philadelphia, PA, 4th edition, 2004. 35. D.A. Hooks, K.A. Tomlinson, S.G. Marsden, I.J. LeGrice, B.H. Smaill, A.J. Pullan, and P.J. Hunter. Cardiac microstructure: Implications for electrical propagation and defibrillation in the heart. Circ Res, 91(4):331–338, 2002. 36. S.R.H. Hoole. Computer-Aided Analysis and Design of Electromagnetic Devices. Elsevier, New York, 1989. 37. L. Ibanez and W. Schroeder. The ITK Software Guide 2.4. Kitware, 2005. 38. SCI Institute, 2010. SCIRun: A scientific computing problem solving environment, Scientific Computing and Imaging Institute (SCI), Download from: http://www.scirun.org. 39. J.D. Jackson. Classical Electrodynamics. John Wiley & Sons, New York, 1975. 40. M.A. Jawson and G.T. Symm. Integral Equation Methods in Potential Theory and Elastostatics. Academic Press, London, 1977. 41. K. Jerbi, J.P. Lachaux, K. N’Diaye, D. Pantazis, R.M. Leahy, L. Garnero, and S. Baillet. Coherent neural representation of hand speed in humans revealed by MEG imaging. Proc Natl Acad Sci USA, 104(18):7676–7681, 2007. 42. C.R. Johnson and R.S. MacLeod. Computer models for calculating electric and potential fields in the human thorax. Ann Biomed Eng, 19:620, 1991. In Proceedings of the 1991 Annual Fall Meeting of the Biomedical Engineering Society. 43. C.R. Johnson and R.S. MacLeod. Expedition in das herz (in German). GEO, 1993. 44. C.R. Johnson, R.S. MacLeod, and P.R. Ershler. A computer model for the study of electrical current flow in the human thorax. Comput Biol Med, 22(3):305–323, 1992. 45. C.R. Johnson, R.S. MacLeod, and M.A. Matheson. Computer simulations reveal complexity of electrical activity in the human thorax. Comput Phys, 6(3):230–237, 1992. 46. C.R. Johnson, S.G. Parker, D. Weinstein, and S. Heffernan. Component-based problem solving environments for large-scale scientific computing. J Conc Comp Prac Exper, 14:1337–1349, 2002. 47. C.R. Johnson and A.E. Pollard. Electrical activation of the heart: Computational studies of the forward and inverse problems in electrocardiography. In Computer Assisted Analysis and Modeling, p. 583–628. MIT Press, Cambridge, MA, 1990. 48. M. Jolley, J. Stinstra, S. Pieper, R.S. MacLeod, D.H. Brooks, F. Cecchin, and J.K. Triedman. A computer modeling tool for comparing novel ICD electrode orientations in children and adults. Heart Rhythm J, 5(4):565–572, 2008. 49. C. Jones, K.-L. Ma, A.R. Sanderson, and L. Myers. Visual interrogation of gyrokinetic particle simulations. J Phys, 78:012033 (6pp), 2007. 50. Y. Kim, J.B. Fahy, and B.J. Tupper. Optimal electrode designs for electrosurgery. IEEE Trans Biomed Eng, 33:845–853, 1986. 51. G. Kindlmann. Superquadric tensor glyphs. In Proceedings of the IEEE TVCG/EG Symposium on Visualization 2004, p. 147–154, May 2004. 52. S. Lankton and A. Tannenbaum. Localizing region-based active contours. IEEE Trans Imag Proc, pp. 2029–2039, 11 2008.

Computational Methods and Software for Bioelectric Field Problems

43-27

53. M. Lizier, J.F. Shepherd, L.G. Nonato, J. Comba, and C.T. Silva. Comparing techniques for tetrahedral mesh generation. In Proceedings of the Inaugural International Conference of the Engineering Mechanics Institute (EM 2008), pp. 1–8, 2008. 54. R.S. MacLeod, C.R. Johnson, and M.A. Matheson. Visualization of cardiac bioelectricity—A case study. In Proceedings of the IEEE Visualization 92, p. 411–418. IEEE CS Press, 1992. 55. R.S. MacLeod, C.R. Johnson, and M.A. Matheson. Visualization tools for computational electrocardiography. In Visualization in Biomedical Computing, p. 433–444. Bellingham, WA, 1992. Proceedings of the SPIE #1808. 56. M. Maddah, W. Grimson, S. Warfield, and W. Wells. A unified framework for clustering and quantitative analysis of white matter fiber tracts. Med Image Anal, pp. 191–202, 04 2008. 57. M. Meyer, P. Georgel, and R.T. Whitaker. Robust particle systems for curvature dependent sampling of implicit surfaces. In Proceedings of the International Conference on Shape Modeling and Applications (SMI), p. 124–133, June 2005. 58. M. Meyer, B. Nelson, R.M. Kirby, and R.T. Whitaker. Particle systems for efficient and accurate finite element visualization. IEEE Trans Vis Comput Graphics 13(5): 1015–1026, 2007. 59. C.E. Miller and C.S. Henriquez. Finite element analysis of bioelectric phenomena. Crit Rev Biomed Eng, 18:181–205, 1990. 60. A.J. Pullan M.P. Nash. Challenges facing validation of noninvasive electrical imaging of the heart. Ann Noninvasive Electrocardiol, 10(1):73–82, 2005. 61. K. N’Diaye, R. Ragot, L. Garnero, and V. Pouthas. What is common to brain activity evoked by the perception of visual and auditory filled durations? a study with MEG and EEG co-recordings. Brain Res Cogn Brain Res, 21(2):250–268, 2004. 62. J. Nenonen, H.M. Rajala, and T. Katilia. Biomagnetic Localization and 3D Modelling. Helsinki University of Technology, Espoo, Finland, 1992. Report TKK-F-A689. 63. S.G. Parker. Component-based multi-physics simulations of fires and explosions. In Proceedings of the 12th SIAM Conference on Parallel Processing for Scientific Computing, 2006. Presented at the Minisymposium on Parallel Dynamic Data Management Infrastructures for Scientific & Engineering Applications. 64. S.G. Parker, D.M. Weinstein, and C.R. Johnson. The SCIRun computational steering software system. In E. Arge, A.M. Bruaset, and H.P. Langtangen, editors, Modern Software Tools in Scientific Computing, p. 1–40. Birkhauser Press, Boston, 1997. 65. S. Pieper, B. Lorensen, W. Schroeder, and R. Kikinis. The NA-MIC kit: ITK, VTK, Pipelines, Grids and 3D Slicer as an open platform for the medical image computing community. In Proceedings of the IEEE International Symposium on Biomedical Imaging, 4 2006. 66. T.C. Pilkington, B. Loftis, J.F. Thompson, S. L-Y. Woo, T.C. Palmer, and T.F. Budinger. HighPerformance Computing in Biomedical Research. CRC Press, Boca Raton, FL, 1993. 67. R. Plonsey. Bioelectric Phenomena. McGraw-Hill, New York, 1969. 68. A. Pullan, L. Cheng, R. Yassi, and M. Buist. Modelling gastrointestinal bioelectric activity. Prog Biophys Mol Biol, 85(2–3):523–550, 2004. 69. Y. Rudy and B.J. Messinger-Rapport. The inverse solution in electrocardiography: Solutions in terms of epicardial potentials. Crit Rev Biomed Eng, 16:215–268, 1988. 70. A.R. Sanderson, C.R. Johnson, and R.M. Kirby. Display of vector fields using a reaction diffusion model. In Proceedings of IEEE Visualization 2004, p. 115–122, 2004. 71. J.A. Schmidt, C.R. Johnson, J.C. Eason, and R.S. MacLeod. Applications of automatic mesh generation and adaptive methods in computational medicine. In I. Babuska, J.E. Flaherty, W.D. Henshaw, J.E. Hopcroft, J.E. Oliger, and T. Tezduyar, editors, Modeling, Mesh Generation, and Adaptive Methods for Partial Differential Equations, p. 367–390. Springer-Verlag, 1995. 72. J.P. Schmidt, S.L. Delp, M.A. Sherman, C.A. Taylor, V.S. Pande, and R.B. Altman. The Simbios national center: Systems biology in motion. Proc IEEE, 96(8):1266–1280, 2008.

43-28

Bioelectric Phenomena

73. W. Schroeder, K. Martin, and B. Lorensen. Visualization Toolkit: An Object-Oriented Approach to 3D Graphics, 4th Edition. Kitware, Clifton Park, NY, 2006. 74. C. Sergent, S. Baillet, and S. Dehaene. Timing of the brain events underlying access to consciousness during the attentional blink. Nat Neurosci, 8(10):1391–1400, 2005. 75. J.F. Shepherd. Topologic and Geometric Constraint-Based Hexahedral Mesh Generation. PhD thesis, School of Computing, University of Utah, May 2007. 76. J.F. Shepherd and C.R. Johnson. Hexahedral mesh generation constraints. J Eng Comput, 24(3):195– 213, 2008. 77. J.G. Stinstra, S. Shome, B. Hopenfeld, and R.S. MacLeod. Modeling the passive cardiac electrical conductivity during ischemia. Med Biol Eng Comput, 43(6):776–782, 2005. 78. M.H. Tawhai, A.J. Pullan, and P.J. Hunter. Generation of an anatomically based three-dimensional model of the conducting airways. Annal Biomed Eng, 28(7):793–802, 2000. 79. J. Thompson, Z. Warsi, and C. Mastin. Numerical Grid Generation Foundations and Applications. North Holland, New York, 1985. 80. J. Thompson and N.P. Weatherill. Structed and unstructed grid generation. In T.C. Pilkington, B. Loftis, J.F. Thompson, S. L-Y. Woo, T.C. Palmer, and T.F. Budinger, editors, High-Performance Computing in Biomedical Research, p. 63–112. CRC Press, Boca Raton, FL, 1993. 81. A. Tikhonov and V. Arsenin. Solution of Ill-Posed Problems. Winston, Washington, DC, 1977. 82. A.N. Tikhonov and A.V. Goncharsky. Ill-Posed Problems in the Natural Sciences. MIR Publishers, Moscow, 1987. 83. D. Weinstein, G. Kindlmann, and E. Lundberg. Tensorlines: Advection-diffusion based propagation through diffusion tensor fields. In Proceedings of IEEE Visualization 1999, p. 249–253, 1999. 84. D.M. Weinstein, S.G. Parker, J. Simpson, K. Zimmerman, and G.M. Jones. Visualization in the scirun problem-solving environment. In C.D. Hansen and C.R. Johnson, editors, The Visualization Handbook, p. 615–632. Elsevier, Burlington, MA, 2005. 85. C.H. Wolters, A. Anwander, X. Tricoche, D.M. Weinstein, M.A. Koch, and R.S. Macleod. Influence of tissue conductivity anisotropy on EEG/MEG field and return current computation in a realistic head model: A simulation and visualization study using high-resolution finite element modeling. Neuroimage, 30(3):813–826, 2006. 86. Y. Wu, S.K. Warfield, I.L. Tan, W.M. Wells, D.S. Meier, R.A. van Schijndel, F. Barkhof, and C.R. Guttmann. Automated segmentation of multiple sclerosis lesion subtypes with multichannel MRI. Neuroimage, 32(3):1205–1215, 2006. 87. Y. Yamashita. Theoretical studies on the inverse problem in electrocardiography and the uniqueness of the solution. IEEE Trans Biomed Eng, 29:719–725, 1982. 88. O.C. Zienkiewicz. The Finite Element Method in Engineering Science. McGraw-Hill, New York, 1971. 89. O.C. Zienkiewicz and J.Z. Zhu. A simple error estimate and adaptive procedure for practical engineering analysis. Int J Num Meth Eng, 24:337–357, 1987. 90. O.C. Zienkiewicz and J.Z. Zhu. Adaptivity and mesh generation. Int J Num Meth Eng, 32:783–810, 1991. 91. CIBC, 2013. Volumetric image segmentation and visualization. Scientific Computing and Imaging Institute (SCI), Download from: http://www.seg3d.org. 92. SCI Institute, 2013. BioMesh3D: Quality mesh generator for biomedical applications. Scientific Computing and Imaging Institute (SCI). Download from http://www.biomesh3d.org. 93. CIBC, 2013. ImageVis3D: A SCIRun Power App for interactive visualization of vary large image volumes. Scientific Computing and Imaging Institute (SCI), Download from: http://www.imagevis3d.org.

44 The Potential Fields of Triangular Boundary Elements 44.1 Introduction.....................................................................................44-1 44.2 Preliminaries....................................................................................44-2 Notation  •  Field Produced by a Line Source  •  Integral of r(λ)

44.3 Potential Field of a Uniform Double Layer..................................44-4 Properties of ΩΔ • Autosolid Angle

44.4 Potential Field of a Uniform Monolayer..................................... 44-6 44.5 Potential Field of a Linearly Distributed Double Layer.............44-9 44.6 Potential Field of a Linearly Distributed Monolayer................44-11 44.7 Analysis...........................................................................................44-12

A. van Oosterom Radboud University Nijmegen

Numerical Aspects • Examples

44.8 Discussion.......................................................................................44-17 References...................................................................................................44-18

44.1 Introduction The boundary element method (BEM) is a well-known method for computing the (quasi-static) potential in field points on the boundaries of piecewise homogeneous media, as well as inside these, arising from applied forces. The principles of the method for two-dimensional (2D) applications can be found in Reference 1, while three-dimensional (3D) applications to bioelectricity are described, for example, in Reference 2. As described in Chapter 20, in bioelectricity, the applied forces are impressed electric currents and the medium is a volume conductor configuration comprising a set of nonintersecting surfaces nested inside the body surface. The surfaces considered are the interfaces between any two regions having a different electric conductivity. In the latter case, the surfaces are taken to carry the so-called secondary sources. These are virtual sources that are placed in a virtual, homogeneous, and isotropic medium having an infinite extent. In the BEM, the strengths of the secondary sources are computed such that the continuity conditions of the electric volume conduction theory at these interfaces are satisfied [3]. The requisite basic computations involved in the BEM are those of the potential fields generated by monolayer and/or double-layer sources distributed over the surfaces. On the basis of the superposition theorem, which applies to quasi-static linear media, the potential at each field point is computed as the sum of the contributions of the primary sources and the secondary current sources on all the small triangles considered (Chapter 20). Initially, in its application to electrocardiography, the BEM was worked out by introducing virtual monolayer current source density at the interfaces [4] and their local strength was expressed in A/m 2. 44-1

44-2

Bioelectric Phenomena

Soon after, dipole layer source densities were introduced [5]. These so-called double-layer sources that may be viewed as an infinite number of current dipoles oriented along the local surface normal of the interface, with their total local strength expressed in Am/m2 = A/m. Another application of the BEM in bioelectricity aims at linking the potential field on a closed internal surface that encompasses all primary sources to the potential field on the surface bounding the conductive medium. An example of this application is the one in which the internal surface is taken to be a surface closely encompassing the heart and the bounding surface is that of the thorax [6–11]. The solving of this type of mixed boundary value problem (Cauchy problem) involves both double layers and monolayers. The interfaces that are relevant in the field of bioelectricity usually have a complex shape. This necessitates a numerical handling of the computation of the fields generated by sources distributed over the surfaces involved. To this end, the surfaces are subdivided into numerous, small planar elements. By choosing a triangular shape for these elements, an optimal fit of the mesh to interfaces is reached. If the primary source involved is distributed over a surface, the same numerical handling can be used for finding the potential field that it generates. In early applications of the BEM, the vertices of each triangular element were placed on the surface to be represented; the local source strength was taken to be uniform over the triangle and the field points considered were the centers of gravity of the triangles. For a single surface bounding a volume conductor represented by NV vertices, this results in Nt = 2NV − 4 triangles. Solving the potential field on the body surface as generated by an internal primary source then demands the solution of a linear system of Nt equations in the Nt unknown field point potentials. In later applications, the field points were taken to be the vertices of the triangular elements; thus, the field points directly coincide with feasible measurement locations such as the electrodes placed on the body surface as used in electrocardiography. The source strength over a triangle was taken to be proportional to the mean value of the field potentials at its vertices [8]. For a single interface, this reduced the size of the linear system to NV equations in NV field point potentials. In such applications, the fields produced by virtual sources on the “elementary” boundary elements, the triangles, need to be computed in the virtual homogeneous volume conductor. In this chapter, an overview is presented of analytical expressions for the fields produced by a uniform monolayer and a uniform dipole-layer distribution on a triangle, as well as for their variants in which the source strength is linearly distributed over the triangle. Particular attention is given to the computation of the value of the potential generated at the triangle’s vertices. The derivations for each of the cases are included. Some of these derivations follow those reported in the literature, while including some more intermediate steps; others are more original. The order in which these topics are presented here is aimed at facilitating the subsequent derivations in this chapter.

44.2 Preliminaries 44.2.1 Notation Throughout, vectors in 3D space are denoted by lower-case variables with an overhead arrow, for   r , and their lengths are denoted by dropping the arrow. The vector product of example, vectors a and     b is denoted by a × b (cross product) and their scalar vector product is denoted as a ⋅ b (dot product).  The source triangle is denoted by Δ its normal n is found from the cross product of two of its edges.   The norm of n , denoted by n, is twice the area of the source triangle. The normalized version of n is  denoted by nn . The variables expressed in the domain of linear algebra are denoted as follows: vectors are denoted in lower-case bold, their norms are denoted using regular font, matrices are denoted in upper-case bold, row vectors are denoted as primed, and column vectors are denoted as unprimed. The transpose of a matrix M is primed: M′. The column vectors having only unit elements are denoted by u.

44-3

The Potential Fields of Triangular Boundary Elements

44.2.2  Field Produced by a Line Source As is evident in the following sections, the expressions for the fields produced by some of the source ­distributions over a triangle contain terms that can be interpreted as the fields resulting from a line source. This problem is discussed here in some detail to provide a correct physical interpretation of such terms. The problem to be solved is illustrated in Figure 44.1. A current line density τ (unit: A/m) is impressed   in a conductive infinite medium surrounding a line segment with length c having endpoints a and b relative to the field point depicted as the origin. The potential at the origin, Φ, is found by integration  (superposition) of the contributions of point current sources at positions r along the line source seg  ment, with strength I (r ) = τ(r ) c dλ , in which λ is a dimensionless integration variable. Accordingly, we have 1 Φ= 4 πσ



1

∫ 0

 τ(r )c dλ r (λ)

(44.1)

with σ denoting the electric conductivity of the medium (unit: S/m), and the potential at infinity taken to be zero is the reference potential. For ease of notation, the factor preceding the integral is dropped. In  the sequel, a uniform line source density is assumed with unit strength, that is, τ(r ) = 1 A/m. This leaves the following integral to be determined: 1

I0 =

c

∫ r(λ) dλ 0

(44.2)

Note that this expression is invariant to an overall scaling of the  geometry (Figure 44.1).   The distance function r(λ) is the length of r = (1 − λ )a + λb , which can be expressed as r(λ) = c 2λ 2 + Qλ + a 2 , in which Q denotes a combination of squared edge lengths: Q = b2 − a2 − c2. The integral is a standard one. By using Dwight (380.001) listed in Reference 12, we have I o = ln(2c λ + Q + c r (λ))| 2



λ =1 λ =0

  bc + b ⋅ c (b + c)2 − a2   = ln 2 = ln ac + a ⋅ c b − (a − c)2

(44.3)

On the basis of the triangle inequalities applied to the triangle with edges (a, b, c), both the numerator and the denominator in the fractions appearing in Equation 44.3 are nonnegative. Moreover, with the →

b

z

λ →

r

→

a

y x

FIGURE 44.1  Diagram introducing the computation of the potential at the origin generated by a line source den   sity along a line segment with endpoints a and b . Here, the vector r is drawn from a source point of the line source to the field point, depicted at the origin.

44-4

Bioelectric Phenomena

zero reference potential at infinity, the integral must be positive. Hence, the fractions forming the arguments of the logarithms are greater than one. Equation 44.3 holds true throughout the 3D space; at field points coinciding with the line source, its value is infinite.

44.2.3 Integral of r(λ) In one of the field problems to be discussed (Section 44.6), the integral over a line segment of r(λ) appears rather than that of its reciprocal value appearing in Equation 44.2. By using the result listed as Dwight (380.201) [12] and employing the same notation, the result is D ⎞ ⎛ I1 = ⎜ 2bc 2 + (b − a)Q − I 0 ⎟ /(4c) 2c ⎠ ⎝



(44.4)



with D = Q  − 4a c , the discriminant of the parabolic expression in r(λ). 2

2 2

44.3  Potential Field of a Uniform Double Layer The first of the fields produced by the sources on the basic, triangular BEM element Δ to be discussed is the one generated by a double layer that is uniformly distributed over Δ. The geometrical configuration involved is depicted in Figure 44.2. The triangle vertices are labeled (k,l,m) in a clockwise order when viewed from the origin. The elementary current dipoles constituting the double layer are lined up in parallel to the triangle normal, pointing into the forward direction of a right-hand cork screw rotated in the order of the vertices k → l → m. Without loss of generality, the field point is taken to be the origin.  The potential at t r follows from taking the integral  of the contributions to the potential of elementary current dipoles (Equation 44.16) dipole strength d dS  Φ(r ) =

  r ⋅d 1 dS 4 πσ r 3

∫

(44.5)

 with d as the current dipole surface density (unit: Am/m2) taken to be uniform over Δ. Note that, as for the line source, the potential is invariant to an overall scaling of the geometry, the tetrahedron formed Δ

z →

rk

r→m

→

r

y →

x

rl

FIGURE 44.2  Diagram introducing the computation of the potential at the origin generated by a uniform current dipole surface source density over a triangle. The nearby curved patch represents the central projection of all  elements of the source triangle onto a sphere with unit radius. Here, the vector r points from a source location on the triangle to the field point, depicted as the origin.

44-5

The Potential Fields of Triangular Boundary Elements

  by the vertex indices of Δ and the field point. The term r ⋅ d dS is the component of the local dipole  strength d dS along the vector specifying the source location. Combined with the preceding note, this means that the contribution to the field potential of the elementary sources d dS is equal to a virtual dipole source at the central projection of dS onto a sphere with unit radius surrounding the field point, now pointing radial, having the same strength as d . This means that the solution of Equation 44.5 is d d  Φ(r ) = dS = Ω 4 πσ ∫Δ 4 πσ Δ



(44.6)

with ΩΔ denoting the solid angle subtended by the triangle at the field point of interest [13]. A numerically efficient and accurate expression for ΩΔ , dating from 1983 [14], reads



Ω Δ = 2arctan

  [r r r ]   k l m    rk rl rm + rk (rl ⋅ rm ) + rl (rm ⋅ rk ) + rm (rk ⋅ rl )



(44.7)

  with [rk rl rm ] the triple vector product of the vectors specifying the triangle vertices relative to the field point. In the sequel, this triple vector product is denoted by T. Its numerical value is denoted by T; it equals that of the determinant of the matrix of size 3 × 3 whose elements are the vertex coordinates of the source triangle relative to the field point; it represents 6 times the volume of the tetrahedron.

44.3.1 Properties of ΩΔ As mentioned above, the potential is invariant to an overall scaling of the geometry as seen from the field point, which is also evident from Equation 44.7. The potential profile along a line crossing the source triangle exhibits a discontinuous jump. This corresponds to the discontinuity in the solid angle observed close to the triangle, which jumps from ΩΔ = − 2π at one side to ΩΔ = 2π at the other side, with a positive sign at the side of the semispace into which the elementary dipoles are pointing. Applied to Equation 44.6, we see that a voltage jump of Vd = d/σ is observed when crossing the double layer, a value that, in a uniform medium with known conductivity, may be used to specify the double-layer strength. Expression 44.7 produces the correct sign of the solid angle in this application provided the arctan function produces angles in the range −π to π and thus accounts for the signs of the numerator and the denominator (e.g., MATLAB •’s atan2 function). When moving away from the source triangle, the potential profile rapidly approaches the profile produced by a single dipole placed at the center of gravity of Δ, with strength D = dSΔ with SΔ the area of Δ, directed along its normal



 Φ(r ) =

  1 r ⋅ dSΔ 4 πσ r 3

(44.8)

which indicates that at increasingly larger distances from Δ, the potential decays as 1/r2.

44.3.2 Autosolid Angle In the early application of the BEM, the field points considered were the centers of gravity of the triangles forming a closed interface. The discontinuity when crossing a double- layer source was treated by using the limit of the solid angle (Ωj → −2π) while approaching any triangle j from the interior part of the interface along its local normal. In later applications, the field points were taken to be the vertices of the triangles [15]. In this situation, the BEM requires the specification of the potentials generated by all individual source triangles at

44-6

Bioelectric Phenomena

all field points, including those at its own vertices. However, the solid angle subtended by a triangle at any of its vertices remains to be defined. The singularity needs to be treated with care since their values have a major impact on the accuracy of the entire computed potential field. In the application of the BEM to a closed interface, the total solid angle subtended by the interface at any interior point is −4π. This has led to the practice of assigning a value of Ωi = −4π −

∑Ω



(44.9)

Δj

j | i ∉Δ j



to any node i (field point), involving the summation over the solid angles subtended by all triangles on the interface carrying node i, but excluding those having node i as a vertex. The solid angle defined in this manner is referred to as the autosolid angle [16]. For a node at an approximately planar patch of the interface, the value of Ωi is close to −2π; for a locally convex patch, it is more negative, and at a concave patch, it is less negative. An improved handling of this complexity results from the application of the results for the linearly distributed double-layer strength (Section 44.5 and Reference 17).

44.4 Potential Field of a Uniform Monolayer Figure 44.3 depicts the basic configuration involved in solving the potential field generated by a uni      form monolayer on a triangle, with vertices as defined previously, and edges ek = rl − rk , el = rm − rl , and    em = rk − rm . At each infinitesimally small part dS of the triangle, an electric current JdS (unit: A) is impressed in the surrounding medium, with J the impressed current surface density (unit: A/m2). The problem to be solved is the computation of the potential at an arbitrary field point. There are a multitude of papers dealing with this problem, or the linearly distributed variant, each exhibiting a different approach to solving the involved surface integrals, and the detail in which the results, or their derivations, are documented [18–23]. The solution presented here, but not the solution method, corresponds to the analytical, closed-form solution described in Reference 24. z

→

rk

em

→

nn

→

rm

→

r

→

el

x

→

ek

y

→

rl

FIGURE 44.3  Diagram introducing some of the variables involved in the computation of the potential at the ori gin generated by a uniform current surface source density over a triangle. Here, the vector r points from a source  location on the triangle to the field point, depicted as the origin. The unit normal, nn of the triangle is drawn starting from an arbitrary source location.

44-7

The Potential Fields of Triangular Boundary Elements

The problem to be tackled is the computation of  Φ(r ) =

1 4 πσ

∫ Δ

 J (r ) J 1 dS = Δ dS r 4 πσ r

∫ Δ

(44.10)



which is similar to the situation treated in Section 44.2.2, but now involves a surface integral. JΔ is the uniform surface source density over Δ, scaling the potential. In the derivation, its value is set at JΔ = 1A/m2. Another difference is that the integral, and, hence, the potential, depends linearly on an overall scaling, say, by a factor α. This property is the key to the solution method described here. In Figure 44.4, the triangle nearest to the field point is the source triangle. Its potential at the field point is denoted by Φ1, the potential required to be computed. The other triangle has vertices that are  obtained by scaling the source triangle vertices by a factor α ≥ 1. Point p is the orthogonal projection of the field point onto the plane of the source triangle; its length h is the height of the tetrahedron as seen from the source triangle. From this point, line segments are drawn orthogonal to the lines carrying the edges of the source triangle; their lengths are denoted by hk, hl, and hm, respectively. In addition, orthogonal projections of the vertex points of the source triangle onto the second triangle are included, outlined by means of their connections shown in white line segments that delineate a triangle having the same size as Δ. In addition, small line segments are shown that connect these projections to the nearby vertices of the source triangle. The latter line segments are parallel to the line connecting the field point  and its projection p on the plane of Δ. On the basis of the overall scaling of the two tetrahedrons, their  length is l = (α − 1)h. Note that in this particular example, the projection of the edge ek runs outside the  second triangle, which relates to the fact that p lies outside the source triangle.

z

→

rk

→

rm

→

p

y x →

rl

FIGURE 44.4  Diagram introducing the configuration involved in the method for computing the potential at an arbitrary field generated by a uniform current surface source density over a triangle. The triangle closest to the field point (at the origin) is the source triangle, the second triangle has vertices that are scaled versions of those of the  source triangle. The vector p is the projection of the field point on the plane of the source triangle. Further details are as described in the text.

44-8

Bioelectric Phenomena

The second triangle is taken to represent a virtual monolayer source with uniform density and unit strength. The potential Φ2 generated at the field point is, as discussed above, Φ2 = α Φ1. When the polarity of the sources at the second triangle is reversed, turning its sources into sinks, the potential Φ at the field point generated by the “imperfect sandwich” formed in this manner is Φ = (1 − α)Φ1 (44.11)



We now consider taking the limit α → 1, which reduces the distance between the two triangles. For small values of l = (α − 1)h, the combination of the uniform source density on the source triangle and the uniformly distributed sinks over its scaled version has the character of a double layer with strength d = J(α − 1)h. For J = 1, this produces a potential ΦDL at the field point equal to



Φ DL =

d (α − 1)h Ω =− ΩΔ 4 πσ Δ 4 πσ

(44.12)

(compare Equation 44.6). By looking at Figure 44.4, we note that there are sinks on two strips on the scaled version of Δ that are  not represented in the double-layer activity. In contrast, the contribution of the strip parallel to edge ek is overrepresented in ΦDL . For values of α close to one, the length of these strips tends to the lengths of the longest edges bounding them and their widths can be seen to be (α − 1)hj, j = (k,l,m). The areas that these strips have in common shrink as (α − 1)2 and the contributions of sources on these areas may be neglected for α → 1. The contributions of each of these strips can be approximated by those of a weighted uniform line source with density wj = (α − 1)hj. For a strip parallel to any edge j, the approximate contribution to the potential at the field point is (Section 44.2.2)



Φj =

1 1 (α − 1)h j γ j wγ = 4 πσ j j 4 πσ

(44.13)

with γj the value of the line integral I0 as in Equation 44.3, here pertaining to edge j. By using an appropriately signed version of the hj distances, the contributions will be positive or negative as required. By combining the results shown in Equations 44.11 through 44.13, we see that Φ = (1 − α) Φ1 =

(1 − α) h 1 ΩΔ + (1 − α) 4 πσ 4 πσ

∑

j =[ k ,l ,m]

hj γ j

(44.14)



  The required signed distances hj are found from hk = [rk rl nn ]/ek, the other two follow by cyclic per  mutations of the vertex indices (k, l, m). The height of the tetrahedron is h = [rk rl rm ]/n. For α → 1, all approximations mentioned tend to be more realistic and after dividing by α − 1 > 0, we find the solution to Equation 44.10 for a uniform density J



 J ⎛ Φ(r ) = Δ ⎜ h Ω Δ + 4 πσ ⎜ ⎝

⎞ J Γ J h j γ j ⎟ = Δ Δ = Δ (h Ω Δ + hʹγ ) 4 πσ 4 πσ ⎟ ⎠ j =[ k ,l ,m]

∑

(44.15)

in which ΓΔ represents the value of the right integral in Equation 44.10; the expression on the right includes the numerical vector representations of hj and γj.

44-9

The Potential Fields of Triangular Boundary Elements

44.5  Potential Field of a Linearly Distributed Double Layer In its application to the BEM, the strength of the double layer, a virtual source in infinite space, is proportional to the local potential of the actual physical problem addressed. For the vertex approach, generally having different potential values at each of the vertices of a triangular element, the uniform double-layer strength over the individual triangles needs to be specified in terms of its vertex values. In the early application of the BEM to bioelectric field problems, Barr et al. [15] took the uniform source strength on a triangle to be proportional to the mean value of its vertex potentials. Assuming the source strength to be uniform over each triangle implies that the potential over the triangle is constant. Generally, this would imply a discontinuity of the potential across edges shared by neighboring triangles, which is unrealistic. This problem was solved by de Munck [25], who derived a closed-form analytical expression for the field generated by a double layer having a strength that varies linearly between the vertex values. This extended the zero-order approximation of the source distribution as used in the solid-angle formulation to a first-order approximation, rendering the source strength across an edge shared by neighboring triangles to be continuous. The method used by de Munck for deriving this expression is not always easy to grasp from his paper. Here, a reconstruction is presented of the derivation of this highly significant expression, cast in the notation used in this chapter. Some notations in Reference 25 that easily lead to confusion have been adapted. The nonuniform variant of Equation 44.5 reads  Φ(r ) =

   r ⋅n 1 d(r ) 3 n dS 4 πσ r

∫ Δ

(44.16)



 with d (r ) as a scalar function specifying the double-layer strength over the triangle. On the basis of     the values at its vertices, d (rk ), d(rl ), and d (rm ), a linear distribution of d (r ) over the triangle can be described as

       d(r ) = d(rk )wk (r ) + d(rl )wl (r ) + d(rm )wm (r )

(44.17)



 in which any of the weighting functions w j (r ), j ∈ (k, l , m), has a value one at vertex j, zero values at the remaining two vertices, and a linear course along any straight line passing through vertex j. For vertex k, such a dimensionless weighting function is

            wk (r ) = [r , rl , rm ]/T = (rl × rm ⋅ r )/(rl × rm ⋅ rk ) = (rl × rm ⋅ r )/T



(44.18)

 a function that is linear in r and satisfies the required values at the vertices of the source triangle. Recall that T is the value of the triple vector product. By inserting Equation 44.17 in Equation 44.16, the integral can be split up into three integrals of the  same type. The one involving w k (r ) is worked out in detail and the other two are found from a cyclic per  mutation of the vertex indices. The integral involving w k (r ), after moving the constant d (rk ) in front of it, is Ωk =

1 T

∫ Δ

    (rl × rm ⋅ r )r ⋅ nn dS r3

(44.19)



 For any r starting from the source, viz the source triangle, and ending at the remaining node of the        tetrahedron, we have r ⋅ nnn = r ⋅ n = r ⋅ el × em = T . This leads to the following integral to be evaluated: Ωk =

   1   r 1 zk ⋅ r rl × rm ⋅ 3 dS = dS n n r r3

∫ Δ

∫ Δ



(44.20)

44-10

Bioelectric Phenomena

     in which z k is the shorthand for rl × rm as used in de Munck’s paper, with variants for z l and z m defined through a cyclic permutation of the indices (k, l, m). These vectors are normals to those faces of the tet rahedrons that do not have a vertex corresponding to their label; their vector sum equals n . The integral in Equation 44.19 can be seen to represent a weighted solid angle. To be valid for a uniform density, the weights should satisfy Ωk + Ωl + Ωm = ΩΔ (44.21)



While solving the integral on the right-hand side in Equation 44.20, de Munck introduced a similar type of integral:  H =

∫ Δ

   r 1 × dS = ∇ × dS = 3 r r

∫ Δ

1 

∫ r dc

(44.22)



Note that this integral is dimensionless. With the scalar vector product replaced by a cross product, the application of Stoke’s law yields the contour integral on the right, the contour being formed by the edges of the source triangle. By using γj as the value of the line integral I0 as in Equation 44.3 pertaining to edge j, we find  H =

∫

1  dc = r

1

∑∫

j = k ,l ,m 0

1  e dλ = r (λ) j

 1 ej ej dλ = e j r (λ)

∑ ∫

j = k ,l ,m

∑

j = k ,l ,m

 ej γ ej j

(44.23)

  An alternative expression for H results from introducing the representation of the vector r as the     sum of its components along vectors rj : r = (1/T ) ∑ j = k ,l ,m (z j ⋅ r )rj into the integral on the left-hand side of Equation 44.22. This yields



 1 H = T

∫∑

Δ j = k ,l ,m

   (z j ⋅ r )rj  n nn × n d S = × n T r3

∑

j = k ,l ,m

0

    1 (z j ⋅ r ) n S = × rj d T n r3

∫ Δ



∑ rΩ j

j = k ,l ,m

j



(44.24)

The most right-hand part of this expression stems from identifying the final part of the preceding expression with the definition of Ωk in Equation 44.20.   By storing the vectors (n /T ) × rj as columns of a matrix B, the expression on the right-hand side of Equation 44.24 reads Bω, with ω a column vector with elements Ωj Equations 44.23 and 44.24 both express H , with the right-hand side of Equation 44.23 being a vector y = Enγ, in which E n is a matrix comprising the normalized edges (k,l,m) as its columns. Combining Equations 44.23 and 44.24 leads to the linear system

Bω = y (44.25)

A straightforward solution of the desired vector ω is impossible since B is underdetermined; n′ is a left eigenvector with zero eigenvalue: n′B = [0 0 0], as follows from the fact that for any vertex index j, the      vector n × rj lies in the plane of the source triangle and, hence, n ⋅ n × rj = 0. Note that this complication is due to the nature of B rather than the nature of y as suggested in Reference 25. The complication is removed by adding Condition 44.21 as a row to the system in Equation 44.25. Finally, ω is found as the least-squares solution to the 4 × 3 linear system



⎡B ⎤ ⎡y ⎤ ⎢ ⎥ω = ⎢ ⎥ ⎣u ʹ ⎦ ⎣Ω Δ ⎦

(44.26)

44-11

The Potential Fields of Triangular Boundary Elements

The solution, Equation 44.19 of de Munck’s paper cast in the notation of this chapter, is ω=



1 (Z ʹn Ω Δ − E ʹcE n γ T ) n2

(44.27)

with Ec a matrix whose columns are the edges of the source matrix stored after one step of cyclic rota tion, [el, em, ek], and Z a matrix in which the columns are the vectors of z j ; recall ΩΔ as found from Equation 44.7.

44.6 Potential Field of a Linearly Distributed Monolayer We now turn to the final topic, the handling of the refinement of Section 44.4, determining the field of a monolayer, the strength of which is linearly distributed over the triangle. This problem is addressed in a manner similar to the one described in detail in the previous section for the double layer. To this        end, the monolayer strength is written as J (r ) = J (rk )wk (r ) + J (rl )wl (r ) + J (rm )wm (r ) (compare Equation 44.17) and after its introduction in Equation 44.10, we have  Φ(r ) =

1 4 πσ

∫ Δ

    J (r ) J wk (r ) J wl (r ) J wm (r ) dS = k dS + l dS + m dS, r r r 4 πσ 4 πσ 4 πσ r

∫

∫

Δ

∫

Δ

Δ



(44.28)

with the integral broken up into three subintegrals of the same type. In the following equation, the integral for the index j ∈ (k, l, m) is denoted by Γj Γj =

∫ Δ

  w j (r ) r 1 1 dS = z j ⋅ dS = z j ⋅ ∇r dS r T r T

∫

∫

Δ

Δ

(44.29)



with the linear weighting function as in Equation 44.18, (dimension: m). Similar to Condition 44.21, the terms Γj should add up to the value of the integral for the uniform distribution:

Γk + Γl + ΓΔ . (44.30)   Next, an auxiliary vector G introduced, similar to the vector F in the previous section  G=



∫ Δ

   r × dS = ∇r × dS = r

∫ Δ



∫ r dc

(44.31)



with the second equality resulting from the application of Stoke’s law (dimension: m2). The value of the contour integral is  G=

∫

 r dc =

1

∑∫

 r (λ) e j dλ =

j = k ,l ,m 0

 1 ej r (λ)e j dλ = ej

∑ ∫

j = k ,l ,m

0

∑

j = k ,l ,m

 ej I e j 1, j

(44.32)

with I1,j the value of the line integral I1 (Equation 44.4) pertaining to edge j.    Similar to the procedure in the previous section, the synthesis  r = (1/T ) ∑ j = k ,l ,m (z j ⋅ r )rj is inserted in the left integral in Equation 44.31, yielding an alternative for G



 1 G= T

∫∑

Δ j = k ,l ,m

  (z j ⋅ r )rj   × nn dS = nn × r

∑

j = k ,l ,m

 1 rj T

∫ Δ

   (z j ⋅ r ) n dS = × n r



∑rΓ j

j = k ,l ,m

j



(44.33)

44-12

Bioelectric Phenomena

  The vectors (n/n) × r are stored as columns of a matrix N, which can be seen to be a scaled version of matrix B introduced in the previous section and hence, like B, is underdetermined. After introducing  y = ∑ j = k ,l ,m (e j /e j )I1, j and applying Constraint 44.30, this leads to the following 4 × 3 linear system, to be solved for the monolayer of the source distribution



⎡N ⎤ ⎡y ⎤ ⎢ ⎥Γ = ⎢ ⎥ ⎣u ʹ ⎦ ⎣Γ Δ ⎦

(44.34)

The least-squares solution of this system produces a numerical column vector Γ, the three elements of which are the three integrals in Equation 44.28, thus yielding the final solution

Γ = (Z′ nΓΔ − E′ E c nI1)/n (44.35)

with matrices E c and En as in Equation 44.27, n and I1 representing column vectors, and the scalar ΓΔ as found from Equation 44.15.

44.7 Analysis 44.7.1 Numerical Aspects The basic results discussed in this chapter are Expressions 44.27 and 44.35. These are closed-form analytical expressions for computing the potential fields produced by current sources that are linearly distributed over a triangle of the double-layer type in Equation 44.27 and the monolayer type in Equation 44.35. In turn, these build on the expressions for the corresponding uniform distributions, Equations 44.7 and 44.15. As a consequence, the implementation of these expressions is less forbidding than may appear at first glance. In fact, the results of several of the intermediate and basic computations involved can be used at different points in large-scale implementations as carried out in the BEM. A careful implementation in any code is essential in such applications. The results in Equations 44.7, 44.15, 44.27, and 44.35 have been tested exhaustively and were found to be accurate. Their values were finite at all points of 3D space as were expected to be from the physical nature of the problem. As discussed in Section 44.3.1, the potential field produced by the double layer on the source triangle itself remains to be defined. All monolayer potentials in Equations 44.15 and 44.35 resulting from a positive monolayer source strength were positive, as required. For field points in the plane of the source triangle as well as for field points very close to it, the results proved to be accurate within machine precision. To ensure this property, when computing factors γj, the absolute value of the denominator in Equation 44.3 was used, after which the machine epsilon was added to the numerator as well as to the denominator. This efficiently suppresses any arguments of the logarithm less than one that may arise due to the rounding-off steps in the numerical handling of the numbers involved in the computation of these essentially positive entities.

44.7.2 Examples In the following section, some examples are presented of potential fields generated by the expressions discussed in the chapter, also aimed at demonstrating the major properties of these fields. In all these examples, unit values are assigned to the source densities dΔ and JΔ as well as to the conductivity σ of the medium. 44.7.2.1 Double Layer The left panel of Figure 44.5 illustrates the potential field in the plane z = 0 of a uniform double layer in the plane z = 0.01 with its normal directed along the z-axis, computed from Equations 44.6 and 44.7. Lying close to the double-layer source, the potential inside the triangle is almost uniform, with its

44-13

The Potential Fields of Triangular Boundary Elements

3

Monolayers, uniform, h = 0.01: max = 0.49401: step:0.05

3

2.5

2.5 B

2

1.5

1.5

1

1

y-axis

y-axis

2

0.5 0

C

A

B

0.5 C

0

–0.5

A

–0.5

–1 –1.5 –2

Double layers V_1, h = 0.01: max = 0.4176: step:0.025

–1 –1.5

–1

–0.5

0 0.5 x-axis

1

1.5

2

2.5

–1.5 –2

–1.5

–1

–0.5

0 0.5 x-axis

1

1.5

2

2.5

FIGURE 44.5  Left panel: Potential field in the plane z = 0.01 generated by a triangularly shaped uniform double layer in the plane z = 0, having vertices A, B, and C at [2 0 0], [−1.5 2 0], and [−1 0 0], respectively. Right panel: Corresponding result, now for a linearly distributed source strength, with unit value at vertex A and zero values at the other two vertices. Note the different step sizes between the contours used in both panels.

maximum (0.494; position indicated by the asterisks) close to the theoretical limit of 0.5 and with values outside the triangle close to zero. As a consequence, the isopotential lines, drawn at 0.05 V intervals, concentrate along the edges of the triangle. On the right panel, the corresponding field is shown, now generated by a linearly distributed source strength, with its unit value at one of the three vertices ([2 0 0]) and zero at the other two vertices. This field was computed from Equation 44.27. Note that, at this closeness to the double-layer source, the pattern of the potential field closely follows the distribution of the source strength; its maximum is somewhat smaller (0.418) than the limit value of 0.5. Moving away from the source, the potential field exhibits a more diffuse image of the edges of the source, as illustrated in Figure 44.6 for the plane z = 0.5, with the maxima of both cases clearly reduced and the maximum observed for the nonuniform case closer to that of the uniform case. When moving further away from Δ, these effects are amplified. 44.7.2.2 Monolayer The field generated by sources on the same triangle as in the previous example, now generated by a monolayer, is illustrated in Figure 44.7. The field potential generated by a monolayer is defined throughout space, and hence, the illustration (based on Equation 44.15 for the uniform case and on Equation 44.35 for the linearly distributed case) could be produced at the plane of observation coinciding with that of the source triangle. Interestingly, the field shown in the right panel, which is directly at the source plane, has its extreme at a location that lies more than a unit away from the position of the maximal source strength. As for the double layer, the field gets more blurred, with reduced voltages, the further one moves away from the source plane, as is illustrated in Figure 44.8. The potentials at the vertices of the source triangle for all three basic linear source configurations, as well as for the uniform case, are listed in Table 44.1. Another view on this basic phenomenon is presented in Figure 44.9. It depicts some potential profiles along a line parallel to the z-axis, and thus directed along the normal of the source triangle, and passing through its center of gravity, generated by uniform densities over the triangle. The solid discontinuous line is the profile of the double layer. Including the applied scaling by 4π (Section 44.3.1), the

44-14

3

Bioelectric Phenomena Monolayers, uniform, h = 0.5: max = 0.24802: step:0.025 3

2.5

2.5 B

2

1.5

1.5

1

1

y-axis

y-axis

2

0.5 0

C

A

–1

–1 –1

–0.5

0 0.5 x-axis

1

1.5

2

C

0 –0.5

–1.5

B

0.5

–0.5

–1.5 –2

Double layers V_1, h = 0.5: max = 0.10041: step:0.0125

2.5

–1.5 –2

–1.5

A

–1

–0.5

0

0.5 x-axis

1

1.5

2

2.5

FIGURE 44.6  As in Figure 44.5, with the plane of observation here at z = 0.5.

discontinuity has magnitude one (−0.5 to 0.5). The solid continuous line is generated by the monolayer. Here, the characteristic feature is the discontinuity in the slope, changing abruptly from 0.5 to –0.5 while crossing the source in the positive z-direction. This corresponds to the symmetric outflow of the current density from both sides of the monolayer. These curves form the quantification for the triangle of the general profiles of these two fundamental source types as discussed in the major textbooks on potential theory (e.g., Figures 1 through 7 in Panofski and Phillips [13]).

3 2.5

3

! B

2

1.5

1.5

1

1

0.5

B

0.5

0

C

0

A

–0.5

–0.5

–1

–1

–1.5 –2

Mono_phi V_1, h = 0: max = 0.18813: step:0.025

2.5

y-axis

y-axis

2

Monolayres uniform, h = 0: max = 0.45854: step:0.05

–1.5

–1

–0.5

0 0.5 x-axis

1

1.5

2

2.5

–1.5 –2

A

C

–1.5

–1

–0.5

0 0.5 x-axis

1

1.5

2

2.5

FIGURE 44.7  Left panel: Potential field in the plane z = 0, the source plane, generated by a triangularly shaped uniform monolayer in the plane z = 0, as in Figure 44.5. Right panel: Corresponding result, now for a linearly distributed source strength, with unit value at vertex A and zero values at the other two vertices. Note the different step sizes between contours used in both panels.

44-15

The Potential Fields of Triangular Boundary Elements

3

Monolayers, uniform, h = 0.5: max = 0.27704: step:0.025 3

!

2.5

2.5 B

2

1.5

1.5

1

1

y-axis

y-axis

2

0.5 0

C

A

0 –0.5

–1

–1 –1.5

–1

–0.5

0 0.5 x-axis

1

1.5

2

B

0.5

–0.5

–1.5 –2

Mono_phi V_1, h = 0.5: max = 0.098542: step:0.0125

2.5

–1.5 –2

C

–1.5

–1

A

–0.5

0 0.5 x-axis

1

1.5

2

2.5

FIGURE 44.8  As in Figure 44.7, here, with the plane of observation at z = 0.5.

The solid lines are accompanied by dotted lines representing the potential profiles generated by a single, equivalent single dipole with strength dSΔ placed at the center of gravity, as well as that of a single, equivalent monopole current source with strength JSΔ . These curves illustrate that the fields that generated the distributed sources at sufficiently large distances may be approximated by these point sources, the current dipole (decay of the potential as 1/r 2) and the current monopole (decay of the potential field as 1/r). Close to the position of such equivalent sources, the correspondence with the fields generated by the surface sources is extremely poor, tending toward infinite values while moving closer to the source location. As a rule of thumb, fields further away than, say, 3 times the size of the triangle expressed, for example, by the radius of the circumscribed circle, may permit field computations based on such equivalent sources. For the computation of the most significant terms in the BEM transfer matrix, the diagonal terms, such approximations are inadequate, as can be seen in Figure 44.9. 44.7.2.3 Singularities As discussed in Section 44.1, the BEM requires the field potentials generated by sources on a triangle to be known at its own vertices. The handling of this problem for the double layer is discussed in Section 44.3.1, with a special reference to the handling of the autosolid angle as described in Reference 16. For the monolayer, on the basis of the expressions presented in Section 44.6, it is seen that the field generated in the plane of the source triangle is continuous and finite, including field points on the TABLE 44.1  Potentials at Vertices A, B, and C of the Triangle Specified in Figure 44.5 [1 0 0] [0 1 0] [0 0 1] [1 1 1]

A

B

C

0.06996 0.03323 0.03676 0.13992

0.03794 0.08582 0.04788 0.17164

0.05942 0.06954 0.12896 0.25791

Note: First three rows: linearly distributed monolayer current source distributions, with vertex source strengths as specified in the row labels, for example, [1 0 0]: a unit strength at vertex A and zero values at vertices B and C. The lower row represents the uniform case, with potential values seen to be equal to the sum of the other column entries, as required.

44-16

Bioelectric Phenomena Phi, mono and double, x = –0.33333 y = 0.66667 max : 0.45851 0.5 0.4 0.3 0.2

V(z)

0.1 0 –0.1 –0.2 –0.3 –0.4 –0.5 –3

–2

–1

0 z

1

2

3

FIGURE 44.9  Potential profiles along a line parallel to the z-axis, passing through the center of gravity of the triangle, generated by uniform source distributions. Solid discontinuous line: double-layer sources; solid continuous line: monolayer sources. Dotted lines: fields generated by a single, equivalent single dipole with strength dSΔ placed at the center of gravity as well as that of a single, equivalent monopole current source with strength JSΔ . The dash–dot line represents one of the two tangents to the potential profile of the monolayer at z → 0; its slope is 0.5.

edges, as well as at the vertices. The potentials at the vertices of a monolayer distribution on the source triangle follow from Equation 44.35. Figure 44.7 illustrates that the handling by the expression of these so-called weak singularities is adequate and that the singularity relates to the gradient of the field only at these locations. This can be explained as follows. The term on the left of this expression includes ΓΔ as computed for the uniform case in Equation 44.15. In its computation, the first term in Equation 44.15 is eradicated by the zero value of the solid angle of the triangle subtended by the observation point in the plane of the triangle and moreover, the factor h is also zero in this case. From the interpretation of the factors hj in Equation 44.15, it can be seen that these are nonzero only for the edge opposite the vertex of interest, yielding positive contributions hjγj for this edge only, while wiping out the singularities in the logarithms γj pertaining to the two edges carrying the node of interest. This also justifies the inclusion of the machine epsilon in the logarithm as described above. A useful set for checking the accuracy of the values found from Equation 44.35 at the critical field points, in the plane of the source triangle, and in particular, those at its vertices, is presented in Table 44.2. Its rows list the values of the vector Γ at the vertices of a rectangular triangle as generated by each of the separate linear distributions. The source triangle is taken to have vertex labels A, B, and C. Its edges form a right angle at vertex C. The lengths of the edges opposite vertices A, B, and C are labeled a, b, and c, respectively. The right angle in this example facilitates the computation of such results by means of direct integration, using, for example, the results Dw.200.01, Dw.610.1, and Dw.635 [12]. The values for more general triangles, as well as at arbitrary field points in the plane of the source triangle, can be found by forming

44-17

The Potential Fields of Triangular Boundary Elements

TABLE 44.2  Values of Γ at the Vertices A, B, and C of a Rectangular Triangle (Right Angle at C) Generated by Linear Monolayer Source Distributions, with Source Strengths Specified in the Leading Column A

B

C

[1 0 0]

b a+c ln 2 b

a(c − a) 2b

ab(a − b) ab3 (a + c )(b + c ) + 3 ln ab 2c 2 2c

[0 1 0]

b(c − b) 2a

a b+c ln 2 a

ab(b − a) a3b (a + c )(b + c ) + 3 ln ab 2c 2 2c

[0 0 1]

b(b − c ) b a + c + ln 2a 2 b

a(a − c ) a b + c + ln 2b 2 a

ab (a + c )(b + c ) ln 2c ab

[1 1 1]

b ln

a+c b

a ln

b+c a

ab (a + c )(b + c ) ln ab c

Note: The variables a, b, and c denote the edge lengths, opposite to vertices A, B, and C, respectively. The lower row represents the uniform case, seen to be equal to the sum of the other three elements of the same column, as required.

triangles between the field point and the edges of the source triangle. The subsequent application of the superposition theorem, forming an appropriately weighted sum of the individual results, yields the desired solution. Note: Table 44.2 has two terms in which the logarithm is absent; also note that, for this rectangular triangle, Γ([111],A) = 2Γ([100]A) and Γ([111],B) = 2Γ([010],B).

44.8 Discussion In this chapter, analytical expressions are described for computing the potential field generated by either a double layer or a monolayer current distribution on a triangle. The pertinent expressions are Equations 44.7, 44.15, 44.27, and 44.35, which remain to be scaled by source strength and 1/4πσ. Next to an application to the computation of the potential field, the BEM can be used in the computation of the magnetic fields outside the body generated by internal electric sources. The virtual, secondary electric sources at the interface may serve for the computation of the effect of inhomogeneities in the electric tissue conductivities on the magnetic field [26]. The numerical handling of the computation of the magnetic fields on the basis of the virtual current source strengths at the triangular elements can be found in Reference 24. In the vertex approach to the BEM, the expressions pertaining to linearly distributed sources can be used, by which the discontinuities of the source strength across the edges are avoided. The proper handling of the contributions of the current sources on the triangles to their vertex potentials is essential. Equation 44.35 is the proper expression for treating this situation. For the double layer, the concept of the autosolid angle as introduced in Reference 16 can be used. The computation of the fields for the linearly distributed cases includes factors that are the endpoints of the uniform cases. For sufficiently distal field points, the fields produced by the uniform distributions may be considered as an approximation to the linearly distributed cases. The suggestions for using higher-order shape functions have been reported in the literature, for example, in Reference 21. When considering their application on any given triangular mesh, one may be well advised to contrast this to a straightforward refinement of the triangulation in which all additional nodes are projections of the triangle refinement onto the actual, generally nonplanar, geometry treated [27]. The interest in the use of the method of fundamental solutions (MFS) appears to be on the increase [28]. This method uses sets of virtual monopolar sources, for which the infinite medium potential field is simple. However, by their nature, these sources have an essential singularity at their locus (Figure 44.9), which necessitates the inclusion of an extremely dense set of nodes in the computation of boundary

44-18

Bioelectric Phenomena

value problems. The claims seen in the literature that the MFS would obviate the complete meshing of the involved surfaces conceal the fact that imaging the results demands the construction of such meshes. This chapter offers a physical interpretation of the dominant role of the solid angle appearing in all of the expressions for the four major analytical expressions treated in Sections 44.3 through 44.6 and of their properties. This insight has led to the full set of these results, also previously published, in more a condensed report [29].

References 1. Brebbia, C.A., The Boundary Element Method for Engineers. 1984, London: Pentech Press. 2. Gulrajani, R.M., Bioelectricity and Biomagnetism. 1998, New York: John Wiley & Sons. 3. Smythe, W.R., Static and Dynamic Electricity. 1968, New York: McGraw-Hill. 4. Gelernter, H.L. and J.C. Swihart, A mathematical–physical model of the genesis of the electrocardiogram. Biophys. J., 1964. 4: 285–301. 5. Lynn, M.S. and W.P. Timlake, The numerical solution of singular equations of potential theory. Numer. Math., 1968. 11: 77–98. 6. Gulrajani, R.M., The forward problem in electrocardiography, in Bioelectricity and Biomagnetism. 1998, New York: John Wiley & Sons. pp. 348–380. 7. Martin, R.O., Inverse Electrocardiography. 1970, Duke University: Duke, NC, USA. 8. Barr, R.C., M. Ramsey, and M.S. Spach, Relating epicardial to body surface potentials by means of transfer coefficients based on geometry measurements. IEEE Trans. Biomed. Eng., 1977. BME-24: 1–11. 9. Colli-Franzone, P. et  al., Inverse epicardial mapping in the human case. In Proceedings of the Symposium on Electrophysiology of the Heart. 1980, New York: Plenum. 10. Rudy, Y. and J.E. Burns, Noninvasive electrocardiographic imaging. Ann. Noninv. Electrocardiol., 1999. 4: 340–359. 11. van Oosterom, A. and T.F. Oostendorp, On computing pericardial potentials and current densities. J Electrocardiol., 1992. 25: 102–106. 12. Dwight, B.H., Tables of Integrals and Other Mathematical Data. 1961, New York: Macmillan. 13. Panofski, W.K.H. and M. Phillips, Classical Electricity and Magnetism. 1962, London: Addison-Wesley. 14. van Oosterom, A. and J. Strackee, The solid angle of a plane triangle. IEEE Trans. Biomed. Eng., 1983. BME-30: 125–126. 15. Barr, R.C. et al., Determining surface potentials from current dipoles with application to electrocardiography. IEEE Trans. Biomed. Eng., 1966. BME-13: 88–92. 16. Meijs, J.W.H. et  al., On the numerical accuracy of the boundary element method. IEEE Trans. Biomed. Eng., 1989. 36(10): 1038–1049. 17. van Oosterom, A., Electrocardiography, in The Biophysics of Heart and Circulation, J. Strackee and N. Westerhof, eds. 1993, Bristol: Institute of Physics Publication. pp. 249–256. 18. Rao, S.M. et al., A simple numerical solution procedure for statics problems involving arbitraryshaped surfaces. IEEE Trans. Ant. Propag., 1979. AP-36: 604–608. 19. Okon, E.E. and R.F. Harrington, The potential due to a uniform source distribution over a triangular domain. Int. J. Numer. Meth. Eng., 1982. 18: 1401–1411. 20. Kuwahara, T. and T. Takeda, An effective analysis for three-dimensional boundary element method using analytical higher order elements. Trans. IEE Japan, 1986. 107-A: 275–282. 21. Kuwahara, T. and T. Tadeka, A formula of boundary integral for potential problem and its consideration. In Proceedings of the 1st Japan-China Symposium on Boundary Element Methods. 1987, Kyota, Japan: Pergamon Press. 22. Medina, D.E. and J.A. Liggett, Exact integrals for the three-dimensional boundary element potential problems. Commun. Appl. Num. Anal., 1989. 5: 555–561.

The Potential Fields of Triangular Boundary Elements

44-19

23. Graglia, R.D., On the numerical integration of the linear shape functions times the 3-D Green’s function or its gradient on the plane triangle. IEEE Trans. Antennas Propag., 1993. 41: 1448–1455. 24. Ferguson, A.S., X. Zhang, and G. Stroink, A complete linear discretization for calculating the magnetic field using the boundary element method. IEEE Trans. Biomed. Eng., 1994. BME-41: 455–460. 25. Munck, J.C.D., A linear discretization of the volume conductor boundary integral equation using analytically integrated elements. IEEE Trans. Biomed. Eng., 1992. BME-39: 986–990. 26. Geselowitz, D.B., On the magnetic field generated outside an inhomogeneous volume conductor by internal sources. IEEE Trans. Magn., 1970, MAG-6: 346–347. 27. Zhou, H. and A. van Oosterom, Mesh refinement and accuracy of numerical solutions. In Engineering solutions to current health care problems. Proceedings of the 15-th Annual International Conference of the IEEE Engineering in Medicine and Biology Society. 1993, Piscataway: IEEE Publishing Services. 28. Fairweather, G. and A. Karageorghis, The method of fundamental solutions for elliptic boundary value problems. Adv. Comput. Math., 1998, 9: 69–95. 29. A. van Oosterom, Closed-form analytical expressions for the potential fields generated by triangular monolayers with linearly distributed source strength. Med Biol Eng Comput. 2012, 25: 1–9.

45 Principles of Electrocardiography 45.1 Introduction.....................................................................................45-1 45.2 Physiology.........................................................................................45-4 45.3 Instrumentation...............................................................................45-5 Applications

Edward J. Berbari Indiana University–Purdue University, Indianapolis

45.4 Conclusions.................................................................................... 45-10 References................................................................................................... 45-10 Further Information.................................................................................. 45-11

45.1 Introduction The electrocardiogram (ECG) is the recording of the electrical activity generated by the heart on the body surface. It was originally observed by Waller in 1889 [1] using his pet bulldog as the signal source and the capillary electrometer as the recording device. In 1903 Einthoven [2] improvised the technology by using the string galvanometer as the recording device and employing human subjects with a variety of cardiac abnormalities. Einthoven is chiefly responsible for introducing some concepts still in use today, including the labeling of the various waves, defining some of the standard recording sites using the arms and legs, and developing the first theoretical construct whereby the heart is modeled as a single time-varying dipole. We also owe the “EKG” acronym to Einthoven writing in German where the root word “cardio” is spelled with a “k.” To record an ECG waveform, a differential recording between two points on the body are made. Traditionally each differential recording is referred to as a lead. Einthoven defined three leads numbered with the Roman numerals I, II, and III. They are defined as:



I = VLA − VRA II = VLL − VRA III = VLL − VLA

where RA = right arm, LA = left arm, and LL = left leg. Because the body is assumed to be purely resistive, at ECG frequencies, the four limbs can be thought of as wires attached to the torso. Hence, lead I could be recorded from the respective shoulders without a loss of cardiac information. Note that these are not independent and the following relationship II = I + III holds. For 30 years the evolution of the ECG proceeded when F.N. Wilson [3] added concepts of a “unipolar” recording. He created a reference point by tying the three limbs together and averaging their potentials so that individual recording sites on the limbs or the chest surface would be differentially recorded with the same reference point. Wilson extended the biophysical models to include the concept of the 45-1

45-2

Bioelectric Phenomena I I = VRA – VLA II = VRA – VLL II

III = VLA – VLL

III

aVL =

2VLA – VRA – VLL 2

2VRA – VLA – VLL 2 2VLL – VLA – VRA aVF = 2 aVR =

Augmented leads

vi

Vi = vi – Vw i = 1 to 6

Σ 3

Vw

FIGURE 45.1  The 12-lead ECG is formed by the three bipolar surface leads: I, II, and III; the augmented Wilson t­erminal referenced limb leads: aVR, aVL, aVF; and the Wilson terminal referenced chest leads: V1, V2, V3, V4, V5, and V6.

cardiac source enclosed within the volume conductor of the body. He erroneously thought that the central terminal was a true zero potential. However, from the mid-1930s until today the 12 leads composed of the 3 limb leads, 3 leads in which the limb potentials are referenced to a modified Wilson terminal (the augmented leads [4]), and 6 leads placed across the front of the chest and referenced to the Wilson terminal form the basis of the standard 12-lead ECG. Figure 45.1 summarizes the 12-lead set. These sites are historically based, have a built in redundancy, and are not optimal for all cardiac events. The voltage difference from any two sites will record an ECG, but it is these standardized sites with the massive 90-year collection of empirical observations that has firmly established their role as the standard. Figure 45.2 is a typical or stylized ECG recording from lead II. Einthoven chose the letters of the alphabet from P–U to label the waves and to avoid conflict with other physiologic waves being studied at the turn of the century. The ECG signals are typically in the range of ±2 mV and require a recording bandwidth of 0.05–150 Hz. Full technical specification for ECG equipment has been proposed by both the American Heart Association [5] and the Association for the Advancement of Medical Instrumentation [6]. There have been several attempts to change the approach for recording the ECG. The vector cardiogram used a weighted set of recording sites to form an orthogonal XYZ lead set. The advantage here was minimum lead set but in practice it gained only a moderate degree of enthusiasm among physicians. Body surface mapping refers to the use of many recording sites (>64) arranged on the body so that isopotential surfaces could be computed and analyzed over time. This approach still has a role in research investigations. Other subsets of the 12-lead ECG are used in limited mode recording situations such as the digitally stored ambulatory ECG (usually 2 leads) or in intensive care monitoring at the bedside ­(usually 1 or 2 leads) or telemetered within regions of the hospital from patients who are not confined to bed (1 lead). The recording electronics of these ECG systems have followed the typical evolution of modern instrumentation, for example, vacuum tubes, transistors, ICs, and microprocessors.

45-3

Principles of Electrocardiography

R 200 ms

1 mV

T

P

U

Q PR interval

S ST segment

FIGURE 45.2  This is a stylized version of a normal lead II recording showing the P wave, QRS complex, and the T and U waves. The PR interval and the ST segment are significant time windows. The peak amplitude of the QRS is about 1 mV. The vertical scale is usually 1 mV/cm. The time scale is usually based on millimeter per second scales with 25 mm/s being the standard form. The small boxes of the ECG are 1 × 1 mm2.

The application of computers to the ECG for machine interpretation was one of the earliest uses of computers in medicine [7]. Of primary interest in the computer-based systems was the replacement of the human reader and the elucidation of the standard waves and intervals. Originally this was performed by linking the ECG machine to a centralized computer via phone lines. The modern ECG machine is completely integrated with an analog front end, a 12–16-bit A/D converter, a computational microprocessor, and dedicated I/O processors. These systems compute a measurement matrix derived from the 12-lead signals and analyze this matrix with a set of rules to obtain the final set of interpretive statements [8]. Figure 45.3 shows the ECG of a heartbeat and the types of measurements that might be made on each of the component waves of the ECG and used for classifying each beat type and the subsequent cardiac rhythm. The depiction of the 12 analog signals and this set of interpretive statements form the final output with an example shown in Figure 45.4. The physician will over-read each ECG and modify or correct those statements that are deemed inappropriate. The larger hospital-based system will record these corrections and maintain a large database of all ECGs accessible by any combination of parameters, for example, all men, above 50 years, with an inferior myocardial infarction. There are hundreds of interpretive statements from which a specific diagnosis is made for each ECG, but there are only about five or six major classification groups for which the ECG is used. The first step in analyzing an ECG requires the determination of the rate and rhythm for the atria and ventricles. Included here would be any conduction disturbances either in the relationship between the various chambers or within the chambers themselves. Then one would proceed to identify features that would relate to the presence or absence of scarring due to a myocardial infarction. There may also be evidence of acute events occurring that would occur with ischemia or an evolving myocardial infarction. The ECG has been a primary tool for evaluating chamber size or enlargement, but one might argue that more accurate information in this area would be supplied by noninvasive imaging technologies. More recently, a high-resolution (HR) ECG has been developed whereby the digitized ECG is signal averaged to reduce random noise [9,10]. This approach, coupled with postaveraging high-pass filtering,

45-4

Bioelectric Phenomena QRSD VAT PArea

+

+

PArea

QRSNotch

R

QRSArea

–

P′Area

ST-shape

TArea

+ –

Type 3

–

T′Area

Type 2 Type 1 Ra STD

P

STE

QDUR

PA P′A PD

P′ P′D

SA

QAMP PR

Segment

Q

RD

STON

STM ST? 80 ms

SD

T TA TD

T′A

T′D

STSlope

J Point QRSP–P

PRInterval

S

QTInterval

FIGURE 45.3  The ECG depicts numerous measurements that can be made with computer-based algorithms. These are primarily durations, amplitudes, and areas. (Courtesy of the Hewlett Packard Co., Palo Alto, CA.)

is used to detect and quantify low-level signals (1.0 μV) not detectable with standard approaches. This computer-based approach has enabled the recording of events which are predictive of future life-threatening cardiac events [11,12].

45.2 Physiology The heart has four chambers, the upper two chambers are called the atria and the lower two chambers are called the ventricles. The atria are thin-walled, low-pressure pumps that receive blood from venous circulation. Located in the top right atrium are a group of cells which act as the primary pacemaker of the heart. Through a complex change of ionic concentration across the cell membranes (the current source) an extracellular potential field is established which then excites neighboring cells and a cell-to-cell propagation of electrical events occur. Because the body acts as a purely resistive medium these potential fields extend to the body surface [13]. The character of the body surface waves depends upon the amount of tissue activating at one time and the relative speed and direction of the activation wave front. Therefore, the pacemaker potentials which are generated by a small tissue mass are not seen on the ECG. As the activation wave front encounters the increased mass of atrial muscle, the initiation of electrical activity is observed on the body surface and the first ECG wave of the cardiac cycle is seen. This is the P wave and it represents activation of the atria. Conduction of the cardiac impulse proceeds from the atria through a series of specialized cardiac cells (the A–V node and the His–Purkinje system), which again are too small in total mass to generate a signal large enough to be seen on the standard ECG. There is a short relatively isoelectric segment following the P wave. Once the large muscle mass of the ventricles is excited, a rapid and large deflection is seen on the body surface. The excitation of the ventricles causes them to contract and provides the main force for circulating blood to the organs of the body. This large wave appears to have several components. The initial downward deflection is called the Q wave, the initial upward deflection is the R wave, and the

45-5

Principles of Electrocardiography

Lastname, Firstname 50 years Male Black 70in 240lbs Room: 222 Loc: 4

ID: 000001234 25-Mar-2004 10:03:07 70 bpm Normal sinus rhythm Vent. rate 136 ms Left bundle branch block PR interval Abnormal ECG QRS duration 126 ms QT/QTc 332/358 ms P-R-T axes 43 72 251 114/71 mmHg BP

Technician: Anne Test ind: Chest pain

Referred by:

GE Healthcare

Unconfirmed

I

aVR

V1

V4

II

aVL

V2

V5

III

aVF

V3

V6

VI

H

V5 150 Hz

25.0 mm/s

10.0 mm/mV

4 by 2.5 s + 3 rhythm lds

MAC5K 008A

= ο =

12SLTMv237

FIGURE 45.4  This is an example of an interpreted 12-lead ECG. A 2.5 s recording is shown for each of the 12 leads. The bottom trace is a continuous 10 s rhythm strip of lead II. Patient information is given in the top area, below which is printed the computerized interpretive statements. (Courtesy of GE Healthcare Technologies, Waukesha, WI.)

terminal downward deflection is the S wave. The polarity and actual presence of these three components depends upon the position of the leads on the body as well as a multitude of abnormalities that may exist. In general, the large ventricular waveform is generically called the QRS complex regardless of its makeup. Following the QRS complex is another relatively short isoelectric segment. After this short segment the ventricles return to their electrical resting state and a wave of repolarization is seen as a low-frequency signal called the T wave. In some individuals a small peak occurs at the end or after the T wave and is called the U wave. Its origin has never been fully established but is believed to be a repolarization potential.

45.3 Instrumentation The general instrumentation requirements for the ECG have been addressed by professional societies through the years [5,6]. Briefly they recommend a system bandwidth between 0.05 and 150 Hz. Of great importance in ECG diagnosis is the low-frequency response of the system because shifts in some of the low-frequency regions, for example, the ST segment, have critical diagnostic value. While the heart rate may only have a 1 Hz fundamental frequency, the phase response of typical analog highpass filters are such that the system corner frequency must be much smaller than the 3 dB corner frequency where only the amplitude response is considered. The system gain depends upon the total

45-6

Bioelectric Phenomena

system design. The typical ECG amplitude is ±2 mV and if A/D conversion is used in a digital system, then enough gain to span the only 20% of the A/D converter’s dynamic range is needed. This margin allows for recording abnormally large signals as well as accommodating base line drift if present and not corrected. To first obtain an ECG the patient must be physically connected to the amplifier front end. The patient/amplifier interface is formed by a special bioelectrode that converts the ionic current flow of the body to the electron flow of the metallic wire. These electrodes typically rely on a chemical paste or gel with a high ionic concentration. This acts as the transducer at the tissue–electrode interface. For short-term applications the use of silver-coated suction electrodes or “sticky” metallic foil electrodes are used. Long-term recordings, such as the case for the monitored patient, require a stable electrode/tissue interface and special adhesive tape material surrounds the gel and an Ag+/Ag+Cl electrode. At any given time, the patient may be connected to a variety of devices, for example, respirator, blood pressure monitor, temporary pacemaker, and so on, some of which will invade the body and provide a low-resistance pathway to the heart. It is essential that the device does not act as a current source and inject the patient with enough current to stimulate the heart and cause it to fibrillate. Some bias currents are unavoidable at the system input stage and recommendations are that these leakage currents be less than 10 μA per device. In recent years, there has been some controversy regarding the level of allowable leakage current. The Association for the Advancement of Medical Instrumentation [5] has written its standards to allow leakage currents as high as 50 μA. Studies [14,15] have shown that there may be complex and lethal physiological response to 60 Hz currents as low as 32 μA. In light of the reduced standards these research results were commented on by members of the American Heart Association Committee on Electrocardiography [16]. There is also a 10 μA maximum current limitation due to a fault condition if a patient comes in contact with the high-voltage side of the AC power lines. In this case, the isolation must be adequate to prevent 10 μA of fault current as well. This mandates that the ECG reference ground not be connected physically to the low side of the AC power line or its third ground wire. For ECG machines the solution has typically been to AM modulate a medium-frequency carrier signal (400 kHz) and use an isolation transformer with subsequent demodulation. Other methods of signal isolation can be used but the primary reason for the isolation is to keep the patient from being part of the AC circuit in the case of a patient to power line fault. In addition, with many devices connected in a patient-monitoring situation it is possible that ground loop currents will be generated. To obviate this potential hazard a lowimpedance ground buss is often installed in these rooms and each device chassis will have an external ground wire connected to the buss. Another unique feature of these amplifiers is that they must be able to withstand the high-energy discharge of a cardiac defibrillator. Older-style ECG machines recorded one lead at a time, then evolved to three simultaneous leads. This necessitated the use of switching circuits as well as analog weighting circuits to generate the various 12 leads. This is usually eliminated in modern digital systems by using an individual single-ended amplifier for each electrode on the body. Each potential signal is then digitally converted and all of the ECG leads can be formed mathematically in software. This would necessitate a 9-amplifier system. By performing some of the lead calculations with the analog differential amplifiers this can be reduced to an 8-channel system. Thus only the individual chest leads V1 through V6 and any two of the limb leads, for example, I and III, are needed to calculate the full 12-lead ECG. Figure 45.5 is a block diagram of a modern digitalbased ECG system. This system uses an amplifier per lead wire and a 16-bit A/D converter, all within a small lead wire manifold or amplifier lead stage. The digital signals are sent via a high-speed link to the main ECG instrument. Here, the embedded microprocessors perform all of the calculations and a hard copy report is generated (Figure 45.4). Note that each functional block has its own controller and the system requires a sophisticated real-time operating system to coordinate all system functions. Concomitant with the data acquisition is the automatic interpretation of the ECG. These programs are quite sophisticated and are continually evolving. It is still a medical/legal requirement that these ECGs be over-read by the physician.

45-7

Principles of Electrocardiography Isolation barrier D S P

.. .

Patient acquisition module

Display Data storage media

Communication port

CPU board w/μ processor Keyboard

ROM Speaker

Writer Thermal printhead Power supply

AC inlet

Motor Battery pack

FIGURE 45.5  This is a block diagram of microprocessor-based ECG system. (Courtesy of GE Healthcare Technologies, Waukesha, WI.)

45.3.1 Applications Besides the standard 12-lead ECG, there are several other uses of ECG recording technology which rely on only a few leads. These applications have had a significant clinical and commercial impact. The following are brief descriptions of several ECG applications that are aimed at introducing the reader to some of the many uses of the ECG. 45.3.1.1 The Ambulatory ECG The evolution of the ambulatory or Holter ECG has an interesting history and its evolution closely followed both technical and clinical progress. The original, analog tape-based, portable ECG resembled a fully loaded backpack and was developed by Dr. Holter in the early 1960s [17], but was soon followed by more compact devices that could be worn on the belt. The original large-scale clinical use of this technology was to identify patients who developed heart block transiently and could be treated by implanting a cardiac pacemaker. This required the secondary development of a device which could rapidly play back the 24 h of tape-recorded ECG signals and present to the technician or physician a means of identifying periods of time where the patient’s heart rate became abnormally low. The scanners had the circuitry to not only playback the ECG at speeds 30–60 times real time, but to detect the beats and display them in a superimposed mode on a cathode ray tube (CRT) screen. In addition, an audible tachometer could be used to identify the periods of low heart rate. With this playback capability came numerous other observations such as the identification of premature ventricular beats (PVBs), which led to the development of techniques to identify and quantify their number. Together with the development of antiarrhythmic drugs a coupling was formed between pharmaceutical therapy and the diagnostic tool for quantifying PVBs. ECG tapes were recorded before and after drug administration and the drug efficacy was measured by the reduction of the number of PVBs. The scanner technology for detecting and quantifying these arrhythmias was originally implemented with analog hardware but soon advanced to computer

45-8

Bioelectric Phenomena

technology as it became economically feasible. Very sophisticated algorithms were developed based on pattern recognition techniques and were sometimes implemented with high-speed specialized numerical processors as the tape playback speeds became several hundred times real time [18]. Unfortunately this approach using the ambulatory ECG for identifying and treating cardiac arrhythmias has been on the decline as the rationale of PVC suppression was found to be unsuccessful for decreasing cardiac mortality. However, the ambulatory ECG is still a widely used diagnostic tool and modern units often have built-in microprocessors with considerable amounts of random access memory. Here, the data can be analyzed on line with large segments of data selected for storage and later analysis with personal computer-based programs. 45.3.1.2  Patient Monitoring The techniques for monitoring the ECG in real time were developed in conjunction with the concept of the coronary care unit or CCU. Patients were placed in these specialized hospital units to carefully observe their progress during an acute illness such as a myocardial infarction or after complex surgical procedures. As the number of beds increased in these units it became clear that the highly trained medical staff could not continually watch a monitor screen and computerized techniques were added which monitored the patient’s rhythm. These programs were not unlike those developed for the ambulatory ECG and the high-speed numerical capability of the computer was not taxed by monitoring a single ECG. The typical CCU would have 8–16 beds and hence the computing power was taken to its limit by monitoring multiple beds. The modern units have the central processing unit (CPU) distributed within the ECG module at the bedside, along with modules for measuring many other physiological parameters. Each bedside monitor would be interconnected with a high-speed digital line, for example, Ethernet, to a centralized computer used primarily to control communications and maintain a patient database. 45.3.1.3  HR Electrocardiography HR capability is now a standard feature on most digitally based ECG systems, or as a stand-alone microprocessor-based unit [19]. The most common application of the HRECG is to record very low level (1.0 μV) signals which occur after the QRS complex but are not evident on the standard ECG. These “late potentials” are generated from abnormal regions of the ventricles and have been strongly associated with the substrate responsible for a life-threatening rapid heart rate (ventricular tachycardia). The typical HRECG is derived from three bipolar leads configured in an anatomic XYZ coordinate system. These three ECG signals are then digitized at a rate of 1000–2000 Hz per channel, time aligned via a real-time QRS correlator, and summated in the form of a signal average. Signal averaging will theoretically improve the signalto-noise ratio by the square root of the number of beats averaged. The underlying assumptions are that the signals of interest do not vary, on a beat-to-beat basis, and that the noise is random. Figure 45.6 has four panels depicting the most common sequence for processing the HRECG to measure the late potentials. Panel (a) depicts a 3 s recording of the XYZ leads close to normal resolution. Panel (b) was obtained after averaging 200 beats and with a sampling frequency of 10 times as that shown in panel (a). The gain is also five times greater. Panel (c) is the high-pass filtered signal using a partially time-reversed digital filter having a second-order Butterworth response and a 3 db corner frequency of 40 Hz [12]. Note the appearance of the signals at the terminal portion of the QRS complex. A common method of analysis, but necessarily optimal, is to combine the filters XYZ leads into a vector magnitude, (X2 + Y2 + Z2)1/2. This waveform is shown in panel (d). From this waveform several parameters have been derived such as total QRS duration, including late potentials, the RMS voltage value of the terminal 40 ms, and the low-amplitude signal (LAS) duration from the 40 μV level to the end of the late potentials. Abnormal values for these parameters are used to identify patients at high risk of ventricular tachycardia following a heart attack. 45.3.1.4  His Bundle Electrocardiography ECG can be directly recorded from the heart surface as in a modern electrophysiology (EP) study where the evaluation of the heart relies on both the body surface ECG and direct recordings obtained from

45-9

Principles of Electrocardiography (c)

(a) 19.250 17.325

0.346

X

15.400

83

0.308

Y

9.625

mV

11.550

0.231

70

0.192

209

Y

211

Z

0.154 0.115

Z

63

60 0

30

0.038

90 0 12 00 15 00 18 00 21 00 24 00 27 00 30 00

1.925

30 0

3.850

0.077

90 12 0 15 0 18 0 21 0 24 0 27 0 30 0

5.775

60

7.700

Time, ms

(b) 3.850

Time, ms

(d) 0.256

Late potentials

3.465

0.231

X

3.080

0.205

Duration, 138 ms RMS, 20 µV LAS, 54 ms

0.179

2.310

Y

1.925

mV

2.695

0.154 0.128 0.102

1.540 1.155

Z

0.770

67

0.077

LAS

0.051

205

0 21 0 24 0 27 0 30 0

18

0

0

15

12

90

0

0

30

0

27

0

24

0

21

0

18

0

15

90

60

30

12

ms

60

0.025

0.385

30

mV

X

197

0.269

13.475 mV

Late potentials

ms

FIGURE 45.6  The signal processing steps typically performed to obtain a HRECG are shown in panels (a–d). See text for a full description.

within the heart using electrode catheters. Such catheters are introduced into a leg or arm vein or artery and advanced, under fluoroscopic control, into the interior of one of the four chambers of the heart. An electrode catheter is an insulated set of wires bundled within a polyurethane sheath. The diameters of these catheters range from about 1.0 to 2.5 mm. As many as 16 wires may be in the total assembly with ring electrodes, exposed on the outer surface of the catheter, attached to each internal wire. In addition, there are usually structural internal wires used to stiffen the catheter. With a proper controller at the rear of the catheter a trained operator can flex the catheter in a loop of almost 180°. Together with the torsional properties of the catheter almost every point within the heart can be probed for electrical events. Direct contact recordings are called electrograms to distinguish them from body surface ECGs. Figure 45.7 shows an example of a His bundle recording. The top two traces are leads II and V6 of the ECG and the bottom trace is the voltage difference from two electrodes on the indwelling electrode catheter. This internal view of cardiac activation combined with the His bundle electrogram has been referred to as His bundle electrocardiography [20]. Atrial activation on the catheter recording is called the “A” deflection and ventricular activation called the “V” deflection. The His bundle potential is the central “H” deflection. Since the catheter is located very close to the His bundle and AV node, it is assumed that the A deflection arises from the atrial muscle tissue close to the AV node. When combined with the surface lead information a number of new intervals can be obtained. These are the PA, AH, and HV intervals. The PA interval is a measure of atrial muscle activation time, the AH interval is a measure of AV nodal activation time, and the HV interval is a measure of the ventricular conduction system activation time.

45-10

Bioelectric Phenomena 90 BPM L-II

V-2

HB (e.g.)

FIGURE 45.7  The top two traces are ECG leads II and V-2 and the bottom trace is a bipolar catheter recording, properly positioned inside the heart, showing the His Bundle deflection (HB), and intracardiac atrial (A) and ventricular (V) activity.

The modern electrophysiological evaluation, or EP study, may involve as many as 64 individual recordings within the heart. In addition, current can be passed through these electrodes to stimulate the heart. A variety of atrial and ventricular stimulation protocols can be used, which then allows the cardiac electrophysiologist to identify pathways and mechanisms involved in most forms of arrhythmias. Besides this diagnostic function, it is now possible to locate abnormal structures or regions of the heart that are critical to arrhythmogenesis. By passing high-energy radio frequency waves through one or more of the internal electrodes it is possible to cauterize or ablate the suspect tissue without causing any widespread injury to the rest of the heart. In many forms of arrhythmias this ablation therapy can produce a cure for the patient. In addition to the EP study and ablation therapy internal electrodes are the primary form of signal recording for both the cardiac pacemaker and implantable defibrillator. These devices both sense cardiac activation from permanent indwelling catheters and deliver energy to the heart through them. In the case of the cardiac pacemaker these are low-level shocks which maintain the patient’s heart rhythm. In the case of the implantable defibrillator the device will monitor the patient’s rhythm until a serious or life-threatening arrhythmia occurs and then a high-energy pulse will be delivered in order to convert the rhythm back to normal. Both devices rely heavily on continuous monitoring of the cardiac signals obtained from internal catheter recordings using sophisticated implanted microprocessors and accurate means of signal detection and analysis.

45.4 Conclusions The ECG is one of the oldest, instrument-bound measurements in medicine. It has faithfully followed the progression of instrumentation technology. Its most recent evolutionary step, to the microprocessor-based system, has allowed patients to wear their computer monitor or provided an enhanced, HRECG, which has opened new vistas of ECG analysis and interpretation. The intracardiac ECG also forms the basis of modern diagnostic EP studies and therapeutic devices, such as the pacemaker and implantable defibrillator.

References

1. Waller A.D. On the electromotive changes connected with the beat of the mammalian heart, and the human heart in particular. Philos. Trans. B, 180: 169, 1889.

Principles of Electrocardiography

45-11



2. Einthoven W. Die galvanometrische Registrirung des menschlichen Elektrokardiogramms, zugleich eine Beurtheilung der Anwendung des Capillar-Elecktrometers in der Physiologie. Pflugers Arch. ges. Physiol. 99: 472, 1903. 3. Wilson F.N., Johnston F.S., and Hill I.G.W. The interpretation of the falvanometric curves obtained when one electrode is distant from the heart and the other near or in contact with the ventricular surface. Am. Heart J. 10: 176, 1934. 4. Goldberger E. A simple, indifferent, electrocardiographic electrode of zero potential and a technique of obtaining augmented, unipolar, extremity leads. Am. Heart J. 23: 483, 1942. 5. Bailey J.J., Berson A.S., Garson A., Horan L.G., Macfarlane P.W., Mortara D.W., and Zywietz C. Recommendations for standardization and specifications in automated electrocardiography: Bandwidth and digital signal processing: A report for health professionals by an ad hoc writing group of the committee on electrocardiography and cardiac electrophysiology of the Council on Clinical Cardiology, American Heart Association. Circulation 81: 2, 730–739, 1990. 6. Safe Current Limits for Electromedical Apparatus: American National Standard, ANSI/AAMI ES1– 1993. Arlington, VA: Association for the Advancement of Medical Instrumentation; 1993. 7. Jenkins J.M. Computerized electrocardiography. CRC Crit. Rev. Bioeng. 6: 307, 1981. 8. Pryor T.A., Drazen E., and Laks M. (Eds.), Computer Systems for the Processing of Diagnostic Electrocardiograms. IEEE Computer Society Press, Los Alamitos, CA, 1980. 9. Berbari E.J., Lazzara R., Samet P., and Scherlag B.J. Noninvasive technique for detection of electrical activity during the PR segment. Circulation 48: 1006, 1973. 10. Berbari E.J., Lazzara R., and Scherlag B.J. A computerized technique to record new components of the electrocardiogram. Proc. IEEE 65: 799, 1977. 11. Berbari E.J., Scherlag B.J., Hope R.R., and Lazzara R. Recording from the body surface of arrhythmogenic ventricular activity during the ST segment. Am. J. Cardiol. 41: 697, 1978. 12. Simson M.B. Use of signals in the terminal QRS complex to identify patients with ventricular tachycardia after myocardial infarction. Circulation 64: 235, 1981. 13. Geselowitz D.B. On the theory of the electrocardiogram. Proc. IEEE 77: 857, 1989. 14. Swerdlow C.D., Olson W.H., O’Connor M.E. et al. Cardiovascular collapse caused by electrocardiographically silent 60 Hz intracardiac leakage current: Implications for electrical safety. Circulation 99: 2559–2564, 1999. 15. Malkin R.A. and Hoffmeister B.K. Mechanisms by which AC leakage currents cause complete hemodynamic collapse without inducing fibrillation. [see comment]. J. Cardiovasc. Electrophysiol. 12: 1154–1161, 2001. 16. Laks M.M., Arzbaecher R., Geselowitz D., Bailey J.J., and Berson A. Revisiting the question: Will relaxing safe current limits for electromedical equipment increase hazards to patients? Circulation 102: 823–825, 2000. 17. Holter N.J. New method for heart studies: Continuous electrocardiography of active subjects over long periods is now practical. Science 134: 1214–1220, 1961. 18. Ripley K.L. and Murray A. (Eds.), Introduction to Automated Arrhythmia Detection, IEEE Computer Society Press, Los Alamitos, CA, 1980. 19. Berbari E.J. and Steinberg J.S. A Practical Guide to High Resolution Electrocardiography. Futura Publishers, Armonk, NY, 2000. 20. Scherlag B.J., Samet P., and Helfant R.H. His bundle electrogram: A critical appraisal of its uses and limitations. Circulation 46: 601–613, 1972.

Further Information A Practical Guide to the Use of the High-Resolution Electrocardiogram, Edward J. Berbari and Jonathan S. Steinberg, Eds., Armonk, NY: Futura Publishers, 2000.

45-12

Bioelectric Phenomena

Cardiac Electrophysiology: From Cell to Bedside, 4th ed., D.P. Zipes and J. Jalife, Eds., Philadelphia: W.B. Saunders & Co., 2004. Comprehensive Electrocardiology: Theory and Practice in Health and Disease, Vols. 1–3, P.W. Macfarlane and T.D. Veitch Lawrie, Eds., England: Pergamon Press, 1989. Medical Instrumentation: Application and Design, 3rd ed., J.G. Webster, Ed., Boston: Houghton Mifflin, 1998.

46 Electrodiagnostic Studies

Sanjeev D. Nandedkar Natus Medical Inc.

46.1 Introduction.....................................................................................46-1 46.2 Anatomy............................................................................................46-1 46.3 Physiology.........................................................................................46-4 46.4 EMG and Force Generation...........................................................46-5 46.5 Pathology......................................................................................... 46-6 46.6 Instrumentation...............................................................................46-7 46.7 EDX Study.........................................................................................46-9 46.8 Motor Nerve Conduction...............................................................46-9 46.9 Sensory Nerve Conduction..........................................................46-11 46.10 Needle EMG...................................................................................46-11 46.11 Single Fiber and Macro EMG......................................................46-14 46.12 Evoked Potentials...........................................................................46-16 46.13 Somatosensory Evoked Potential................................................46-16 46.14 Brainstem Auditory Evoked Response.......................................46-17 46.15 Visual Evoked Potential................................................................46-18 46.16 Engineering in EDX......................................................................46-19 References...................................................................................................46-19

46.1 Introduction Neuromuscular disease is suspected when a patient complains of abnormal sensation (numbness, tingling, and pain), weakness, or difficulty with movements (e.g., tremor and foot drop). Electrodiagnostic (EDX) studies have been used successfully over the last six decades to identify or to refute a neuromuscular pathology to explain the patient symptoms (Dumitru et al., 2002). The EDX studies are often performed in conjunction with other diagnostic procedures such as imaging (MRI, x-ray), blood work (biochemistry), nerve or muscle biopsy, and so on. The EDX studies offer many advantages. The EDX studies are relatively noninvasive, the study can be repeated easily, the cost of procedures is relatively low, and the study characterizes the “function” of the neuromuscular system. Imaging studies reveal the structure and thus help the overall assessment of the patient condition. In this chapter, we will review the physiologic basis and principles of EDX studies, and discuss the contributions of biomedical engineers in this exciting field of neurophysiology. The study of brain using electroencephalograph (EEG) is discussed in a separate chapter.

46.2 Anatomy The EDX study is often described as an extension of the patient’s medical history and physical examination. It is essential to understand the anatomy and the physiology of the neuromuscular system to plan and interpret the test results. 46-1

46-2

Bioelectric Phenomena (a)

Motor neuron

Concentric needle

Axon

(c)

Terminal branches

Muscle fiber and end-plate (b) 0 mV

–80 mV

(d)

c

b

a

0

d e

Time (ms)

1

2

2

FIGURE 46.1  Schematic of MU and MUP. (a) The MU shows muscle fibers in a longitudinal view. A cross-sectional view is shown in Figure 46.3. (b) The resting and action potential in intracellular space are illustrated. (c) The extracellular AP of all muscle fibers shows variation in amplitude and arrival time at the electrode. The concentric needle tip is better seen in Figure 46.9. (d) The sum of all muscle fiber APs is the MUP. Markers 1 and 2 indicate the beginning and end of the MUP. The time difference between these points is the MUP duration. The number of phases is obtained by adding 1 to the number of baseline crossings. Hence, this MUP has five phases. (Copyright Nandedkar Productions LLC, 2010.)

A muscle is made of thousands of cells, called muscle fibers. They are organized into functional entities called motor units (MUs). An MU consists of all muscle fibers innervated by one motor neuron (MN) (Figure 46.1a). The MN is located in the spinal cord (Figure 46.2), and is also called the lower MN. The upper MN is located in the brain. The nerve fiber from the lower MN exits from a small opening between the disks separating the vertebrae. All nerve fibers exiting such an opening form the so-called root (Figure 46.2). The root is described by its anatomic location in the spinal cord, for example, the C5 root contains fibers exiting the spinal cord at the C5 level. The nerve fibers from different roots combine and separate to form distinct bundles (trunk, division, cord) and finally the individual nerve (Figure 46.2). A nerve supplies many different muscles. Note that a muscle is innervated by a single nerve and has multiple roots. Also, a nerve consists of fibers (or axons) from many roots. The lesion of individual roots or nerves will give a corresponding pattern of weakness in the muscles innervated by them. A nerve fiber begins at the MN and upon reaching the muscle divides into many branches to connect with individual muscle fibers. The contact is called the “end-plate” or “neuromuscular junction” (Figure 46.1a). In most muscles, there is only one end-plate per muscle fiber. In large muscles such as the biceps or the tibialis anterior, the MU muscle fibers are distributed randomly over a roughly circular territory (Figure 46.3a) with 5–10 mm diameter. Most fibers are separated from other fibers of the same MU by a few hundred micrometers. There is no tendency to form groups. The fiber diameter varies slightly among different fibers of the MU. The mean muscle fiber diameter is 50–60 μm. The MU size refers mainly to the number of muscle fibers in the MU. A muscle has MUs of different sizes. The small MUs are fatigue resistant and are activated first. Large MUs have more fibers and have larger territory (Figure 46.3b). This gives them the same “fiber density (FD)” as the smaller MUs. The larger MUs are activated when a higher force is required and they fatigue easily.

46-3

Electrodiagnostic Studies

Musculocut N

D

PT (C6, C7)

V Trunk

C7

Axillary N

Division

C6

Cord

Cord

Trunk

Trunk

Deltoid (C5, C6) Radial N

EDC (C7, C8) EIP (C7, C8)

Triceps (C6, C7, C8)

FCU (C8, T1)

T1

Root

Neck

Thumb C6 Ring C8 Small C8

FDI (C8, T1)

Cord

Ulnar N

Spinal cord

Thumb C6 Index C6,C7 Middle C7 Ring C8

APB (C8, T1)

Sensory

Division

C8

Median N

Sensory

C5

Biceps (C5, C6)

Sensory

Sensory ganglion

Shoulder

Upper arm

Forearm

ADM (C8, T1)

Hand

FIGURE 46.2  Illustration of the beginning of motor nerve fibers in the spinal cord and their path to reach different muscles in the upper limb. All nerves and muscles are not shown. The sensory innervation to fingers is shown. The dorsal and ventral roots are indicated by “D” and “V.” The shaded area is called the brachial plexus. The knowledge of this anatomic structure is essential to plan and interpret the EDX procedures. (Copyright Nandedkar Productions LLC, 2010.)

(a)

(b)

(c)

(d)

FIGURE 46.3  Cross section of a motor unit shown schematically. A single fiber electrode is superimposed on the MU cross section in (b) and (d). The shaded semicircular area near the recording tip represents the recording territory. The concentric needle (a, c) records from a much larger circular recording area. In both types of recordings, the needle is placed close to fibers of the MU. (a) A normal small MU contains fibers distributed randomly in a roughly circular territory. (b) A normal large MU. The MU in (a) is shown after (c) myopathy and (d) reinnervation (neuropathy). Note the significant difference in MU architecture that will affect the MUP waveform (shown in Figure 46.10). (Copyright Nandedkar Productions LLC, 2010.)

46-4

Bioelectric Phenomena

The axons connecting the lower MNs to the muscle fibers constitute the “motor” component of a nerve. Most nerves also contain sensory axons. The sensory axon cell body lies outside the spinal cord in the sensory ganglion (Figure 46.2). Their axons terminate in various sense organs, for example, for touch, sight, sound, and so on. The sensory innervation to fingers and thumbs is shown in Figure 46.2. Note that the hand receives sensory innervation by different nerves and roots. The lesion of individual roots or nerves will affect the sensation in different digits. Thus, the patient symptoms and physical examination will allow the clinician to select the appropriate nerves for testing. The sensory axons convey information from the periphery toward the spinal cord and the brain, while the motor axons provide activation to the muscles located in the periphery. Together, they form a feedback system that allows a smooth coordination of muscular activity. Note that the motor fibers form the ventral root while the sensory fibers make up the dorsal root (Figure 46.2). The roots, nerves, and muscles are considered as the peripheral nervous system. The MNs (upper and lower) and their spinal connections make up the central nervous system. The “autonomic” nervous system is responsible for other neuromuscular functions, for example, respiration and circulation, that occur subconsciously. The assessment of this system requires a different battery of tests that is beyond the scope of this chapter.

46.3 Physiology The nerve and muscle cells are electrically “active.” In their “resting” state, the cell maintains a voltage difference of 80 mV across the cell membrane, the intracellular being negative (Figure 46.1b-a). If the cell depolarizes, that is, the intracellular potential increases from −80 to −50 mV (Figure 46.1b-b), an action potential (AP) is generated. It begins by opening the voltage-dependent sodium channels in the membrane, causing a flux of sodium ions from the extracellular space to the intracellular space. The intracellular space becomes positive with respect to the extracellular space by roughly 30 mV (Figure 46.1b-c). The sodium channels then close while potassium channels open. The movement of potassium ions from the intracellular space to the extracellular space (Figure 46.1b-d) restores the cell to its normal state (Figure 46.1b-e). This event lasts for only a millisecond or two. The depolarization also spreads along the muscle or nerve fiber, causing the propagation (or conduction) of the AP. The initial depolarization of the cell membrane to produce the AP occurs via the release of neurotransmitters such as acetylcholine. The cell membrane can also be depolarized by applying an external electrical or magnetic field. This forms the basis for the nerve (or muscle) stimulation to perform conduction studies. The nerve fibers are surrounded by an insulating tissue called myelin (Figure 46.4). The myelin is absent at the “node of Ranvier.” Owing to the low impedance at the exposed region, the nerve can depolarize easily at the node. The net effect is that the AP “jumps” from one node to another in contrast to a smooth propagation seen in muscle fibers. This mechanism, called “saltatory” conduction, gives a higher velocity in nerve fibers (30–60 m/s) than in muscle fibers (2–6 m/s). The larger the fiber diameter, the higher is the conduction velocity. The voluntary muscle activity begins by the depolarization of the MN. A nerve AP is generated and it propagates from the neuron to the periphery along the axon. When the nerve AP arrives in the endplate, the neurotransmitter “acetylcholine (Ach)” is released from the nerve ending. The Ach diffuses to the muscle membrane and causes its depolarization. The muscle fiber AP propagates from the endplate to the tendons (Figure 46.1c). Its passage activates the contractile elements of the fiber, causing it to twitch and generate a force. Thus, every time the MN discharges, all fibers of that MU respond by producing a mechanical twitch and their AP. The sum of APs of all fibers in the MU is the motor unit potential (MUP) (Figure 46.1d). The EDX recordings are made in extracellular space. The relationship between intracellular AP (ICAP) and extracellular AP (ECAP) has been investigated using mathematical models and computer simulations (Plonsey, 1964; Andreassen and Rosenfalck, 1981; Henneberg and Plonsey, 1994; Henneberg and Roberge, 1997). The ECAP has a triphasic waveform that is quite different from the ICAP. When

46-5

Electrodiagnostic Studies (a)

(b)

(c)

Proximal site

Distal site

Normal

Focal demyelination

Diffuse demyelination (d)

Conduction block (e)

Axon

Node of Ranvier

Myelin

Axonal degeneration

FIGURE 46.4  A normal axon (a) and its structural changes with pathology (b−e). Curved arrows indicate the saltatory conduction of AP from one node to the next. The conduction block is indicated by “X.” The distal and proximal stimulation sites are shown to match abnormalities shown in Figure 46.7. (Copyright Nandedkar Productions LLC, 2010.)

the ICAP approaches the recording electrode, the electromyograph records a positive voltage (Figure 46.1c). This, by convention in EMG, produces a downward deflection on the instrument display. The main spike of the ECAP occurs when the ICAP passes the electrode. When the ICAP moves away from the electrode, the terminal positive phase is seen. The amplitude of the ECAP decreases with the distance between the fiber and the recording electrode (Figure 46.1c). The rate of decline depends on the size of the recording surface. Small electrodes (e.g., single fiber needle) have a high rate of amplitude decline and allow “selective” recording from muscle fibers near the electrode tip (Figure 46.3b,d). Large recording surface (e.g., concentric needle) has a slower radial decline of amplitude. Hence, they can record from a much larger portion of the muscle (Figure 46.3a,c). Using electrodes of different sizes, one can obtain complementary information about the changes in MU with pathology and disease progression.

46.4 EMG and Force Generation The MU twitch from a single MN discharge lasts only for a short period of time (LCST

FIGURE 87.5  Smart drug-delivery systems using thermoresponsive polymers. (a) Diffusion-controlled drug release below LCST. (b) “Squeezing out” effect above LCST. (c) “On–off” control of drug release. (d) Heterogeneous microgels with a thermo-responsive shell. (Adapted from Bromberg, L. E., and Ron, E. S. 1998. Temperatureresponsive gels and thermogelling polymer matrices for protein and peptide delivery. Adv. Drug Deliv. Rev., 31: 197–221.)

87-7

Environment-Responsive Hydrogels for Drug Delivery

the membranes that contain thermoresponsive hydrogel segments. Swollen gel blocks drug passage through the pores, and allows permeation when collapsed. Figure 87.5d describes another pulsatile drug release system. When a shell layer is made of thermoresponsive hydrogels with LCST, it may form a dense shell layer of the collapsed component while the core remains swollen. The drug release behavior from PEG–PLGA–PEG in situ forming hydrogels has been extensively studied. For example, two low-molecular-weight compounds, ketoprofen and spironolactone, were used as model drug molecules having different hydrophobicities. The relatively hydrophilic ketoprofen was released monotonously through diffusion mechanisms, with approximately 90% of the drug released within 5 days. In contrast, the more hydrophobic spironolactone showed a sigmoid curve, with the release extending over 50 days. Given that the polymeric micellar structure was maintained within the triblock copolymer gels, the spironolactone molecules in PEG shell layers were released mainly by a diffusion process, while drugs preferentially existing in the hydrophobic micelle core were released via diffusion and bulk micelle matrix degradation. Thus, the longer-term sustained release of drugs was achieved using PEG–PLGA–PEG triblock copolymer hydrogels (Jeong et al. 2000, 2002b).

87.3  pH-Responsive Hydrogels 87.3.1  Structure and Property The pH sensitivity has been one of the important parameters in designing a smart drug-delivery system because the pH change frequently occurs at pathological sites. For ionic hydrogels, the degree of swelling and drug release significantly depend on the environmental pH. The pH-responsive polymers can be classified as acidic weak polyelectrolytes containing pendant acidic groups (e.g., carboxylic and sulfonic acids) and basic weak polyelectrolytes with pendant basic (e.g., amine) groups (Figure 87.6). They accept or release protons in response to changes in environmental pH. Typical acidic pH-sensitive polymers containing carboxylic groups include poly(acrylic acid) (PAA), poly(methacrylic acid) (PMA), poly(lglutamic acid), and alginate (Figure 87.7). Typical examples of the basic polyelectrolytes containing amine groups include poly(tertiary amine methacrylate), poly(2-vinylpyridine), poly(l-lysine), poly(lhistidine), poly(β-amino ester), and chitosan (Figure 87.7). The presence of ionizable groups on polymer chains results in swelling of the hydrogels; far beyond that, it can be achievable by nonelectrolyte polymer hydrogels. Since the swelling of polyelectrolyte hydrogels is mainly due to the electrostatic repulsion among charges present on polymer chains, the extent of swelling is influenced by any changes that reduce or enhance electrostatic repulsion, such as pH, ionic strength, and type of counterions (Qiu and Park 2001). Swelling of ionic hydrogels sharply

NH3+

Low pH

Neutral pH

High pH

NH3+

X

NH2 NH2

NH2 NH2

+

COOH COOH

COOH COOH

COO– COO–

NH3

NH3+

X

NH2 NH2

COOH COOH

NH2

COOH

NH2

COOH

COO– COO–

H+ H+

H+

H+

H+

H+ H+

H+

H+

OH–

H+

OH–

H+

OH–

OH–

H+

H+

H+ H+

H+

H+

H+

H+

Cationic hydrogel OH–

OH– OH–

H+

H+

Anionic hydrogel

OH–

H+

H+

OH–

OH– OH– OH– OH– – OH

OH–

OH– OH– OH–

OH– OH–

FIGURE 87.6  ​ Schematic illustration of swelling/deswelling behaviors of different types of pH-responsive hydrogels.

87-8

Drug Design, Delivery Systems, and Devices OH

HO

OH O

O

HO

HO

NH2

O

HO

NH2

OH

O

OH

O

O n

OH

O

O

HO

NH2

Chitosan HO O

O

HO OH

O

m

n Alginate

HO O

O O

O

O

N O O

N

n

O

O Poly(b-amino ester)

OH

n O

n

Poly(2-vinylpyridine)

O

NH

NH N N Poly(histidine)

NH

n

n

n

Poly(methacrylic acid)

Poly(acrylic acid) O

O

OH

O H2N Poly(lysine)

n

OH

Poly(glutamic acid)

FIGURE 87.7  Structural formula of various pH-responsive polymers.

changes in the vicinity of their pKa or pKb values. Anionic hydrogels deprotonate and swell more when external pH is higher than pKa of the ionizable groups bonded on polymer chains, while cationic hydrogels protonate and swell more when external pH is lower than the pKb of the ionizable groups. By using two or more ionic monomers, the pH-dependent swelling curves can exhibit two or more inflection points near the pKa/pKb of the ionizable groups. As described above, the pendant acidic or basic groups on polymers undergo ionization such as acidic or basic groups of monomers. However, it should be noted that the ionization on the polymer is more difficult due to electrostatic effects exerted by other adjacent ionized groups. This tends to make the apparent dissociation constant (Ka) different from that of the corresponding monoacid or monobase. The pH-responsive swelling/deswelling of polyelectrolyte hydrogels can be further manipulated by adding nonionic comonomers, such as 2-hydroxyethyl methacrylate (HEMA), methyl methacrylate (MMA), and maleic anhydride (MA) (Zentner et  al. 2001). Different comonomers provide different hydrophobicity to the polymer chain, leading to different pH-responsive behaviors (Kim et al. 2001). At low pH, the acidic protons of the carboxyl groups of PMA interact with the ether oxygen of PEG through hydrogen bonding, and such complexation results in shrinkage of the hydrogels. As the carboxyl groups of PMA become ionized at high pH, the resulting decomplexation leads to the swelling of the hydrogels. Cross-linked copolymer hydrogels of poly(l-glutamic acid) and PEO showed rapid swelling and deswelling behavior. The swelling of this hydrogel varied with pH and increased at higher ionization of the poly(l-glutamic acid), which resulted from not only the electrostatic effects but also the secondary

Environment-Responsive Hydrogels for Drug Delivery

87-9

structural change associated with the polypeptide backbone. By modifying the hydrophobicity of polypeptide and the degree of ionization, the overall extent of pH-responsive swelling could be controlled. Just like temperature-responsive sol–gel transition polymers, block copolymers composed of pH-responsive polymers and neutral polymers exhibit pH-sensitive sol–gel transition. Some triblock copolymers, such as poly(diphenylamine)–poly(2-methacryloyloxyethyl phosphorylcholine– poly(diphenylamine) (PDPA–PMPC–PDPA), form physical hydrogels at 37°C. At pH of 8 or less, the amino group is protonated and the block copolymers remain in solution, while under alkaline pH conditions, PDPA is sufficiently hydrophobic to form physical hydrogels. Triblock and three-arm star diblock copolymers can be synthesized with atom transfer radical polymerization (ATRP) initiated by bifunctional and trifunctional initiators, respectively, with the central block, poly(glycerol methacrylate) (PGMA), and the outer pH-responsive PDEA or PDPA blocks. The hydrogel from these block copolymers showed reversible, pH-responsive sol–gel transition; the free-standing gel formation was observed at neutral or higher pH, but dissolved in acidic solution. Armes and coworkers synthesized pH-responsive microgels with a diameter of approximately 250 nm by the emulsion polymerization of 2-(diethylamino)ethyl methacrylate (DEAEMA) with a bifunctional oligo(propylene oxide)-based diacrylate cross-linker and a PEO-based macromonomer. The microgels showed reversible swelling properties in response to pH. At low pH, microgels swelled due to the protonation of the tertiary amine units. On the contrary, compact latex particles due to the deswelling occurred when pH was >7.

87.3.2 ​Application to Drug Delivery pH-responsive hydrogels have been frequently used to develop controlled-release formulations for oral administration. The gastrointestinal tract is known to possess a wide pH range, from a gastric pH of 1−2 to an intestinal tract pH of 7−8. Such significant changes can be utilized for the design of pH-responsive drug-delivery devices. Tumor sites and some sites of infection are known to have local acidic pH values amenable to pH-responsive release systems (Ghandehari et  al. 1997). For polycationic hydrogels, the swelling is minimal at neutral pH, thus minimizing drug release from the hydrogels. Hydrogels made of polyanions (e.g., PAA) cross-linked with azoaromatic cross-linkers were developed for colon-specific drug delivery. Swelling of such hydrogels in the stomach is minimal and thus, the drug release is also minimal. The extent of swelling increases as the hydrogel passes down the intestinal tract due to increase in pH leading to ionization of the carboxylic groups. But, only in the colon, can the azoaromatic cross-links of the hydrogels be degraded by azoreductase produced by the microbial flora of the colon (Ghandehari et al. 1997; Akala et al. 1998). The degradation kinetics and pattern can be controlled by the cross-linking density. The kinetics of hydrogel swelling can also be controlled by changing the polymer composition (Akala et al. 1998). pH-responsive hydrogels can be placed inside capsules (Gutowska et al. 1997) or silicone matrices (Ghandehari et  al. 1997; Akala et  al. 1998) to modulate drug release. The release patterns of several model drugs having different aqueous solubilities and partitioning properties (including salicylamide, nicotinamide, clonidine HCl, and prednisolone) were correlated with the pH-dependent swelling pattern. At pH 1.2, the hydrogel swelling was low and the release was limited to an initial burst. At pH 6.8, the network became ionized and higher swelling resulted in increased release (Qu et al. 2006). ABA-type triblock copolymers showing pH-responsive micelle formation and gelation were prepared through an ATRP. The A block consisted of either poly(2-(diisopropylamino) ethyl methacrylate) (PDPEA) or poly(2-(diethylamino) ethyl methacrylate) (PDEMA), and the B block contained poly(2methacryloyloxyethyl phosphorylcholine) (PMPC). At low pH regions, the amino groups in the A blocks were protonated and highly soluble in water, whereas they were deprotonated at neutral or higher pH ranges. At neutral pHs, the triblock copolymers became micelles in which the A blocks formed hydrophobic aggregated cores and the neutral hydrophilic B blocks formed the outer shell. At higher polymer concentrations in the basic pH solution, physical gels were formed. Thus, at physiological pH, drugs

87-10

Drug Design, Delivery Systems, and Devices

could be incorporated into the micelle cores, and a slow release of the drugs was achieved. At pH 2, the polymer gels immediately dissolved and released drugs rapidly (Ma et al. 2003).

87.4 ​Light-Responsive Hydrogels Photoresponsive polymers are macromolecules that change their physicochemical properties by irradiation with an appropriate wavelength (Kumar and Neckers 1989; Dai et al. 2009). Potential applications of the photoresponsive polymers include reversible optical storage, polymer viscosity control, photomechanical transduction and actuation, bioactivity switching of proteins, tissue engineering, and pulsatile drug- delivery devices (Shimoboji et al. 2002a,b). It is an important aspect of photoresponsive hydrogel systems that irradiation as a stimulus is a relatively straightforward and noninvasive method of inducing responsive behaviors. These types of polymers have been investigated for many years, but there has been a recent expansion in research to create complex macromolecular architectures. Typically, the photoresponsive polymer is constructed by incorporating chromophores that can transfer light energy into a change in conformation. The chromophore should show a property change during isomerization large enough to cause a conformational change in the polymer. The chromophore is transformed under photoirradiation into isomers that return to the initial state either thermally or photochemically. This isomerization is called “photochromism.” During the photochromism, some physicochemical properties of the chromophores are changed including geometrical structures, dipole moment, and charge generation. Figure 87.8 shows the typical chromophores that are often incorporated into the photoresponsive polymers (Irie 1990; He et al. 2009) into the backbone or side chains. Azobenzene is the most frequently used chromophore. It undergoes isomerization from the transto the cis-form under ultraviolet (UV) irradiation (300−400 nm). The cis-form can return thermally or photochemically to the trans-form. The trans-to-cis isomerization causes three important physical property changes: (1) a change in the absorption spectrum—a decrease in the intense absorption at 320 nm and an increase in absorption at 440 nm, (2) a change in geometry—a shortening of the distance between the 4- and 4′-carbon from 0.9 nm (trans) to 0.55 nm (cis), and (3) a change in dipole moment from 0.5 D (trans) to 3.1 D (cis). The photomechanical effect of photoresponsive hydrogels that show a reversible contraction and expansion is based on the geometrical change of azobenzene embedded in the polymer hydrogel network. When the polymer hydrogel network containing azobenzene chromophores as a cross-linker is stretched, the azobenzene chromophores are preferentially oriented parallel to the stretching axis. With irradiation of such an oriented sample with UV light, the conformational change of azochromophores is expected to cause a macroscopic change in the overall hydrogel shape.

N

hv

N

N

N

Azobenzene H3C

CH3 N O CH3

H3C N H3C

C CN

hv

H3C + N CH3

NO2 Spirobenzopyran

N

CH3 CH3

hv Triarylmethane

FIGURE 87.8  ​Structural formula of representative chromophores.

H3C N H3C

NO2

CH3 O

C + CN–

N

CH3 CH3

87-11

Environment-Responsive Hydrogels for Drug Delivery λ2

λ1

Length

λ1

Time

FIGURE 87.9  Schematic illustration of the photomechanical behavior of azobenzene-containing hydrogels on irradiation.

A typical photomechanical behavior of the polymer hydrogel network is described in Figure 87.9. By changing the irradiation wavelength to the visible region, the cis-form changes to the trans-form, and the dimension recovery is observed. This contraction recovery can be repeated many times. Spirobenzopyran undergoes ring opening on UV irradiation, with the production of intensely colored merocyanine. The merocyanine can return thermally or photochemically to colorless spiropyran. Physical property changes associated with this isomerization are as follows: (1) a change in absorption spectrum, (2) a change in dipole moment, and (3) a geometric structural change. Spirobenzopyran can be incorporated into backbone or pendant groups to polymer hydrogel networks. A change in dipole moment caused by spiropyran–merocyanine isomerization would be expected to alter intramolecular interaction of polymer chains. The change of intramolecular interaction induces a conformational change in the polymer and thus causes swelling or shrinking polymer hydrogels. A change in dipole moment on irradiation could affect the adsorption–desorption behavior of drugs, particularly proteins on the polymer. This feature may be useful for the design of “on–off” control of drug release in a pulsatile delivery system. The photoresponsive hydrogels can also be synthesized by introducing triarylmethane into the polymer network (Mamada et al. 1990). The triarylmethane can be ionized upon UV irradiation. The hydrogels discontinuously swell in response to UV irradiation but shrink when the UV light is removed. The UV light-induced swelling is attributed to an increase in osmotic pressure within the gel due to the appearance of cyanide ions formed by UV irradiation. A typical function of photoresponsive hydrogels is to change their volume reversibly on irradiation of UV or visible lights. Photoresponsive hydrogels respond to “on–off” stimulus of lights, which induces the gel swelling–shrinking that contributes to the release of drug molecules (Qiu and Park 2001). The molecular weight of the polymer may affect the photoresponsive property; in polymers with smaller molecular weight, the photoresponsive macroscopic change is induced more effectively. While the action of stimulus (light) is instantaneous, the reaction of hydrogels in response to such action is still relatively slow.

87.5 Electroresponsive Hydrogels Electroresponsive hydrogels transform electrical energy directly into mechanical energy. Basically, electroresponsive hydrogels are made of polyelectrolytes, swellable polymer networks that carry cations or anions. The electroresponsive hydrogels change a macroscopic shape in response to an electric field (Figure 87.10) (Filipcsei et al. 2000). When a hydrogel is negatively charged, it swells near the anode and contracts near the cathode. Generally, the response rate is proportional to the external electric current. The commonly used electroresponsive polymers include conducting polymers, polyelectrolyte gels, and ionic polymer–metal composites. Electroresponsive polymers are an increasingly important class of smart materials (Kim et al. 1998; Ramanathan and Block 2001; Bajpai et al. 2008). They have promising

87-12 V = 0 kV

Drug Design, Delivery Systems, and Devices V =+ kV

V =++ kV

+

–

–

+

–

+

+

–

+

–

+

+

–

+

–

+

+

–

–

+

– –

–

+

FIGURE 87.10  ​Schematic illustration of the bending phenomena of an electroresponsive polymer hydrogel.

applications in biomechanics, artificial muscle actuation, sensing, energy transduction, sound dampening, chemical separations, and controlled drug delivery. Gel deformation in an electric field is influenced by a number of factors, including variable osmotic pressure based on the voltage-induced motion of ions in the solution, pH or salt concentration of the surrounding medium, position of the gel relative to the electrodes, thickness or shape of the gel, and the applied voltage (Gao et al. 2008). Transforming the application of an electric field into a physical response by a polymer generally relies on collapse of a gel in an electric field, electrochemical reactions, electrically activated complex formation, ionic ­polymer–metal interactions, electrorheological effects, or changes in electrophoretic mobility (Filipcsei et al. 2000; Kim et al. 1998, 2004). A typical function of electroresponsive hydrogels is to change their volume reversibly under the influence of an electric field. The volume change can be utilized for solute permeation control through hydrogels in controlled drug delivery. Electroresponsive hydrogels respond to “on–off” stimulus of electrical currents, which induces the gel swelling–shrinking that contributes to the release of drug molecules. The control of “on–off” drug release can be achieved by varying the intensity of electric stimulation. Hydrogels made of poly(2-acrylamido-2-methylpropane sulfonic acid-co-n-butylmethacrylate) were able to release edrophonium chloride and hydrocortisone in a pulsatile manner in response to electric current (Gong et al. 1994). Poly(sodium acrylate) microparticle gels containing pilocarpine showed a current-dependent pilocarpine release. However, a complete “on–off” drug release regulation is still challenging since it is difficult to completely stop drug release upon termination of the electrical stimulus (Kulkarni et al. 2010). Kwon et al. prepared cross-linked poly(2-acrylamide-2-methylpropanesulfonic acid-co-butyl methacrylate) [P(AMPS-co-BMA)] hydrogels and evaluated the feasibility of these hydrogels for electroresponsive drug-delivery devices (Kwon et al. 1991). They used a cationic drug molecule, edrophonium chloride, within the negatively charged hydrogel. Rapid drug release from the hydrogels resulted from an application of electric fields through the ion exchanges between positively charged drug molecules and protons at the cathode. The squeezing effects arising from the electric field application induced rapid drug release from the gels, which increased as the voltages increased in a dose-dependent manner. Using the P(AMPSco-BMA) hydrogels, an “on–off” drug release regulation was achieved under an “on–off” application of electric current. The group further investigated the electric current-induced release of anionic heparin from a positively charged polyallylamine polyion complex. Rapid structural changes and an apparent dissociation of the polyion complex occurred upon application of an electric current. During the electric current application, the positively charged polyallylamine was neutralized at the cathode owing to the microenvironmental pH changes, and apparent dissociation of the polyion complex occurred. Although bioactive heparin was released by electric current application, polyallylamine was also released.

87.6 ​Glucose-Responsive Hydrogels Insulin-dependent diabetes mellitus patients lack the pancreatic function that releases insulin in response to blood glucose levels. These patients require daily self-injections of an appropriate amount of insulin that helps them to avoid hyperglycemia. Diabetic patients suffer from a gradual decline in the efficiency of various organs, leading to vision loss and long-term diseases. Severe conditions may even

Environment-Responsive Hydrogels for Drug Delivery

87-13

lead to patient death. Thus, injection of properly dosed insulin at proper times is required for insulindependent diabetes mellitus therapy. Self-injection of insulin, however, results in patient discomfort, varied bioavailability, and sometimes a hypoglycemic coma due to an overdose of insulin. Alternatively, insufficient insulin induces hyperglycemia and related complications. Therefore, the precise control of blood glucose levels with an effective, stimuli-responsive insulin release would be of great utility. A large number of formulations incorporating hydrogels for glucose concentration-dependent insulin release have been reported. Glucose-responsive hydrogel systems are based on: (1) enzymatic oxidation of glucose by glucose oxidase (GOx), (2) binding of glucose to concanavalin A (Con A), and (3) reversible sol–gel phase transition hydrogels. In the glucose-responsive systems using GOx, the glucose sensitivity is not caused by direct interaction of glucose with the responsive polymer, but rather by the response of the polymer to the by-products that result from the enzymatic oxidation of glucose. The substrate glucose reacts with GOx, which produces gluconic acid and H2O2. Typically, a pH-responsive moiety is incorporated into glucose-responsive hydrogel networks, and the gluconic acid induces a pH-responsive swelling or collapse of the hydrogel matrix that contains insulin. Several insulin-release systems utilize the glucoseresponsive hydrogels based on glucose–GOx. For example, Chu et al. reported the covalent modification of a cellulose film with GOx-conjugated PAA (Chu et al. 2004). At neutral and high pH levels, the carboxylate units of the PAA chains were negatively charged and extended due to electrostatic repulsion, which resulted in occlusion of the pores in the cellulose membrane. The gluconic acid that resulted from the addition of glucose led to a local pH reduction, protonation of the PAA carboxylate moieties, and concomitant collapse of the chains obscuring the membrane pores, with the latter event facilitating the release of entrapped insulin. Con A has also been frequently used in modulated insulin delivery. In this type of the system, insulin molecules are attached to a support or carrier through specific interactions that can be interrupted by glucose itself. Kim and coworkers reported the synthesis of monosubstituted conjugates of glucosylterminal PEG (G-PEG) and insulin (Liu et al. 1997). The G-PEG–insulin conjugates were bound to Con A that was grafted along a PEG–poly(vinylpyrrolidone-co-acrylic acid) backbone. When the concentration of glucose in the surrounding aqueous media increased, competitive binding of glucose with Con A led to displacement and release of the G-PEG–insulin conjugates. Obaidat and Park reported glucose-responsive systems that underwent sol–gel phase transition depending on the glucose concentration in the environment (Obaidat and Park 1996). The reversible sol–gel phase transition required glucose-responsive cross-linking. Since diffusion of insulin through the sol phase was an order of magnitude faster than that through the gel phase, the insulin release could be controlled by the glucose concentration in the environment. Another type of sol–gel transition polymers responsive to glucose was prepared using a water-soluble copolymer of acrylamide and allyl glucose. The resulting polymers were cross-linked in the presence of lectin and Con A. Since binding constants of native glucose molecules are higher than those of glucose moieties on the copolymer side chains, an exchange reaction occurred between added glucose and copolymer glucose moieties, inducing a gel-to-sol phase transition. Such changes can be utilized for the permeation control of insulin. All the above-mentioned examples used proteins such as GOx and Con A. The exposure of these proteins and peptides to the body may cause an undesirable immune response upon contact. Therefore, these naturally derived proteins and peptides, and their whole systems, should be separated from the body using semipermeable membranes. Matsumoto et al. prepared synthetic polymers with glucose-­ responsive functions (Matsumoto et al. 2003). They focused on the unique characteristics of phenylboronic acid as a glucose-responsive moiety. Boronate is known to form reversible bonding with polyols such as cis diol sugar compounds such as glucose. They prepared water-soluble copolymers containing phenylboronic acid side chains using m-acrylamidophenylboronic acid (AAPBA) and various water- soluble monomers, including N-vinylpyrrolidone, acrylamide, and (N,N-dimethylacrylamide) DMAAm. The resulting copolymers formed reversible complexes with polyol compounds such as poly(vinyl alcohol) (PVA). These complexes dissociated with the addition of glucose in a concentration-dependent

87-14

Drug Design, Delivery Systems, and Devices

manner. Such complex formation and dissociation could be attributed to the different dissociation constants of phenylboronate anions with PVA or glucose.

87.7 Enzyme-Responsive Hydrogels Enzymes play a critical role in most biological pathways. Enzymes are highly selective and work under mild conditions present in vivo (aqueous, pH 5 − 8, 37°C). Generally, enzyme-responsive hydrogels consist of two components: (i) an enzyme-responsive substrate and (ii) a component that directs or controls interactions that cause macroscopic transitions (Figure 87.11) (Thornton et al. 2005; Ulijn 2006). The molecular interactions include hydrogen bonding, electrostatic interactions, van der Waals forces, hydrophobic interactions, π–π interactions, and their combinations. Catalytic action of the enzyme on the substrate can lead to changes in surface properties, self-assembly, supramolecular architectures, and swelling/collapse of gels (Ulijn 2006). In situ depot-forming enzyme-responsive hydrogels were synthesized by using enzymatic dephosphorylation to induce a sol–gel transition (Yang et al. 2004; Yang and Xu 2004; Thornton et al. 2007). When fluorenylmethyloxycarbonyl (FMOC)–tyrosine phosphate was exposed to a phosphatase, the phosphate groups were removed, which resulted in reduction in electrostatic repulsions, supramolecular assembly by π-stacking of the fluorenyl groups, and eventually gelation. The incorporation of functional moieties that can react with enzymes is another typical approach to produce enzyme-responsive hydrogels. Exposure of the functional groups to a specific enzyme can lead to the creation of new covalent linkages that cause a change in macroscopic properties. For example, transglutaminase, a bloodclotting enzyme, had the ability to cross-link the side chains of lysine (Lys) residues with glutamine (Gln) residues. Various approaches have been studied to prepare protease-responsive hydrogels. When the hydrogels are exposed to a protease, hydrolysis of protein or peptide leads to gel degradation and subsequent release of encapsulated drugs. Moore and coworkers prepared chymotrypsin-responsive hydrogels by incorporating a degradable (cysteine–tyrosine–lysine–cysteine) CYKC tetrapeptide sequence as a crosslinker within polyacrylamide hydrogels (Plunkett et al. 2005). The CYKC sequence contains a terminal cysteine conjugation site, a tyrosine residue that can be cleaved at the carboxyl side by chymotrypsin, and a Lys residue. When subjected to α-chymotrypsin, the micron-sized gels dissolved due to the degradation of CYKC by α-chymotrypsin. Ulijin reported protease-responsive hydrogels that were applicable to the removal of toxins or entrapment of drug molecules (Ulijn 2006). In this case, the response was caused by a change in osmotic pressure instead of cross-link degradation. Copolymer beads composed of acrylamide and PEG–macromonomers were modified via an enzyme-cleavable tripeptide comprising combinations of glycine, phenylalanine, and positively charged arginine residues that imparted swelling due to electrostatic repulsions. Upon the addition of proteases, the tripeptide was cleaved, and the resulting loss of arginine groups led to a reduction in electrostatic repulsions and subsequent collapse of the hydrogel.

Enzyme

Ionized hydrogels

Neutral hydrogels

FIGURE 87.11  Enzymatic cleavage and drug release from enzyme-responsive hydrogels. (Adapted from Thornton, P. D., McConnell, G., and Ulijin, R. V. 2005. Enzyme responsive polymer hydrogel beads. Chem. Commun., (47): 5913–5.)

87-15

Environment-Responsive Hydrogels for Drug Delivery

87.8 ​Inflammation-Responsive Hydrogels Inflammatory reactions are commonly observed at injury sites. Inflammation-responsive cells such as macrophages and polymorphonuclear leukocytes (PMNs) play a key role in normal healing processes after injury. The oxygen metabolites such as hydroxyl radicals (•OH) are produced from the inflammation-responsive cells at the injured tissues. Yui et al. designed a hydroxyl radical-responsive drug- delivery system (Yui et al. 1992,1993). They used hyaluronic acid (HA), a linear mucopolysaccharide consisting of repeating units of N-acetyl-d-glucosamine and d-glucuronic acid, for preparing inflammation-responsive hydrogels because the hydroxyl radicals produced at injured sites can effectively degrade HA. HA was cross-linked with ethylene glycol diglycidylether or polyglycerol polyglycidylether. HA degradation in response to hydroxyl radicals was observed only at the surface of the gel, indicating surface erosion degradation. Further utilization of these hydrogels involved the introduction of microspheres as model drug carriers in the hydrogels. The release of microsphereencapsulating drugs followed the surface erosion of the gels. These HA gels could be useful in vivo for inflammation-induced drug-delivery systems, specifically for chronic inflammatory problems including rheumatoid arthritis.

87.9  Antigen-Responsive Hydrogels Antigen–antibody interactions are highly specific and are associated with complex immune responses that help recognize and neutralize foreign infection-causing objects in the body. The high affinity and specificity of their interactions have been extensively used to yield a variety of antigen-­responsive polymer systems. In most cases, antigen-responsive hydrogels have been prepared by physically entrapping antibodies or antigens in networks, chemical conjugation of the antibody or antigen to the network, or using antigen–antibody complexes as reversible cross-linkers within networks (Lu et al. 2003). A typical antigen-responsive polymer can be synthesized by copolymerization of vinyl-­ functionalized antigen or antibody with acrylamide or N,N′-methylenebisacrylamide (MBA). The copolymerization results in a hydrogel cross-linked both covalently and by antigen–antibody interactions. When free antigen molecules are added to the solution with immersed antigen-immobilized hydrogels, the antibodies in the hydrogel network change partners with free antigen, owing to the difference in the binding constants. This antigen-competitive exchange results in a decreased number of cross-linking points in the hydrogels, and thus promotes the swelling of hydrogels. This antigenresponsive swelling behavior of an antigen-immobilized hydrogel is irreversible (Figure 87.12a), but, when both antigen and antibody are immobilized on polymer hydrogel networks, reversible swelling and deswelling occur (Figure 87.12b). Such changes are very antigen specific, so that the addition of other antigens does not alter hydrogel swelling.

(a)

Antigen

Antibody Antigen immobilized polymers Free antigen

(b)

Antigen

Antibody immobilized polymers Antigen immobilized polymers Free antigen

FIGURE 87.12  ​Irreversible (a) and reversible (b) antigen-responsive hydrogels. (Adapted from Miyata, T., Asami, N., and Uragami, T. 1999. Nature, 399: 766–9.)

87-16

Drug Design, Delivery Systems, and Devices

87.10 ​Magnetoresponsive Hydrogels For designing a magnetoresponsive hydrogel delivery system, several factors should be considered, including the magnetic properties of the delivery systems, field strength, field geometry, drug/genebinding capacity, and physiological parameters such as the depth to target, the rate of blood flow, vascular supply, and body weight. Generally, inorganic magnetic particles are physically entrapped within or covalently immobilized to a 3D cross-linked network. In principle, in the presence of a magnetic field gradient, a translational force is exerted on the drug-delivery hydrogel complexes. This effectively traps the complex in the field at the target site and pulls it toward the magnet (Pankhurst et al. 2003). A major challenge of chemotherapeutic approaches to cancer treatment is that they are nonspecific. Magnetoresponsive hydrogels have been explored extensively as possible drug carriers for site-specific drug delivery and controlled release. Although theoretically very effective, magneto drug-delivery systems still have numerous obstacles. Magnetoresponsive hydrogel systems generally require a relatively strong gradient in an external field. There is also the potential for embolization as the fraction of magnetoresponsive hydrogels may accumulate and block flow or they may also concentrate in the liver (Dobson 2006). There are other limitations such as the depth that the magnet may function, as is encountered when scaling up from small animals with near-surface targets to larger animals and humans. Another type of magnetoresponsive hydrogels exhibit the shape and size distortions that occur reversibly and instantaneously in the presence of a nonuniform magnetic field (Zrinyi et  al. 1997; Starodoubtsev et al. 2003; Wang et al. 2006). Such hydrogels have received significant attention for use as soft biomimetic actuators, sensors, cancer therapy agents, artificial muscles, switches, separation media, membranes, and drug-delivery systems (Zrinyi et al. 1997; Szabo et al. 1998, 2000; Zrinyi 2000; Babinocova et al. 2001; Starodoubtsev et al. 2003; Wang et al. 2006; Pyun 2007).

87.11 ​Ultrasound-Responsive Hydrogels The application of stimuli-responsive polymers to drug delivery needs the target-specific delivery and the controlled release of therapeutic compounds at a specified rate. The drug-delivery systems are generally guided to the target site—which has an environment that stimulates release—by passive or active transport mechanisms. The change in environmental conditions spontaneously induces drug release at the target site. However, in most cases, to locally apply the stimulus at the targeted site is not simple. For instance, a change in temperature could lead to release in thermoresponsive hydrogels in vitro, but localized heating and cooling in vivo are not always trivial at sites deep within the body. Ultrasound is a particularly effective stimulus that can be applied externally on demand and has proven to be effective at triggering drug release within the body. One of the pioneering approaches of exploiting ultrasound in drug delivery involves directing the ultrasound directly at the hydrogel matrix (Sershen and West 2002). This approach of ultrasound-responsive drug delivery achieved a 27 times increase in the release of 5-fluorouracil from a poly(ethylene-co-vinyl acetate) (PEVAc) matrix (Miyazaki et al. 1985). Ultrasound regulated drug delivery in which the release rates were repeatedly responsive (Kost and Langer 1988). Biodegradable polymers that have been used for ultrasound-­responsive systems include poly(d,l-lactide) (PGA), poly(d,l-glycolide) (PLA), poly(bis(p-carboxyphenoxy))alkane–anhydrides (PCPX), and their copolymers with sebacic acid. When induced to ultrasound, these bioerodible polymer hydrogels responded rapidly and reversibly. It is believed that the ultrasound causes an increase in temperature in the delivery system, which facilitates diffusion (Mathiowitz and Cohen 1989). The concept of using ultrasound-responsive hydrogels for controlled drug delivery is attractive because the method is essentially noninvasive and has been successfully used in other areas of medical treatment and diagnostics (Noriis et al. 2005). The success of ultrasonic mediation of drug delivery is generally ascribed to cavitation, which is the alternating growth and shrinkage of gas-filled microbubbles that results from high- and low-pressure

Environment-Responsive Hydrogels for Drug Delivery

87-17

waves generated by ultrasound energy (Lentacker et al. 2006). Eventually, these cavitating microbubbles implode, generating local shock waves that can disrupt polymer assemblies in their vicinity.

87.12 ​Redox/Thiol-Responsive Hydrogels Redox/thiol-responsive hydrogel materials are another class of responsive hydrogels that have recently received increased attention, especially in various fields of controlled drug delivery (Meng et al. 2009a). The interconversion of thiols and disulfides is a key step in many biological processes, plays an important role in the stability and rigidity of native proteins in living cells (Castellani et al. 1999), and has been commonly used for various bioconjugation protocols (Saito et al. 2003). Since disulfide bonds can be reversibly converted into thiols by exposure to various reducing agents (e.g., mercaptoethanol, dithiothreitol (DTT), and glutathione (GSH)) and/or undergo disulfide exchange in the presence of other thiols, polymers containing disulfide linkages can be considered both redox and thiol responsive (Oh et al. 2007). GSH, the most abundant reducing agent in most cells (Bulmus et al. 2003), has a typical intracellular concentration of about 10 mM, whereas its concentration is only about 0.002 mM in the cellular exterior (Jones et al. 1998). This significant variation in concentration has been utilized to design thiol/redox-responsive drugdelivery systems that specifically release therapeutics upon entry into cells (Ghosh et al. 2009).

87.13 ​Concluding Comments Development of smart hydrogels as effective drug-delivery systems has been limited, mainly due to a few reasons. First, the chemical structures of most smart hydrogels contain functional groups that have not been used in clinical applications. This makes it rather difficult to use them in humans, as their safety has not been unequivocally demonstrated. Until the safety is proven, the pharmaceutical, as well as biomedical, industries are not willing to develop clinical products. Second, the smart hydrogels are obviously smarter than ordinary hydrogels by being able to sense the environmental changes and react to them, but they cannot overcome the inherent limitations of hydrogels in terms of drug loading and release. Unless a hydrogel can deliver a drug at a therapeutically significant level for a sufficiently long period of time, any control on drug release has no clinical meaning. Third, most of the smart hydrogels are not biodegradable, although they may be biocompatible. Thus, it is not practical using the smart hydrogels as implantable drug-delivery systems. Without biodegradation in the body, the utilization of smart hydrogels will be limited. Biodegradability can be achieved by employing synthetic polymers with biodegradable backbones or natural polymers. Synthesizing new polymers to make environment-responsive hydrogels will continue. Synthetic polymers possess attractive potential because experts in the field can easily alter their design to achieve the desired characteristics of hydrogels that respond to different stimuli (Kwon 2005). The single ­environmental-responsive property of intelligent hydrogels would limit their practical applications. It would be favorable if the intelligent hydrogels could respond to more than one stimulus simultaneously. For example, more effective drug therapies for complicated diseases may require polymeric materials, the functions of which are variable or switchable in response to several kinds of stimuli. Indeed, the diagnosis of patients suffering from some diseases is generally achieved by monitoring several physiological changes. Therefore, multiresponsive hydrogels have attracted more and more attentions (Ji et al. 2007; Ju et al. 2009). The combination of two or more responses is particularly useful to optimize the control of drug release. Recent advances in nanofabrication have allowed utilization of smart hydrogels in the nano-/microsystems. Application of smart hydrogels to microfluidic systems, bioseparation, and biosensors is a good example. Their application has been extended to high-throughput screening, such as peptide, protein, and deoxyribonucleic acid (DNA) array. Micropatterned hydrogels can be employed as a template for preparing nano-/microparticles of predefined size and shape. Nanofabricated smart hydrogels can be used in various aspects in tissue engineering, including cell sheet technique, artificial extracellular matrix materials, and 3D scaffolds with chemical patterning or microchannels.

87-18

Drug Design, Delivery Systems, and Devices

Abbreviations DEA 2-(diethylamine) DPA 2-(diisopropylamine) MPC 2-methacryloyloxyethyl phosphorylcholine

References Akala, E. O., Kopeckova, P., and Kopecek, J. 1998. Novel pH-sensitive hydrogels with adjustable swelling kinetics. Biomaterials, 19: 1037–47. Babinocova, M., Leszczynska, D., Sourivong, P., Cicmanec, P., and Babinec, P. 2001. Superparamagnetic gel as a novel material for electromagnetically induced hyperthermia. J. Magn. Magn. Mater., 225: 109–12. Bajpai, A. K., Bajpai, J., and Soni, S. N. 2008. Preparation and characterization of electrically conductive composites of poly(vinyl alcohol)-g-poly(acrylic acid) hydrogels impregnated with polyaniline (PANI). Express Polym. Lett., 2: 26–39. Bromberg, L. E., and Ron, E. S. 1998. Temperature-responsive gels and thermogelling polymer matrices for protein and peptide delivery. Adv. Drug Deliv. Rev., 31: 197–221. Bulmus, V., Woodward, M., Lin, L., Murthy, N., Stayton, P., and Hoffman, A. 2003. A new pH-responsive and glutathione-reactive, endosomal membrane-disruptive polymeric carrier for intracellular delivery of biomolecular drugs. J. Control. Release, 93: 105–20. Castellani, O. F., Martinez, E. N., and Anon, M. C. 1999. Role of disulfide bonds upon the structural stability of an amaranth globulin. J. Agric. Food Chem., 47: 3001–8. Chu, L.-Y., Li, Y., Zhu, J.-H., Wang, H.-D., and Liang, Y.-J. 2004. Control of pore size and permeability of a glucose-responsive gating membrane for insulin delivery. J. Control. Release, 97: 43–53. Dai, S., Ravi, P., and Tam, K. C. 2009. Thermo- and photo-responsive polymeric systems. Soft Matter, 5: 2513–33. Dobson, J. 2006. Magnetic nanoparticles for drug delivery. Drug Develop. Res., 67: 55–60. Filipcsei, G., Feher, J., and Zrinyi, M. 2000. Electric field sensitive neutral polymer gels. J. Mol. Struct., 554: 109–17. Gao, Y., Xu, S., Wu, R., Wang, J., and Wei, J. 2008. Preparation and characteristics of electric stimuli responsive hydrogel composed of polyvinyl alcohol/poly(sodium maleate-co-sodium acrylate). J. Appl. Polym. Sci., 107: 391–5. Ghandehari, H., Kopeckova, P., and Kopecek, J. 1997. In vitro degradation of pH-sensitive hydrogels containing aromatic azo bonds. Biomaterials, 18: 861–72. Ghosh, S., Yesilyurt, V., Savariar, E. N., Irvin, K., and Thayumanavan, S. 2009. Redox, ionic strength, and pH sensitive supramolecular polymer assemblies. J. Polym. Sci. A Polym. Chem., 47: 1052–60. Gong, J. P., Nitta, T., and Osada, Y. 1994. Electrokinetic modeling of the contractile phenomena of polyelectrolyte gels. One-dimensional capillary model. J. Phys. Chem., 98: 9583–7. Gutowska, A., Bark, J. S., Kwon, I. C., Bae, Y. H., Cha, Y., and Kim, S. W. 1997. Squeezing hydrogels for controlled oral drug delivery. J. Control. Release, 48: 141–8. Hamidi, M., Azadi, A., and Rafiei, P. 2008. Hydrogel nanoparticles in drug delivery. Adv. Drug Deliv. Rev., 60: 1638–49. He, J., Tong, X., and Zhao, Y. 2009. Photoresponsive nanogels based on photocontrollable cross-links. Macromolecules, 42: 4845–52. Irie, M. 1990. Properties and applications of photoresponsive polymers. Pure Appl. Chem., 62(8): 1495–502. Jeong, B., Bae, Y. H., and Kim, S. W. 1999a. Biodegradable thermosensitive micelles of PEG–PLGA–PEG triblock copolymers. Colloids Surf. B, 16: 185–93. Jeong, B., Kim, S. W., and Bae, Y. H. 2002a. Thermosensitive sol–gel reversible hydrogels. Adv. Drug Deliv. Rev., 54: 37–51.

Environment-Responsive Hydrogels for Drug Delivery

87-19

Jeong, B., Lee, K. M., Gutowska, A., and An, Y. H. 2002b. Thermogelling biodegradable copolymer aqueous solutions for injectable protein delivery and tissue engineering. Biomacromolecules, 3: 865–8. Jeong, B. M., Bae, Y. H., and Kim, S. W. 1999b. Thermoreversible gelation of PEG–PLGA–PEG triblock copolymer aqueous solutions. Macromolecules, 32: 7064–9. Jeong, B. M., Bae, Y. H., and Kim, S. W. 2000. Drug release from biodegradable injectable thermosensitive hydrogel of PEG–PLGA–PEG triblock copolymers. J. Control. Release, 63: 155–63. Ji, S. C., Kwon, I. K., and Park, K. 2007. Smart polymeric gels: Redefining the limits of biomedical devices. Prog. Polym. Sci., 32: 1083–122. Jones, D. P., Carlson, J. L., Samiec, P. S., Jr., Mody, V. C., Jr., Reed, R. L., and Brown, L. A. S. 1998. Glutathione measurement in human plasma evaluation of sample collection, storage and derivatization conditions for analysis of dansyl derivatives by HPLC. Clin. Chem., 275: 175–84. Ju, X.-J., Xie, R., Yang, L., and Chu, L.-Y. 2009. Biodegradable intelligent materials in response to chemical stimuli for biomedical applications. Expert Opin. Ther. Pat., 19(5): 683–96. Kim, S. J., Kim, H. I., Shin, S. R., and Kim, S. I. 2004. Electrical behavior of chitosan and poly(hydroxyethyl methacrylate) hydrogel in the contact system. J. Appl. Polym. Sci., 92: 915–19. Kim, S. W., Bae, Y. H., and Okano, T. 1992. Hydrogels: Swelling, drug loading, and release. Pharm. Res., 9(3): 283–90. Kim, S. Y., Shin, H. S., Lee, Y. M., and Jeong, C. N. 1998. Properties of electroresponsive poly(vinyl alcohol)/poly(acrylic acid) IPN hydrogels under an electric stimulus. J. Appl. Polym. Sci., 73: 1675–83. Kim, Y. J., Choi, S., Koh, J. J., Lee, M., Ko, K. S., and Kim, S. W. 2001. Controlled release of insulin from injectable biodegradable triblock copolymer. Pharm. Res., 18(4): 548–50. Kojima, C. 2010. Design of stimuli-responsive dendrimers. Expert Opin. Drug Deliv., 7(3): 307–19. Kost, K., and Langer, R. 1988. Ultrasonically controlled polymeric drug. Macromol. Chem. Macrom. Symp., 19: 275–85. Kulkarni, R. V., Setty, C. M., and Sa, B. 2010. Polyacrylamide-g-alginate-based electrically responsive hydrogel for drug delivery application: Synthesis, characterization, and formulation development. J. Appl. Polym. Sci., 115: 1180–8. Kumar, G. S., and Neckers, D. C. 1989. Photochemistry of azobenzene-containing polymers. Chem. Rev., 89: 1915–25. Kwon, G. S. 2005. Polymeric Drug Delivery Systems. Taylor & Francis Group, Boca Raton, FL, 680 pp. Kwon, I. C., Bae, Y. H., and Kim, S. W. 1991. Electrically erodible polymer gel for controlled release of drugs. Nature, 354(28): 291–3. Lentacker, I., Geest, B. G. D., Vandenbroucke, R. E., Peeters, L., Demeester, J., Smedt, S. C. D., and Sanders, N. N. 2006. Ultrasound-responsive polymer-coated microbubbles that bind and protect DNA. Langmuir, 22: 7273–8. Li, M. H., and Keller, P. 2009. Stimuli-responsive polymer vesicles. Soft Matter, 5: 927–37. Liu, F., Song, S. C., Mix, D., Baudys, M., and Kim, S. W. 1997. Glucose-induced release of glycosylpoly(ethylene glycol) insulin bound to a soluble conjugate of concanavalin A. Bioconjug. Chem., 8: 664–72. Lu, Z.-R., Kopeckova, P., and Kopecek, J. 2003. Antigen responsive hydrogels based on polymerizable antibody Fab’ fragment. Macromol. Biosci., 3(6): 296–300. Ma, Y., Tang, Y., Billingham, N. C., and Armes, S. P. 2003. Synthesis of biocompatible, stimuli-responsive, physical gels based on ABA triblock copolymers. Biomacromolecules, 4: 864–8. Mamada, A., Tanaka, T., Kungwatchakun, D., and Irie, M. 1990. Photoinduced phase transition of gels. Macromolecules, 23: 1517–9. Mathiowitz, E., and Cohen, M. D. 1989. Polyamide microcapsules for controlled release: I characterization of the membranes. J. Membr. Sci., 40: 1–26. Mathiowitz, E., and Cohen, M. D. 1989. Polyamide microcapsules for controlled release: II release characteristics of the micro capsules. J. Membr. Sci., 40: 27–41.

87-20

Drug Design, Delivery Systems, and Devices

Matsumoto, A., Ikeda, S., Harada, A., and Kataoka, K. 2003. Glucose-responsive polymer bearing a novel phenylborate derivative as a glucose-sensing moiety operating at physiological pH conditions. Biomacromolecules, 4: 1410–6. Meng, F., Hennink, W. E., and Zhong, Z. 2009a. Reduction-sensitive polymers and bioconjugates for biomedical applications. Biomaterials, 30: 2180–98. Meng, F., Zhong, Z., and Feijen, J. 2009b. Stimuli-responsive polymersomes for programmed drug delivery. Biomacromolecules, 10(2): 197–209. Miyata, T., Asami, N., and Uragami, T. 1999. A reversibly antigen-responsive hydrogel. Nature, 399: 766–9. Miyazaki, S., Hou, W. M., and Takada, M. 1985. Controlled drug release by ultrasound irradiation. Chem. Pharm. Bull., 33: 428–31. Noriis, P., Noble, M., Francolini, I., Vinogradov, A. M., Stewart, P. S., Ratner, B. D., Costerton, J. W., and Stoodley, P. 2005. Ultrasonically controlled release of ciprofloxacin from self-assembled coatings on poly(2-hydroxyethyl methacrylate) hydrogels for Pseudomonas aeruginosa biofilm prevention. Antimicrob. Agents Chemother., 49: 4272–9. Obaidat, A. A., and Park, K. 1996. Characterization of glucose dependent gel–sol phase transition of the polymeric glucose-concanavalin A hydrogel system. Pharm. Res., 13: 989–95. Oh, J. K., Lee, D. I., and Park, J. M. 2009. Biopolymer-based microgels/nanogels for drug delivery applications. Prog. Polym. Sci., 34: 1261–82. Oh, J. K., Siegwart, D. J., Lee, H.-i., Sherwood, G., Peteanu, L., Hollinger, J. O., Kataoka, K., and Matyjaszewski, K. 2007. Biodegradable nanogels prepared by atom transfer radical polymerization as potential drug delivery carriers: Synthesis, biodegradation, in vitro release, and bioconjugation. J. Am. Chem. Soc., 129: 5939–45. Onaca, O., Enea, R., Hughes, D. W., and Meier, W. 2009. Stimuli-responsive polymersomes as nanocarriers for drug and gene delivery. Macromol. Biosci., 9: 129–39. Pankhurst, Q. A., Connolly, J., Jones, S. K., and Dobson, J. 2003. Applications of magnetic nanoparticles in biomedicine. J. Phys. D: Appl. Phys., 36: 167–81. Plunkett, K. N., Berkowski, K. L., and Moore, J. S. 2005. Chymotrypsin responsive hydrogel: Application of a disulfide exchange protocol for the preparation of methacrylamide containing peptide. Biomacromolecules, 6: 632–7. Pyun, J. 2007. Nanocomposite materials from functional polymers and magnetic colloids. Polym. Rev., 47: 231–63. Qiu, Y., and Park, K. 2001. Environment-sensitive hydrogels for drug delivery. Adv. Drug Deliv. Rev., 53: 321–39. Qu, J. B., Chu, L.-Y., Yang, M., Xie, R., Hu, L., and Chen, W.-M. 2006. A pH-responsive gating membrane system with pumping effects for improved controlled release. Adv. Funct. Mater., 16: 1865–72. Ramanathan, S., and Block, L. H. 2001. The use of chitosan gels as matrices for electrically-modulated drug delivery. J. Control. Release, 70: 109–23. Roy, D., Cambre, J. N., and Sumerlin, B. S. 2010. Future perspectives and recent advances in stimuliresponsive materials. Prog. Polym. Sci., 35: 278–301. Saito, G., Swanson, J. A., and Lee, K.-D. 2003. Drug delivery strategy utilizing conjugation via reversible disulfide linkages: Role and site of cellular reducing activities. Adv. Drug Deliv. Rev., 55: 199–215. Sershen, S., and West, J. 2002. Implantable, polymeric systems for modulated drug delivery. Adv. Drug Deliv. Rev., 54: 1225–35. Shimoboji, T., Ding, Z. L., Stayton, P. S., and Hoffman, A. S. 2002a. Photoswitching of ligand association with a photoresponsive polymer–protein conjugate. Bioconjug. Chem., 13: 915–9. Shimoboji, T., Larenas, E., Fowler, T., Kulkarni, S., Hoffman, A. S., and Stayton, P. S. 2002b. Photoresponsive polymer enzyme switches. Prog. Natl. Acad. Sci. USA, 99(26): 16592–6. Starodoubtsev, S. G., Saenko, E. V., Khokhlov, A. R., Volkov, V. V., Dembo, K. A., Klechkovskaya, V. V., Shtykova, E. V., and Zanaveskina, I. S. 2003. Poly(acrylamide) gels with embedded magnetite nanoparticles. Microelec. Eng., 69: 324–9.

Environment-Responsive Hydrogels for Drug Delivery

87-21

Stuart, M. A. C., Huck, W. T. S., Genzer, J., Muller, M., Ober, C., Stamm, M., Sukhorukov, G. B. et al. 2010. Emerging applications of stimuli-responsive polymer materials. Nature Mater., 9: 101–13. Szabo, D., Czako-Nagy, I., Zrinyi, M., and Vertes, A. 2000. Magnetic and Mossbauer studies of magnetiteloaded polyvinyl alcohol hydrogels. J. Colloid. Interface. Sci., 221: 166–72. Szabo, D., Szeghy, G., and Zrinyi, M. 1998. Shape transition of magnetic field sensitive polymer gels. Macromolecules, 31: 6541–8. Thornton, P. D., Mart, R. J., and Ulijn, R. V. 2007. Enzyme-responsive polymer hydrogel particles for controlled release. Adv. Mater., 19: 1252–6. Thornton, P. D., McConnell, G., and Ulijin, R. V. 2005. Enzyme responsive polymer hydrogel beads. Chem. Commun., (47): 5913–5. Ulijn, R. V. 2006. Enzyme-responsive materials: A new class of smart biomaterials. J. Mater. Chem., 16: 2217–25. Wang, C., Adrianus, G. N., Sheng, N., Toh, S., Gong, Y., and Wang, D.-A. 2009a. In vitro performance of an injectable hydrogel/microsphere based immunocyte delivery system for localized anti-tumor activity. Biomaterials, 30: 6986–95. Wang, G., Tian, W. J., and Huang, J. P. 2006. Response of ferrogels subjected to an AC magnetic field. J. Phys. Chem. B., 110: 10738–45. Wang, Y.-C., Xia, H., Yang, X.-Z., and Wang, J. 2009b. Synthesis and thermoresponsive behaviors of biodegradable pluronic analogs. J. Polym. Sci. A. Polym. Chem., 47: 6168–79. Yang, Z., Gu, H., Fu, D., Gao, P., Lam, J. K., and Xu, B. 2004. Enzymatic formation of supramolecular hydrogels. Adv. Mater., 16: 1440–4. Yang, Z., and Xu, B. 2004. A simple visual assay based on small molecule hydrogels for detecting inhibitors of enzymes. Chem. Commun., 2424–5. Yui, N., Okano, T., and Sakurai, Y. 1992. Inflammation responsive degradation of crosslinked hyaluronic acid gels. J. Control. Release, 22: 105–16. Yui, N., Okano, T., and Sakurai, Y. 1993. Regulated release of drug microspheres from inflammation responsive degradable matrices of crosslinked hyaluronic acid. J. Control. Release, 25: 133–43. Zentner, G. M., Rathi, R., Shih, C., McRea, C. J., Seo, M.-H., Oh, H., Rhee, B. G., Mestecky, J., Moldoveanu, Z., Morgan, M., and Weitman, S. 2001. Biodegradable block copolymers for delivery of proteins and water-insoluble drugs. J. Control. Release, 72: 203–15. Zhao, S. P. and Xu, W. L. 2010. Thermo-sensitive hydrogels formed from the photocrosslinkable polypseudorotaxanes consisting of β-cyclodextrin and pluronic F68/PCL macromer. J. Polym. Res., 17: 503–510. Zrinyi, M. 2000. Intelligent polymer gels controlled by magnetic fields. Colloid. Polym. Sci., 278: 98–103. Zrinyi, M., Barsi, L., and Szabo, D. 1997. Direct observation of abrupt shape transition in ferrogels induced by nonuniform magnetic field. J. Chem. Phys., 106: 5685–92.

88 Biodegradable PLGA Scaffolds for Growth Factor Delivery Yusef Khan University of Connecticut Health Center

Cato Laurencin University of Connecticut Health Center

88.1 Introduction.....................................................................................88-1 88.2 Elements of Drug Delivery Related to Tissue Engineering.......88-2 88.3 Tissue Engineering Scaffolds as Drug Delivery Vehicles..........88-2 Material Choices  •  Techniques of Incorporation

88.4 Musculoskeletal Tissue Engineering............................................88-6 Bone • Cartilage • Ligament and Tendon • Vascular Tissue

88.5 Conclusion...................................................................................... 88-11 References................................................................................................... 88-11

88.1 Introduction One of the most widely studied strategies for tissue regeneration and repair is that of tissue engineering. The strategy behind tissue engineering is to replicate the tissue to be repaired or regenerated by adding each element of that tissue separately, the extracellular structure, the cells, and the proteins and factors that provide cellular cues for healing, to essentially build a temporary tissue [1]. The extracellular structure, natural or synthetic, is designed to mimic or resemble the three-dimensional hierarchical structure and mechanical behavior of the tissue to be repaired. These structures, referred to as matrices or scaffolds, are designed to either (1) accommodate cells that are seeded in vitro and subsequently encouraged to migrate and proliferate through the 3-D pore structure prior to implantation or (2) to accommodate cells that may migrate from tissues adjacent to the site of repair after being implanted in vivo. The biological cues and signals that govern cell proliferation, migration, and differentiation toward whole intact tissues are not inherent to scaffolds and thus need to be added [2]. In practice these cues are often made available to cells by adding them to the surrounding milieu for in vitro experiments [2], but for in vivo applications are more typically incorporated into the scaffold structure itself. This way the implanted scaffold can provide and maintain site-specific delivery of necessary cues at the tissue repair/ regeneration site, a key element to successful tissue engineering. This concept also overlaps with the general strategy of drug delivery for the repair of tissues but presents an added challenge when designing tissue engineered scaffolds for tissue and organ repair. It is not enough to design a structure that simply resembles the three-dimensional form of the native tissue and is capable of sustaining cell attachment and migration. Indeed, the tissue engineer must simultaneously design a drug or factor delivery vehicle as well, and incorporate the three-dimensional form of the native tissue that is capable of sustaining cell attachment and migration.

88-1

88-2

Drug Design, Delivery Systems, and Devices

88.2 Elements of Drug Delivery Related to Tissue Engineering The goal of drug delivery is to administer therapeutic compounds in a manner such that the therapeutic value of the compound is realized. This relatively simple definition becomes more and more challenging as the layers of complexity of a particular condition, location within the body, or desired physiological response are considered. For tissue engineering, much of the goal of drug delivery is to influence the behavior of cells that are required to form new tissues. These compounds may include: (1) bioactive proteins such as growth factors and cytokines to influence the proliferation and differentiation of cells within or around the scaffold, (2) peptide sequences that represent the active region of larger growth factor proteins but are stable and less susceptible to degradation than proteins, (3) antibiotics to prevent or minimize infection or foreign body response, (4) anticoagulants to prevent blood clotting of vascular tissue, and (5) nucleic acids using viral or nonviral strategies to manipulate the expression of a specific gene. Once the payload for delivery has been established, the nature in which these compounds are released, or if they are released at all, must be determined. There is a considerable body of literature describing techniques to vary the nature of release of compounds from materials for systemic or local delivery, short-term or long-term release, passive or active release of a compound, temporal, sequential, or simultaneous release of compounds from either natural and or synthetic materials that can be either degradable and nondegradable.

88.3 Tissue Engineering Scaffolds as Drug Delivery Vehicles 88.3.1  Material Choices When designing and constructing a tissue engineering scaffold, there are a number of fundamental scaffold design criteria that must be considered and adapted based on the tissue being repaired or regenerated. For instance, the three-dimensional scaffold should have an interconnected pore structure [3], it should have suitable mechanical properties that represent the tissue being restored, and it should be resorbable within reasonable time frames (depending on the application) via suitable degradation mechanisms. Some of these parameters depend on the overall design of the scaffold and others depend on the material chosen. When considering a tissue engineered scaffold that would also function as a drug delivery vehicle an additional set of criteria are included that largely, although not exclusively, depend on the material choice alone [4]. Certain design criteria such as pore structure and available scaffold surface area will influence overall drug delivery from a tissue engineered scaffold, but the material alone will govern much of the relevant parameters such as hydrophobicity/hydrophilicity, degradation rate, degradation mechanism, and drug elution kinetics. Materials suitable for drug delivery include polymers from both natural and synthetic origins, ceramics, and composites of the two. Here is a brief summary of some of the synthetic polymers commonly used for tissue engineering and drug delivery applications. 88.3.1.1 Polyanhydrides Polyanhydrides are synthesized using an anhydride linkage between monomers. The anhydride bond is unstable in water or other aqueous environments and is readily cleaved through the process of hydrolysis [5,6]. While this makes polyanhydrides unstable in aqueous environments, it makes it well-suited for drug delivery applications [7]. To control the overall stability and rate of degradation in water, polyanhydrides can be synthesized to incorporate hydrophobic monomers in various concentrations, allowing for some degree of control over degradation and drug release. This overall instability that makes polyanhydrides so well-suited for drug delivery also makes it less well-suited for certain scaffold-based tissue engineering applications. 88.3.1.2 Polyphosphazenes The polyphosphazenes are a broad family of inorganic polymers characterized by a backbone of alternating nitrogen and phosphorus atoms to which a wide variety of organic or organometallic sidegroups

Biodegradable PLGA Scaffolds for Growth Factor Delivery

88-3

can be attached [8]. Varying these sidegroups changes the physicochemical and mechanical properties of the resulting polymer, and for scaffold-based drug delivery applications allows for the variation of degradation rates, mechanical properties, and cell-material compatibilities [9,10]. The simple structure and high variability of potential polymers has led to the development of over 700 different polyphosphazenes, many of which are currently being evaluated for both tissue engineering and drug delivery capabilities [11]. Although still relatively new to the tissue engineering forum, polyphosphazenes have tremendous potential for future development. 88.3.1.3 Polyhydroxyalkanoates Another biodegradable polymer family that has potential in both the tissue engineering and drug delivery fields is the polyhydroxyalkanoates (PHAs) [12–14]. These thermoplastic linear polyesters are produced naturally as a by-product of bacterial fermentation. One of the more common PHAs seen in tissue engineering applications is a co-polymer of 3-hydroxybutyrate and 3-hydroxyvalerate to form poly(hydroxybutyrate-co-valerate) (PHBV) [14]. PHBV is a biocompatible, biodegradable polymer that degrades through the hydrolysis of its ester linkage. Like other degradable polyesters this degradability, as well as the polymer mechanical properties, can be tuned by varying the content of its constituent materials, specifically the valerate content. As valerate content of the co-polymer increases, the crystallinity, glass transition temperature, melting temperature, tensile strength, and elastic modulus all decrease. Although most of the literature describes PHBV as a polymer for tissue engineering there are a few studies that have evaluated it for drug delivery applications suggesting potential for the PHAs as scaffold-based drug delivery vehicles. One reason that there are fewer studies evaluating polymers like the PHAs in the tissue engineering and drug delivery realm is not necessarily due to their form or function, but in part due to the larger challenge of tissue engineering. Whether it is regenerating orthopedic, vascular, or organ tissue or delivering therapeutic molecules directly to the injury or repair site, the research undertaken to solve these challenges is often guided by a specific clinical deficiency and subsequent need. For this reason much of the work in both tissue engineering and drug delivery has been centered on the use of a particular subset of polyesters; polylactide, polyglycolide, and poly(lactide-co-glycolide). 88.3.1.4  Polylactide, Polyglycolide, and Poly(Lactide-co-Glycolide) Polylactide (PLA), polyglycolide (PGA), and their co-polymer poly(lactide-co-glycolide) (PLGA) are the most widely used polymers for tissue engineering applications [15–17]. This wide use is due to a number of positive aspects of these polyesters including their biocompatibility, biodegradability, tunable degradation rate, mechanical properties, formability, and perhaps most important, the FDA approval for a select number of PLA and PLGA orthopedic devices. PLA, PGA, and PLGA are linear polyesters that degrade through the hydrolysis of the ester linkage along the backbone of the polymer chain into lactic acid (LA) and glycolic acid (GA), which are further broken down to CO2 and H2O (see Figure 88.1). Degradation times of each polymer vary, where PLA typically degrades in 12–24 months, PGA in 6–12 months, and PLGA anywhere from 1 to 6 months. This range of degradation times can be controlled to a certain extent by manipulating several factors. For PLGA, degradation times can be tuned by varying the LA:GA ratio. Typically equal ratios of LA and GA (often referred to as 50:50) result in the shortest degradation time. As the LA content of the copolymer increases (65:35, 75:25, 85:15) degradation time follows in part due to the greater hydrophobicity of LA than GA. For PLA, PGA, and PLGA increases in molecular weight will also increase degradation time. External environmental conditions like ambient pH and temperature can also influence degradation time, with extremes of pH and elevations in temperature increasing the rate of degradation. Since these polymers degrade through hydrolysis, the amount of polymer surface area exposed to aqueous environments can influence the rate of degradation as well. Taking into consideration the amount of surface area available to interact with the surrounding aqueous milieu thus becomes relevant when

88-4

Drug Design, Delivery Systems, and Devices O

O

O CH C O CH3

CH C

O

O

O CH2 C O CH2 C

O

CH3 Poly(lactide-co-glycolide) H2O

O H

O

O CH C O

CH C

O OH

O

HO CH2 C O CH2 C

O

CH3

CH3

Polylactide

Polyglycolide

H2O

H2O O

HO CH C

O OH

HO CH2 C

OH

CH3 Lactic acid

Glycolic acid

FIGURE 88.1  ​Poly(lactide-co-glycolide) degrades through hydrolysis to polylactide and polyglycolide, which is further broken down to lactic and glycolic acid, which is released from the body harmlessly as H2O and CO2.

considering both the necessary pore structure for adequate cellular infiltration and the need to control the rate of factor delivery which is often tied to the rate of degradation. Although both PLA and PGA do have the positive attributes mentioned PLGA is more commonly utilized in tissue engineering scaffolds due to the tunable degradation via LA:GA ratio. As mentioned above when PLGA degrades it is reduced to its constituent parts; lactic acid and glycolic acid, each of which are easily tolerated by the body and further broken down to CO2 and H2O and harmlessly excreted. As these polyesters are essentially hydrophilic polymers they degrade through bulk degradation, where water seeps into the polymer structure faster than the surface can degrade, and high molecular weight polymer chains are broken down from the inside out. This degradation mechanism is relevant for both the structural and factor delivery needs of a tissue engineered scaffold as it allows the larger three-dimensional structure of the scaffold to be retained as it degrades, but accelerates toward the end of the degradation cycle through buildup of acidic degradation products within the material. This buildup further accelerates degradation through an autocatalytic process and results in a sudden collapse of the structure at the tail end of healing. While PLGA is not perfectly suited for tissue engineering and drug delivery applications and the drawbacks have prompted the pursuit of many alternatives, the many positive attributes mentioned above have led to its overwhelming prevalence in the literature as a building block for tissue engineered scaffold drug delivery.

88.3.2 Techniques of Incorporation To deliver drugs and proteins from tissue engineered scaffolds they must first be integrated into the scaffold. Given the sensitivity of proteins and the importance of their stability to their function, particular care must be taken when loading them into scaffolds. How proteins are loaded into scaffolds can also dictate how they are released, or if they are released at all. There are three broad methods of incorporating drugs and proteins into scaffolds; encapsulation, surface adsorption/coating, and surface tethering. Each method has both advantages and disadvantages inherent to the approach, but each method also possesses numerous variations that allow for relative levels of control over release kinetics [15].

Biodegradable PLGA Scaffolds for Growth Factor Delivery

88-5

88.3.2.1 Encapsulation Encapsulation involves the incorporation of the molecule to be delivered into the bulk of the polymeric scaffold itself, either by adding the molecule to the polymer solution prior to scaffold synthesis if the molecule can endure the solvent environment without losing its bioactivity, or, if incompatible with solvent systems, by adding the molecule to an aqueous phase that is subsequently incorporated as water droplets into a water/oil/water emulsion system. This method would protect the molecule from the harmful solvent and incorporate the molecule into the bulk of the scaffold. Release kinetics for these encapsulation methods are more or less governed by rates of polymer degradation. As the polymeric scaffold degrades it releases the molecule accordingly. Encapsulation within the polymer bulk during or prior to scaffold fabrication must consider the preservation of the molecule bioactivity, which may limit certain scaffold fabrication strategies that include certain solvents or elevated temperatures [18]. One way around this challenge, however, is to load the molecule after scaffold formation by bonding it to the surface of the scaffold. This can be achieved through surface adsorption. 88.3.2.2  Physical Immobilization-Surface Adsorption Typically, surface adsorption techniques of drug loading involve soaking the fabricated scaffold in an aqueous solution containing the molecule which allows it to diffuse into small pores on the surface of the scaffold. After soaking, the aqueous scaffold coating is rapidly frozen and lyophilized, removing the aqueous phase but leaving the molecule behind. Additional pores can be introduced to the surface of the scaffold using porogens, but often this method alone is less capable of retaining high concentrations of molecules than other techniques. Additional materials, however, can be added to the polymer structure such as ceramics which may have higher affinities for proteins than the polymer itself. Ceramics like calcium phosphate are known to bond well with proteins and have higher capacities to retain molecules after a similar soaking process. Release kinetics of molecules from surface-adsorbed polymers typically exhibit a burst effect, but the addition of ceramic materials can temper this burst and extend the release over longer periods of time. 88.3.2.3 Chemical Immobilization-Surface Tethering A greater degree of control over release kinetics may be necessary than is afforded by either encapsulation or surface adsorption. Indeed for certain applications it may be beneficial to retain the molecule on the scaffold temporarily or permanently rather than release it into the surrounding milieu. For greater control over release kinetics an additional method for incorporating biologically relevant molecules involves immobilizing the molecule onto a polymeric scaffold via functional chemical groups on the surface of the scaffold material. Functional groups may be (1) inherent to the molecular structure of the polymer chains, (2) incorporated into the molecule during polymer synthesis, or in polymers that lack naturally occurring functional groups (3) can be introduced to the surface using various surface modification techniques. For PLGA scaffolds option (3) is quite common in which the surface of the scaffold is partially hydrolyzed, in a sense partially degraded to break molecular bonds between polymer molecules, using solutions of extreme pH to expose functional hydroxyl groups capable of binding to proteins, peptides, or other materials. Similarly plasma treatments can be used to introduce functional hydroxyl groups as well. Another technique that has been used to create functional groups is to graft a separate polymer that possesses necessary functional groups for binding molecules of interest onto the surface of a bulk material. Rather than modifying the underlying material the added material contains the necessary functional groups. The above-mentioned techniques have been utilized in the field of tissue engineering to enhance the effectiveness of scaffolds designed to repair human tissue. Much of the work reported in the literature centers around musculoskeletal tissue engineering but also includes cardiovascular, organ, and neural tissue engineering. Much of the reported work has utilized one or more of the techniques described above. Below is a summary of the literature that describes PLGA as a platform for drug and growth factor delivery in tissue engineering.

88-6

Drug Design, Delivery Systems, and Devices

88.4  Musculoskeletal Tissue Engineering Musculoskeletal tissue engineering comprises a significant portion of the literature that discusses PLGA as a scaffold material. This is in part due to the range of musculoskeletal tissues that have shown considerable potential for repair and regeneration using tissue engineering. Bone, cartilage, ligament, and tendon have all been evaluated as candidates for tissue engineering repair, each employing unique scaffolds, delivery schemes, and payloads.

88.4.1 Bone The factors and other proteins that exist in bone are responsible for regulating cellular activity. Growth factors bind to receptors on cell surfaces, stimulating the intracellular environment to act [19]. Generally this activity translates to a protein kinase that induces a series of events that result in the transcription of mRNA and ultimately into the formation of a protein to be used intra- or extracellularly [19]. The combination and simultaneous activity of many factors results in the controlled production and resorption of bone. These factors, residing in the extracellular matrix of bone, include insulin-like growth factor (I and II) (IGF), platelet-derived growth factor (PDGF), transforming growth factor-β (TGF-β), fibroblast growth factor (FGF), vascular endothelial growth factor (VEGF), and the bone morphogenetic proteins (BMPs) [19]. Researchers have been able to isolate, and in some cases synthesize, these factors and thus examine the specific function of each factor to enhance normal bone development. The ability to isolate appropriate factors from bone, synthesize them in large quantities, and reapply them in concentrated amounts to accelerate bone healing has produced many possibilities for drug delivery in tissue engineering. Much research has been done and continues to be done, while some products have already appeared on the market for clinical use [20]. Each factor, however, has specific roles and has been applied both alone and in conjunction with other factors, in some cases through the controlled sequential release from scaffold material. 88.4.1.1 Insulin-Like Growth Factor Insulin-like growth factor I and II have been shown to stimulate osteoblast proliferation and type I collagen expression [21]. IGF levels in cells of developing bone and periosteum are higher than in nondeveloping equivalents, suggesting that they are involved with bone development and repair [21]. IGF has also been linked to osteoclast formation, which, in turn, would result in an upregulation of osteoblasts to complete the remodeling process [21]. The levels of IGF found in bone vary between both bone site and age of the individual, with lower amounts found as the individual ages and lower amounts in cortical bone as compared to trabecular bone. Studies, however, have examined the relationship between IGF dose and bone healing and have found that when rats were administered varying amounts of IGF, the higher doses resulted in stronger and more energy-absorbing bones [22]. 88.4.1.2  Platelet-Derived Growth Factor Platelet-derived growth factor exists as three similar molecules, PDGF-AA, -BB, and - AB, with molecular shape and locus of activity distinguishing them from one another (-BB and -AB act systemically while -AA acts locally). PDGF is synthesized by platelets, endothelial cells, and macrophages and stimulates the proliferation of osteoblasts and other cells derived from mesenchymal stem cells [23]. PDGF also increases collagen and noncollagenous protein production. Although its role is not entirely clear, elevated levels have been noted during fracture healing [23]. 88.4.1.3 Transforming Growth Factor-β Of the factors that have been isolated, TGF-β has been one of the more widely studied for bone repair. TGF-β is a generic name that refers to three structurally and functionally related growth factors TGFβ1, -β2, and β3, all of which are found in mammals [24,25]. Osteoblasts produce both TGF-β1 and -β2,

Biodegradable PLGA Scaffolds for Growth Factor Delivery

88-7

and both are incorporated into the mineralized bone matrix with large amounts of TGF-β in its latent form and very little in its active form [21]. The activation of TGF-β within the matrix may be stimulated by the acidic environment created by osteoclasts resorbing bone matrix, indicating that bone remodeling may trigger TGF-β activity [21]. It has been suggested that one function of TGF-β is to stimulate the proliferation of cells that have been committed to the osteoblastic lineage, but may not yet be osteoblasts [26,27]. However, TGF-β has also been found to be a stimulator of collagen synthesis as well as a recruiter of osteoblasts [27,28]. Generally, TGF-β increases alkaline phosphatase, collagen I, and osteonectin production, while it decreases osteocalcin synthesis. It has also been found to have an inhibitory effect on the endogenous production of BMPs in vivo [29]. 88.4.1.4  Fibroblast Growth Factor FGF acts on both stem cells and those cells already differentiated, inducing proliferation, differentiation, and migration [23]. Depending on the dose, and the form (acidic or basic), FGF can either inhibit or accelerate bone repair [30,31]. 88.4.1.5  Vascular Endothelial Growth Factor VEGF is a well-established angiogenic growth factor. That is, VEGF is a key molecule in the formation of new blood vessels from existing blood vessels [31A]. The VEGF family is subdivided into VEGF-A, VEGF-B, VEGF-C, VEGF-D, VEGF-E, VEGF-F, and placental growth factor (PlGF), with VEGF-A being most commonly associated with angiogenesis and vasculogenesis, and others more commonly associated with lymphogenesis [31A]. Overexpression of VEGF-A, as one may anticipate when delivering VEGF from a tissue engineered scaffold, can result in a pronounced angiogenic response. Given the dependence of bone healing and long-term survival on adequate vascularization, the delivery of VEGF has been investigated for not only vascular applications but also musculoskeletal repair. 88.4.1.6  Bone Morphogenetic Protein The bone morphogenetic proteins represent a unique subgroup of growth factors in that some of them have been patented. First isolated and reported by Urist in 1965 [32], BMP-7, also known as osteogenic protein-1 (OP-1), has been patented which limits the availability of the molecule for research purposes. BMP-7 is a member of the TGF-β superfamily of factors, and has been shown to not only increase the healing of bony defects, but also to induce bone formation in heterotopic sites [33,34]. Numerous studies have been performed showing the effectiveness of BMP-7 in healing bone defects, and subsequently has gained approval for use in limited clinical applications for long bone nonunions and related trauma [35]. Another potent protein, BMP-2, has similar bone inducing capabilities to BMP-7 and is also the subject of much study in the research laboratory and application in the field of bone tissue engineering. A considerable number of studies describing factor delivery from a PLGA scaffold for bone repair have incorporated one or more of the BMPs into the scaffold. There are also several reports of other growth factors being delivered both alone and in combination with the BMPs (see Table 88.1). For instance, Jayasuriya et al. used an elegant strategy to load and deliver IGF-I from porous three-dimensional PLGA scaffolds by incorporating the IGF-I protein into simulated body fluid (SBF), a solution of ions that closely mimics the ionic concentrations of various salts found in human plasma [36,37]. Soaking the scaffold in the factor-loaded SBF resulted in the formation of a precipitated calcium phosphate layer that contained the IGF-I, thereby forming the delivery vehicle for the encapsulated IGF-I directly onto the PLGA scaffold. Release kinetics data showed a steady gradual release of IGF-I over 30 days with a slight burst release over the first 3 days. Cell studies revealed that the IGF-I release resulted in enhanced cell proliferation on IGF-I loaded scaffolds over pure PLGA scaffolds and scaffolds plus calcium phosphate minus the IGF-I [36]. Anusaksathien et al. used PLGA to deliver PDGF via scaffold-seeded transfected cells. Briefly, Anusaksathien et al. examined the effectiveness of PDGF in cementogenesis, the formation of the mineralized tissue lining adjacent to tooth roots, by transfecting cells to overexpress PDGF while seeded on porous PLGA foams. Results indicated that the addition of PDGF to the scaffold via

88-8

Drug Design, Delivery Systems, and Devices

TABLE 88.1  Summary of Tissue Engineering Scaffolds Used as Drug Delivery Vehicles Application Bone Bone Bone Bone Bone Bone Cartilage Cartilage Cartilage Cartilage Ligament/tendon Ligament/tendon Vascular tissue

Polymer(s) PLGA PLGA PLA, alginate PLGA, alginic acid, poly(4-vinyl pyridine) PLGA PLGA PLGA, polylysine-heparin PLGA PLA, PCL, Fibrin gel PLGA PLA, gelatin PLGA PLGA, ePTFE

Payload

Incorporation Method

Reference

BMP-2, IGF-I PDGF BMP-2, TGF-β BMP-2, BMP-7

Loaded into precipitated CaP layer Transfected cells to overexpress PDGF RGD-functionalized alginate Alginic acid and poly(4-vinyl pyridine)

36 38 42 44

BMP-2 VEGF TGF-β TGF-β TGF-β TGF-β, IGF bFGF bFGF paclitaxel

Surface adsorption, encapsulation Transfected cells to overexpress VEGF Encapsulation, surface adsorption Encapsulation Surface adsorption Encapsulation Surface adsorption Encapsulation Encapsulation

45, 46 47 66 68 72 73 77 78, 79 92

transfected cells was not necessarily beneficial as the PDGF inhibited healing, while the scaffold alone showed greater mineralization and less inflammatory response [38]. As mentioned, numerous studies have delivered BMP-2 and BMP-7 from a variety of scaffolds for bone repair [39–41]. More recently, several new approaches to delivering the effects of the BMPs to cells via scaffolds have emerged. These include combining BMPs with other factors to reduce the necessary dose, combining BMPs together to induce an additive effect, delivering BMP peptides vs entire proteins, and loading plasmids onto scaffolds. Oest et al. combined BMP-2 with TGF-β on PLA scaffolds with a hope of reducing the necessary dose of BMP-2 alone with the same or better results [42]. Typically, BMP-2 has a relatively short half-life and therefore requires doses higher than seen physiologically to be effective, but this creates concerns when considering clinical applications as higher doses and may have undesired side effects [43]. For this study PLA scaffolds with oriented pore structures were formed and subsequently infiltrated with an RGD-functionalized alginate solution that contained both BMP-2 and TGF-β together. The alginate was fully crosslinked after infiltration and composite structures were implanted into 8 mm rat femoral segmental defects that were externally fixated and allowed to heal for 16 weeks. Results after healing indicated that the reduced dosage used was not sufficient to fully heal the defect, minimizing the likelihood that the synergistic effect of these two growth factors reported elsewhere to be effective for ectopic bone formation would have the same effect in large-scale orthotopic bone defects [42]. In a similar study evaluating the combinatorial delivery of two factors, Basmanav et al. loaded BMP-2 and BMP-7 into the same PLGA scaffold and evaluated the effectiveness of sequential delivery. BMPs were loaded into complexes of alginic acid and poly(4-vinyl pyridine) to avoid contact with organic solvents used with PLGA [44]. Microsphere composition was modified to control release kinetics and once optimized were loaded into PLGA foams. Sequential delivery of BMP-2 and BMP-7 resulted in enhanced differentiation of seeded cells over either factor alone, while each factor delivered alone decreased proliferation and increased differentiation over scaffolds with no factor loaded. As mentioned above another approach to delivering the beneficial effects of BMPs to sites of bone repair is through the delivery of plasmid DNA. Nie et al. examined the effectiveness of this approach and its correlation to delivery methodologies using three methods: surface adsorption of naked DNA plasmids for BMP-2 onto PLGA fibers, encapsulating DNA into chitosan nanoparticles and coating PLGA fibers with the nanoparticles, and encapsulating the DNA-loaded nanoparticles into the PLGA fibers themselves [45]. Fiber–nanoparticle constructs were implanted into 1 mm mouse tibial defects and were allowed to heal for 6 weeks. Periodically both healing and DNA release was assessed, and it was determined that surface adsorbed naked plasmid DNA was released the quickest over the first 2 weeks, but after 4 weeks

Biodegradable PLGA Scaffolds for Growth Factor Delivery

88-9

of healing DNA encapsulated in chitosan nanoparticles and coated onto PLGA fibers showed the best results, suggesting a longer release period was more beneficial than a burst release into the defects site. The final group, DNA loaded nanoparticles encapsulated within fibers, was theorized to result in the longest sustained release but due to the brevity of the study its potential was not realized as the release kinetics resulted in longer delivery times than expected. Nevertheless, this was an elegant examination of three delivery schemes each with distinct release kinetics and temporal expression [45]. Nie et al. also examined another approach to attaching BMP-2 plasmids to PLGA scaffolds; functionalizing the PLGA scaffold by modifying both the surface charge and relative surface hydrophobicity [46]. Increased positive surface charge was seen to increase DNA plasmid binding and also lead to a more sustained release of the plasmid over time, suggesting a degree of control over traditional burst release kinetics with the modification to the surface of the scaffold [46]. A slightly different use of PLGA scaffolds as delivery vehicles is described in Jabbarzadeh et al. in which a sintered microsphere scaffold was used as a scaffold for bone repair but also as a vehicle for cells that had been transfected to overexpress VEGF [47]. VEGF has been incorporated both alone and in combination with BMPs and other growth factors due to the necessity of vascularization to the long-term maintenance of bone tissue [48–51]. In this study however, rather than load VEGF into microspheres, transfected adipose-derived stem cells (ADSCs) were used as delivery vehicles for VEGF and were co-cultured on the scaffolds with endothelial cells. The release of VEGF from ADSCs influenced endothelial cells to produce vasculature in subcutaneously implanted scaffolds in the dorsum of rats. Vascularization was evident across the surface and through the pore structure of the porous scaffold after 21 days of implantation. This unorthodox but elegant use of PLGA scaffolds demonstrates the diversity of applications.

88.4.2 Cartilage Like bone, cartilage repair can be driven by various hormones, cytokines, and growth factors, often the same as those found to have value in bone repair. For instance, TGF-β, IGF, and the BMPs have been implicated in the differentiation of chondrogenic progenitor cells and cartilage matrix synthesis [52– 54], while TGF-β, IGF, and FGF have been found to induce chondrocyte proliferation [55–60]. Scaffolds to repair cartilage largely fall into the hydrogel category due to the aqueous nature and compressible mechanical properties of native cartilage and hydrogels, which can be developed to match the mechanical nature of cartilage better than rigid three-dimensional PLGA scaffolds. Efforts to reproduce the elastic and fibrous matrix of cartilage have been reported using various techniques [61,62]. TGF-β has been found to increase cartilage expression of type II collagen, DNA, and glycosaminoglycans [63], all suggesting greater cartilage regeneration [64]. Given this prominent role in cartilage formation, TGF-β has been the payload for several PLGA-based scaffolds [65–76]. Given the native structure of cartilage, a composite of collagen and elastin fibers in an aqueous, compressible matrix, it has been the strategy of many groups to use PLGA in combination with other scaffolds and materials to in part mimic the mechanical nature of natural cartilage tissue. Park et al. used PLGA microspheres as a form of scaffold for cartilage repair and bound TGF-β to the surface by loading the growth factor into ­polylysine–heparin nanoparticles (20–80 nm), which were subsequently attached to the surface of the larger (50–100  µm diameter) PLGA microspheres. Effects of TGF-β delivery on rabbit mesenchymal stem cells showed significant increases in type II collagen and aggrecan after four weeks in culture [66]. It was felt that the protein was stabilized by loading them into the nanoparticles, and when combined with the larger PLGA microspheres formed a suitable two-dimensional matrix onto which cartilage cells could attach and proliferate. Emin et al. took a different approach to cartilage formation and rather than just examining the effects of growth factor release on cells incorporated the effects of a three-­dimensional scaffold and shear forces applied to seeded cells. It is well recognized that both three-dimensional cell culture and the application of physical forces can impact cartilage regeneration and repair [67]. To this end, Emin et al. combined the use of PLGA (85:15) 3-D scaffolds, TGF-β release, and dynamic culture using a bioreactor determined that dynamic culture increased cell infiltration into the scaffold, while

88-10

Drug Design, Delivery Systems, and Devices

the addition of TGF-β increased proteoglycan production. Immunohistochemistry verified the formation of hyaline cartilage, vs fibrocartilage, with TGF-β supplemented media. Defail et al. took a slightly different approach to delivering TGF-β by encapsulating the protein in PLGA (50:50) microspheres but then embedding the microspheres in a poly(ethylene glycol) (PEG) hydrogel [68]. The PEG hydrogel served two purposes; (1) to better mimic the mechanical properties of intact cartilage and (2) to temper or better control the burst release of TGF-β typically seen from PLGA microspheres. PEG is a commonly used polymer for hydrogels in drug delivery and tissue engineering and while typically nondegradable, can be made degradable through proper synthesis and variations in cross-linkers [68–71]. Burst release of TGF-β from PLGA microspheres was seen to be controlled by adding the hydrogel phase to the scaffold, with further control of release seen by varying the concentration of cross-linking agent genipin, which varied the rate and nature of PEG degradation [68]. Using a combination of approaches Jung et al. combined polylactide and polycaprolactone, both hydrolytically degradable polyesters used to generate tissue engineering scaffolds, to form a copolymer that has a slow degradation time and is more elastic than pure PLGA scaffolds, to form a scaffold [72]. To this was added fibrin gel and heparinized, TGFβ-loaded PLGA nanoparticles as the delivery vehicle. Adipose derived stem cells were added to this composite structure and formation of cartilage was evaluated. Results of TGF-β showed a suppression of a burst release with the use of PLGA nanoparticles. It was this sustained delivery that was credited for the chondrogenic differentiation of the adipose derived stem cells noted in the study [72]. Despite the bounty of evidence supporting TGF-β as an important element of cartilage generation and regeneration, relying on one growth factor alone may present limitations. When considering the use of more than one growth factor the role of the drug delivery vehicle becomes more pressing, as spatiotemporal and dose-dependent considerations arise. For instance, the release of one growth factor may stimulate proliferation while a secondary one may stimulate cell differentiation [73–76]. Given the varied roles of growth factors the sequence and duration of release becomes an important parameter. To this end, Jaklanec et al. evaluated the release of IGF-I and TGF-β by encapsulating each growth factor to separate populations of PLGA microspheres, each modified by either introducing bovine serum to the growth factor to stabilize it prior to encapsulation or by using slightly modified PLGA polymer that promoted polymer/growth factor interactions. These variations allowed for the sequential control of release over a two-month time frame, with either the IGF-I or TGF-β being released more or less rapidly than the other [73].

88.4.3  Ligament and Tendon Although modest in volume compared to the fields of bone and cartilage, PLGA-based tissue engineering of ligament and tendon has gained momentum in recent years. The number of studies utilizing PLGA as a drug or factor delivery vehicle for ligament or tendon regeneration is similarly small but growing. Kimura et  al. combined bFGF that was surface adsorbed to gelatin hydrogels, which were subsequently placed between two braided synthetic polylactide fibrous structures designed to replicate the anterior cruciate ligament. This gelatin-PLA structure was then wrapped with a collagen layer that had been loaded with PLA microspheres for added mechanical integrity [77]. Results indicated better mechanical properties with the PLA microsphere loaded collagen wrap than without, and better mechanical properties with the addition of bFGF after 8 weeks of in vivo implantation and healing, suggesting that the best mechanical integrity arose from a combination of factor delivery and structural modifications to the ligament itself [77]. Sahoo et al. evaluated a knitted silk synthetic ACL that had been coated with PLGA nanofibers loaded with bFGF via encapsulation [78,79]. The nanofibers served as the delivery vehicle for bFGF to the silk ACL and supported the attachment, proliferation, and tenogenic differentiation of mesenchymal progenitor cells, increases in type I and type II collagen, and increased mechanical strength of the composite ligament structure over non-bFGF loaded scaffolds. This biohybrid scaffold demonstrated the utility of PLGA purely as a factor delivery vehicle rather than as the bulk material for the scaffold.

Biodegradable PLGA Scaffolds for Growth Factor Delivery

88-11

88.4.4  Vascular Tissue The regeneration of vascular tissue in the realm of scaffold-based tissue engineering often occurs in conjunction with bone formation since the long-term success of tissue engineered bone is largely dependent on whether that new tissue becomes vascularized. For this reason many of the strategies to tissue engineer vasculature have been in conjunction with the development of a scaffold designed for bone regeneration but with the combined delivery of VEGF, as described above [47]. There are, however, numerous reports of tissue engineered vessels focused on the repair and replacement of native vessels [80–90]. In general, clinical strategies to repair damaged blood vessels include harvesting autograft vessels from human saphenous vein, allograft vessel transplantation, or replacement with a synthetic vessel. The synthetic vessels are formed form either Dacron for larger diameter vessels or expanded polytetrafluoroethylene (ePTFE) for medium sized vessels. To date there is no suitable replacement for vessels 99.995% consensus accuracy at >20× coverage ≤5% (~0.5% for substitutions) Consistent from 20 through 80% GC content of target DNA Independent of read length and template Size 25–5000 bases

molecule is present at the bottom of the ZMW and a high concentration of four nucleotides (A, C, G, and T), each linked to a different colored fluorophore at the phosphate group, is added to the ZMW. As each nucleotide is incorporated in the DNA strand, the nucleotide fluorophore is briefly brought to the bottom of the ZMW, where the excitation is stimulated and emission is read by a photometer. As incorporation is completed, the fluorescent group is cleaved and quickly diffuses out of a tiny detection volume. The presence of the incorporated fluorophore-linked nucleotide in the detection volume for tens of milliseconds produces a bright flash of light which is terminated once the natural cleavage of phosphate takes place. The light emitted by each fluorophore passes through a prism dispersive element, where it is separated by its color-specific wavelength and is detected on a single-photon CCD array (Figure 90.6). The process is repeated thousands of times over the area of the CCD array. Each sequencing chip contains more than 100 K ZMW, allowing for simultaneous and continuous detection across all ZMW in real time. Currently, the technology only populates 30–40% of the theoretically available ZMWs during a run, limiting the number of sequence reads to 30–40 K. 90.3.3.3 Ion Torrent Systems Inc.: Personal Genome Machine Ion Torrent Systems Inc. is a major developer of third-generation SMS technology. As its proprietary name, “Personal Genome Machine” (PGM™), suggests, the main target of Ion Torrent is an individual’s genome, which could be sequenced in a very short time at the point of care during a visit to a healthcare

90-9

The Evolution of Massively Parallel Sequencing Technologies

Polymerase

DNA template

Nucleotide analogs

Bioinformatics Multiplex zero-mode waveguide chip Zero-mode waveguide chip

Objective lens

Data processing

ZMW 1

Color separation

ZMW 3

Dichroic Prism

Lens

Light source

ZMW 5

Monochrome detector

FIGURE 90.6  PacBio ZMW single molecule sequencing.

provider. The initially announced price of PGM is in the range of $50 K USD, which, along with its compact size and light weight of about 50 lbs, makes the machine affordable for private medical practices, hospitals, diagnostic labs, and small research labs. PGM technology is based on a high-density array of wells containing different DNA templates, beneath which is placed an ion-sensitive layer, followed by a proprietary ion sensor. The principle of sequencing (Figure 90.7) is based on the release of H+ ions that occurs during nucleotide incorporation into the synthesized molecule and detection of the subsequent pH changes by an ion-sensitive layer and sensor. The sensor converts the chemical reaction into digital information, which is deconvolved into sequence. 90.3.3.4 Nanopore-Based Technologies Nanopore-based SMS, a novel technology in development, is believed to be capable of sequencing the whole human genome for under $1 K USD within 24 h. The main principle of existing variations is modulation of current changes by nucleotide of DNA/RNA molecules driven by electrophoresis through a nanopore while the technology measures the ionic current through the pore. The nanopore-based ioncurrent modulating sequencing approaches presently in development (17) include • Detection of ionic current fluctuation through an α-hemolysin pore created by a blockage of a pore by a strand of synthesized DNA • Blockage delay of current caused by exonuclease cleavage of dNMP off the DNA strand driven into an adaptor lodged within the nanopore • Sequencing using synthetic DNA stripped off as it passes through a nanopore, detected as a shortlived photon bursts • Detection of tunneling currents that traverse through the nucleotides of DNA electrophoretically driven through the nanopore

90-10

Personalized Medicine

Nucleotide incorporates into DNA

Hydrogen ion is released H+

FIGURE 90.7  Ion Torrent personal genome machine.

90.4  Short Read Alignment and Cluster Computing The vast technical improvements in DNA/RNA sequencing are necessitating equally transformative improvements in the computational aspects of genomics. For the foreseeable future, long DNA strands like chromosomes will be broken into smaller pieces, sequenced, and then reassembled. The first assembly of the human genome in 1998 required more than 700 CPUs and 70 TB of storage. By comparison, in 2010 the alignment of 40 million short reads of RNA to the known genome can be accomplished on a fast desktop computer in hours with only 4 GB of RAM. Nonetheless, the computational success of alignment is a critical element of success in NGS, and nearly inherent problems of alignment and statistical analysis will limit this strategy for years to come. Vladimir Levenshtein’s 1965 manuscript detailed a method to measure the amount of distance between two strings of characters (18). Later improved in 1970 by Needleman and Wunsch and in 1981 by Smith and Waterman (19), sequence alignment has been a daily operation in almost every biomedical research laboratory. In 1990, the algorithm “basic local alignment search tool” (BLAST) demonstrated notable speed enhancements over prior algorithms, while maintaining nearly the same level of accuracy. BLAST quickly became the most widely used bioinformatics program in history (20). BLAST “seeds” the alignment by finding small segments from the query and target sequences that are highly similar and then attempting to increase the alignment from there. Segments that are highly similar are called “maximal segment pairs” (MSP) or “high-scoring segment pairs” (HSP). In this way, local maximums are found and returned as probable alignments. The previously discussed alignment algorithms were more than sufficient for the individual DNA and RNA sequences of up to 800 bp obtained using Sanger sequencing. However, with the advent of NGS, the alignment problems became significant. To align millions of short reads by traditional means would require intensive time and computational resources. Thus, new heuristic alignment algorithms, such as

The Evolution of Massively Parallel Sequencing Technologies

90-11

those used by the software package Bowtie, have been developed (21). Bowtie can align 35-bp reads at a rate of greater than 25 million reads per CPU-hour. To allow Bowtie to run at such speeds on a PC, it employs a Burrows–Wheeler index on the full-text minute-space (FM) index, requiring a memory footprint of only about 1.3 GB for the entire human genome. Once next-generation sequence reads are aligned, they serve as input for many other bioinformatic approaches to understanding the biological implications of these genome-wide measurements. Some of the major algorithms evaluate: sequence conservation between organisms, expression patterns within a single study or between studies (22), secondary structure predictions for RNAs, biological annotation such as splice sites protein coding regions, gene ontology, pathway enrichment (23), and network analysis (24). The vast information content of the NGS dataset is critical for the outcome of these bioinformatic algorithms. Computationally, these more sophisticated algorithms are being implemented on increasingly powerful computer architectures. The NGS platforms typically include multiblade cluster computers, which divide the alignment problems into parallel problems, with each problem assigned to separate compute “nodes.” Compute nodes are typically blades with quad processors, 4–8 GB RAM and an on-board hard drive. These nodes perform alignment and then return the results to a master node for a “meta assembly.” Increasingly, these physical compute nodes are being replaced by virtual machines residing on: “cloud” computers like Amazon’s Elastic Compute Cloud (EC2), which harness the aggregate computing power of interconnected servers around the world. Cloud computing has the advantages of essentially no investment in physical infrastructure or personnel, on-demand scalability, and nearly complete software flexibility, but is somewhat hindered by concerns over the security of the highly sensitive personal data which reside within the cloud.

90.5 The Limitations of Genomics and NGS 90.5.1 The “Curse” of Dimensionality While these massively parallel methods provide impressive power to generate new hypotheses and potentially understand and cure diseases, there are limitations that require consideration. A major limitation to the NGS methods is a direct function of their major strength. By measuring millions of independent genetic events, one has excellent coverage, but each measurement has low, but significant random noise. When the random noise of millions of events is accumulated, it essentially insures that false-positive and false-negative results will occur. For instance, in a conventional statistical analysis involving measurements of blood pressure in two groups of people, one accepts a 5% risk of a given difference occurring by random chance. However, if one measures 54,000 transcript levels, and accepts the same 5% risk for each measure, then by chance alone, 2700 transcripts will be observed to change randomly between any two groups. The problem is further enhanced at the genomic level, where it might be necessary to measure 1–3 million SNPs or more to even roughly cover the genome at sufficient resolution. Known as the false discovery rate (FDR), this intrinsic limitation of highly dimensional data can only partially be overcome by using large numbers of subjects so that the random noise is averaged out, leaving the true signal to emerge. For example, several large genome-wide association studies have employed 10–15,000 patients per study in order to have sufficient power to detect SNPs associated with CAD (25, (26), diabetes, Crohns, and bipolar disorder (27). The agreement between studies on some of these markers strongly suggest that sufficient power was reached in each of the studies. Fortunately, NGS technologies offer a level of measurement precision unattainable with microarrays, reducing the FDR and increasing the statistical significance of genome-wide experiments. Especially at lower levels of transcript expression, microarray platforms suffer from a background level of hybridization that reduces the signal-to-noise characteristics. In contrast, because each individual aligned sequence reads in an NGS study depends on multiple independent experimental observations (as many

90-12

Personalized Medicine

as the length of the sequence read itself), the net information content provided by the experiment increases 10–50-fold over microarrays. This additional information content permits higher resolution at low expression levels, better overall quantitation, lower p-values, and a lower FDR.

90.5.2 The Human Genome Contains Repeated Sequence Unlike a large novel, in which any 35 sequential letters might occur in only a single position within the book, as much as 70% of the human genome is composed of nearly identical sequences called “repeats” and otherwise low complexity sequences such as GCGCGCGC. By analogy, the letters “and the” occur more than 20 times in this short chapter. While repeated sequences may be necessary for chromatin structure and function, repeated sequence is problematic for alignment because they can be aligned to thousands of positions in the genome, and thus, are typically discarded by “filtering.” For this reason, longer reads are easier to align because they are more likely to contain unique sequence that “seeds” the alignment to a unique location. Currently, as much as 70% of RNA reads are discarded because they do not align uniquely to the genome.

90.5.3 Identifying True Phenotypes A major impediment to fully discovering the genotype–phenotype relationship lies in the definition of clear and singular phenotypes. While genotypes can now be completely characterized by NGS, phenotypes, in the form of traits or diseases, are often far less clear. Take one of the simplest traits: Is there only one type of blue eyes? Evidence to date indicates that potentially hundreds of genes may define precise eye color, a trait once thought to have a single gene or a few at best. Diseases such as cancer and cardiovascular or autoimmune diseases may be many times more complicated. For instance, breast cancer is defined clinically as a mass in the breast, which then can be separated into several finer phenotypes, such as estrogen receptor positive or negative, benign or metastatic, and so on. Genetically, however, there may be hundreds of “disease genotypes” that are associated with particular functional phenotypes. It will be essential to track the behavior of precise genetic subtypes of a disease. Another challenge for using NGS to characterize phenotypes pertains to multiple cell types. Even relatively simple physiological functions rely on a number of different cell types functioning within a specific anatomical microregion in a coordinated, goal-oriented fashion. More complex functions such as inflammation can recruit dozens of cell types from peripheral blood flow and drive the ­context-specific differentiation of many other cell types from recruited cells. The genomic characterization of disease phenotypes requires a simultaneous understanding of gene expression in these many cell types that participate in the physiological functions relevant to disease etiology. Many current experimental frontiers focus on the enrichment of specific cell types for genomic analysis within a disease context.

90.6  Proteomic Strategies When DNA transcribes RNA, the complexity of the signal is actually significantly reduced because the mRNA is simpler than the DNA which produced it. However, as mRNA is translated into protein, the protein is typically modified by cleavage, dimerization, phosphorylation, glycosylation, lipid modification, and protein–protein interactions, which all drastically increase the complexity of the proteome. Current methods of protein identification and quantitation, such as mass spectrometry, are extremely sophisticated but are still far short of determining all of these potential protein variations in a complex protein mixture such as serum. Nonetheless, there are increasingly useful strategies for fractionating complex biological samples, cleaving the proteins into peptide fragments, and then analyzing the peptides by one of several mass spectrometry methods.

The Evolution of Massively Parallel Sequencing Technologies

90-13

90.7  Future Directions Genomics, proteomics, and bioinformatics are by far the most explosive areas of biomedical research, and they are quickly making inroads into clinical practice. By 2011, it is likely that complete sequencing of individual human genomes will be affordable to the average American, probably for less than the cost of a laptop computer. However, fully interpreting the massive amounts of information, especially the gene– gene interactions that modify diseases, will be a sizeable task. Further, not all diseases can be diagnosed by DNA sequence alone, and so RNA profiling and improved proteomic methods will be crucial to advancing biomedical research. In addition, recent discoveries have demonstrated that the human transcriptome contains far more transcripts than originally predicted from the approximately 25,000 protein coding genes (28, 29). While most of these transcripts do not code for proteins, some have important functionality in cellular physiology, such as micro-RNAs (miRNAs) (30), piwi associated RNAs (piRNAs) (31), long intergenic noncoding RNAs (lincRNAs) (32), and natural antisense transcripts (NATs) (33). As a result of such emerging complexity, large-scale, well-controlled prospective studies will be required to determine whether genomic information is actually useful in informing the diagnosis and treatment of patients. In some cases, it is quite possible that clinical “titration” (to test and adjust the levels) of coumarin doses, for instance, may be advantageous. Once the empirical value of genetic information is established in specific indications, it should be easier to engage physicians and patients in its routine use (34). There is little doubt, however, that a genomic era of medicine is beginning in which the physician will have intricate knowledge of the genetic anatomy of the patient. As with any tool, it is the task of the physicians and scientists to apply that knowledge for the greatest good of the patient.

References 1. Helgadottir, A., Thorleifsson, G., Manolescu, A., Gretarsdottir, S., Blondal, T., Jonasdottir, A., Sigurdsson, A., Baker, A., Palsson, A., Masson, G. et al. 2007. A common variant on chromosome 9p21 affects the risk of myocardial infarction. Science 316:1491–1493. 2. Helgadottir, A., Thorleifsson, G., Magnusson, K.P., Gretarsdottir, S., Steinthorsdottir, V., Manolescu, A., Jones, G.T., Rinkel, G.J., Blankensteijn, J.D., Ronkainen, A. et al. 2008. The same sequence variant on 9p21 associates with myocardial infarction, abdominal aortic aneurysm and intracranial aneurysm. Nat Genet 40:217–224. 3. Gudbjartsson, D.F., Arnar, D.O., Helgadottir, A., Gretarsdottir, S., Holm, H., Sigurdsson, A., Jonasdottir, A., Baker, A., Thorleifsson, G., Kristjansson, K. et al. 2007. Variants conferring risk of atrial fibrillation on chromosome 4q25. Nature 448:353–357. 4. Ackerman, M.J. 2004. Cardiac channelopathies: It’s in the genes. Nat Med 10:463–464. 5. Glas, A.M., Floore, A., Delahaye, L.J., Witteveen, A.T., Pover, R.C., Bakx, N., Lahti-Domenici, J.S., Bruinsma, T.J., Warmoes, M.O., Bernards, R. et  al. 2006. Converting a breast cancer microarray signature into a high-throughput diagnostic test. BMC Genomics 7:278. 6. Knauer, M., Mook, S., Rutgers, E.J., Bender, R.A., Hauptmann, M., van de Vijver, M.J., Koornstra, R.H., Bueno-de-Mesquita, J.M., Linn, S.C., and van’t Veer, L.J. 2010. The predictive value of the 70-gene signature for adjuvant chemotherapy in early breast cancer. Breast Cancer Res Treat 120:655–661. 7. Kim, C. and Paik, S. 2010. Gene-expression-based prognostic assays for breast cancer. Nat Rev Clin Oncol 7:340–347. 8. Oldenburg, J., Bevans, C.G., Fregin, A., Geisen, C., Muller-Reible, C., and Watzka, M. 2007. Current pharmacogenetic developments in oral anticoagulation therapy: The influence of variant VKORC1 and CYP2C9 alleles. Thromb Haemost 98:570–578. 9. Helb, D., Jones, M., Story, E., Boehme, C., Wallace, E., Ho, K., Kop, J., Owens, M.R., Rodgers, R., Banada, P. et al. Rapid detection of Mycobacterium tuberculosis and rifampin resistance by use of on-demand, near-patient technology. J Clin Microbiol 48:229–237.

90-14

Personalized Medicine

10. Calvano, S.E., Xiao, W., Richards, D.R., Felciano, R.M., Baker, H.V., Cho, R.J., Chen, R.O., Brownstein, B.H., Cobb, J.P., Tschoeke, S.K. et al. 2005. A network-based analysis of systemic inflammation in humans. Nature 437:1032–1037. 11. Zohlnhofer, D., Richter, T., Neumann, F., Nuhrenberg, T., Wessely, R., Brandl, R., Murr, A., Klein, C., and Baeuerle, P. 2001. Transcriptome analysis reveals a role of interferon-g in human neointima formation. Mol Cell 7:1059–1069. 12. McCaffrey, T.A., Fu, C., Du, B., Eksinar, S., Kent, K.C., Bush, H., Jr., Kreiger, K., Rosengart, T., Cybulsky, M.I., Silverman, E.S. et al. 2000. High-level expression of Egr-1 and Egr-1-inducible genes in mouse and human atherosclerosis. J Clin Invest 105:653–662. 13. Avramopoulos, D., Szymanski, M., Wang, R., and Bassett, S. 2011. Gene expression reveals overlap between normal aging and Alzheimer’s disease genes. Neurobiology of Aging 32(12):2319.e27–2319. e34. 14. Wennmalm, K., Wahlestedt, C., and Larsson, O. 2005. The expression signature of in vitro senescence resembles mouse but not human aging. Genome Biol. 6:R109. 15. Gagarin, D., Yang, Z., Butler, J., Wimmer, M., Du, B., Cahan, P., and McCaffrey, T.A. 2005. Genomic profiling of acquired resistance to apoptosis in cells derived from human atherosclerotic lesions: Potential role of STATs, cyclinD1, BAD, and Bcl-XL. J Mol Cell Cardiol 39:453–465. 16. Ozsolak, F., Ting, D.T., Wittner, B.S., Brannigan, B.W., Paul, S., Bardeesy, N., Ramaswamy, S., Milos, P.M., and Haber, D.A. 2010. Amplification-free digital gene expression profiling from minute cell quantities. Nat Methods 7:619–621. 17. Branton, D., Deamer, D.W., Marziali, A., Bayley, H., Benner, S.A., Butler, T., Di Ventra, M., Garaj, S., Hibbs, A., Huang, X. et  al. 2008. The potential and challenges of nanopore sequencing. Nat Biotechnol 26:1146–1153. 18. Levenshtein, V.I. 1966. Binary codes capable of correcting deletions, insertions, and reversals. Sov Phys Dokl 10:707–710. 19. Smith, T.F., and Waterman, M.S. 1981. Identification of common molecular subsequences. J Mol Biol 147:195–197. 20. Altschul, S.F., Gish, W., Miller, W., Myers, E.W., and Lipman, D.J. 1990. Basic local alignment search tool. J Mol Biol 215:403–410. 21. Langmead, B., Trapnell, C., Pop, M., and Salzberg, S.L. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biol 10:R25. 22. Cahan, P., Ahmad, A.M., Burke, H., Fu, S., Lai, Y., Florea, L., Dharker, N., Kobrinski, T., Kale, P., and McCaffrey, T.A. 2005. List of lists-annotated (LOLA): A database for annotation and comparison of published microarray gene lists. Gene 360:78–82. 23. Salomonis, N., Hanspers, K., Zambon, A.C., Vranizan, K., Lawlor, S.C., Dahlquist, K.D., Doniger, S.W., Stuart, J., Conklin, B.R., and Pico, A.R. 2007. GenMAPP 2: New features and resources for pathway analysis. BMC Bioinformatics 8:217. 24. Bogner, V., Leidel, B.A., Kanz, K-G., Mutschler, W., Neugebauer, E.A.M., and Biberthaler, P. 2011. Pathway analysis in microarray data: A comparison of two different pathway analysis devices in the same dataset. Shock 35(3):245–251. 25. Samani, N.J., Erdmann, J., Hall, A.S., Hengstenberg, C., Mangino, M., Mayer, B., Dixon, R.J., Meitinger, T., Braund, P., Wichmann, H.E. et al. 2007. Genomewide association analysis of coronary artery disease. N Engl J Med 357:443–453. 26. McPherson, R., Pertsemlidis, A., Kavaslar, N., Stewart, A., Roberts, R., Cox, D.R., Hinds, D.A., Pennacchio, L.A., Tybjaerg-Hansen, A., Folsom, A.R. et al. 2007. A common allele on chromosome 9 associated with coronary heart disease. Science 316:1488–1491. 27. Burton, P., Ahmad, T., Attwood, A., Ball, S., Balmforth, A., Ban, M., Barbour, J., Barrett, J., Barton, A. et al. 2007. Genome-wide association study of 14,000 cases of seven common diseases and 3000 shared controls. Nature 447(7145):661–678.

The Evolution of Massively Parallel Sequencing Technologies

90-15

28. Katayama, S., Tomaru, Y., Kasukawa, T., Waki, K., Nakanishi, M., Nakamura, M., Nishida, H., Yap, C.C., Suzuki, M., Kawai, J. et al. 2005. Antisense transcription in the mammalian transcriptome. Science 309:1564–1566. 29. Kapranov, P., Cheng, J., Dike, S., Nix, D.A., Duttagupta, R., Willingham, A.T., Stadler, P.F., Hertel, J., Hackermuller, J., Hofacker, I.L. et al. 2007. RNA maps reveal new RNA classes and a possible function for pervasive transcription. Science 316:1484–1488. 30. Krol, J., Loedige, I., and Filipowicz, W. 2010. The widespread regulation of microRNA biogenesis, function and decay. Nat Rev Genet 11:597–610. 31. Thomson, T. and Lin, H. 2009. The biogenesis and function of PIWI proteins and piRNAs: Progress and prospect. Annu Rev Cell Dev Biol 25:355–376. 32. Huarte, M., Guttman, M., Feldser, D., Garber, M., Koziol, M.J., Kenzelmann-Broz, D., Khalil, A.M., Zuk, O., Amit, I., Rabani, M. et al. 2010. A large intergenic noncoding RNA induced by p53 mediates global gene repression in the p53 response. Cell 142:409–419. 33. Faghihi, M.A., Modarresi, F., Khalil, A.M., Wood, D.E., Sahagan, B.G., Morgan, T.E., Finch, C.E., St Laurent, G., 3rd, Kenny, P.J., and Wahlestedt, C. 2008. Expression of a noncoding RNA is elevated in Alzheimer’s disease and drives rapid feed-forward regulation of beta-secretase. Nat Med 14:723–730. 34. Scheuner, M.T., Sieverding, P., and Shekelle, P.G. 2008. Delivery of genomic medicine for common chronic adult diseases: A systematic review. JAMA 299:1320–1334.

91 Computational Methods and Molecular Diagnostics in Personalized Medicine Contents Roland Valdes, Jr. University of Louisville School of Medicine PGXL Laboratories

Mark W. Linder University of Louisville School of Medicine PGXL Laboratories

91.1 Introduction..................................................................................... 91-1 91.2 The Problem...................................................................................... 91-2 91.3 Fundamentals (PGx and Pharmacology)..................................... 91-3 CYP2C9 PGx  •  VKORC1 PGx

91.4 Modeling and Clinical Applications............................................. 91-6 Interpretive Guidance of PerMIT:Warfarin  •  Estimation of Maintenance Dose  •  Practical Support for Dosage Adjustment

91.5 Future Extensions of Genotype–Phenotype Modeling............. 91-8 91.6 Summary........................................................................................... 91-9 References................................................................................................... 91-10

91.1 Introduction The future of linking molecular information to clinical outcomes requires a substantial change in present paradigm, where practice is based on intuitive knowledge, toward a more targeted practice now referred to as “precision medicine.” One example of this concept is in the implementation of pharmacogenetics (PGx) as a basis for providing individualized therapy. A major challenge in this application is in providing clinically actionable information to practitioners. In the area of drug therapeutics, one solution involves optimizing the dosing of medications which requires establishing quantifiable relationships between the genotype of an individual and their anticipated response to a particular drug. Combining both metabolism and receptor genotypic information is advantageous; however, it is not sufficient unless kinetic and dynamic parameters are both integrated into quantifiable decision-making approaches. In this chapter, we review the development of a decision-support tool based on combining PGx genotyping with both pharmacokinetic and -dynamic parameters to optimize dosing decisions in real time (Figure 91.1). This model is applied to relationships designed to predict optimum dosing for warfarin, the most commonly prescribed oral anticoagulant for the treatment and prevention of thromboembolic events. The correct maintenance dose of warfarin for a given patient is difficult to predict; the drug carries a high risk of toxicity, and variability among patients means that the safe dose-range differs widely between individuals. Recent PGx studies indicate that the routine incorporation of genetic testing into warfarin therapy protocols could substantially ease both the financial and health risks currently associated with this treatment. In particular, the variability in warfarin dose requirement is now recognized to be due in large part to polymorphisms in two genes: cytochrome P4502C9 (CYP2C9) 91-1

91-2

Personalized Medicine Pharmacokinetic

Pharmacodynamic

Metabolism

Receptor

CYP2C9

VKORC1

Actionable information

FIGURE 91.1  Combined insight into inherited contributions to variability in pharmacokinetic and pharmacodynamic properties of medications provides the foundation for comprehensive clinical decision support systems.

• CYP2C9 sets the rate: accumulation and elimination – Influences warfarin clearance and is also associated with need for decreased maintenance dosages • VKORC1 sets the amount: effective concentration – Influences warfarin pharmacodynamic response and is also associated with specific warfarin maintenance dose

FIGURE 91.2  Conceptual summary of the inherited sources of variance in S-warfarin pharmacology.

Convergence Molecular information

Computational tools

Diagnostic informatics

Decision support tools utilizing genetic biomarkers to fine-tune Personalized medicine

FIGURE 91.3  Computational tools to assist with the integration of diagnostic information are increasingly ­ tilized in clinical decisions. u

and the vitamin K epoxide reductase complex subunit 1 (VKORC1) (Figure 91.2). The development of computational decision support tools, which integrate all the relevant genetic and physical factors into comprehensive, individualized predictive models for warfarin dose selection, may be used to translate the results of PGx testing into actionable clinical application, Figure 91.3. Of substantial interest is that similar computational models have application in other therapeutic settings.

91.2 The Problem Warfarin is the most commonly prescribed oral anticoagulant, with four million U.S. patients taking the drug for treatment and prevention of atrial fibrillation, stroke, deep vein thrombosis, or pulmonary embolism, and for those who have had heart valve replacement surgery. Adverse reactions to warfarin

Computational Methods and Molecular Diagnostics in Personalized Medicine

91-3

precipitated 43,000 emergency room visits in 2004–2005, a number second only to that of adverse reactions to insulin (http://biotech.seekingalpha.com/article/10378). Current warfarin dosing practices involve initiating dosing at a daily dose of 5–10 mg for 3–4 days, followed by dosing adjustments based on the results of international normalized ratio (INR) testing to measure the degree of anticoagulation. This process is fundamentally flawed and commonly results in suboptimal care for up to 70% of patients who have an inherited deficiency in warfarin metabolism or increased sensitivity for warfarin response [1]. Inherited differences in the cytochrome P450 2C9 (CYP2C9), and vitamin K epoxide reductase complex protein 1 (VKORC1) genes can produce delayed metabolic clearance of S-warfarin, and a lower concentration threshold for response, respectively [2]. These inherited characteristics have a profound effect on the clinical pharmacology of warfarin and defeat the utility of standard dosing and monitoring practices [3]. The ideal induction and maintenance dosage rate of medications is dictated by the rate of drug metabolism (clearance, half-life) and target therapeutic concentration. Knowledge of these variables establishes the basis for calculation of tailored induction and maintenance dosing regimens. It is also important to ensure that therapeutic monitoring is done when drug concentrations remain constant over the dosing interval, otherwise known as steady state (see figure in section below). Steady-state blood concentrations of warfarin develop over a period of time equal to seven elimination half-lives of the medication. Approximately 40% of patients have diminished CYP2C9 capacity and have not yet achieved steady state when standard therapeutic monitoring is performed during therapy initiation and following dosage changes. Standard warfarin dosing and monitoring practices are fundamentally inappropriate for application to patients who possess these genetic variants.

91.3  Fundamentals (PGx and Pharmacology) To begin, a brief introduction to the field of PGx is warranted. PGx links inherited gene structure variants with drug metabolism and response. PGx can be utilized to provide phenotype prediction based on genotype as a means to decrease the incidence of adverse drug reactions (ADRs). Ideally, a patient’s PGx information would be known prior to initiation of a new therapeutic regimen so that the physician could base decisions of medication selection and dosing on the patient-specific genotype. The utilization of PGx a priori would allow for identification of patients with an increased risk of ADRs before they experience an event. Genotyping as a retrospective diagnostic analysis, on the other hand, can also provide useful information as to the potential cause and mechanistic basis of an ADR.

91.3.1  CYP2C9 PGx Inherited genetic polymorphisms in hepatic drug-metabolizing enzymes have been linked to increased risk of ADRs associated with a multitude of common medications [4,5]. The polymorphic cytochrome P450 2C9 enzyme metabolizes 6–10% of commonly prescribed medications including S-warfarin, phenytoin, several of the NSAIDs, and sulfonylurea [5,6,7]. Approximately 20% of the wide interindividual variability in warfarin dosage is due to the metabolic capacity of CYP2C9 [8,9]. The CYP2C9 gene contains many single nucleotide polymorphisms (SNPs) represented by over 30 alleles, many of which result in altered enzymatic activity. A complete and up-to-date list of all known CYP2C9 alleles can be found on the Human Cytochrome P450 Allele Nomenclature Committee website (http:/­­/­­www.­­cypalleles.­­ki.­ se/­­c yp2c9.­­htm).­­ The most common allele is CYP2C9*1 and represents the reference “normal” active allele. The frequency of variant alleles differs depending on the ethnic diversity of a population. Among Caucasian populations, approximately 82% of all alleles are CYP2C9*1, while the remaining alleles are comprised primarily of the CYP2C9*2 and CYP2C9*3 variants [5,10]. In contrast, greater than 95% of alleles in African–American and Asian populations are CYP2C9*1. In these ethnic groups, the CYP2C9*2 and *3 alleles are less common, comprising only 1–2% of the alleles. Several other variant SNPs are rare and will not be described here [6,10,11].

91-4

Personalized Medicine

The functional consequences of the CYP2C9*2 and *3 alleles on enzyme activity have been well characterized. CYP2C9*2 has been shown to have as little as 12% of the metabolic capacity of CYP2C9*1, and as much as 70% capacity, with most studies demonstrating ~70% [12–14]. The CYP2C9*3 allele, however, has consistently been shown to have roughly 5% of the enzymatic activity of CYP2C9*1 [2,5,13]. Patients with these variants are intrinsically hypersensitive to CYP2C9 substrates, including warfarin, in an apparent gene-dose manner. The primary pharmacokinetic change associated with CYP2C9 metabolic deficiency is a decreased S-warfarin clearance rate [2,6,13]. Decreased clearance subsequently leads to an increased elimination half-life, increased time to reach steady-state plasma concentrations, and ultimately lower dose requirement. The different pharmacokinetic responses to a given dose of warfarin associated with the CYP2C9*2 and CYP2C9*3 variants are illustrated in Figure 91.4. In a patient without a CYP2C9 deficiency (CYP2C9*1/*1), the S-warfarin plasma concentration would be expected to reach both the therapeutic range, corresponding to an INR between 2.0 and 3.0, and steady state within 3–5 days following dose initiation or adjustment. However, the decreased S-warfarin clearance and increased half-life associated with CYP2C9 deficiency lead to significantly higher plasma concentrations and a prolongation of the time required to reach steady-state concentrations of the medication following dose initialization or adjustment, the magnitude of each being dependent on which variant is present. For a patient with the CYP2C9*1/*2 genotype, the expected plasma concentration and time required to reach steady state would be approximately twice that of a CYP2C9*1/*1 patient on the same dose (Figure 91.4). Even more severe is the case of a patient with at least one CYP2C9*3 allele, in which the plasma concentration and time to steady state are at least threefold greater than that of a wild-type patient for a given dose (Figure 91.4). Because a priori genotyping is not yet standard of care, a lower dose requirement typically is not identified until after the lengthy trial and error dosing strategies have been utilized, wherein resides the highest risk of adverse events described earlier in this review. Indeed, warfarin ADRs and low dose requirement are significantly associated with the presence of at least one CYP2C9 variant [15,16]. Several studies have demonstrated that patients with either the CYP2C9*2 or *3 variants were 2–4 times as likely to experience a bleeding event as those with the CYP2C9*1 allele [14,15,17]. Presence of the CYP2C9*2 Dynamic approach to guide INR interpretation

S-warfarin (mg/L)

3.00 Time to steady state

2.40

CYP2C9*1/*3

1.80

Accumulation CYP2C9*1/*2

1.20 0.60 0.00

CYP2C9*1/*1

0

3

6

9

12

15

18

21

24

27

30

Time (days)

FIGURE 91.4  Impact of CYP2C9 genotype-dependent changes in S-warfarin clearance on plasma concentration of S-warfarin resulting from a fixed dosage and on the rate of achieving steady state. Scenarios are presented for a 65 y/o female subject, weighing 150 lbs who is administered 4 mg daily dosages. Note the effects of this individual of having a single CYP2C9*2 allele or CYP2C9*3 allele. Plasma concentrations accumulate to supra-therapeutic levels and do not achieve steady state until 12–18 days following initiation of dosing. (Adapted from Linder MW et al. J Thromb Thrombolysis 14(3), 227–232, 2002.)

Computational Methods and Molecular Diagnostics in Personalized Medicine

91-5

and/or CYP2C9*3 variants also conferred up to a sixfold increased risk of supra-therapeutic INR during the induction phase of warfarin therapy over that of the *1 genotype [15,18,19]. Although CYP2C9 genetic variation has been established as an independent risk factor for warfarin low dose requirement and adverse events, CYP2C9 genotype only accounts for 5–20% of the variability in warfarin dose depending on the ethnic population in question [9,20–24]. Approximately 80% of variability in dose cannot be predicted by CYP2C9 genotype alone. Other factors that affect dose include age (17%), gender (13%), body surface area (15–25%), and the pharmacodynamic changes associated with genetic variation in the gene that encodes VKOR [22,25,26].

91.3.2  VKORC1 PGx The target enzyme of warfarin inhibition, VKOR, is encoded by the recently identified vitamin K epoxide reductase complex subunit 1 gene (VKORC1) [27,28]. Numerous recent studies have identified several noncoding region polymorphisms that have been associated with warfarin sensitivity and low dose requirements [25,29,30]. In 2005 Rieder et al. determined that by haplotyping warfarin patients using 10 different VKORC1 SNPs, they could stratify patients into low, intermediate, or high dose groups, and could explain 25% of dose variability [29]. Concurrent studies found that the VKORC1 1173 C > T SNP of intron 1, significantly affected warfarin dose requirement [22,25]. This SNP was included in the low dose haplotype described by Rieder at position 6484 [29]. However, additional analysis has demonstrated that this SNP is in tight linkage disequilibrium with the promoter variant −1639 G > A, which has the strongest association with low-dose warfarin requirement [9,25,26,30]. Patients with the homozygous −1639 GG genotype have been reported to require on average 4.5 mg/day of warfarin, significantly greater than that of the heterozygous GA genotype group, who required 3.8 mg/day, and the homozygous AA genotype group who required 2.2 mg/day [9,30,31]. Other studies have reported similar differences in warfarin dose according to the VKORC1 −1639 genotype. Figure 91.5 summarizes the distribution of warfarin daily dose requirements across VKORC1 −1639 G > A genotypes in Caucasians [9,22,24,29], and illustrates that presence of the −1639 A allele is associated with a lower warfarin dose than the −1639 G allele. The pharmacodynamic variability is attributed to the fact that the variant lies within the promoter of VKORC1, potentially resulting in decreased transcription of the gene product. Decreased expression of the VKOR enzyme results in decreased warfarin demand to maintain adequate

S-warfarin (mg/L)

0.8 0.7 0.6 0.5 0.4 0.3

A/A

A/G

G/G

VKORC1

FIGURE 91.5  Association between VKORC1 −1639 genotype, warfarin maintenance dose, and plasma concentration of S-warfarin required to maintain therapeutic anticoagulation. (Adapted from Zhu, Y. et al. Clin Chem 53:1199–1205, 2007.)

91-6

Personalized Medicine

anticoagulation. In other words, the effective warfarin concentration is lower in the presence of the −1639 A allele. In Caucasians, the VKORC1 −1639 G and A allele frequencies are approximately 58% and 42%, respectively [32]. This corresponds to genotype frequencies of approximately 39% for GG, 47% for GA, and 14% for AA in the general Caucasian population [26,32].

91.4  Modeling and Clinical Applications 91.4.1 Interpretive Guidance of PerMIT:Warfarin The application of PGx diagnostics to warfarin therapy is hindered by the absence of clear guidance on whether and how genotyping may be used to improve patient therapy. The Personalized Medicine Interface (PerMIT:Warfarin) applies PGx modeling as a method for the interventional application of CYP2C9 and VKORC1 genetic diagnostics to individually tailored warfarin dosing and evaluation of therapeutic response. PerMIT:Warfarin calculates a warfarin maintenance dose estimate based on a multivariate equation that accounts for the effects of CYP2C9 and VKORC1 genotypes [33]. Then, based on the relationship between CYP2C9 and warfarin elimination half-life, PerMIT models the influence of repeated dosing on plasma drug concentration. This model provides guidance during the transition from induction to maintenance therapy and limits the potential for misinterpretation of INR measurements by clearly displaying the relationship between a patient’s dosing regimen and their progress toward steady state.

91.4.2 Estimation of Maintenance Dose The PGx panel of CYP2C9 and VKORC1 (−1639 G > A) accounts for both the pharmacokinetic and pharmacodynamic aspects of warfarin therapy. While CYP2C9 sets the rate of drug accumulation and elimination, VKORC1 sets the amount, or effective concentration required to achieve therapeutic success. As indicated above, together, the two genes account for approximately 35–40% of the variability in warfarin dose requirement. Even with this improvement, the majority of variability is unaccounted for with genotyping alone. Several recent multivariate analyses, like the one presented in Table 91.1, have shown that the addition of patient characteristics such as age, gender, height, weight, and other medications to CYP2C9, VKORC1, and/or other genomic information accounts for approximately 50–60% of warfarin dose variability [9,21,22,34,35]. However, the study by Sconce et al. was the first to promote the use of a published regression equation that included both CYP2C9 and VKORC1 as “a new dosing regimen” [9]. These types of mathematical algorithms may be used currently to estimate an individual patient’s maintenance dose requirement, typically to within 1 mg/day of the actual optimal dose [36]. It is important to note that the maintenance dose estimates that can be achieved with an algorithm approach are not expected to replace standard loading induction therapy practices at this time. Application of a genotype-guided maintenance dose at the onset of therapy could result in a long lag before the plasma concentration accumulates to the therapeutic level (dictated by VKORC1) and reaches steady state (dictated by CYP2C9) Figure 91.6. This would result in a significant risk that the onset of anticoagulation would be delayed, particularly in patients requiring acute therapy. Delayed anticoagulation could lead to thrombosis and/or a misinterpretation by the physician to prematurely increase the dose, leading to a possible overshoot of the target INR. Support for standard initial doses was demonstrated by a study in 2004 which confirmed that significant differences in dose requirements based on CYP2C9 genotype do not diverge until day four [19]. Therefore, a physician who needs to start a patient on warfarin in the emergent setting can do so regardless of the patient’s genotype. When results of genetic testing are not immediately available, our recommended scenario is that patients begin therapy based on standard induction protocols (e.g., 5 mg/day) with careful INR monitoring for the first 3–4 days. Samples for genotyping should be collected and sent to laboratory on the first

91-7

Computational Methods and Molecular Diagnostics in Personalized Medicine

TABLE 91.1  Calculated Estimation of Warfarin Maintenance Dose Based on Clinical and Genetic Attributes of Individual Patients Predictor(s)

Regression Equation

Age Sex Weight VK3673 2C9* Full model (all variables)

Model P-value

R2

0.0003 0.0024

log(D) = 2.870 − 0.020 (Age) log(D) = 1.276 + 0.415 (Sex) log(D) = 0.298 + 0.006 (Weight) log(D) = 1.349 − 0.426 (VK3673-M) + 0.426 (VK3673-W) log(D) = 1.659 − 0.248(2C9*2) − 0.625 (2C9*3) log(D) = 1.35 − 0.008 (Age) + 0.116 (Sex) + 0.004 (Weight) − 0.376 (VK3673-M) + 0.271 (VK3673-W) − 0.307 (2C9*2) − 0.318 (2C9*3)

0.18 0.13 0.28 0.27 0.22 0.61