Bone Remodeling Process: Mechanics, Biology, and Numerical Modeling [1 ed.] 0323884679, 9780323884679

Table of contents :
Front Cover
Bone Remodeling Process
Copyright Page
Contents
Introduction
1 Bone multiscale mechanics
Abbreviations
1.1 Bone multiscale and hierarchical organization
1.1.1 Bone elementary components
1.1.2 Structural components level
1.1.3 Arrays and array patterns levels
1.1.4 Superstructure level
1.1.5 Material patterns level
1.1.6 Tissue elements level
1.1.7 Tissue and the organ (whole bone) levels
1.1.7.1 Cortical bone tissue
1.1.7.2 Trabecular bone tissue
1.2 Cortical bone macromechanical properties
1.2.1 Preparation of bones samples for handling
1.2.2 Preparation of bone samples for mechanical testing
1.2.3 Cortical bone characteristics
1.2.4 Cortical bone ailments
1.2.5 Genetic disorders
1.2.6 Triggered bone ailments
1.2.7 Fractures
1.2.8 Osteoporosis
1.3 Bones as a composite structure
1.4 Concluding remarks
References
2 Bone remodeling biology
Abbreviations
2.1 Bone cells
2.1.1 Osteoblasts
2.1.2 Osteoclasts
2.1.3 Osteocytes
2.1.4 Reversal cells
2.1.5 Bone lining cells
2.2 Bone remodeling cycle
2.2.1 Activation phase
2.2.2 Resorption phase
2.2.3 Reversal phase
2.2.4 Formation phase
2.2.5 Termination phase
2.3 Bone cell interactions
2.3.1 Effects of osteoblasts on osteoclasts
2.3.2 Effects of osteoclasts on osteoblasts
2.3.3 Bidirectional regulations between osteoblasts and osteoclasts
2.3.4 Osteocyte contribution to the osteoblasts and osteoclasts
2.3.5 Reversal cell contribution to the osteoblast-osteoclast interplay
2.3.6 Lining cell contribution to the osteoblast-osteoclast interplay
2.3.7 Bone matrix contribution to the osteoblast-osteoclast interplay
2.3.8 Signals to and from other marrow components
2.4 Factors influencing bone from a biological point of view
2.4.1 Age1
2.4.2 Sex steroids
2.4.3 Alcohol
2.4.4 Body size
2.5 Concluding remarks
References
3 Bone diseases and associated therapeutic solutions
Abbreviations
3.1 Metabolic bone diseases
3.1.1 Osteoporosis
3.1.1.1 Clinical features of osteoporosis
3.1.1.2 Etiology of osteoporosis
3.1.1.3 Diagnosis of osteoporosis
3.1.1.4 Management of osteoporosis
3.1.2 Rickets
3.1.2.1 Clinical features of rickets
3.1.2.2 Etiology of rickets
3.1.2.3 Diagnosis of rickets
3.1.2.4 Management of rickets
3.1.3 Osteomalacia
3.1.3.1 Clinical features of osteomalacia
3.1.3.2 Epidemiology of osteomalacia
3.1.3.3 Diagnosis of osteomalacia
3.1.3.4 Management of osteomalacia
3.1.4 Paget disease of bone
3.1.4.1 Clinical features of Paget disease of bone
3.1.4.2 Etiology of Paget disease of bone
3.1.4.3 Diagnosis Paget disease of bone
3.1.4.4 Management of Paget disease of bone
3.1.5 Osteogenesis imperfecta
3.1.5.1 Clinical features of osteogenesis imperfecta
3.1.5.2 Etiology of osteogenesis imperfecta
3.1.5.3 Diagnosis of osteogenesis imperfecta
3.1.5.4 Management of osteogenesis imperfecta
3.2 Multiple myeloma
3.2.1 Clinical features of multiple myeloma
3.2.2 Etiology of multiple myeloma
3.2.3 Diagnosis of multiple myeloma
3.2.4 Management of multiple myeloma
3.3 Recent rare case reports
3.4 Concluding remarks
References
4 Bone remodeling mathematical models
Abbreviations
4.1 Bone remodeling in vitro
4.2 Mathematical modeling in bone remodeling
4.2.1 Mechanical models
4.2.1.1 Isotropic models
4.2.1.2 Anisotropic models
4.2.2 Biological models
4.2.3 Biomechanical models
4.2.4 Mechanobiological models
4.3 Modeling of bone remodeling during treatments
4.4 Conclusion and remarks
References
5 Bone and bone remodeling finite element modeling
Abbreviations
5.1 Finite element modeling healthy bone
5.2 Finite element modeling of pathologic bone
5.3 Finite element method improvement and validation studies
5.4 Finite element modeling of bone remodeling
5.5 Concluding remarks
References
6 Bone remodeling: analysis, discussion, and perspectives
Abbreviations
6.1 Analysis and discussion of the current state
6.2 Toward a bone diseases modeling via bone remodeling
6.2.1 Mathematical models treating bone diseases
6.2.2 Toward a bone diseases treatments modeling
6.2.2.1 Osteoporosis
6.2.2.2 Paget’s disease
6.2.2.3 Osteogenesis imperfecta
6.2.2.4 Cancer-associated bone diseases
6.2.2.4.1 Treatment for metastatic breast cancer
6.2.2.4.2 Treatment for metastatic prostate cancer
6.2.2.4.3 Treatment for multiple myeloma
6.3 Conclusion remarks
References
Conclusion
Index
Back Cover

Citation preview

Bone Remodeling Process Mechanics, Biology, and Numerical Modeling

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Bone Remodeling Process Mechanics, Biology, and Numerical Modeling

Rabeb Ben Kahla Laboratoire de Syste`mes et de Me´canique Applique´e (LASMAP), Ecole Polytechnique de Tunis Universite´ De Carthage, La Marsa, Tunisie Laboratoire de Me´canique Applique´e et Inge´nierie (LR-MAI), Ecole Nationale d’Inge´nieurs de Tunis Universite´ Tunis El Manar, Tunis, Tunisie

Abdelwahed Barkaoui Laboratoire des Energies Renouvelables et Mate´riaux Avance´s (LERMA), Universite´ Internationale de Rabat, Rabat-Sala El Jadida, Morocco

Academic Press is an imprint of Elsevier 125 London Wall, London EC2Y 5AS, United Kingdom 525 B Street, Suite 1650, San Diego, CA 92101, United States 50 Hampshire Street, 5th Floor, Cambridge, MA 02139, United States The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, United Kingdom Copyright © 2021 Elsevier Inc. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions. This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein). Notices Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary. Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility. To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein. British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress ISBN: 978-0-323-88467-9 For Information on all Academic Press publications visit our website at https://www.elsevier.com/books-and-journals

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Contents Introduction........................................................................................................................................... ix

CHAPTER 1 Bone multiscale mechanics ................................................................. 1 Abbreviations.............................................................................................................. 1 1.1 Bone multiscale and hierarchical organization ......................................................... 1 1.1.1 Bone elementary components.......................................................................... 3 1.1.2 Structural components level ............................................................................ 6 1.1.3 Arrays and array patterns levels ...................................................................... 7 1.1.4 Superstructure level ....................................................................................... 10 1.1.5 Material patterns level ................................................................................... 11 1.1.6 Tissue elements level ..................................................................................... 12 1.1.7 Tissue and the organ (whole bone) levels..................................................... 14 1.2 Cortical bone macromechanical properties ............................................................. 27 1.2.1 Preparation of bones samples for handling ................................................... 28 1.2.2 Preparation of bone samples for mechanical testing .................................... 30 1.2.3 Cortical bone characteristics.......................................................................... 31 1.2.4 Cortical bone ailments ................................................................................... 32 1.2.5 Genetic disorders............................................................................................ 32 1.2.6 Triggered bone ailments ................................................................................ 33 1.2.7 Fractures ......................................................................................................... 34 1.2.8 Osteoporosis ................................................................................................... 34 1.3 Bones as a composite structure................................................................................ 34 1.4 Concluding remarks ................................................................................................. 42 References................................................................................................................. 42

CHAPTER 2 Bone remodeling biology.................................................................... 49 Abbreviations............................................................................................................ 49 2.1 Bone cells ................................................................................................................. 51 2.1.1 Osteoblasts ..................................................................................................... 51 2.1.2 Osteoclasts...................................................................................................... 53 2.1.3 Osteocytes ...................................................................................................... 53 2.1.4 Reversal cells ................................................................................................. 55 2.1.5 Bone lining cells ............................................................................................ 55 2.2 Bone remodeling cycle............................................................................................. 56 2.2.1 Activation phase............................................................................................. 56 2.2.2 Resorption phase ............................................................................................ 56 2.2.3 Reversal phase................................................................................................ 56

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2.2.4 Formation phase............................................................................................. 57 2.2.5 Termination phase.......................................................................................... 57 2.3 Bone cell interactions............................................................................................... 58 2.3.1 Effects of osteoblasts on osteoclasts ............................................................. 58 2.3.2 Effects of osteoclasts on osteoblasts ............................................................. 60 2.3.3 Bidirectional regulations between osteoblasts and osteoclasts ..................... 62 2.3.4 Osteocyte contribution to the osteoblasts and osteoclasts ............................ 64 2.3.5 Reversal cell contribution to the osteoblast-osteoclast interplay.................. 65 2.3.6 Lining cell contribution to the osteoblast-osteoclast interplay ..................... 66 2.3.7 Bone matrix contribution to the osteoblast-osteoclast interplay................... 66 2.3.8 Signals to and from other marrow components ............................................ 67 2.4 Factors influencing bone from a biological point of view...................................... 70 2.4.1 Age1 ............................................................................................................... 70 2.4.2 Sex steroids .................................................................................................... 70 2.4.3 Alcohol ........................................................................................................... 71 2.4.4 Body size........................................................................................................ 72 2.5 Concluding remarks ................................................................................................. 72 References................................................................................................................. 72

CHAPTER 3 Bone diseases and associated therapeutic solutions....................... 89 Abbreviations............................................................................................................ 89 3.1 Metabolic bone diseases........................................................................................... 90 3.1.1 Osteoporosis ................................................................................................... 90 3.1.2 Rickets ............................................................................................................ 95 3.1.3 Osteomalacia .................................................................................................. 98 3.1.4 Paget disease of bone................................................................................... 101 3.1.5 Osteogenesis imperfecta .............................................................................. 104 3.2 Multiple myeloma .................................................................................................. 109 3.2.1 Clinical features of multiple myeloma ........................................................ 109 3.2.2 Etiology of multiple myeloma..................................................................... 110 3.2.3 Diagnosis of multiple myeloma................................................................... 110 3.2.4 Management of multiple myeloma.............................................................. 112 3.3 Recent rare case reports ......................................................................................... 113 3.4 Concluding remarks ............................................................................................... 117 References............................................................................................................... 118

CHAPTER 4 Bone remodeling mathematical models........................................... 125 Abbreviations.......................................................................................................... 125 4.1 Bone remodeling in vitro ....................................................................................... 125 4.2 Mathematical modeling in bone remodeling......................................................... 127 4.2.1 Mechanical models ...................................................................................... 127

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4.2.2 Biological models ........................................................................................ 133 4.2.3 Biomechanical models ................................................................................. 139 4.2.4 Mechanobiological models .......................................................................... 143 4.3 Modeling of bone remodeling during treatments .................................................. 152 4.4 Conclusion and remarks......................................................................................... 160 References............................................................................................................... 161

CHAPTER 5 Bone and bone remodeling finite element modeling ...................... 165 5.1 5.2 5.3 5.4 5.5

Abbreviations.......................................................................................................... 165 Finite element modeling healthy bone .................................................................. 166 Finite element modeling of pathologic bone......................................................... 179 Finite element method improvement and validation studies ................................ 185 Finite element modeling of bone remodeling ....................................................... 193 Concluding remarks ............................................................................................... 201 References............................................................................................................... 201

CHAPTER 6 Bone remodeling: analysis, discussion, and perspectives............. 207 Abbreviations.......................................................................................................... 207 6.1 Analysis and discussion of the current state.......................................................... 207 6.2 Toward a bone diseases modeling via bone remodeling ...................................... 210 6.2.1 Mathematical models treating bone diseases .............................................. 210 6.2.2 Toward a bone diseases treatments modeling............................................. 212 6.3 Conclusion remarks................................................................................................ 215 References............................................................................................................... 215 Conclusion ......................................................................................................................................... 219 Index .................................................................................................................................................. 221

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Introduction

The skeletal system plays an essential support role for the entire human body. It supports the gravity forces and the stresses produced by daily activities. The bone thus optimizes and adapts its mass and geometry through the remodeling process. Mechanically, bone is a living, nanocomposite material with a complex hierarchical structure that gives bone remarkable mechanical properties: light weight, high rigidity, toughness, and fracture resistance. The imbalance in bone remodeling is responsible for certain bone pathologies such as osteoporosis and Paget’s disease. In particular, osteoporosis induces a loss of bone mass as well as a reduction in the quality of bone tissue (microarchitecture). The architecture and the structural properties of the bone are thus degraded, which causes a decrease in bone quality and therefore, an increase of fractures risk. Throughout life, bone is constantly remodeled through the complementary resorption and formation activities, establishing what is known as bone remodeling process (Fig. 1). This process requires a highly coordinated regulation in time and space to consistently maintain bone amount and quality. This coordination mainly incorporates bone-resorbing osteoclasts and bone-forming osteoblasts, which are the major two actors in the remodeling event. The delicate balance between the resorbed bone amount and the subsequent deposited amount requires a strict coordination of the resorption and the formation activities, allowing to generate the appropriate osteoblast number in

FIGURE 1 Cartoon representing the bone remodeling process with the osteoblast-mediated bone formation and the osteoclast-mediated bone resorption driven by osteocytes. Bahia, M. T., Hecke, M. B., Mercuri, E. G. F., & Pinheiro, M. M. (2020). A bone remodeling model governed by cellular micromechanics and physiologically based pharmacokinetics. Journal of the Mechanical Behavior of Biomedical Materials, 104, 103657.

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Introduction

remodeling area, which is referred to as the coupling mechanism. Moreover, the coordination between osteoblast and osteoclast activities involves other cells from diverse origins, in addition to several hormones, cytokines, and growth factors that tightly interlink osteoblast- and osteoclastlineage cells through a complex interaction network throughout the remodeling cycle. The remodeling process is an integral part of the calcium homeostatic system and provides a crucial mechanism for old bone removal, as well as for bone damage repair and adaptation to physical stress, allowing to maintain the skeleton mechanical integrity. The remodeling process manifests at anatomically distinct sites known as bone multicellular units, each unit functioning asynchronously and independently from other units throughout the skeleton. It should however be noted that the bone multicellular units in cortical and in trabecular bones greatly differ in their structure, as well as in the way the bone is removed and replaced. The concept of bone remodeling compartment consists of initiating the remodeling process within a canopy, and intercellular communication occurs in this compartment among the component bone cells, from vascular and endothelial cells, and probably from immune cells reaching the remodeling sites via the blood supply. Bones occupy about 15% of the whole body weight, a fraction that does not deserve any consequence interpretation. Interestingly, human body ambulation, ventilation, and protection are primarily associated with bone, which highlights bone mechanical function. Therefore bone represents a structural material with mechanical characteristics resembling any other material with a mineralbased structure, even if the discovery process and the investigation of the relation between microcomponents and bulk material is opposite for the two types of material. After more than 2000 years of improvements, we now have enough knowledge of the right components to make a high quality steel, but still do not know yet how to efficiently treat bone metabolic disorders and age-related diseases, including osteoporosis. Steel is inert material, whereas bone is a living material. Steel is a mineral material, whereas bone is a biological material. Steel structure alters with higher mechanical loads, whereas bone strengthens with higher mechanical loads. All of these are differential features clearly show that bone mechanics do not necessarily follow the same classic rules of continuum damage mechanics as the remaining structures. This goes back to several poorly known factors and mechanisms, according to which bone structure is maintained. By browsing the literature, one can find numerous studies attempting to better clarify these mechanisms and identify the origin of lunching the remodeling phenomenon, which might hopefully be tantamount to unlock the treatment stalemate of bone metabolic disorders, if such treatments exist. Except for neurons, bone cells are no different from the other body cells that are in constant renewing until the process dramatically seizes up. So, characterization of bone mechanical behavior is not dependent on the bone age, as bone is always “young,” but on the age of the cell division process, in addition to biological disorders and mechanical disruptions bone is subjected to. Besides shape and appearance, bone is often subdivided into two main categories: cortical bone, robust and compact, and trabecular bone, spongy and flexible, with plenty of biological processes taking places and some not yet elucidated. The molecular mechanisms of osteoblast
osteoclast interplay, which occur at several differentiation stages, represent one of the main issues in bone cell biology. This second chapter aims to set up an overall image of the remodeling process and the coupling mechanisms ensuring the preservation of bone biomechanical integrity. Therefore, the first part of the second chapter deals with the origins, the function, and the differentiation process of bone cells; the second part reviews the

Introduction

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sequential remodeling phases within the basic multicellular unit; the third part focuses on the actors and factors of the intercellular signaling pathways and coupling mechanism; and the fourth part presents the factors affecting bone biology. When bone biological mechanisms are disturbed, metabolic diseases manifest. This disease category encompass a large group of disorders related to alterations in mineral homeostasis. Despite their quite common occurrence, a lot still needs to be investigated. This has led to develop diverse diagnostic procedures, involving physical examination, family history, and imaging investigation. In clinical practice, metabolic diseases are often silent until bone fractures, which represent the ultimate complication of such pathologic conditions. Still, clinical history of back pain and nonspecific radiological features may reflect the development of one of them. At this stage, understanding the different mechanisms and specific features of each one of these potentially debilitating conditions is crucial to provide the appropriate therapeutic solution. Bone may also be subjected to malignancies and the cancer cells may originate from the bone tissue or marrow, or may metastasize from a tumor developed elsewhere in the body. In these cases, the most common treatment options consist of surgery, chemotherapy, and radiation therapy or their combinations, according to type and extent level of the tumor. However, specific cases may involve both a tumor and a metabolic disease. Therefore the investigation and the appropriate therapeutic solutions may require diverse types of testing and imaging. To achieve this, researchers had to start by investigating physiologic bone behavior and adaptation processes in response to the surrounding physiologic and mechanical environment. This has been a subject of research and discussion for more than a century. In 1892, Julius Wolff enunciated that bone architecture is directly associated with the principal stress directions. This statement is currently known as Wolff’s law, and represents the first explicit statement that directly related bone microstructure and mechanical loading. This law established the tendency of bone trabeculae to be aligned with the principal stress directions. Since, mathematical description of bone behavior has enjoyed a spectacular expansion. At first, most models were phenomenological or purely mechanical, lacking biological grounding. Afterwards, models started gaining insight into bone remodeling biological processes and the relationship between them and the mechanical environment. Concepts, such as bone multicellular unit activity, metabolic activity, mineralization process, and damage accumulation have been introduced and included in the mathematical models. To better visualize and interpret the latter, computational techniques and modalities have been involved in the investigation of bone biomechanics. Computational modeling and numerical simulation of the musculoskeletal system can represent an interesting tool to address biomechanical questions, particularly those targeting bone biomechanical behavior, allowing to provide information that is not amenable to direct measurements, such as bone strength and joint loading. This type of information is required for several clinical applications, including designing assistive devices, analyzing pathology, such as osteoporosis and osteoarthritis, designing implants, and preventing fractures. In recent years, partition of unity methods, explicitly using finite element (FE) mesh, has become popular owing to its easy applicability. The FE method is one of the most used numerical analysis techniques based on FE mesh, allowing to obtain approximate solutions to a wide range of engineering problems. During the past years, the FE method has experienced a phenomenal expansion in the field of bone biomedical engineering, owing to its flexibility and diversity as an analysis tool, but also because it easily handles complex and evolving cellular domains, and can be generalized to multidimensions with little complication.

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Particularly, the FE method has been widely used to analyze and predict bone mechanical behavior, in physiologic and pathologic conditions, based on mathematical models describing the cellular mechanisms governing the remodeling process, including more factors and actors each time, with aim of providing a more realistic description of cell interactions. This book provides a literature review of bone remodeling process, with the aim of drawing a link between the key factors in bone remodeling mechanical and biological process, in order to provide an overall image of the current knowledge in the field of bone biomechanics, and highlight the limitations of many of the developed prospection procedures. Hopefully, the bone may help gathering data for a better progress in bone heath and healing. Thus the first chapter of the book focuses on bone multiscale and hierarchical organization, along with mechanical properties in cortical, trabecular, and the whole bone. The second chapter establishes an overall image of the current knowledge about bone remodeling process and cell dynamics, in addition to the complex communication network between the diverse remodeling actors, based on overwhelming control evidence revealed over recent years. The third chapter deals with bone metabolic diseases and cancer types, with the currently revealed features, the etiology, the diagnostic measurements and the existing therapeutic solution for each condition. The fourth chapter collects the main mathematical models developed to describe bone mechanical, biological, biomechanical, and mechanobiological behaviors, in physiologic and pathologic states. The fifth chapter represents a review of the FE modeling attempts to investigate and analyze bone behavior. Finally, the sixth chapter summarizes the collective data from the different fields, with a critical presentation of the limitations and the requirements for each field.

CHAPTER

Bone multiscale mechanics

1

Abbreviations ACP ARC ATP BMP BMU BRC CLB CRISPR GAGs HA HCs HRpQCT HSCs IR M-CSF MSCs NCPs OPG pQCT QCT PTH NPY RANK RGD RPI SERT SEM SSI VC VMH μCT

amorphous calcium phosphate arcuate nucleus adenosine triphosphate bone morphogenetic protein basic multicellular unit bone remodeling compartment circumferential lamellar bone clustered regularly interspaced short palindromic repeats proteoglycans hydroxyapatite Haversian canals high resolution peripheral quantitative computed tomography hematopoietic stem cells infrared macrophage colony stimulating factor mesenchymal stem cells noncollagenous proteins osteoprotegerin peripheral quantitative computed tomography quantitative computed tomography parathyroid hormone neuropeptide Y receptor activator of nuclear factor kappa beta arginine-glycine-aspartic reference point indentation serotonin transporter scanning electron microscopy strain stress index Volkman canals ventromedial hypothalamus microcomputed tomography

1.1 Bone multiscale and hierarchical organization Following the hierarchical scheme proposed by Weiner and Wagner (1998), representing seven hierarchical organization levels of the lamellar bone, Reznikov et al. (2014) adapted the same scheme while Bone Remodeling Process. DOI: https://doi.org/10.1016/B978-0-323-88467-9.00005-9 © 2021 Elsevier Inc. All rights reserved.

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Chapter 1 Bone multiscale mechanics

taking into account the existence of ordered and disordered materials (Fig. 1.1). The new resulting scheme is mainly related to the lamellar bone, as the latter is the most abundant structural type found in the adult skeleton. According to this figure, bone is arbitrarily subdivided into nine hierarchical levels, which only applies to lamellar bone. Some other types of bone materials, such as woven bone, could well be divided into fewer hierarchical levels. Still, more work is definitely required to confirm the existence of both ordered and disordered materials in other bone types. Besides, levels 1, 2 and 3 are assumed to be common to all bone types, which also requires further investigations. Fig. 1.1 illustrates the classification proposed by Reznikov et al. (2014), that describes the set of bone scale levels, taking a human femur as an example: (I) longitudinally cut femur, (II) SEM of trabecular and cortical tissue, (III) a single trabeculae and osteon, (IV) lamella, (V) fibular organizations, (VI) mineralized collagen fibril (VII) collagen molecules and mineral nanostructure and (VIII) atomic structure of the main bone components. Table 1.1 summarizes different classifications of the multiscale structure of the bone. Each of the multiscale structure nine levels proposed by Reznikov et al. (2014) is elaborated separately below.

FIGURE 1.1 Hierarchical organization levels of the lamellar bone.

Table 1.1 Classification and definition of the hierarchical levels of bone proposed in different studies. Study

Level

Main components

Reznikov et al. (2014)

Components Structural components Arrays Arrays patterns Superstructure Material patterns Tissue elements Tissue Organ

Collagens, mineral, water, NCPs Mineralized collagen fibrils Mineralized collagen fibrils ordered array Unidirectional array, fanning array, limited alignment Bundles Lamellar bone, Parallel-fibered bone Trabecula, osteon, fibrolamellar unit Trabecular bone, compact bone Whole bone

1.1 Bone multiscale and hierarchical organization

3

Table 1.1 Classification and definition of the hierarchical levels of bone proposed in different studies. Continued Study

Level

Main components

Barkaoui et al. (2014)

Nanoscale Ultrastructure Microscale Mesoscale Macroscale Level 1

Mineral, collagen, water, noncollagenous proteins Microfibril, fibril, fiber Lamellas, osteon, trabecular element Cortical and trabecular bones Whole bone Isolated crystals and part of a collagen fibril with the triple helix structure Mineralized collagen fibrils The array of mineralized collagen fibrils with a cross-striation periodicity of nearly 60
70 nm Two fibril array patterns of organization as found in the zebrafish skeleton bone The lamellar structure in one vertebra A vertebra Skeleton bone Fibril and molecules of collagen, mineral components Layers Individual trabeculae and osteons Cortical or trabecular and osteons bone representative of both subtypes Molecules Fibrils of collagen and minerals Collagen fibers Patterns of the fibers (mature bone vs interstitial bone) Osteons Cortical and trabecular bone Whole bone Molecular structure of the different elements Fibrilar collagen and mineral components Layers Individual osteons and trabeculae Cortical and trabecular bone

Cui et al. (2007)

Level 2 Level 3 Level 4

An and Draughn (1999)

Weiner and Wagner (1998)

Rho et al. (1998)

Level 5 Level 6 Level 7 Nanostructure Laminar level Tissue level Architectural level Whole bone level Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Level 7 Sub-nanostructure Nanostructure Sub-microstructure Microstructure Macrostructure

1.1.1 Bone elementary components At this coarse description level, the mineral and biomolecular components of both the ordered and disordered materials are similar. The ordered material mainly comprises type I collagen, mineral carbonated HA and water, in addition to minor amounts of other collagen types, NCPs and GAGs. The disordered material mainly contains type I collagen and carbonated HA, in addition to

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Chapter 1 Bone multiscale mechanics

relatively large amounts of NCPs, GAGs and water, forming what can be loosely called “ground mass.” Yet, the specific molecular components of the disordered material should be the subject of deeper studies (Reznikov et al., 2014). Mineral phase: The mineral phase of mature bone is made up of carbonated HA in the form of thin (Fig. 1.2) plate-shaped crystals. At the atomic level, the mature carbonated HA crystals are relatively disordered, in part because of the highly disordered precursor phase, from which the crystals form, the several included additives, such as carbonate, that these crystals contain, and the very thin thickness characterizing the mature crystals, resulting in a large surface-to-bulk ratios. The crystal surface is known to be relatively disordered compared to the bulk (Reznikov et al., 2014). The size and shape of HA crystals were observed using transmission electron microscopy (TEM) (Landis et al., 1996; Weiner & Traub, 1992) and small angle X-ray scattering (SAXS) (Fratzl et al., 1992; Paris et al., 2000). The majority of research studies considered that the HA molecules were gathered in the form of plaques (Fratzl et al., 2004; Jackson et al., 1978; Landis et al., 1993; Rubin et al., 2003). A range of geometric dimensions is given to HA crystals. The thickness varies from 2 to 7 nm, the length from 15 to 200 nm and the width from 10 to 80 nm (Eppell et al., 2001). An average size is accepted for almost all researchers, taking its dimensions as follows: 50 nm  25 nm  3 nm (Rho et al., 1998). The largest dimension of the mineral is oriented along the mineralized collagen fibril axis (Rubin et al., 2003). Several experimental and numerical studies have been carried out to define the mechanical behavior of HA and to determine its mechanical properties (Barkaoui et al., 2015; Katz & Ukraincik, 1971; Lees & Rollins, 1972; Zamiri & De, 2011). Table 1.2 groups the elastic

FIGURE 1.2 Plate-shaped crystals of bone HA: (A) SEM scanning electron microscopy of HA particles showing the diversity of their shapes and sizes, (B) SEM of HA particles showing their porous structure, (C) The arrangement of the different atoms of HA (Peccati et al., 2018), (D) A medium height is accepted for almost all researchers: 50 nm  25 nm  3 nm.

1.1 Bone multiscale and hierarchical organization

5

Table 1.2 Elastic mechanical properties of the mineral HA (Barkaoui et al., 2015). References

Young’s modulus (GPa)

Poisson’s ratio

Shear modulus(GPa)

Weiner and Wagner (1998) Katz and Ukraincik (1971) Zamiri and De (2011) Cowin and Telega (2003) Currey (1969) Lees and Rollins (1972)

114 165 150.38 150 170 —

0.30 2.28 0.45 0.27 0.33 0.23

44.5 — — — — 33

FIGURE 1.3 Collagen triple helix structure: (A) crystal structure of a collagen triple helix, (B) ball-and-stick image of a segment of collagen triple helix, (C) stagger of the three strands in the segment in panel (Bella et al., 1994).

mechanical properties of the mineral reported in the literature. The modulus of elasticity of HA crystals varies from 111 to 170 GPa and its Poisson’s ratio from 0.23 to 0.45. Collagen: Type I collagen, made up of the triple helical molecules (Fig. 1.3), is the most abundant protein in mature bone, despite the existence of other collagen types, such as types III, VI and V. The staggered array structure of the triple helical molecules generates the formation of spaces, often referred to as holes, within the fibril. In bone, these holes are aligned to form thin extended slots, named grooves, in which the intrafibrillar crystals form. Based on the presence of the characteristic repeat structure in the collagen fibrils from both ordered and disordered materials, type I collagen is assumed to be a major component of both of these material types (Kraiem et al., 2018; Reznikov et al., 2014). Several studies on mechanical behavior (Buehler & Wong, 2007; Buehler et al., 2008) and mechanical properties (An et al., 2004; Sun et al., 2004) of collagen molecules have been realized. Sasaki and Odajima (1996) studied the stress-strain behavior of collagen in the case of tensile loading, using the X-ray diffraction technique. They deduced that in its hydrated state, collagen has a linear behavior and its Young’s modulus has been estimated to be between 2.8 and 3.0 GPa. Sun

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Chapter 1 Bone multiscale mechanics

FIGURE 1.4 Mechanical behavior of collagen: (A) Force displacement curve of a collagen molecule (B) enlargement of the first regime of the displacement force curve characterized by entropic elasticity (Buehler & Wong, 2007).

et al. (2004) studied its behavior using an optical technique, finding that the modulus of elasticity of collagen ranges from 0.35 to 12. Buehler and Wong (2007) isolated and tested a single molecule of collagen under tensile loading and suggested that the collagen behaves nonlinearly following four regimes (Fig. 1.4). Water: Water is an essential component of bone and is present in various types that should also be integrated into the different hierarchical organizational levels. At level I, designating the crystal level, water bounds to the crystal surface. This is particularly prevalent when this surface comprises a disordered ACP-like layer. The absence or the partial presence of mineral is associated to the presence of water molecules between the collagen triple helical molecules. Interestingly, dehydration of lamellar bone causes a more pronounced contraction of the lamellae in the direction perpendicular to the lamellar boundary compared to the orthogonal direction, which indicates the presence of liquid water in the collagen channels, even in mineralized bone. Unbound water is likely to be present in the canaliculi, lacunae, and blood vessels (Reznikov et al., 2014). Noncollagenous proteins and proteoglycans: Numerous noncollagenous proteins are present in bone, but most of them are not unique to it. However, several bone-related GAGs, such as decorin and biglycan, and a series of bone-related NCPs, such as osteocalcin, osteonectin, matrix gla protein, alkaline phosphatase, RGD and BAG-75 containing proteins, including bone sialoprotein and osteopontin, are thought to be crucial factors in bone formation. Surprisingly, little is known about the precise specific NCP macromolecule locations in bone and their specific functions (Reznikov et al., 2014).

1.1.2 Structural components level The collagen molecules are organized into fibrils and may well be oval shaped. Crystals of carbonated HA nucleate from a disordered precursor phase within the gaps inside the fibril, and extend into the overlap zones while growing. This leads to the production of the mineralized collagen fibril that contains layers of plate-shaped crystals that span the fibril cross-section. Therefore, the fibril has no radial symmetry, but holds an essentially orthotropic crystalline structure (Fig. 1.5).

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FIGURE 1.5 Mineralized collagen fibril: (A) TEM illustrating the collagen fibrils seen in the longitudinal section, (B) collagen molecules and mineral HA structural organization (Facca et al., 2010).

Mineralized collagen fibrils represent the major ordered material component. The crystal c-axes are well aligned with the collagen fibril axis. Mineralized collagen fibrils are also present in the disordered material, and together with the abundant ground mass and the canaliculi, these fibrils contain only one of the major constituents. In the ordered material, the collagen fibrils are intimately associated with most of the crystals, whether in the interior or on the surface. In the disordered material, crystals were observed both within and between the collagen fibrils. Other studies also concluded the existence of crystals within and between the collagen fibrils, but did not notice the existence of the disordered material, which led to assume that this intrafibrillar and extrafibrillar crystal motif characterizes all lamellar bone types (Reznikov et al., 2014). The mechanical behavior of mineralized collagen fibril is sensitive to several factors like the geometry and the mechanical properties of its various components (Hamed et al., 2010). The study of the mechanical behavior and the determination of the mechanical properties of mineralized collagen fibril have been the subject of multiple experimental and numerical analyses. Experimental work has been carried out to estimate the mechanical properties of mineralized collagen fibril (Eppell et al., 2006; Van Der Rijt et al., 2006). Akiva et al. (1998) and Akkus (2005) have developed mechanical models to estimate the elastic orthotropic properties of mineralized collagen fibril. Nikolov and Raabe (2008) have proposed a homogenization method that models the elastic properties of the bone at a nanometric level. Ja¨ger and Fratzl (2000) proposed a geometric model of fibril. This model is a particular arrangement of HA crystals deposited inside of gap areas between collagen molecules (collagen matrix) (Fig. 1.5). It has been used in all the finite element models proposed for the bone modeling at the nanoscopic scale.

1.1.3 Arrays and array patterns levels In vitro, type I collagen fibrils showed a high tendency to self-assemble into arrays, with the fibril long axes aligned, whereas in vivo, the assembly process is complex, apparently starting in

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Chapter 1 Bone multiscale mechanics

osteoblast endoplasmic reticulum, then in compartments outside the cytoplasm, and finally moving to the extracellular space. The diameters of these arrays can vary from less than a micron to several microns and fibril arrays are only present in the ordered material (SV1). The majority of fibrils in the disordered material appear as individual fibrils and show little preferred orientation compared to the ordered material (Fig. 1.6). The fibril arrays may be organized in a variety of ways to form different patterns, which is effectively the first hierarchical level at which differences in structure in the ordered material appear between different bone types, and even within the same bone type. The simplest and most anisotropic pattern is essentially an extension of the single array with all the fibril axes aligned to much larger dimensions. This so-called unidirectional array pattern is common in lamellar bone, parallel-fibered bone and Sharpey’s fibers, in addition to tendon and other bone types. The fanning array is a second pattern in which the fibril array orientations vary in a gradational manner. This structural pattern has is common in lamellar bone and its formation in vitro was found to be associated with relatively high collagen concentrations. The disordered material can whether form thin layers between the aligned collagen fibril arrays, or form extensive layers, in which the collagen fibrils are mainly present as individual fibrils with no preferred spatial orientation. The spaces between these individual fibrils are filled with ground mass. This pattern reminisces woven bone, with a major difference regarding the individuality of the fibrils instead of randomly oriented arrays (Reznikov et al., 2014). Weiner and Wagner (1998) defined this level as “fibril array patterns.” Collagen fibril array organization patterns were observed in different bone types such as: parallel, disordered, plywoodlike and radial fibril arrays (Fig. 1.7).

FIGURE 1.6 Selected images of ordered and disordered materials in lamellar bone from stacks. Four pairs of images were taken from rat circumferential lamellar bone (A and A0 ), human cortical osteonal (B and B0 ) and circumferential lamellar bone (C and C0 ) and human trabecular lamellar bone (D and D0 ). Each pair was selected from one continuous volume and the two images in each pair are separated by 0.5
1.0 μm. Scale bars: 1 micron (Reznikov et al., 2014).

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FIGURE 1.7 Patterns of fibrils organization: SEM illustrations: (A) parallel array pattern, (B) femur disordered array patter, (C) tibia plywood-like lamellar bone, (D) human dentin radial array pattern (Weiner & Wagner, 1998).

In parallel with the observations made by Weiner and Wagner (1998), Rho et al. (1998) suggests the existence of collagen fiber, which is the assembly of collagen fibrils. The work of Fratzl (Fratzl & Weinkamer, 2007; Fratzl, 2008) and his coauthors confirm the existence of the collagen fibril. They worked a lot on its geometry, behavior, and mechanical properties.

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Chapter 1 Bone multiscale mechanics

FIGURE 1.8 The hierarchical structure of a self-assembled HA-collagen composite: (I) mineralized collagen fibril formed by collagen and HA in gaps zones (phase I), (II) mineralized collagen fibril with HA in gaps zones and between collagen molecules enveloped by Polycrystal of nano-HA (phase II) and (III) mineralized collagen fiber formed by collagen fibrils (Cui et al., 2007).

Cui et al. (Cui et al., 2007; Zhang et al., 2003) introduced a new concept of mineralized collagen fibril. They described the phases of mineralized collagen fibril formation and distinguished between two types of mineral HA (Fig. 1.8). The collagen fibrils are created by self-assembly of collagen triple helices, and the HA crystals are formed initially within the gap zones between the collagen molecules. The collagen fibril’s size should be about 4.0 mm based on the collagen molecule’s size which is 1.5 mm. The second phase of formation or growth of the collagen fibril consists of the development of HA crystals, in sheet form, on the surface to surround the mineralized collagen fibril (phase I) along its longitudinal axis (Cui et al., 2007).

1.1.4 Superstructure level In the ordered material, the 3D structure of human lamellar bone reveals the presence of unidirectional collagen fibril bundles. Within a single bundle, neighboring fibrils are mainly in register with respect to the repeating structure, with a tight and space filling fibril packing in the bundles. Thus, the fibrils form a highly anisotropic and cooriented array. These cylindrical arrays are aligned sideby-side to form extensive parallel bundle sheets and the sheets of differently oriented bundles stack in such a way that any other set of parallel bundles follows a similar orientation. Adjacent coaligned bundle sets have an angular offset of 40
80 degrees. A canonical orthogonal bundle organization has never been documented. However, bundles also include small amounts of ground mass and ordered collagen fibril arrays are intimately associated to proteoglycans (Reznikov et al., 2014). In human bone, the bundles are separated by thin disordered material layers that often include the osteocyte processes. Indeed, bundles in fibrolamellar bone are bounded by the thin disordered material layers. Yet, much remains to be learned about the structure, composition and function of these bundles. Fiber bundles were also observed in tendon and their presence was found to be intimately implicated in the intracellular synthesis and assembly of collagen. In some bones, bundle

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FIGURE 1.9 Reconstruction of part of an osteocyte and its associated canaliculi in human osteonal bone. Note that the kinks in the canaliculi (arrowheads) often occur when the bundles of ordered collagen fibril arrays (not visible in this image) change direction (Reznikov et al., 2014).

presence might reflect the way in which the cells produce, package and export collagen fibrils. Therefore, a special hierarchical level was included for collagen bundles. It should be noted that the term “bundle” is frequently fairly used in the bone literature. Bone types were classified according to bundles with varying properties and, in alveolar bone, there is a bone structural type named “bundle bone,” but it likely resembles the mineralized insertions of collagen fibers from the periodontal ligament (Reznikov et al., 2014). In the continuous disordered material, the combination of the embedded osteocyte lacunae and canaliculi, confined within the disordered material, and the material itself, containing the mineralized collagen fibrils and the ground mass, form what is called the superstructure. The lacunae and the canaliculi contain the osteocytes and the processes extending out from them, respectively. Thus, a tight structural relationship relates the collagen matrix arrangements and the osteocyte network organization. In human bone, the spaces between bundles are filled with the disordered material. Therefore, the canaliculi 3D geometry also reflects the overall bundle distribution. During bone formation, the spaces in which the ordered material is deposited are likely to be defined by the locations of the cell processes and their surrounding disordered material. The canalicular network 3D organization and a part of an osteocyte in osteonal bone are illustrated in Fig. 1.9.

1.1.5 Material patterns level This level refers to the materials or tissues forming an organ, such as bone. Since these materials result from cell activities and some of them also contain cell components, they are also referred to as tissues. Lamellar bone is the most common material that forms bone, whereas woven bone forms a material in its own right. This section focuses on discussing the materials/tissue types in bones (Reznikov et al., 2014).

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Chapter 1 Bone multiscale mechanics

Woven bone: The term “woven bone” is used in different ways. Woven bone is made of mineralized collagen fibril bundles, with a little or no preferred 3D orientation. This bone type may not present any higher hierarchical organization levels. It is rather a transient tissue type usually deposited during bone development and fracture repair, and appears to provide an optimal solution when a scaffold is required for subsequent formation of a more structured bone or for early callus formation stages during fracture healing. This is due to the relatively high speed with which it is deposited, in addition to its mechanical property similarity in all directions. Still, woven bone 3D structure needs to be more investigated (Reznikov et al., 2014). Lamellar bone: Lamellar bone, as its name implies, is made of a series of lamellae. Each lamella includes both the ordered material and the disordered material with its embedded canaliculi. The lamella contains differently oriented bundles of both unidirectional mineralized fibril arrays and fanning arrays, and the spaces separating these bundles are filled with the disordered material. The canaliculi embedded in the disordered material are generally aligned perpendicular to the lamellar boundary plane, and the crystal layers within an individual lamella likely have different orientations. Particularly, CLB is a primary bone type containing a series of lamellae that have a large radius of curvature and are all parallel to the forming cortical and trabecular bone surfaces. These lamellae are deposited on bone surface by osteoblast and removed by osteoclasts (bone remodeling process). Indeed, CLB is later replaced by secondary osteonal bone, and its presence on a bone surface indicates that this specific zone has not been remodeled. At the fibril organization level, no significant differences were revealed between CLB and osteonal bone 3D structures in human femur. The bone remodeling is a continuous process of resorption and formation of bone tissue during life time. the cells involved in this process are mainly osteocytes, osteoblasts and osteoclasts (Fig. 1.10).

1.1.6 Tissue elements level Lamellar bone is by far the most common structural element in mammalian bone. Furthermore, lamellar bone replaces woven bone during the remodeling process. The continued description of hierarchical organization levels is therefore confined to lamellar bone elements. According to bone formation time and location, the lamellae adopt many different structural motifs, besides the circumferential lamellar motif (Reznikov et al., 2014). Lamellar packets: The term “lamellar packets” refers to an assemblage of slightly differently oriented series of lamellae, which characterizes trabecular bone. Adjacent series truncate each other at low angles (Fig. 1.10E), owing to some lamellar bone removal. This is followed by new lamellar bone deposition to fill in the consequent resorption defect. Hence, the most superficially deposited lamellar packet is aligned with the trabecular bone strut surface, but is not necessarily aligned with the earlier surface, which reflects the adaptational history. Osteons: Osteons are often classified as primary or secondary osteons, and the latter are also referred to as Haversian systems (Fig. 1.10C). Secondary osteons are the products of bone remodeling and are most abundant in mature skeletons, particularly of large animals. Primary osteons have the same concentric lamellar structure but they do not have a cement line, the outer layer of the secondary osteon. The cement line forms where resorption ceased and new lamellae started being laid down. Primary osteons form de novo around blood vessels such that the preexisting cavity is

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FIGURE 1.10 Bone hierarchical levels 1
3: (A) whole bone; (B) section of long bone; (C) osteon—cortical bone unit; (D, E) lacuna-canaliculi network; (E) trabecula—trabecular bone unit and (F) bone remodeling cells.

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Chapter 1 Bone multiscale mechanics

centripetally filled with lamellar bone. Primary osteons are common in fibrolamellar bone when a vascular cavity is being filled in and at the interface of compact and trabecular bone of large animals. The secondary osteons, or Haversian systems, are roughly cylindrical structures with a central canal. The central canals may branch or merge and are often coaligned in long bones with the prevailing direction being along the bone axis. Historically the longitudinal Haversian canals (HCs) were distinguished from the transverse Volkmann’s canals. However, high resolution μCT reconstructions show the continuity of these canals and indicate that they are parts of the same system. Alternating orientations of fibrils in adjacent lamellae of an osteon and noted that the angular offset varies. It follows from Gebhardt’s study that none of the lamellar layers in an osteon contain collagen fibrils oriented strictly parallel or strictly perpendicular to the cylinder axis. Therefore, following Gebhardt, the lamellae that form an osteon could be viewed as a set of nested “coil springs” with alternating pitches. The average pitch of lamellae may differ between osteons, resulting in the characteristic appearance of dark and bright osteons in the polarized-light microscope. This phenomenon was extensively studied from the viewpoint of local adaptation of cortical bone to the dominant mode of loading. Secondary (but not primary) osteons are surrounded by cement lines. In trabecular bone, each aligned series of lamellae within the lamellar packet is also bound by a cement line. The cement line is thinner than an individual lamella and appears crenulated. The material deposited in the cement line and its structure are still poorly understood. Although some controversy still exists regarding its degree of mineralization, the prevailing view is that it is more highly mineralized than the associated lamellar bone (Reznikov et al., 2014). An osteon has a cylindrical shape (Fig. 1.10C) with a central canal called the Haversian canal (about 50 μm in diameter). The diameters of the osteons that forms the cortical bone can vary from 200 to 500 μm depending on their location. Blood vessels and nerve fibers pass through the HCs. These channels are enclosed by concentrically arranged lamellae with thicknesses ranging from 3 to 7 μm. Osteocytes cells are located inside of cavities named vacancies with volumes of about B300
500 μm3. These vacancies are connected by fluid-filled channels and canaliculi of diameter ranging from 100 to 500 nm (Fig. 1.10C and D). Trabecular or cancellous bone is formed by an irregular and random gathering of trabeculae that are approximately 50 μm in diameter (Fig. 1.10E). These trabeculae are oriented in the main direction of the mechanical load on the bone. A single trabecula is composed of lamellar tissue with osteocytes lying in lacunae with a network of canaliculi similar to that of the cortical tissue.

1.1.7 Tissue and the organ (whole bone) levels All bones contain an outer shell of compact bone that can vary greatly in thickness even within an individual bone (Fig. 1.11). Trabecular bone (also known as spongy or cancellous bone) may fill up the entire inner volume of some bones such as vertebrae, ribs and calvarial bones, or may only be present in parts of bones, such as the epiphyses of long bones. Structurally both compact and trabecular bone are composed of lamellae, and a comparison of the 3D structures up to Level VI reveals only subtle differences. One such difference is that in compact bone from human femora repeating sets of unidirectional fibril bundles show a variety of alternating orientations, whereas in a trabecular bone lamella one of the two unidirectional fibril sets is more or less aligned with the long axis of the individual trabecular strut. Another difference is that on average trabecular bone

1.1 Bone multiscale and hierarchical organization

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FIGURE 1.11 Bone hierarchical levels 8 and 9 for long bone: (A) long whole bone, (B) cancellous bone, (C) cortical bone and bone marrow.

material contains less mineral than the associated compact bone. Probably the most investigated structural attribute of bone is at Level VII, namely whether or not the overall texture of trabecular bone reflects the predominant stress directions to which the whole bone is subjected. Julius Wolff was one of the first to propose that indeed it does and D’Arcy Thompson was one of the wellknown proponents of this idea. There are several compelling studies that, in our opinion, do support the notion that there is a relation between the applied stress field and trabecular texture, including two experimental studies in which the mode of the applied stress field was changed and the trabecular orientation changed accordingly. Fig. 1.11A illustrates the components of long bones such as the femur or tibia. The long bones are formed by the epiphyses which occupies the two extremities and the diaphysis that represents the central cylindrical part. As seen before, bone tissue is divided into two types (Fig. 1.11B and C) considering its structure, location, and properties: (1) cortical or compact bone tissue and (2) trabecular spongy tissue. The long bones are composed from a dense cortical shell (that provides the organ with required strength and stiffness) with a porous trabecular interior (that ensures stress reinforcement and

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lightness). Flat bones such as frontal bone have a sandwich structure: dense cortical layers on the outer surfaces and a thin reinforcing trabecular structure within. Both bone types are easily distinguished by their degree of porosity or density, but the true differentiation comes from histological evaluation of the tissue’s microstructure (Fig. 1.12). Table 1.3 summarizes a comparison between the two types of bone, the cortical one and the trabecular one (Hollister, 2014).

1.1.7.1 Cortical bone tissue Cortical bone also named compact bone (Fig. 1.11C and 1.12C) constitutes the main scaffold of the body by being the structural element of our skeleton. Also we know much about it, many puzzling unknowns are still to be solved and resolved. It is not inherent only to the bone but to our body as

FIGURE 1.12 Hip femur cortical and trabecular bone: (A) human femoral structure, (B) hip femur lines of stress, and (C) scanning electron micrograph of a part of hip femur.

Table 1.3 Comparison of structural features and mechanical properties of cortical and trabecular bone. Young’s modulus (GPa) Strength (MPa) Volume fraction (mm3) Surface fraction (mm2) Porosity (%) Density Total skeletal (mass%)

Cortical bone

Trabecular bone

7
30 100
230 0.85
0.95 2.5 5
10 1.6
2.0 80

0.7
20 1
7 0.05
0.60 20 50
90 0.03
0.12 20

1.1 Bone multiscale and hierarchical organization

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a whole and saying “the function is creating the organ” (or you may say Wolff’s law for bones) is just stating what we see and not what we know. Detailing cortical structure (or trabecular by the same token) is detailing an average composition with variations of known causes and some of unknown causes. The abusive use of the above adage lets to rest the endeavor to elucidate what can be called a secret of life, endeavor probably leaving the scientific realm for some inroads into the metaphysical domain. Cortical bone is mainly organized in so-called cylindrical osteons (about 210 6 40 μm diameter, a few mm length) arranged in so called Haversian system. In the name of Clopton Havers (1657
1702) who, by the way, has shown that even without the heavy and expensive technical paraphernalia of nowadays one can achieve scientific progress. This structure is built around a vascular (about 75 6 15 μm in diameter) canal in concentric layers of mineral lamellae (5
30). This canal is also the road for nerves so it is both a communication and a supply route of blood for nutrients necessary for the maintaining and the renewing of the bone structure. Description doesn’t stop here for it is much more intricate for these canals are connected transversely by other canals named VC which apparently, but to a level not yet neither fully investigated nor fully understood, insure the interconnectivity of HCs. Recent study shows that VC canals result from small osteon branches bifurcating off of HC canals with path which could be either linear or oblique or even circular (Maggiano et al., 2016). More than that, analysis shows that the VC canal can be a doubling on an existing canal case more frequent with advancing age. Synchroton μCT processed image on the left of an about 3 mm3 of cortical bone shows the complexity of osteon. Canals and voids colored orange actualize the importance of draining and communication inside the bone. It is already worth to note that this arrangement is for mature bone. In immature bone there are not HC cells but a woven structure around collagen fibers that eventually during a first bone remodeling process of first bone resorption and then new bone formation creates osteons. The triggering of this remarkable event is yet to be deciphered even if precursor actions have been tentatively proposed avoiding the next level of understanding which is what determines the precursors actions. The same study proves that a high redundancy exists in VC canals between osteons which are partially age dependent not on the average of about 6 between osteons but on the type of VC canals with transverse connections found in youngster (up to 27 y) and intro-osteonal branching as age increase. Lateral and dichotomous VC were found not age related. Main HC connected by the numerous VCs constitute a complex network of information with a lot of redundancy, which overall reminds us of Internet and therefore this parallel raises a fundamental questioning: is the same message affecting the bone managing, like start of remodeling (of yet of unknown nature and unknown source), going straight to the chosen target through a single path or going through multiple paths, overriding clogged (for whatever reasons) paths? The above mentioning brings the next questioning (keeping the start of remodeling for the sake of simplicity); is the message arriving in the bone structure pertaining to a specific bone address or a general message which is treated and address-decided locally? Known are the magnetoelectric effects in bone, both in the mineral and the collagen parts. Investigations are running with some interesting findings, some found that stressed (bending) wet cortical bones emit signals much larger than expected from known magnetoelectric effects from dry bone collagen (Maggiano et al., 2016). And some assert that the use of magnetoelectric materials (like erfenol-D/poly(vinylidene fluoride-co-trifluoroethylene) composites) can provide mechanical and electrical stimuli to MC3T3-E1 cells presented as pre-osteoblast cells by applying a magnetic field (Ribeiro et al., 2016). They noted a 25%

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enhancement of cell production. It is important to note that it is an in vivo study of a bone fracture. From the latter we do not know if in this experiment if the applied magnetoelectric field is the trigger of the remodeling/repair of the fracture or probably the boosting of the natural process of healing. From what has been said above we know that electric signals are produced inside the bone but their meanings are not established and therefore we cannot decide is they are signals for the osteoclast, osteoblast and osteogenic cells found on the endosteum, signals sent elsewhere, inside or outside the bone to inform the nearby cells or request from remote locations. Anyway, are osteons assembled in clusters? For some, yes is the answer and curiously not age dependent (Bell et al., 2001). This has been detected in fibulae not on the forming bone phase but on the eliminating phase which results in large deleterious cavities in the bone. This phenomenon more pronounced in the shaft than in the neck of the bone. Some other study suggests that hip fracture occurrence is associated to weakened bone by merging of osteons resulting in HC canals of abnormal size (more than 350 μm in diameter). Said with the necessary prudence, the above occurrences might suggest that remodeling is rather a local affair for the said bone as apparently no remote external triggered process is engaged into a corrective action. MSCs, produced in the mesenchyme of the bone marrow close to HSCs, source of different blood cells, maintain the homeostasis of the bone marrow and control the rate of production of both hematopoietic and bone cells, osteocytes, osteoblasts, bone marrow adipocytes, cartilage chondrocytes. MSCs, associated with existing osteoblast and osteocytes on the bone endosteum, are the main actor in the cell differentiation and transcription based on received signals from the environment through not yet established routes and probably chemicals signals transiting in the blood and it may be prudent to let open other possibilities. One main cellular is missing: osteoclast cells. Coming from the bone marrow as well by merging hematopoietic precursor cells (mononuclear) under the expression of OPG, M-CSF, and RANK factors (themselves modulated by different hormones) into multinucleated giant cells (10
20 nuclei and size up to 200 μm diameter). For some they compare to macrophages having quite identical qualities notably on surface antigens (FranzOdendaal et al., 2006). For some, they have the ability of travel along the endosteum and then sticking to the bone to erode it with degrading enzymes and metalloproteases through the point of contact (Baron, 2001). Essential acidification is maintained by ions channels under a complex process. They are found in pits named Howship’s lacunae where they encroach into the bone. They have a very special wrinkled cell membrane with a high surface sealed in contact with the bone through which they inject acid phosphatase and other degrading chemicals found in vacuoles stuck to the osteoclast. The process is much more complex and understanding is down to the molecular biology level which is not our priority. Osteoblast cell work in team. A single osteoblast can do nothing. How this team of cell is put to work? Osteoblast cells connect between them through tight junctions (preventing extracellular fluid passage) against the old bone and gap junctions (cytoplasm connection) unifying the cell block in one active component. This cell team enters action after osteoclastic phase which has left cavities in the bone. Triggered by different and numerous growth factors, bone morphogenic proteins. . .osteoblast block cells synthetize osteoid which is a dense network of collagen type I fibers parallel to the ancient bone with crosslinks every few μm. Some specialized proteins, osteocalcin and osteopontin are deposited as well in much smaller quantities which are the bonding agent with the mineral part coming in the next step. This osteoid is the core of the tensile strength of the future bone. The

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osteoblast team is then actively producing compounds containing phosphate, calcium salts, ATP and secreting alkaline phosphatase (osteoblast membrane anchored) which is supposed to create a high phosphate concentration in the space created by the osteoblast block and the ancient bone. It is generally proposed that a further process is involved in the making of the HA bone mineral. In a slightly alkaline medium HA is precipitating from water, calcium and phosphate under the formula: 21 1 6HPO22 4 1 2H2 O 1 10Ca "Ca10 ðPO4 Þ6 ðOHÞ2 1 8H

(1.1)

This production of acid in the sealed space of the osteoblast block against the former bone should rapidly stop the HA precipitation which is not the case. As a consequence, the actual removal of those acid H1 is one more phenomenon to be deciphered. The osteoblast blocks forming a new osteon are separated by impermeable spaces without cellular connections, called cement lines which area thin layer of calcified mucopolysaccharides. What is stopping the remodeling? During concentric mineral depositing the osteoblast cells undergo what we may call a decay process even if only part of them disappear through apoptosis. Part of the osteoblasts slows the production of mineral, and are slowly embedded in the new bone by the other still depositing mineral, in the process becoming osteocytes. For others, their shape switches from cubic to flat, stops the mineral deposit, finally laying along the surfaces of the new bone (on both endosteum and periosteum). Apparently, the embedded osteoblasts then osteocytes cells in ellipsoidal holes, lacunae, (5 by 7 μm) filled by extracellular fluid are connected through dendritic elongated gap junctions (tiny channels about half of a μm in diameter for about 5 μm in length called canaliculi) to others new osteocytes and former ones. Nearly a hundred of canaliculi is associated with each lacunae. Each mm3 of bone comprises a very large (hundreds of thousand) canaliculi. The role of the embedded osteocytes is to monitor and to maintain the bone matrix homeostasis for they can synthesize or resorb the matrix. It is said that about 13 days are necessary to fill up the cavities made by osteoclast cells, but 4
6 months are required to consolidate the bone, with noted variance depending on the body bone concerned and the place inside the bone. Suffice to say that a very long list of known factors, proteins, hormones, etc. are acting during this process with yet some not estimated unknowns. Communications to and fro understanding is still in development and this is an in-depth analysis outside of our aim to present the mechanical behavior of the bone. Osteoblast cells deposit HA in a very ordered manner in the collagen network with needle like element along the bone and also in the transverse dimension following the osteoid fibers. Deposited bone crystals are minute, flat of about 5 3 25 3 50 nm with apparent “flawed” crystals with ions sodium, potassium, magnesium, etc. substituting for the ion Ca in the carbonate part of the mineral matrix. The exact role of each actor is yet to be revealed. Nevertheless, the tiny size of the crystals fits with the network of collagen adhering to it and capable to make any turn in the structure. Even if we’ve said that some proteins are the bonding agent, it is remarkable to have such a consolidated lattice of carbonated HA with so many apparent flawed crystals. This probably means that they are necessary for whatever role. A perfect example of “we see but we don’t know.”

1.1.7.2 Trabecular bone tissue Bones and particularly long bones are hollow biological composite entities made of a hard external envelop with remarkable stiffness and resistance qualities with a filling of an altogether

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Chapter 1 Bone multiscale mechanics

composition and behavior. As a whole trabecular bone is less than 20% in weight of the bone, even less for the bone matrix. But this figure widely spread in literature is really approximate for it is very difficult to analyze bone composition and establish the detail of its components, including mineral, collagen, vascular vessels, marrow, and nerves, more so as the variance from bone to bone, age, sex, etc. can be expected to be high, no talking even of diseases effects. Current available literature is void of such studies that would better specify and clarify bone composition and more particularly the trabecular bone. With a sponge-like appearance (Fig. 1.11B and 1.12C), trabecular bone don’t look potentially a structural element, filling the bone external shell of hard cortical bone in its epiphyses and metaphyses zones. In volume of the trabeculae, bone is only about 20%. This 3D skeleton is made of collagen interspersed of mainly rod shaped but also plate shaped mineral struts. It is very difficult in view of the shape to estimate proportions of bone content versus overall trabeculae volume. It is estimated that the bone structure is only about 20%, figure with a significant variance. All the investigative means, such as using HRpQCT and μCT, have been used to evaluate trabecula components proportions. Older methods, painstakingly mixing automatic recognition and manual delimiting of borders (with collagen, cortical, marrow zones) were mainly working with standard X-ray imaging. From literature, dimensioning got a kind of normalization (source unknown) at the level of labeling of dimensions (Fig. 1.13).

FIGURE 1.13 Trabecular bone labeling dimensions. Tb-Th 5 trabecular thickness plate shaped (mm). Tb-Td 5 trabecular thickness diameter for rod shape (mm). Tb-Sp 5 trabecular spacing (mm). Tb-Nd 5 trabeculae nodes (per mm3). Tb-N 5 trabeculae number (inverse of mean distance between mid-axis in mm). Tb-Tm 5 number of termini (per mm3).

1.1 Bone multiscale and hierarchical organization

21

On average and high variance Tb-Th and Tb-Dm are of the order of 0.01 to 0.3 mm, Tb-Sp from 0.06 to 0.5, Tb-Nd from 2 to 8. Some values are not very well established and audited and should only be taken as an order of amplitude, no more. Typically, it is said that trabecular bone porosity is about 80% (75%
95% in literature) with a wide range of density (035 6 0.3 g/cm3). Density of the HA strut (either flat or round) is estimated at 1.9 g/cm3 with crystal size slightly ˚ (decreasing with osteoporosis). It is worth noting that the trabecular HA has a less than 700 A lower level of calcium than the cortical bone but contains more water. Water, 30% of the total bone, has numerous roles, some already seen in the cortical bone, and has a suspected mechanical role (not yet completely unfolded) in the trabecular as participating at the hydraulic damping of stresses applied to the bone. Vascularity is much developed in the trabecular with blood coming near the center of the bone, irrigating marrow and trabecular bone (Fig. 1.14), then exiting trough HCs and VCs and canaliculi as well where embedded osteocytes monitor the bone stability (Marenzana & Arnett, 2013). Blood pressure, about 13 kPa in artery, goes down to around 5 (3
9) kPa in veins and capillary while trough the bone marrow pressure should be 6.6 kPa with small tolerance. Any straying too far from this value has important consequences through a complex chemical-biological process. To make it

FIGURE 1.14 Schematic representation of trabecular bone microarchitecture.

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simpler, remodeling of the trabecular bone is strongly affected by the fluctuations of the blood pressure. Already much stronger in trabecular than in cortical bone (estimation of a yearly 26% trabecular remodeling to 3% cortical remodeling), remodeling increases sharply with hypoxia like for the other macrophages and decreases with hyperoxygenaemia. Other physical parameters, such as pH, are concerned as well and also osteoblasts creating. Not only hypoxia increases number of osteoclasts it decreased the number of osteoblasts enhancing the remodeling disequilibrium. It is said that metabolism in trabecular is 4 times (whatever it means) the cortical metabolism. It is certainly neither chance, nor coincidence even less accident that red marrow fills up the porous space of the trabecular. Marrow is a powerful biological engine which can provide on demand (we don’t hint that marrow control est external although there are enough knowledge of external control, blood flow to start with) biological local “workers,” osteocytes, osteoblasts, osteoclasts. . . “workers” which are on top of it pluripotent and able to play several scenario. Marrow is also capable to provide help and means to the entire body but our focus is bones and in particular trabecular. It is widely recognized that macroscopic change of bone tissue by remodeling is conditioned by the cellular network of osteocytes embedded in the bone matrix interconnected to osteocytes on bone surface, which network transmits the information of stress through the interstitial canaliculi and VC. Then some are speaking of interstitial fluid flowing (Adachi et al., 2010), some other (above mentioned) of blood (Marenzana & Arnett, 2013). Then, if we got overall the same scenario (with quite a lot of unknown covered by the widely recognized and very practical Wolff’s law), particulars differ. Some work on the assumption that osteocytes are sensitive to fluid flow (flow shear stress) and therefore capable of mechanotransduction, apparently observed and noted by some more than 20 years ago, and some other base the scenario on restriction of blood flow in canaliculi by shrinkage of the passage cross section due to stress on the bone (Adachi et al., 2010). And the preferred detection hypothesis is differential pressure increase due to flow speed increase. Not on a particular osteocyte but on a chain of osteocytes linked by dendritic cytoplasmic gap junctions. Other options are available but basically the accepted principle is that stress load or unload from equilibrium applied to the trabecular bone results in a modified remodeling increasing or decreasing it with amplitude. From this starting point and using all what mathematics (even Bessel functions) and fluid physics may offer in terms of equations, algorithms coupled to the finite elements simulation power offer a very attractive theoretical model of stress affected remodeling. Unfortunately, and this is even recognized by the promoters of this model, surface osteocytes, osteoclasts and osteoblasts are left out of the work in terms of communication. Like they don’t communicate between them and others. And we know they do and they do it a lot. It is said that our World is governed by mathematics which is proved again and again (black hole, tomography. . .) and it is likely that the entire chain of command of remodeling is going to be established one day and possibly translated in mathematics. We have seen already numerous close loop-like systems embed and nested one into the other and it might be the case in remodeling. It is left much to understand the remodeling process but we can nevertheless pinpoint some already observed and confirmed points. One of them is that remodeling is a local affair affecting a specific bone region (even if location and size determination is not yet sourced) which is called BMU kept during initiation, transition and termination of remodeling (Matsuo & Irie, 2008). This BMU is supposed to be a group made during remodeling and mineralization and is a fixed spatial and duration unit of cells until a remodeling starts again.

1.1 Bone multiscale and hierarchical organization

23

Communication between osteoclasts and osteoblasts are redundant in terms of number of channels (apparently 3) and plural for the 3 channels are of different nature altogether: (1) communication trough ligands (RANK/OPG foremost), (2) communication through gap junctions allowing cytoplasmic interchanges, and (3) communication by diffusion of molecules produced par a cell, such as cytokine. In vitro experimenting has largely verified this communication phenomenon. Then it is left to know who decided on the location and size of BMU. We have already seen that embedded osteocytes are the scouts of remodeling and by chaining can bring information to the surface cells and by way of myriads of canaliculi can form a network to bring apparently to the surface osteoblasts the information of what has to be done (Adachi et al., 2010). Osteoblasts which in turn communicate with osteoclasts precursors which on differentiation process become full bone eating osteoclasts. Action of bone resorption is coming to an end when osteoclast are in turn sending “signals” to osteoblast precursors to become full osteoblasts rebuilding the BMU now named BRC which is lined with flattened cells delimiting a space against the nude (after cleaning by specific cells) bone. Typically this line-up of flattened cells separates the BRC from the bone marrow. We have said that embedded osteocytes respond to stress load or unload and affect the remodeling process in the wake. But, if it makes sense that a constant stress could keep those specialized osteocytes “aware” of this state and affect accordingly the remodeling process what about repeated stress or ephemeral or random? Wolff’s law states that all these stresses occurrences are accounted for before proceeding to remodeling. Obviously a memory is necessary. Then we have different approaches. Some, and they are numerous, say that microcracks are the memory and it makes sense that may be embedded osteocytes would therefore be compressed in those deformations and keep the information like an electronic memory switching to 1 or even an analog value. What happens next time a stress signal is felt? Resetting the memorized value or better have a value register and an event counter? And do I need systematic microcracks, meaning that under even “normal” load I get them? May be it is the reason why remodeling occurs many times more in the trabecular bone than in the cortical bone to erase the “memory,” although the structure of the trabecular looks pretty elastic and mechanical characteristics high enough. How microcracks can happen: it is not only stress as a cause, it can be mineral crystals crumbling locally, the protein “gluing” coming off, collagen fibrils breaking, etc. and age. Still about microcracks, noted that they happen more in the trabecular than in the cortical, more in interstitial bone (old bone of sort) even reported in canaliculi occurring with apoptosis of embedded osteocytes. We know that remodeling is influenced by microcracks but in appreciating the wide spectrum of possible causes, it looks unlikely that memory can be only confined to embedded osteocytes. Then, some others propose an altogether different explanation, a higher layer of communication, neuronal-like, between all the actor cells involved in the remodeling, including MSCs, HSCs, precursors, and osteocytes (Spencer & Genever, 2003; Turner et al., 2002). The process of mechanotransduction in bones is largely accepted beyond the Wolff’s law but a good part of it is not plainly explained and that is the most important part. How this process integrates history of strain episodes some quite normal (like originating from walking) and some just transient and/or random. After all, we have already a functioning cellular memory system in our brain, a synaptic nuerotransmission based on glutamate signals which coordinates synapses to support memory formation and the necessary learning associated to. As for neurons, osteoblasts (and other cells as well) release glutamate and signaling pathways which can be evidence of endogenous

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receptor activation. The finality could be regulation of cell differentiation. In vitro, testing shows that glutamate receptor antagonism inhibit differentiation between osteoblasts and osteoclasts, evidence which has yet to be transposed in vivo. Another hint of this assumption, which can translate to having some type of cell different behavior depending on their location, has been found in in vitro testing of osteoblasts extracted from skull and tibia. Osteoblasts from skull have shown a significantly lower sensitivity to loading. In the same perspective, PTH hormone fragment (1
34) associated with the glutamate expression, has a much less anabolic effect on skull osteoblasts in culture, this PTH fragment inducing BMP gene transcription. Mechanical influences on the bones cells and their adaptation to recent loading to improve bones structural stability is one thing but what about the effect of transient or random loads? Apparently these brief episodes of mechanical strain are also “memorized” and trigger as well an osteogenic response well after those events. “Memorized” for it is obvious that some kind of memory should exist. As for uninterrupted strain loading, which can be a repetitive loading but at short time intervals, finding are that the mechanotransduction is less osteogenic, less sensitive to the stimulus. More sensitive to separated episodes with rest between and less sensitive for (apparently) uninterrupted loading has been demonstrated in vivo by a widely accepted model of loading induced bone formation. A complex chain of bio-chemical events has been proposed to consolidate this fact of habituation or desensitization on the repetitive mechanotransduction episodes. It has been first observed, researched and explained in the neurones environment around glutamate activity. As for now, no synaptic activity has been observed in bone cells and neither in the nerves linking the bone cells. Which put the role of glutamate in question. Another molecular reactions chain could explain why bone cells could be desensitized by prolonged mechanical or prolonged-like (repetitive with little rest time between) strain: osteoblast and osteoblast-like cells can communicate through autocrine activity of ATP on certain receptors, such as purinergic P2Y2, and strain initiates intercellular calcium signaling mediated by ATP receptors and the secreted ATP desensitizes those receptors. There is also a possibility of type G protein action. Although experimental evidence of desensitization both in vitro and in vivo exists, consolidation of the process particulars has to be done. Another aspect of memorized mechanotransduction within bone cells is the sensitization of the bone cells to transient and random strain. In neurons network the neurotransmitter serotonin plays a key role which through also a complex chain of reactions involving the G protein results in enhance glutamate secretion from the activated neuron opening calcium channels. The question is if there is a parallel in bones; it is likely for serotonin (as 5hydroxytriptamine, 5-HT) receptors have been found in precursors of osteocytes, osteoblasts and osteoclasts in the periosteum. Periosteal fibroblasts and apparently preosteoblasts enhanced production in periosteum by agonists for 5-HT serotonin receptor have been noted. Osteoblasts express a SERT and are capable of uptaking serotonin, serotonin which coupled with PTH increases AP-1 activity in osteoblastic cells, indicating, not with certainty but at least potentially, sensitization. Gap junctions, existence of which was established more than 20 years ago, put in physical communication the cytoplasm of two cells that are not distant than more 3,5
4 nm. It is divided in two sub-connections called connections, themselves dividing up to sub-canals named connections. Neurotransmitters signaling is important in bone cells albeit there is no evidence of chemical synapses, hinting that if not yet identified, they should exist. Connections between osteocytes and osteoblasts have been established with no further conclusion as the nature of it. Glutamate could

1.1 Bone multiscale and hierarchical organization

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make the chemical connection for, like a cytokine, it doesn’t need a synaptic connection. The above assumptions and hypothesis, if even corroborated by experimental and observational events, have to be comforted and confirmed. Long term memory could come with changing intercellular connections changing in turn the neuronal-like network of bone cells. As osteocytes are buried by active osteoblasts, it may be that the information in these osteocytes is fixed at the time of burial and that the information held in the network of osteocytes is coming out at the time of the next resorption work and exploited. Not having a glutamate receptor, osteocytes are unlikely exchanging and pooling information but both osteoclasts and osteoblasts have glutamate receptors allowing chemical communication. Apparently, osteocytes are left outside of this communication but looking further it appears that osteocytes do express GLAST which means the possibility to trap and/or release glutamate. Overall, glutamate (and the swarm of connected molecular activities) appears to be a major actor of bone cells communications and memory. If supposed neuronal, the bone cells network should have a central command post. Immunocytochemistry applied to bones cells has revealed their possessing of peptides receptors and innervation receptors as well. Coupled with the discovery of neural pathways between bone marrow and the central nervous system this has led to a new opening for the determination of the control of bone remodeling which in a vagueness of sort was thought local if not regional. Leptin is the main actor (quite a few studies deny leptin of any role in remodeling in spite of evidence). Leptin, secreted in the peripheral circulation by adipocytes interacts with the hypothalamus through the appropriate receptor behind the membrane separating blood and hypothalamus. Mainly involved in the control of body mass (with which it has a positive correlation) trace of action has been found in bone tissue, but with no definitive deciphering of process. Apparently leptin action differs with cortical and trabecular bones. Connection between trabecular and the ventromedial part of the hypothalamus was found by a complex chemical and genetic experience showing the hypothalamus the main source of leptin signaling to the trabecular bone. Leptin signaling has been verified but heavy parabiosis experiment showed that it is not humoral signaling so the high probability of neural signaling is considered. The leptin action is very much dependent on another peptide, NPY, found in quantity in the central and peripheral nervous systems, in sympathetic and parasympathetic nerve fibers and in blood. Regulator of homeostasis, NPY is strongly associated with leptin in the hypothalamus showing a surge of NPY when leptin depletes. This has a direct implication on body mass regulatory system but also on bone remodeling through a very complex (with some blur) chain reaction. NPY-ergic neurons are concentrated in the ARC (hypothalamic arcuate nucleus) and VMH regions of hypothalamus where endocrinal factors communicate more easily with resident neurons due to thinness of the brain-blood barrier and they express leptin receptors as well. NPY autonomic loaded nerves can be found in the bone tissue but sticking to the blood vessels which may be hinting that they have to do with the blood vessels and not the bone tissue proper. But osteoblasts have been proven of NPY production which is more than a hint of connection between bone cells and hypothalamus. Concerning the central effect of leptin, another actor has been discovered: neuromedin U, NMU, a neuropeptide expressed in both the hypothalamus and the small intestine which is regulated through sympathetic activation. NMU and its receptors haven’t been found in bones but in vivo experiments have shown a definite action on cancellous bone with yet complete NMU action scenario to be written. Undoubtedly, the ultimate map of hypothalamus-bone coupling is still to be drawn with the lingering question of division of command power and where the remodeling campaign plans are safely

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Chapter 1 Bone multiscale mechanics

stored. This means that bone remodeling is neither a local or regional body affair but part of the complete body regulatory system. Local bone homeostasis is affected and controlled by the central nervous system which regulate according to the overall status of the body in terms of energy available primarily (deprived body won’t make good bones) and balanced/unbalanced situations of others organs. And this control concerns as well nutrients, minerals. . . We know that if calcium is too low is the blood, the central system don’t hesitate to take it from the bone which is the central calcium store. Calcium is unlikely to be the only one to which this rule applies. Pres-supposing a bilateral communication bones/hypothalamus, the subject of “memory” is not yet entirely solved, Experiments based on cutting off or upping some particular molecular actor shows the direct influence of this actor on remodeling, but with or without memory? To date memory sharing between bone and hypothalamus (and why not other brain location) is still open to investigation. It is noted that Alzheimer’s patients suffer a bone mass loss which could be hastily explained by the partial/ total loss of remodeling memory. But in the same time many other functions are affected which could explain the phenomenon and many others affected by some different kind of dementia are not affected. This is to say that finding the brain memory site of remodeling by switching off brain compartments one after the other would be futile more so as brain compartments are far from being isolated from each other. One option is left: as it is quite obvious that remodeling is more than likely programmed in DNA, might that possible than stain/stress history is recorded in bone cell DNA to be transmitted to the next generations of bone cells? Evolution is the ultimate proof of DNA memory, dynamic memory registering yesterday and today events for tomorrow use. The use of DNA based recorders which, after some CRISPR adjustments for recording biological events, records which can kept even during a long time, is becoming part of the biologic laboratory equipment. It could be a short DNA memory or not for we know the adaptability of remodeling to strain/stress fluctuations could be fast (may be a few Hz), although rate of DNA duplication can be high (several hundred nucleotides/s). Then, beside memory, the precise path from brain to bone, the link hypothalamus-trabecular bone, has been well established contrary to the hypothalamuscortical which is still questionable and it has been seen that some actions enhancing trabecular bone are diminishing cortical bone. Blurred as well is the connection between higher metabolisms in trabecular bone versus a much higher remodeling rate (more than 5 times) than cortical. Is there a hierarchy between bones? Meaning a prominent role for one type of bone, meaning bone serial role, or no hierarchy, parallel mode. Looking at the bone topography, we see that marrow, blood vessels are inside and trabecular bone as well and that blood is basically flowing from the inside to the periosteum through the cortical bone. We know that any type of arrangement in the living is not random, therefore the bone topography has a meaning. It may be different for the mechanical aspect and for the metabolism aspect. Some experiments, among many others, have shown some interesting results: in one experiment, a low intensity (below regular activity level) 30 Hz sonic transmitter was irradiating the hind leg of sheep some 20 minutes per day (Rubin et al., 2002). Results against the control group, show that only the trabecular bone was influenced in its spatial definition: trabeculae spacing decreased by more than 30% and trabeculae number increased almost 50% with about 30% increase on bone density. The cortical bone didn’t show any variation with the control group. We can easily speculate on why only the trabecular bone did show a reaction to the stress but we could say as well that, even if the cortical was irradiated, the trabecular bone is the “recording” space. We can add that the trabecular bone is adapting its configuration to

1.2 Cortical bone macromechanical properties

27

the actual stress, 30 Hz is a very high frequency compared to a few Hz for regular repetitive stress. Measuring apparatus should be geometrically adapted to the measured physical quantity hence a reducing of dimensions of the basic trabeculae. And consequently from shape increase of bone content and density. In another experiment, a low (0.05%) calcium diet was imposed on test animals with control group fed with a normal 0.5% calcium diet (Seto et al., 1999). From day 1, damage was witnessed on the trabecular with increase of PTH hormone and in the coming days, osteoclasts and osteoblasts increased on the trabecular surface of the test group and not in the control group. Ex vivo study showed that, in the test group, the bone marrow was churning out progenitors of osteoclasts and osteoblasts and the following days, all the armada necessary to repair the loss of trabecular bone was at work. Meanwhile, nothing to report cortical bone wise. This experiment didn’t enter the stage but what we report is a sign that both bones don’t work in parallel. As a wild interpretation, the latter experience could mean that in a shortage situation of calcium, the trabecular bone take the full brunt of the bad situation to protect the cortical bone which is after all, the structural frame of the body and make do with what calcium is left. These two experiments, however small is the group, coupled with the well-established link of the trabecular bone with the hypothalamus and the topography of the entire bone/marrow space may be indication that the trabecular bone may be hierarchically above the cortical bone and certainly not just the stuffing of the cortical bone. To be verified without no doubt. In the previous part, we have made a quick review of bone diseases but we want to make a point with osteoporosis in relation with what has just be said. In the case of “no more available calcium in the body,” osteoporosis starts. Where? In the trabecular bone, always at the fore-front. It cannot be a coincidence.

1.2 Cortical bone macromechanical properties Cortical bone is compact, dense with a rather low porosity (significantly lower than 30%) which can be found primarily at the diaphysis of long bones with a notable thickness decrease to a thin layer encapsulating the trabecular bones of metaphyses and epiphyses, thinner even on vertebrae. Cortical bone accounts for 80% of the bone weight, making it about 12% of the body weight. Cortical bone is a composite of many components, mineral and biologic, forming basic cells, named osteon, which are arranged primarily as Haversian systems which we shall further detail. Before reviewing studies which aim to connect microstructure to macrostructure, one may evaluate the cortical bone as a homogeneous component for structural purposes which it is for the human skeleton. Bulk Cortical bone is an anisotropic material, stronger in the longitudinal direction of long bones and weaker in the transversal and circumferential dimensions. It should be noted that transversal and circumferential do not divert much in characteristics so the bone material can be taken as isotropic in the transversal direction. This assumption is correct for bones like tibia, fibula, etc. questionable for other bones. It is without saying that mechanical characteristics of the bone material is found dependent on age, sex and physical activity leaving for further analysis effects from biological repeated stress accumulation (fatigue) or accidental degeneration. One may address as well the effect or permanent remodeling which affects without no doubt what we could call the apparent bulk mechanical characteristics. Evaluating bone mechanical

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characteristics has been done for already a long time and we are not planning to participate to the competition of who has the actual value of this mechanical parameter or this other one for there is no actual value. Bone variance is so large in all his composition, metabolism and state of health, that group averages versus age, gender, first degree bone diseases (at the level of the bone itself), typical second degree of bone alteration triggered by elsewhere in the body malfunction are a better choice in characterization of bones. Like for any nominal physical parameter, measuring bone means samples are to be prepared, preparation which could have a bearing on the results hence an overview of bone sample preparation.

1.2.1 Preparation of bones samples for handling Bones are biological, meaning that apart the mineral content, all other components are subject to decay, decay non compatible with laboratory manipulation, so bones have to be cleaned of biological tissues or have them neutralized. Plentiful of human bones are for the taking but they are not readily available for administrative steps are to be processed with respect to ethical (and others) laws before getting them. Therefore there is no fresh bones shopping (letting medical universities apart) only “prepared” bones, for quite some time may take place between donor’s death and eventual testing. As donor’s bodies or body parts are likely to be frozen, some think the frozen preparation as the only valid way adding even the fresh-frozen quality adjective to the preparation which is quite problematic (Stefan et al., 2010). We all have the knowledge that freezing results in the secondary phenomenon of drying. Does this drying affects the mechanical characteristics of bones and of cortical bone in particular? What about rehydration after thawing? Literature shows that at a whole, freezing, thawing and rehydration of bones are of no consequence albeit some changes in the microstructure under SEM are observed but did not alter the structural integrity of the microstructure (Tersigni, 2007). Some finds that a 5% decrease in water content (thermal drying in vacuum) starts an increase of bone strength switching to a decrease when drying goes up and above 9% (Nyman et al., 2006). Stiffness increases with the loss of water and toughness decreases above 9% of water loss. Depending on temperature, drying affects two types of water, water as a collagen content and water associated with the bone mineral content as drying temperature is increased. It is suggested that toughness decrease in the first phase (up to 9% water loss) is the result of a loss of plasticity, explained by the loss of the water connected to the collagen, loss occurring at lower temperature and before loss of the water connected to the bone mineral. Some, in drying and rewetting bone experiment, found effect on Young’s modulus very small and bending strength reduced statically by 5%, a rather modest figure, not significant (Cornu et al., 2000). The author concludes that drying/rewetting doesn’t affect the bone mechanical characteristics. To emphasize freezing effects to bone, some went through a multiple cycling freezing/thawing and estimating effects par use of RPI instrument to add another dimension to their study (Kaye et al., 2012), the RPI measuring directly key mechanical properties in vivo to assess bone, hence the added value to compare human tibiae (and bovine femurs) before and after freezing (220 C) and so after several cycles to verify the assumption that implants usually obtained frozen have the same quality than the “fresh” bone implant. Although some degradation were observed, mechanical characteristics didn’t show a spread of more than 15% which is no more than the level of the spread across the samples before freezing. It can be said that freezing affects the bone mechanical characteristics only marginally. Some have repeated the same type of

1.2 Cortical bone macromechanical properties

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testing (femoral sections) but using Raman spectroscopy (McElderry et al., 2011). Beside noting amide I and amide III levels diminishing after 2 freezing/thawing cycles, crystallinity values of bone mineral diminish slightly only after the first freezing. Therefore they recommend allowing only one freezing before bone testing. Some went even a step further, freezing tibiae at 220 C for 21 days, boiling segments for 3 days, finally degreasing with trichloroethylene at 82 C for 3 days (Lander et al., 2014). Using the SEM technology, there were no significant differences between freezing, boiling and degreasing quantitatively. However, qualitative differences were observed after freezing the bone displayed cracks at the microstructure level. Handling of fresh human body parts not germs neutralized in a laboratory is a big endeavor. You have to establish a very stringent process of manipulator protection with all the adequate equipment to wear and tackle the problem of the testing machinery cleansing. This machinery is normally used in the mineral mechanical testing field where there are very few hazardous situations (dust mainly) to confront. They are not at a whole designed to be sanitized biological wise so preparing and testing samples from fresh bones demands certainly a heavy planning starting with the headache of transportation logistics followed by a hectic schedule of testing commanded by the time constraint of acceptable biological decay accumulation in your samples. In that sense cortical bone has the advantage over the trabecular for having a significantly lower biological content. Using animal bones as a starter to round up characterization of bones makes sense for global handling is much lighter but characteristics differ sensibly in bone density and porosity. Even if some bone shapes are very similar to human shapes as to be mistaken one for the other for we have common ancestors, evolution has resulted in quite different metabolisms hiding below the same appearance leading to diverging mechanical characteristics. More practically, human samples are to be sanitized and embalmed. Different ways and sanitizing products are on the taking. Apparently, there is no general agreement on the effects of disinfection. At least, all agree that with some degree that there is an effect on cortical bone mechanical characteristics. The most common way is embalming with a 4% or more formalin solution, an acceptable treatment if it is for no more than 4 ¨ hman et al., 2008) while some others measured alteration (decrease) of the plasweeks for some (O tic energy absorption parameter (Stefan et al., 2010) and some finding no goat bone parameters alteration even after 1 year (van Haaren et al., 2008). By direct mechanical trial (inserting orthopedic screws) some cannot find a difference between fresh and embalmed bone strength (Topp et al., 2012). It is clear that formalin use translates in light opinion discrepancy but discrepancy do exist and is a slight point of contention to remember. Thiel fixation and alcohol-glycerin fixation are on the menu as well (Stefan et al., 2010), with results no better than for the formalin. Water is structurally transparent and besides being incompressible at earth level pressures it can hardly be thought of in terms of strength. May be in general terms of damping, lubrication. But some understanding seems to be found that mechanical testing of bones should be done with wet bone, apparently all are users of Ringel solution, even the cutting, grinding polishing of samples should be performed under drops of Ringel solution. Some consensus exists that dry bone have higher stiffness, less plasticity and are brittle. Some using a heavy set of investigation technical means (X-rays, neutron diffraction, IR and Raman spectroscopies and nuclear magnetic resonance spectroscopy) came to the conclusion that water performs three main roles, roughly first inside the complex mineral content as structurally connected water to the crystal, second as a filling material in the bone porosity dedicated to nutrient supply route and third as an interface between the mineral part and the collagen matrix (Wilson et al., 2006).

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Using wet bones for bone bulk characteristics seems pertinent. Evidently, some may question the confidence that rewetting bones after freezing leads to the equivalent of an in vivo bone for mechanical characterization. Most studies pinpoint the difference in dry bone, consent somehow that rewetting bones fills up partially the gap and finally one must accept the fact that testing mechanically bones can be hardly performed by using fresh cut bones. Up to now, only RPI helps to characterize mechanically bone in vivo. Some show that values of RPI measurements correlate with the ex vivo toughness, with discrepancies due to diabetes or bisphosphonate treatment (Gallant et al., 2013). On the contrary some don’t agree and even question the use of RPI in the potential clinical use of RPI measurements in determining fracture risk for a single patient (Krege et al., 2016).

1.2.2 Preparation of bone samples for mechanical testing By what we overview above we know that cortical bone is a complex composite with main actors but also a plaid of small actors not automatically evenly distributed in the bone. Beside, variance of characteristics is to be expected from location of analysis and size of the sample (Fig. 1.15). It is a

FIGURE 1.15 Cutting scheme for bone samples preparation.

1.2 Cortical bone macromechanical properties

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simple and puzzling fact that there is no standardization of bone testing in mechanical characterization. Knowing the history of testing of industrial structural material which has been standardized a long time ago in view of the results discrepancies resulting from a jumble of testing apparatus and methods, we can only be skeptical of the measurements presented by many which by the way don’t show a large span of results as can be expected. Another important factor is that the thickness of cortical bone can be low even very low so comparing to trabecular bone size results in suggesting that it is very difficult to unify sample size. Dimensions of the bone samples is yet to be determined but the bone must first undergo a treatment to make it acceptable for manipulation. Some went through a meta-analysis of some 4712 abstracts supported by 177 papers, 20 studies directly analyzed (Zhao et al., 2018). It results that freezing is the main method of storing bones before testing, bones being in either physiological saline solution or Ringer’s solution in majority. Grinding, polishing, gluing, encasing the sample, etc. are standard manipulations of specimen. Obliviously samples are to be extracted with caution not to induce local failures and cracks and best are diamond tools abundantly lubricated by water or better Ringel’s solution (anyway the same in which the bone has been frozen). Care should be taken to precisely retrieve the sample with the desired geometry, along the fiber or normal to it, samples mixing different directions should be discarded for interpretation of any mechanical test would be complicated. As for dimensions some in meta-study comes with the conclusion (for local testing) to have rather a cylindrical specimen with ratio height/Ø between 1 to 2 to avoid buckling and a cross section of about 100 mm2 (Zhao et al., 2018). This is not concerning complete bone testing which is even more complicated to perform and a complete subject in itself.

1.2.3 Cortical bone characteristics As any structural material, the standard characteristics to be known are measured in the 3 directions with respect the shape of the bone or the direction of fibers with others parameters deducted from measurements. The same study mentioned above pinpoints the problems of actual measurements coming from drawbacks of the testing equipment and nature of the bone with overall results questionable and which have to be interpreted in perspective (Zhao et al., 2018). The study focus only on the compression strength to define the bone stiffness but the methodology applies for other parameters, tension, shear, etc. Basically everybody is working identically as per the graph below (Fig. 1.16). Value of the Young modulus is then by drawing a parallel to line 1
2 through the coordinate 0.2%. Up to point 3 we are in the elastic phase the in the plastic phase. Another important testing parameter is the strain rate which affects also results. The same meta-study spoke of a range of 0.005 to 0.08 s21 with some higher values used in shock testing (Zhao et al., 2018). Strain rate is important as bone is a visco-elastic material and above a certain value, deduced Young modulus, the most important mechanical parameter, is affected. Consequently strain rate should be below 0.1 s21. As for the average long bones of Young modulus is between 15 and 20 GPa. Other parameters follow the same testing process but the important variation of protocols and results would need a meta-analysis and we see no point to refer to this value or another one.

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FIGURE 1.16 Typical cortical and trabecular bones stress-strain curves.

It is worth noting that two new ways of measurements, not yet mature but promising, are already in use: • •

RPI already referred to for it is used in vivo to give immediate results SSI which is a heavy analysis of images given by scan (QCT and pQCT) and are compared to the standard 3 point bending test.

1.2.4 Cortical bone ailments Cortical bone being the structural element of our skeleton, any disorder will have a direct effect on the freedom of movement, forcing even to a halt when accidental fracture happens. Like an electromechanical closed loop control system, bone is a quasi-perfect machinery when working nominally but becomes erratic when the loop is opened or when outside interference occurs or overwhelms the system in both mechanical and biological fields. This outside interference includes medical treatment which can quite regularly either pushes the system in overshot or trigger a nasty secondary effect which can force to enter into a chain of medication.

1.2.5 Genetic disorders We’ll start with a review of “original” defects meaning genetic defects. There is a long (still opened) list of genetic diseases. As the actual complete functioning of bone formation, evolution and remodeling is not yet known, the witnessing of the wrong in bones don’t systematically lead to know where represents the source of the problem. In Pyle’s disease, leading to thinning of the cortical bone, deformity of

1.2 Cortical bone macromechanical properties

33

and eventually fracture, a candidate gene has been pinpointed. Genic treatment is not yet available (if scientifically accepted may be philosophically denied) but there is questioning about it for we already know that when genes are concerned, you may have one central with most action but in need of peripheral actions of others genes making the solving very complicated. The nest questioning is on the possibility of drug treatment knowing (still partially today) that the disease is based on the lack of a certain protein. It is noted that at the same time that cortical bone is thinning trabecular bone is fattening opening the possibility of a second control loop or better said that that the complete bone control loop is branching between cortical and trabecular bones. Paget’s disease concerns the speed of bone remodeling which is too fast in this occurrence but still balanced. So bones and particularly cortical bone have no time enough to strengthen (we already know that 4
6 months are necessary to cure the new bone) resulting in a weaken structure that is going if not to crumble, to collapse resulting in bow legs for example. Supposed genetic, no real treatment besides giving bisphosphonate with questionable results, coming with age, progressively. Then the cohort of osteogenesis imperfecta, which is a group of genetic disorders of yet unknown causes that translate into brittle bones. Globally all this group concern first the lack of collagen type I in the connective tissue which affects the cohesion mineral/collagen, other disorders of this group focus on different missing or muted proteins resulting in osteoporosis at young age. No cure and again hopeless administration of bisphosphonate. Recourse to surgery to strengthen bones with metallic rods. All those ailments have a heritability component but can appear spontaneously. The above examples are just a very little part of the more than 372 dysplasia have been documented but without knowing the causes and as a consequence without known treatment. Cancer cells coming with the blood from infected organs find a perfect terrain with the bone marrow and their MSC’s cells to accomplish a devastating destruction of the bone and dispatching metastases back in the entire body. Momentary relief is sometimes the use of bisphosphonate to try and make a hasty local repair as cancer trigger some osteoporosis.

1.2.6 Triggered bone ailments Osteomyelitis is most common and results from infection either local through open wound or transferred through blood from another wound. If treated quickly with antibiotics heals pretty fast if not dire consequences are in the line. Leads up to local debridement or total amputation. It is worth to note that debridement hollow space however small it is won’t be refilled by the bone remodeling system, memory of it has been lost and you have to fill it up by other biological material (muscle, skin, etc.) until bone graft (if necessary). Lizard and earthworm have some advantages on us even if partial. Other ailment concern dysfunction of the body organs, erratic supply of mainly chemical and biological agents necessary to the bone stability and brought by the blood. Mainly centered on the lack of calcium, magnesium, phosphorus, potassium, vitamin D that are necessary for the bone remodeling. This lack is disrupting the good loop control of remodeling. Lack of calcium concentrates the bone problem: as calcium is carefully monitored in blood, if the amount is too low the system takes calcium from bones, slowing the remodeling process triggering osteoporosis. This lack of calcium could come from a poor diet or a thyroid malfunctioning. We have seen that bisphosphonate, which as a strong affinity with the cortical bone main structural material, can be treated as a medicine with spectacular effects on osteoporosis of all sort. But not appropriately associated with calcium and vitamin D it can have deleterious effects: osteonecrosis and hindering of the proper remodeling by slowing the osteoblastic process which in turn slow the replacement of ancient bone. There is as

34

Chapter 1 Bone multiscale mechanics

well a long list of medicines which through still unknown processes have a bearing on bone health. It makes sense as blood is irrigating all the body and any deviance from normal equilibrium of concentrations of components due to lack of or excess of impacts correct functioning. We are still at the step of piling up pills triggering a new problem after treating one. Consequence of our enormous lack of knowledge whatever progress has been made to date.

1.2.7 Fractures Fracture are accidental, a violent occurrence and it is astonishing and not (evolution transcript in our DNA of thousands of years memories of broken bones) to see that the “bone” has a check list for repair: first a blood clot (first few days) to protect the broken zone and bring the necessary repair materials and to eliminate residues of the fracture, then the formation (first 7
10 days) of a fibrocartilaginous callus to maintain both sides of the fracture following by a harder, light bonelike callus for the first month partly consolidating the bone. Remodeling has already started after 2
3 weeks replacing the hard callus and last for a long time up to a few years. It is worth noting that this accident is interestingly near the bone marrow and that MSC’s cells are the major actors in all those phases making cartilage and fibers then converting cartilage to real bones, a very complex set of actions but with still not knowing from where the orders are coming from.

1.2.8 Osteoporosis Significant of bone aging, commercial considerations have led numerous people to tackle the double endeavor, understand and explain the phenomenon and the how to slow this natural occurrence without creating a new problem. It is just part of the general mankind search to reach older age and osteoporosis is one among a long list of body parts to be treated for this aim. Noted is that if like expectancy is about roughly 80 and creeping slowly above, life expectancy in good health stagnates at the lower 60 seconds and don’t move much up with even a down tendency. Osteoporosis is when the control system loop of bone remodeling is apparently going in destruction mode, osteoclasts becoming berserk in destroying bone and osteoblasts not up to the task to compensate. Beside juvenile and triggered osteoporosis, the “normal” osteoporosis coming with age is a natural phenomenon like wrinkles, white hair and a thousand others. Commercial aspects are blurring the scientific research.

1.3 Bones as a composite structure Most big body organs, such as heart, liver, and lung, are biological and chemical factories, Some others give us a link with the physical world, ear, eyes, skin, tongue, although it is a brain virtual link where nerves and cell brains play to give us impressions of the physical world. But skeleton is not in the world of impressions, it is the real world, it has to support a few tens of kilos even many more and in a dynamic system where forces can be of all types (tension, compression, torque) directions and amplitudes (constant, repetitive, combined).

1.3 Bones as a composite structure

35

The skeleton is composed of many bones of all shapes and sizes and our purpose is not a study of all of them. Simply taking a typical bone, rather big, with a simple shape and which support intense stress. The leg bones are the stronger, all the body weight is on them. Tibia and fibula are associated and tibia is the foremost in the taking of forces during walking, running, jumping and what else. This is not to say that the feet are outside the brunt of the task of absorbing energy and shocks from outside and from inside due to the mechanical inertia of the body but it is a too intricate zone to show simply how bones (or better said) Nature has adapted to have fitting structural basic materials to build a support for flesh and blood “thinking” mass of biological tissues. We remind that the skeleton, with all the directly associated components, including cartilage, tendons, and ligaments, takes about 20% of the body weight. In bone proper we are down on average to 14% for male and 10% for female reflecting the evolutionary life of man and woman with higher necessary man physical activity for survival during history. This ratio compares favorably with modern car chassis. Concerning human tibia bone, Fig. 1.17 is a reminder of it through a longitudinal cut. It is a composite structure, adjoining a hard compact envelope with a filling of different materials, some for the biological functioning of the bone and other body parts (marrow, blood vessels, nerves) without any mechanical standing, some to finish the mechanical structure, mainly the trabecular bone. The first mechanical quality of the trabecular bone is its bulk lightness compared to the cortical bone. Lightness made by its composition of a 3D minuscule strut lattice amply sufficient mechanically wise, leaving cargo space. A good copy of airspace composite components or better say the opposite when conception times are contemplated. As a real space saver, Nature put the trabecular bone cargo space to good usage by lodging the very necessary red marrow, which is now well protected from external aggression and more, placed at the very best nearest point of bone remodeling functioning. At a lower level of dimensions, both cortical and trabecular bones are similar composite materials or better said sandwiched materials. Both are made with fibers of collagen type I with HA struts glued to them by proteins, each component supporting a specialized force, tensile for the collagen fibers, compressive for the HA chain of struts much like reinforced concrete. To be sure to confront all forces, this arrangement is spatially changing to accommodate natural forces. Beside the pure tensile/compressive force, other physical parameters of importance, shock damping, elasticity, toughness, ductility are taken care of, with and without correlation between them. For example it has been found that the tensile yield is not dependent of the Young modulus. Supposing an elementary tensile/compressive force on an idealized tibia (Fig. 1.18), we see that the structure can be divided in two parallel systems where F 5 F1 1 F2: Very simple at the first look but what could be the ratio F1/F2? Here things got more complicated for this ratio varies first with the mechanical characteristics of each bone material. That said, we have to enter a rapid overview of measures of those mechanical characteristics and the difficulties attached to the task. We have already seen in the first part that albeit some variance among the countless measuring tests made up to now with a lot of them with native measurement shortcomings, the average Young modulus of cortical bone along the length of the bone for compressive forces is between 15 and 20 GPa.

36

Chapter 1 Bone multiscale mechanics

FIGURE 1.17 Longitudinal cut of the human tibia bone.

Some are giving results taking out vascular space, some others applying corrective factors for so and so and many more manipulations to try and estimate the “ultimate” parameter of bone even knowing that age, sex and individual diversity muddy the results. Correlation has been established between the bone volume against the total volume (BV/TV) ratio and the ultimate yield stress which don’t initiate any practical comment. About trabecular Young modulus, it is considered to be down about (again average) 10%, up to 15% at the 0.2% strain point (0.2% strain is now a field recognized reference for the detection of the yield point is difficult and imposes a cycling of load/unload of finely incremented stress) against the cortical bone. Young modulus is defined as the ratio of stress, σ to strain, ε, E 5 σ/ε which is a pressure. Saying that the trabecular bone has a 10% less E than cortical means that for the same strain, you need 10% less force to obtain it. When giving the value of Young modulus for cortical or trabecular bone, we don’t suppose isotropy simply giving the “best” value for the

1.3 Bones as a composite structure

37

FIGURE 1.18 Tibia structure divided into two parallel systems where F 5 F1 1 F2 to determine elementary compressive force on an idealized tibia representation.

material in the main direction of stress. Unfortunately for the scientist bone material is strongly anisotropic which translates in a very long list of mechanical characteristics if some have ever been measured. In 3D engineering calculus, strain/stress computations for material following Hooke’s law (strain is proportional to stress, strain/ stress graph is a line) stress and strain are represented by matrix sensor of order 2. Then Poisson’s coefficient, ν, enters the game. Any force applied in one direction modifies the orthogonal dimension. Compressing in one direction fatten in the perpendicular direction. This leads to some interesting standard relation between Young modulus and shear modulus: E 5 2ð1 1 ν ÞG

(1.2)

where E denotes the Young modulus, ν Poisson’s ratio and G shear modulus. And definition of the bulk modulus: K5

E 3ð1 2 2νÞ

(1.3)

where K denotes the bulk modulus, which links change of volume under change of pressure. Then another actor, anisotropy, brings its own action, complicating the computation which needs now 21 elastic parameters for the material. To sustain cautiousness with publicized precise bone mechanical characteristics, we have collected from literature values of bone density with a range of 0.4
0.8 g/cm3 for trabecular up to a range of 1.6
2 g/cm3 for the cortical. Remodeling is constant with yet unveiled laws of BMU constitution in numbers and location besides apparently faster cycling in epiphyses. We know consolidation of remodeled bones is a matter of months and figures of evolution of parameters during this “curing” time are rare. Overall,

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Chapter 1 Bone multiscale mechanics

stability of bone volume inside the BMU (which could be about a million at any given time) is at least agreed upon and somehow we can accept the concept to have Nature watching on having a more or less constant strength bone (evidently outside the effects of diseases). This is to say that caution should be used in proposing mechanical parameter values which should be rather proposed as a range of values. According to the literature, many proposition on the trabecular bone helping the cortical bone in sharing the load, even helping to bring part of the compression force to the mid-bone exempt of trabecular bone. In traditional engineering calculus, such set-up, cancellous/cortical arrangement leads to forget the trabecular bone in view of its inferior Young module. By consequence, advance spreading of force to mid trabecular bone could be a rather wild suggestion. In real world, pure compression (or tension) doesn’t exit. Natural forces and accidental forces are a set of different forces with any mix that you can think of. Then, computation of such a set of tensors is difficult. All the more that bone material parameters are changing with the stress meaning that they don’t follow the Hooke’s law (some are taking second degree fit curve) and using the classical additive way of separate stress modes is baseless. The computational machine power of today combined with algorithms and finite elements software can cope with the problem but three difficulties still impair solid results. First of all, getting a well-defined geometry of the bone, then having physical parameters mapped on it and finally the stress loading conditions. Left are the values at the limits which choice can be tricky for it can explode literally the results and otherwise is used sometimes to fit the actual results. Another factor to tackle for bone mechanical characteristics is fatigue. Overall fatigue is changing the stress/strain graph for with fatigue strain increases with less stress than before until fracture happens (aeroplane structural potential is fatigue determined). Apparently microcracks are appearing mainly in the interstitial zones (between HCs) of the cortical bone for they are supposed to be made of ancient bone and they are considered the main source and in the bulk of the trabecular bone with no very clear origin other than stress which is just what we consider a gapfilling answer. They are rather divergent opinions on the effects of microcracks in bones (both in the purely mechanical point of view and the biological point of view) which could be simply the result of the difficulties to investigate microdamage and evaluate precisely numbers and sizes of microcracks and correlate these characters to the bulk damage. We have in our opinion that the trabecular bone is not a direct structural direct element, at least as far as long bones are concerned, then is left the role of its existence. In part 2, we proposed that the trabecular bone is hierarchically above the cortical bone biologically. We have seen that its structure of 3D lattice adapts to change of load cycling frequency so it might be the stress captor network measuring for the command center (wherever it is). Besides, trabecular bone is at the epiphyses of the bones where cortical thickness is low but the diameter (average for sure) is high then ratio thickness/ diameter is very low. Some made extensive measurements with serial pQCT (Lu¨scher et al., 2019). In the middle of tibia diaphysis average values are a 90 mm perimeter with a 7 mm cortical thickness and at the metaphysis proxima 120 mm perimeter for a 3.5 mm thickness. Ratio thickness/diameter is then 0.25 in the middle of the bone and 0.09 at 80% of the bone from heel. Ratio of 0.09 is very low for a structural “tube”: it might be that the trabecular bone is filling the epiphysis for stability against

1.3 Bones as a composite structure

39

external transverse chock which could collapse the epiphysis. As wild as it sounds, other explanations, from a mechanical point of view don’t make sense. Concerning damping of forces which some think the trabecular bone an actor, we are still in the same configuration of having two parallel systems, not the best set for damping which is serial configuration. Shock with any amplitude results in an acoustic wave in the bone. Some tested the bones for acoustic propagation and found the acoustic wave speeds to be in the range 3400
4200 m/s in the cortical and 2200
2700 m/s in the porous trabecular bone tissue (Otani & Shimoi, n.d.). This means that the shock wave in the cortical is ahead of the shock wave in the trabecular bone, situation rendering damping of any sort difficult is even possible. Going further, and taking account of the hollow bone geometry, it might be possible for a shock to trigger shear waves on the endosteum, waves with slower speed then some damping might be possible as the acoustic propagation in the trabecular is complicated with two types of waves, slow and fast. Should be investigated. We are in the mechanical field where structural systems are designed with a safety coefficient. What about bones? If we look at the simple set of a 100 daN man and calculate the stress at the diaphysis of the tibia we find very roughly 2.5 MPa for about 100 1 MPa for the compressive yield strength of the cortical bone. So we are in a good situation even if dynamic forces can be many fold this value and a composite tensor can concentrate stress in certain locations. In fact, if muscles problems occur quite frequently, bone fractures are mainly the consequences of accidents with excessive shocks and bone problems, beside diseases, are often located in the joints and cartilages. We have briefly reviewed general aspects of bones and how they function above, talking about modulus of elasticity and other mechanical characteristics without looking at the very nature of bone, cortical and cancellous. In a simple way, when we look at the two bones that are made with the sandwich of the same materials, we would expect them to share the same graph for one parameter versus another, for example Young’s modulus relative to the bulk density. For bone, this is not the case. These are what are considered nominal bone characteristics, used in most mathematical and scientific analyzes and widely accepted. For the cortical bone, Table 1.4 summarizes the values of elastic mechanical properties found in the literature. Longitudinal compression, as indicated above, has its modulus of elasticity ranging from 15 to 20 or even 25 GPa (Reilly & Burstein, 1975; Van Buskirk et al., 1981; Yoon & Lawrence Katz, 1976). Given the complexity and diversity of forms of trabecular bone, its mechanical properties show great variability (Table 1.5). To adapt the elastic properties of bone via bone remodeling using a mechanobiological model, the most important thing is to relate the elastic modulus to the apparent density of the bone. Podshivalov et al. (Podshivalov et al., 2011) proposed a multiscale finite element (FE) model to compare between homogenized macroscale and high resolution micro FE modeling. Their multiscale model has several scale levels, in which bone material characteristics are updated based on the change of porosity in different material scales (Fig. 1.19). Effective mechanical properties vary from level to level due to the changes in geometry and porosity. Table 1.6 resumes several mathematical relationships between elastic modulus and apparent density based on specimen boundary conditions, specimen geometry, and anatomic site.

40

Chapter 1 Bone multiscale mechanics

Table 1.4 Elastic characteristics of human cortical bone. Transverse isotropy Mechanical tests E1 (GPa) E2 (GPa) E3 (GPa) G12 (GPa) G13 (GPa) G23 (GPa) Ѵ12 Ѵ13 Ѵ23 Ѵ21 Ѵ31 Ѵ32

11.7 11.7 18.2 — — — 0.63 — — 0.63 0.38 0.38

Ultrasound 18.8 — 27.4 — 8.7 — 031 — — — 0.28

Orthotropy Mechanical tests

Ultrasound

12.8 12.8 17.7 — 3.3 3.3 0.53 — — 0.53 0.41 0.41

13 14.4 21,5 4.74 5.85 6.56 0.37 0.24 0.22 0.42 0.40 0.33

Table 1.5 Elastic characteristics of human trabecular bone. References

Testing technique

Bone type

Elastic modulus (GPa)

Townsend et al. (1975)

Buckling

Human proximal tibia

Morgan and Keaveny (2001)

Experiment-FEA

Human Human Human Human Human Human Human Human Human Human Human Human Human Human Human Human Human Human Human

11.38 (wet) 14.13 (dry) 23.6 6 6 3.34 24.4 6 2.0 21.4 6 2.8 18.0 6 2.8 6.6 6 1.0 5.7 6 1.6 10 6 2.2 13.0 6 1.47 17.5 6 1.12 14.8 6 1.4 9.98 6 1.31 14.8 6 1.4 11.4 6 5.6 18.1 6 1.7 13.4 6 2.0 21.8 6 2.9 21.3 6 2.1 13.75 6 1.67 8.02 6 1.31

Bayraktar et al. (2004) Ladd et al. (1998) Hou et al. (1998) Homminga et al. (2002) Ashman and Rho (1988) Turner et al. (1999) Nicholson et al. (1997) Nicholson et al. (1997) Rho et al. (1993) Zysset et al. (1999) Turner et al. (1999) Roy et al. (1996) Chevalier et al. (2007) Hoffler et al. (2000)

Ultrasonic technique

Nanoindentation

proximal tibia greater femoral neck femoral neck vertebra vertebra proximal femur femur femur tibia vertebra tibia femoral neck distal femur vertebra femoral head femur distal radius vertebrae

1.3 Bones as a composite structure

41

FIGURE 1.19 Schematic flowchart of computing multiscale material properties: (A) representative elementary volume (RVE) homogenization for estimation of the effective material properties of the bone model at all intermediate levels; (B) a correlation between the porosity of the geometrical models and their respective effective material properties; (C) inverse local material properties model as a function of porosity. Adapted from Podshivalov, L., Fischer, A., & Bar-Yoseph, P. Z. (2011). 3D hierarchical geometric modeling and multiscale FE analysis as a base for individualized medical diagnosis of bone structure. Bone, 48(4). https://doi.org/10.1016/j.bone.2010.12.022.

Table 1.6 Mathematical relationships between Young’s modulus and bone density. References

Bone site

Elastic modulus (GPa)

Kopperdahl and Keaveny (1998) Morgan et al. (2003)

Human vertebra Human vertebra

E 5 2:1ρα 2 0:08

Human proximal tibia

E 5 15:520ρ1:93 α

Human proximal neck

E 5 4:730ρ1:56 α

Ciarelli et al. (2000)

Human proximal femur

E 5 6:850ρ1:49
α  E 5 7:541 BV=TV 2 0:637

Kaneko et al. (2004)

Human distal femur

E 5 10:88ρ1:61 α

Schaffler and Burr (1988)

Compact bone

E 5 0:09ρ7:4 α

Carter and Hayes (1977)

Compact bone specimens

E 5 3790_ε0:06 ρ3α (Continued)

42

Chapter 1 Bone multiscale mechanics

Table 1.6 Mathematical relationships between Young’s modulus and bone density. Continued References

Bone site

Elastic modulus (GPa)

Cory et al. (2010) Ashman et al. (1989)

Rat femur Human tibia

E1 5 3:711ρ1:87 E1 5 0:52ρ1:16 E2 5 0:79ρ1:14 E3 5 2:84ρ1:07

Human femur

E 5 10:89 ðBV=TVÞ2:84

Human femur

E 5 84:37 ðBV=TVÞ2:58 α2:74

Hernandez et al. (2001)

1.4 Concluding remarks • • • • • • •

Bone tissue is characterized by a multiscale structure of many scales levels. Bone quality depends on the structural properties of each of these scales. Bone is commonly classified in two main types: cortical and trabecular bones. Several research studies have been carried out to provide a better understanding of the mechanical composition and behavior of bone as a composite and multiscale material. A general law which expresses the modulus of elasticity as a function of the apparent density for trabecular bone is difficult to justify given the variations in trabecular structure observed experimentally. Bone modeling and remodeling are defined by laws that control external shape changes as function of the mechanical usage. A good mastery of the mechanobiological behavior of the bone over time requires a better understanding of its mechanics.

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Eppell, S. J., Tong, W., Lawrence Katz, J., Kuhn, L., & Glimcher, M. J. (2001). Shape and size of isolated bone mineralites measured using atomic force microscopy. Journal of Orthopaedic Research, 19(6). Available from https://doi.org/10.1016/S0736-0266(01)00034-1. Eppell, S. J., Smith, B. N., Kahn, H., & Ballarini, R. (2006). Nano measurements with micro-devices: Mechanical properties of hydrated collagen fibrils. Journal of the Royal Society Interface. Available from https://doi.org/10.1098/rsif.2005.0100. Facca, S., Cortez, C., Mendoza-Palomares, C., Messadeq, N., Dierich, A., Johnston, A. P. R., Mainard, D., Voegel, J. C., Caruso, F., & Benkirane-Jessel, N. (2010). Active multilayered capsules for in vivo bone formation. Proceedings of the National Academy of Sciences of the United States of America, 107(8). Available from https://doi.org/10.1073/pnas.0908531107. Franz-Odendaal, T. A., Hall, B. K., & Witten, P. E. (2006). Buried alive: How osteoblasts become osteocytes. Developmental Dynamics: An Official Publication of the American Association of Anatomists, 235(1), 176
190. Fratzl, P. (2008). Collagen: Structure and mechanics, an introduction. Collagen: Structure and Mechanics. Available from https://doi.org/10.1007/978-0-387-73906-9_1. Fratzl, P., Groschner, M., Vogl, G., Plenk, H., Eschberger, J., Fratzl-Zelman, N., Koller, K., & Klaushofer, K. (1992). Mineral crystals in calcified tissues: A comparative study by SAXS. Journal of Bone and Mineral Research, 7(3). Available from https://doi.org/10.1002/jbmr.5650070313. Fratzl, P., Gupta, H. S., Paschalis, E. P., & Roschger, P. (2004). Structure and mechanical quality of the collagen-mineral nano-composite in bone. Journal of Materials Chemistry. Available from https://doi.org/ 10.1039/b402005g. Fratzl, P., & Weinkamer, R. (2007). Nature’s hierarchical materials. Progress in Materials Science, 52(8). Available from https://doi.org/10.1016/j.pmatsci.2007.06.001. Gallant, M. A., Brown, D. M., Organ, J. M., Allen, M. R., & Burr, D. B. (2013). Reference-point indentation correlates with bone toughness assessed using whole-bone traditional mechanical testing. Bone, 53(1), 301
305. Hamed, E., Lee, Y., & Jasiuk, I. (2010). Multiscale modeling of elastic properties of cortical bone. Acta Mechanica, 213(1
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78. Hoffler, C. E., Moore, K. E., Kozloff, K., Zysset, P. K., Brown, M. B., & Goldstein, S. A. (2000). Heterogeneity of bone lamellar-level elastic moduli. Bone, 26(6). Available from https://doi.org/10.1016/ S8756-3282(00)00268-4. Hollister, S. J. (2014). BME 332: Introduction to biosolid mechanics. Constitutive Equations: Viscoelasticity. Homminga, J., McCreadie, B. R., Ciarelli, T. E., Weinans, H., Goldstein, S. A., & Huiskes, R. (2002). Cancellous bone mechanical properties from normals and patients with hip fractures differ on the structure level, not on the bone hard tissue level. Bone, 30(5). Available from https://doi.org/10.1016/S8756-3282 (02)00693-2. Hou, F. J., Lang, S. M., Hoshaw, S. J., Reimann, D. A., & Fyhrie, D. P. (1998). Human vertebral body apparent and hard tissue stiffness. Journal of Biomechanics, 31(11). Available from https://doi.org/10.1016/ S0021-9290(98)00110-9. Jackson, S. A., Cartwright, A. G., & Lewis, D. (1978). The morphology of bone mineral crystals. Calcified Tissue Research, 25(1). Available from https://doi.org/10.1007/BF02010772. Ja¨ger, I., & Fratzl, P. (2000). Mineralized collagen fibrils: A mechanical model with a staggered arrangement of mineral particles. Biophysical Journal. Available from https://doi.org/10.1016/S0006-3495(00)76426-5. Kaneko, T. S., Bell, J. S., Pejcic, M. R., Tehranzadeh, J., & Keyak, J. H. (2004). Mechanical properties, density and quantitative CT scan data of trabecular bone with and without metastases. Journal of Biomechanics, 37(4). Available from https://doi.org/10.1016/j.jbiomech.2003.08.010.

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CHAPTER

Bone remodeling biology

2

Abbreviations AKT ALP AP-1 ATF4 ATPase Atp6v0d2 Bcl-XL BGLAP BMI BMP BMPR1 BMU BRC BSP cAMP CCAAT CC3 CC3aR CD95L Col1α1 Cthrc1 CT1 c-Fos c-Fms c-Myc c-Src Dlx5 DMP1 Elk Endo180 Eph Ephrin ErbB2 ERK FARP2 Fas Fasl

protein kinase B alkaline phosphatase activating protein-1 activating transcription factor 4 adenosine triphosphatase V0 complex V-type proton ATPase subunit B-cell lymphoma-extra large bone gamma-carboxyglutamate protein bone mass index bone morphogenetic protein BMP receptor type 1 basic multicellular unit bone remodeling compartment bone sialoprotein cyclic adenosine monophosphate cytidine-cytidine-adenosine-adenosine-thymidine complement component 3 complement component 3a receptor CD95 ligand collagen, type I, alpha 1 collagen triple helix repeat-containing protein 1 cardiotrophin-1 proto-oncogene proto-oncogene proto-oncogene proto-oncogene distal-less homeobox 5 dentin matrix acidic phosphoprotein 1 erythroblastosis (ETS) like-1 protein endocytic recycling glycoprotein related to the macrophage mannose receptor erythropoietin-producing human hepatocellular (receptor) Eph receptor-interacting protein Erb-B2 receptor tyrosine kinase 2 extracellular signal-regulated kinase FERM, ARH/RhoGEF and pleckstrin domain protein 2 transmembrane protein Fas ligand

Bone Remodeling Process. DOI: https://doi.org/10.1016/B978-0-323-88467-9.00002-3 © 2021 Elsevier Inc. All rights reserved.

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GM-CSF GPI GPR48 GTPase HGF HSCs IGF IκK IL IRS-1 ITAM JNK LGR4 LPA LRP5 MAP MCP-1 M-CSF MEPE miR-214
3p MITF MKK6 MMP mTOR MT1-MMP MSCs NFATc1 NF-κB NO Nrp1 OCIF OCN ODF OPG OPGL OSCAR OSM Osx PC PDGF PDGF-BB PI3K PTH PTHrP p38 RANK RANKL Rac

granulocyte-macrophage colony-stimulating factor glycosylphosphatidylinositol leucine-rich repeat containing G-protein coupled receptor 48 guanosine triphosphatase hepatocyte growth factor hematopoietic stem cells insulin-like growth factor inhibitory-κB Kinase interleukin insulin receptor substrate 1 immunoreceptor tyrosine-based activation motif c-Jun N-terminal kinase leucine-rich repeat-containing G-protein-coupled receptor 4 lipoprotein (A) low density lipoprotein receptor-related protein 5 microtubule-associated proteins monocyte chemoattractant protein 1 monocyte colony-stimulating factor matrix extracellular phosphoglycoprotein microRNA-214
3p microphthalmia-associated transcription factor mitogen-activated protein kinase kinase 6 matrix metallopeptidase mechanistic target of rapamycin membrane type-1 matrix metalloproteinase mesenchymal stem cells nuclear factor of activated T cells 1 nuclear factor-kappa B nitric oxide neuropilin-1 osteoclastogenesis inhibitory factor osteocalcin outer dense fiber osteoprotegerin osteoprotegerin ligand osteoclast-associated receptor oncostatin M osterix polycystin platelet-derived growth factor platelet-derived growth factor-BB phosphoinositide 3-kinase parathyroid hormone parathyroid hormone related protein mitogen-activated protein kinase signal transduction pathway receptor activator of nuclear factor kappa-B receptor activator of nuclear factor kappa-B ligand Ras-related C3 botulinum toxin substrate 1

2.1 Bone cells

RGD RhoA Runx2 Satb2 SCF SCL Sema Shc SMAD SOST Sox9 Sp7 Src S1P S1PR TGFβ TNF TNFR TNK TRAcP TRAF TRANCE TRIP-1 uPARAP VDR VRVG Wnt W9

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arginine-glycine-aspartic acid Ras homolog family member A Runt-related transcription factor 2 special AT-rich sequence-binding protein-2 stem cell factor sclerostin semaphoring Src homology and collagen suppressor of mothers against decapentaplegic sclerostin enconding gene SRY (sex determining region Y)-box 9 specificity protein proto-oncogene tyrosine-protein kinase sphingosine-1-phosphate S1P receptor transforming growth factor beta tumor necrosis factor TNF receptor tyrosine kinase non receptor tartrate-resistant acid phosphatase tumor necrosis factor receptor-associated factor tumor necrosis factor (TNF)-related activation-induced cytokine TGFβ receptor interacting protein-1 urokinase plasminogen activator receptor
associated protein vitamin D3 receptor verorabvax wingless-related integration site W9 peptide

2.1 Bone cells 2.1.1 Osteoblasts Osteoblasts are cuboidal cells located on the newly synthesized bone interface and are strongly basophilic in their cytoplasm. They account for 4%
6% of the total bone cells and have two functions: a bone-building function, performed by producing matrix proteins, including Alp, OCN, and Col1α1, and an endocrine function, performed by releasing a large range of regulation factors that influence energy metabolism, as well as male fertility and cognition by producing OCN (Capulli et al., 2014; Rutkovskiy et al., 2016). Osteoblastic cells occupy the BMU tail portion and secrete and deposit osteoids, which are unmineralized bone matrixes. Osteoid formation and mineralization is directed into mature lamellar bone (Raggatt & Partridge, 2010). Osteoblast activity takes about 4 months, from their maturation until the synthesized bone matrix is detected by the cell (Canalis, 2008). Bone-forming osteoblasts are, in fact, post-mitotic cells, but not fully differentiated (Fig. 2.1). After surrounding themselves by the newly synthesized matrix, they differentiate into osteocytes, whereas the remaining osteoblasts on the bone surface facing the periosteum differentiate into inert bone-lining cells or undergo apoptosis (Rutkovskiy et al., 2016).

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FIGURE 2.1 Mature osteoblast final differentiation.

Osteoblasts originate from mesenchymal stromal cells (MSCs), also known as mesenchymal stem cells or as bone marrow stromal cells (Bernhardt et al., 2010), according to two distinct embryonic populations. For the first embryonic population, that is myogenic lineage, osteoblastlineage cells originate from the neural ectoderm. In this case, the mesenchymal progenitors directly differentiate into preosteoblasts, and the derived mature osteoblasts build calvarian bones and clavicles through intramembranous ossification. For the second embryonic population, that is adipogenic lineage, the MSCs differentiate into perichondral cells and chondrocytes, and a subsequent chondrocyte hypertrophy drives the perichondral cell differentiation into preosteoblasts. Then, osteoblasts build bone in the axial skeleton and extremity bones through endochondral ossification (Fedarko, 2014; Nishimura et al., 2012; Yang et al., 2014). The differentiation of mesenchymal progenitors into preosteoblasts involves a number of the socalled master transcriptional regulators, such as (1) Sox9, required for chondrogenesis and endochondral bone development, marking the MSCs that differentiate into osteoblasts and participating in preosteoblast commitment, and (2) Runx2, an osteoblast differentiation master gene that upregulates osteoblast-related genes (Col1α1, Alp, BSP, BGLAP) and modulates bone-specific marker expression (Capulli et al., 2014; Fedarko, 2014; Long, 2012; Zhou et al., 2010). In the endochondral pathway, Runx2 activation is preceded by Sox9, which limits the stem cell potential to differentiate into osteoblasts and chondroblasts (Rutkovskiy et al., 2016). Following Runx2 activation, the defined preosteoblasts become mature osteoblasts through a three stage differentiation process, during which a number of molecular markers is expressed, including fibronectin, collagen, TGFβ1, osteopontin, Alp, and OC, and after which osteoblasts acquire their characteristic cuboidal shape (Long, 2012; Stein et al., 2004). Moreover, Osx, also known as SP7, is a Runx2 downstream target that regulates the development and homeostasis of osteoblast and osteocyte differentiation and functions, and promotes Satb2 transcriptional expression required for the transcription regulation and chromatin emodeling (Celil & Campbell, 2005; Dobreva et al., 2003; Tang et al., 2011). Satb2 is also related to BSP and OCN expression and its interaction with Runx2 and ATF4 provides a positive regulation of osteoblast markers (Yang et al., 2004). Fig. 2.2 illustrates the different stages of osteoblast differentiation form MSCs.

2.1 Bone cells

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FIGURE 2.2 Osteoblast differentiation stages.

2.1.2 Osteoclasts Osteoclasts are giant multinucleated cells that hydrolyze and solubilize both of the inorganic and organic bone components, owing to their polarized secretion of acid and proteolytic enzymes, such as cathepsin K. Therefore, osteoclasts provide bone with a unique characteristic of being the only tissue in the body able to undergo a self-destruction, fulfilling thereby a crucial physiological process for bone homeostasis. Osteoclast-secreted protons and enzymes target the resorption lacunae, and the osteoclast apical membrane is surrounded by a sealing zone of densely packed podosomes to partition the resorption lacunae from the rest of the bone microenvironment (Charles & Aliprantis, 2014). Osteoclasts derive from the fusion of monocyte-macrophage precursors (Heinemann et al., 2011) originating from HSCs in the marrow (Wang et al., 2015). The hematopoietic precursors for osteoclast formation are provided through the capillary blood supply closely associated with and penetrating the BRC (Kristensen et al., 2013), as well as from nearby marrow precursors (Sims & Martin, 2014). Indeed, factors, such as SCF, IL-3 and IL-6, stimulate HSCs to give rise to common myeloid progenitors. The latter are then stimulated by GM-CSF to differentiate into granulocyte/ macrophage progenitors that are, in turn, stimulated by M-CSF to differentiate into monocyte/macrophage-lineage cells, considered as preosteoclasts. Afterwards, osteocytes recruit the preosteoclasts to the BRC. These precursors must be attached to the bone matrix in order to differentiate into mature osteoclasts (Xu & Teitelbaum, 2013). The programming of osteoclast formation involve the actions of osteoblast-lineage cells, endothelial cells, and BRC microenvironment, which produce M-CSF, RANKL, VRVG, and NO (Kristensen et al., 2013).

2.1.3 Osteocytes Osteocytes are easily identified in a bone section, owing to the matrix in which they are completely embedded. In the adult skeleton, they are the most abundant cells, accounting for 90%
95% of all

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bone cells, and the most-long lived ones, with up to 25-year-lifespan. Their cell surface is approximately 400-fold larger than that of the whole Haversian and Volkmann system, and more than 100fold larger than that of the trabecular bone (Capulli et al., 2014). Osteocytes are trapped within the matrix during skeletal maturation of previous remodeling cycles (Bonewald, 2011), and are characterized by a stellar/spider-shape, forming an extensive interconnected network of up to 50 long and branched cellular processes within a fluid-filled canalicular system (Buenzli & Sims, 2015). These processes contact each other, and probably other cell populations, through gap junctions, providing a cell-cell interaction mediated by an intercellular exchange of small signaling molecules, such as NO and prostaglandins. This network plays a crucial role in regulating bone material turnover, by coordinating bone response to mechanical signals, as well as to endocrine and paracrine biological signals (Civitelli, 2008; Schaffler et al., 2014). Indeed, osteocytes are the dominant mechanosensory and RANKL-producing cells (Xu & Teitelbaum, 2013). They have both local and systemic effects, through responding to the strains generated by mechanical stimuli and translating the load into biochemical signals via a mechanotransduction mechanism (Bonewald, 2011; Noble, 2008), which is one of the main factors initiating the remodeling process. The mechanosensing property is mediated by PC1, PC2, and the osteocyte cytoskeleton (Santos et al., 2010; Xiao et al., 2006). Osteocytes sense the increase in the strain owing to the resorption-related progressive bone weakening (McNamara et al., 2006), detect the relieved strain during bone formation, and provide the final refining control to ensure a sufficient new deposited bone amount by osteoblasts, which is generated in response to osteoclastic messages, whether directly or via other cells within the BMU (Sims & Martin, 2015). Osteocytes also regulate and modulate osteoblast and osteoclast behaviors, as explained below. Osteocytes emerge from the differentiation of a subset of mature osteoblasts that are embedded in the newly synthesized osteoid matrix before its mineralization (Tate et al., 2004). Indeed, mature osteoblasts undergo a four-stage differentiation process to become mature osteocytes (Fig. 2.3): (1) type I preosteocytes,

FIGURE 2.3 Osteocyte differentiation steps.

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named osteoblastic osteocytes, (2) type II preosteocytes, named osteoid-osteocytes, (3) type III preosteocytes, named young osteocytes, and (4) old osteocytes (Franz-Odendaal et al., 2006). Type I and II preosteocytes occur before the osteoid mineralization and are able to synthesize and secrete collagen. Type III preosteocytes occur when the matrix is still not completely mineralized, and the old or mature osteocytes are formed after the complete matrix mineralization. At this final stage, osteocyte markers, such as DMP1 and SOST, are highly expressed, whereas the previously expressed osteoblastic markers, including Alp, collagen type I, BSPII, and OCN, are downregulated or switched off (Capulli et al., 2014).

2.1.4 Reversal cells The phenotype of the reversal cells had long been unclear until recent years. Due to systematic investigations, the reversal cells were found to belong to osteoblast-lineage cells that seem to particularly be preosteoblasts (Abdelgawad et al., 2016). In trabecular bone, the reversal cells are, indeed, preosteoblastic cells that progressively mature into bone-forming osteoblasts (Andersen et al., 2013; Kristensen et al., 2014) and that play a crucial role in the resorption-to-formation coupling mechanism (Andersen et al., 2013, 2014; Jensen et al., 2015). Moreover, the late reversal cells positioned proximal to osteoblasts are more mature than the early ones positioned proximal to osteoclasts (Abdelgawad et al., 2016). The reversal cell intermediate position between osteoblasts and osteoclasts suggests their obvious contribution to the osteoblast-osteoclast interplay (Delaisse, 2014). Even though all the reversal cells are osteoblastic cells, the early ones located next to osteoclasts appear to be quite different from the late ones located next to osteoid surfaces, in terms of morphology, ultrastructure, and immunohistochemistry. These differences reflect their diverse cellular interactions, varied functions, and distinct differentiation states (Abdelgawad et al., 2016; Andersen et al., 2013; Kristensen et al., 2014).

2.1.5 Bone lining cells When examining bone surfaces by electron microscopy, a flat cell layer with a thin nonmineralized matrix seam is distinguished. The cells forming this layer are known as bone lining cells (Dierkes et al., 2009). As mentioned above, these lining cells are an osteoblast subpopulation. Interestingly, osteoclastogenesis initiation was found to be tightly related to an interaction established between the lining cells and the osteoclasts attached to bone, due to a close contact between the two cell types (Everts et al., 2002; Matsuo & Irie, 2008). Besides, the lining cells were found to be able to establish physical homotypic connections with osteocytes through gap functions. This suggests that the lining cells form a functional membrane separating bone from interstitial fluids (Wein, 2017). Particularly during the remodeling cycle, bone lining cells persist over the remodeling sites to isolate osteoblasts and osteoclasts from bone marrow (Parfitt, 2001). In fact, at the very beginning of a remodeling cycle, the lining cells separate and raise from the underlying bone surface, forming a canopy above the site to be resorbed. This initiating phenomenon might result from osteocyte signaling to surface cells through their canaliculae when they recognize the need for replacing a specific bone area (Verborgt et al., 2000). Subsequent signals could come from osteocyte apoptosis or

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from the lining cells themselves, generating the release of paracrine factors and chemokines, which attract the precursors of both osteoblasts and osteoclasts, as well as other required vascular elements (Sims & Ng, 2014).

2.2 Bone remodeling cycle 2.2.1 Activation phase The activation phase is the first stage of the remodeling cycle. It implies the detection of a signal that initiates the remodeling process and that may result from diverse actions, such as a direct mechanical strain, to which bone is subjected, and which leads to structural damage, or a hormone action, to which bone cells are subjected, and which occurs in response to systemic changes in homeostasis (Raggatt & Partridge, 2010). Under basal conditions, the activation phase is controlled by two main factors, TGFβ and PTH. The secretion of TGFβ inhibits osteoclastogenesis and the decrease of its levels promotes osteoclast formation (Heino et al., 2002), whereas the bending of PTH to its receptor, expressed on osteoblastic cell membranes, spearheads the production/modulation of the secretion of specific molecules that recruit preosteoclasts, generate osteoclast differentiation and activation, and establish bone resorption (Swarthout et al., 2002).

2.2.2 Resorption phase In response to direct endocrine activation signals or to osteocyte-generated signals, osteoblasts recruit preosteoclasts to the activated BMU. Likewise, in response to PTH-induced bone remodeling, osteoblasts produce MCP-1 that chemically attracts preosteoclasts and enhances RANKL-induced osteoclastogenesis (Li et al., 2007). In addition, PTH reduces OPG expression by osteoblasts, and increases MCSF-1 and RANKL expression by the same cells, which stimulates osteoclast formation and activity (Ma et al., 2001). Osteoblasts also secrete MMP13 in response to endocrine and mechanical signals, altering thereby the unmineralized osteoid lining the bone surface and exposing RGD adhesion sites within the mineralized bone, which facilitates osteoclast attachment to the bone surface. Then, osteoclasts anchor RGF-binding sites via v3 integrin molecules (McHugh et al., 2000) and create an isolated microenvironment beneath the cell, called the “sealed zone.” Afterwards, hydrogen ions are pumped into the sealed zone and the mineralized matrix is dissolved in this acidic zone, resulting in the production of Howship’s resorption lacunae. A number of collagenolytic enzymes degrade the remaining organic matrix, using a low pH optimum, in particular, cathepsin K (Teitelbaum, 2000).

2.2.3 Reversal phase In the reversal phase, the reversal cells remove the remaining undigested demineralized collagen matrix that covers the Howship’s resorption lacunae, and then prepare the bone surface for the subsequent formation phase. Interestingly, it was reported that the events taking place during the

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reversal phase are facilitated by the cooperative activities of both osteomacs and mesenchymal bone lining cells. It was suggested that osteomacs remove the matrix debris and that macrophages can produce MMPs required for the matrix degradation (Newby, 2008; Raggatt & Partridge, 2010). Macrophages are also able to produce osteopontin (Takahashi et al., 2004), which is incorporated into the mineralized tissue. Nevertheless, the collagenous matrix formed along the osteopontin rich cement lines within the Howship’s resorption lacunae is likely to be deposited by mesenchymal lining cells. The final contribution of the reversal cells is the production of coupling signals that allows the transition from the resorption phase to the formation one (Everts et al., 2002).

2.2.4 Formation phase The nature of the coupling signal that coordinates the transition from the resorption phase to the formation one at the precise same sites remains controversial. Several candidate coupling mechanisms have been proposed. For instance, the soluble molecule S1P secreted by osteoclasts induces preosteoblasts recruitment and promotes mature osteoblast survival (Pederson et al., 2008). Besides, EphB4-ephrinB2 bidirectional signaling complex, detailed below, consists of a forward signaling through EphB4 into osteoblasts, improving osteogenic differentiation, and a reverse signaling through ephrinB2 into preosteoclasts, inhibiting osteoclastogenic c-Fos/ NFATc1 cascade and suppressing thereby osteoclast differentiation (Zhao et al., 2006). Thus, the EphB4-ephrinB2 signaling complex govern the simultaneous bone resorption inhibition and bone formation initiation. However, preosteoblasts are likely a more susceptible target for coupling factors than mature osteoblasts. Interestingly, preosteoblasts can detect the eroded area size and shape without the mediation of any accessory cell and preferentially deposit new bone matrix in those areas (Sims & Martin, 2015). Therefore, the information required to initiate and complete the formation phase requires the input arising from the existence of pits formed by osteoclasts, but also the input arising from other cell populations, as detailed in the next section.

2.2.5 Termination phase The termination phase concludes the remodeling cycle. It is initiated when an appropriate new bone quantity is formed and marks the release of largely unknown termination signals that inform the remodeling actors to cease work. Nevertheless, the inhibition of SCL expression that was found to lunch bone formation appears to be one of the events marking the end of the remodeling cycle. The termination phase takes places after bone matrix mineralization, when mature osteoblasts undergo apoptosis, differentiate into osteocytes when embedded in the mineralized matrix, and revert back to form lining cells otherwise. The bone surface environment establishes and maintains its resting state until the initiation of the next remodeling cycle (Raggatt & Partridge, 2010) (Fig. 2.4). Fig. 2.4 illustrate the four main phases of the remodeling cycle: the activation, the resorption, the formation, and the termination phases, without taking into account the reversal phase, which is intermediate between the resorption and the formation phases, since most of the events target the formation-to-resorption coupling mechanisms.

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FIGURE 2.4 Bone remodeling cycle.

2.3 Bone cell interactions 2.3.1 Effects of osteoblasts on osteoclasts Osteoblastic-lineage cells govern the bone mass variation. Over the years, clear evidence have demonstrated osteoblast ability to influence osteoclast formation in a paracrine manner. Indeed, osteoblasts modulate osteoclast formation and activity by synthesizing a number of cytokines and growth factors. This is achieved through a direct contact between the two cells, established by exchanging small water-soluble molecules through formed gap junctions (Chen et al., 2018). Osteoblasts produce two main osteoclastogenesis activators; M-CSF and RANKL. M-CSF is a cytokine that binds to its receptor c-Fms expressed on preosteoclast membranes (Chen et al., 2018), promoting their survival, proliferation, differentiation, migration, function, and cytoskeletal reorganization (Capulli et al., 2014; Heinemann et al., 2011). Besides, M-CSF up-regulates RANK expression in bone marrow precursors and enhances their differentiation into preosteoblasts (Sambandam et al., 2010), activates MITF, up-regulates Bcl-XL expression, and inhibits the activity of both caspases 3 and caspases 9, preventing thereby osteoclast apoptosis (Boyce, 2013;

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Tanaka et al., 2006; Woo et al., 2002). In turn, RANKL, also called ODF, TRANCE, and OPGL, is the most potent osteoclastogenic cytokine (Takayanagi, 2012). It is highly secreted by osteoblasts, but also by preosteoblasts and osteocytes. Typically, RANKL membrane bounds on osteoblasts, but may, as well, be secreted as a soluble cytokine in low quantities (Capulli et al., 2014; Tamma & Zallone, 2012). RANKL expression is regulated by a number of hormones, cytokines, and growth factors, such as estrogen, PTH, and inflammatory cytokines. RANKL binds to its receptor RANK located on osteoclast progenitor cell membranes (Heinemann et al., 2011). RANK is a type I transmembrane protein highly secreted by preosteoclasts and mature osteoclasts, among other cell types and tumors (Fata et al., 2000; Kim et al., 2006). The RANK/RANKL complex forms a crucial pathway for osteoclast differentiation, mainly relying on a cell-cell communication between osteoblasts and preosteoclasts (Capulli et al., 2014). This complex activates preosteoclast fusion and differentiation into mature osteoclasts, by activating the downstream signaling pathway transcription factors NFATc1, c-FOS, and NF-κB (Wang et al., 2015), and also activates the TRAF family, including TRAF2, TRAF5, and TRAF6. RANK/TRAF use different signaling pathways to regulate osteoclast formation, survival and function, among which calcineurin/NFATc1, IκK/NF-κB/c-Myc and JNK/ AP-1 participate in osteoclast formation, while src and MKK6/p38/MITF participate in their activation (Boyle et al., 2003; Takayanagi, 2007). However, RANKL effects are inhibited by OPG. OPG, also known as OCIF, is a soluble member of the TNFR superfamily (Tamma & Zallone, 2012) produced by osteoblasts, along with several other cell types. Its expression in osteoblasts is controlled by several growth factors, cytokines, and hormones, such as estrogen, TNK, and 1,25(OH)2D3 (Theoleyre et al., 2004). OPG is a soluble protein antagonist for RANKL. Hence, the interaction between RANKL and its RANK is blocked by the binding of OPG to RANKL (Boyle et al., 2003). Moreover, OPG can inhibit TNF-related apoptosis-induced ligand, causing osteoclast apoptosis inhibition (Chamoux et al., 2008). Therefore, OPG can inhibit the major signaling pathway of osteoclast differentiation and activation, that is, bone resorption is governed by the quantitative synthesis of RANKL and OPG by osteoblast-lineage cells (Kadow-Romacker et al., 2013), and a balanced osteoclastogenesis rate relies on a balanced RANKL/OPG ratio (Asagiri et al., 2005; Kadow-Romacker et al., 2013; Nakashima et al., 2011; Takayanagi, Kim, Koga, et al., 2002; Takayanagi, Kim, Matsuo, et al., 2002; Wang et al., 2015). Collectively, RANK/RANKL/OPG signaling pathway represents the best-established regulatory mechanism that controls osteoclast development and activity. It should also be noted that LGR4, also known as GPR48, is another decoy receptor for RANKL. LGR4 is expressed in osteoclasts and directly interacts with RANKL, and inhibits its binding with RANK in a dose-dependent manner. Hence, LGR4 and RANK compete in binding with RANKL (Luo et al., 2016). In response to most of the hormones and cytokines, including 1,25(OH)2D3, osteoclast formation is tightly associated with the presence of osteoblast-lineage cells and their RANKL production rate (Sims & Ng, 2014). A number of osteoblast-derived local factors that promote RANKL production was also found to be required for 1,25(OH)2D3-induced osteoclast formation, such as OSM (Walker et al., 2010), Sema3B (Sutton et al., 2008; Walker et al., 2010), and glycoprotein 130 (Shin et al., 2004). The expression pattern of RANKL, OPG, and M-CSF is also influenced by various regulation players (Boyle et al., 2003), such as PTH that induces RANKL expression in osteoblasts (Martin et al., 2006). Moreover, the bending of FasL, also known as CD95L and expressed in osteoblast-lineage cells, with its Fas receptor, expressed in osteoclast-lineage cells, forms an important paracrine apoptotic

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signal (Hohlbaum et al., 2000; Micheau & Tschopp, 2003; Zhang et al., 2008). Indeed, FasL expression is upregulated by estrogen and affects osteoclast survival, while giving rise to osteoblast-mediated osteoclast progenitor apoptosis (Krum et al., 2008). 17b-estradiol (E2) can also upregulate the expression of MMP3 that cleaves the full-length FasL into soluble FasL, which mediates the E2-induced osteoclast apoptosis. The presence of MMP3 specific inhibitor decreases extensive cleavage (Garcia et al., 2013) and soluble FasL concentrations, and a conditional knockout of FasL in osteoblasts increases osteoclast number and function. Besides, osteoclast progenitors express lower Fas levels than mature osteoclasts (Wang et al., 2015). Therefore, osteoclast progenitors may have a low sensitivity to osteoblast-induced osteoclast apoptosis via the FasL/Fas pathway (Chen et al., 2018). This same osteoblast-dependent mechanism also induces preosteoclast apoptosis through raloxifene and tamoxifen (Kousteni et al., 2002; Krum et al., 2008; Nakamura et al., 2007). Furthermore, osteoblasts produce LPA (Hosogaya et al., 2008; Sims et al., 2013), required in osteoclastogenesis and in the enhancement of osteoclast progenitor cell fusion (David et al., 2010; McMichael et al., 2010). It can regulate osteoclast activity and calcium signaling, and can induce NFATc1 nuclear accumulation in osteoclasts, which is an essential signaling pathway in osteoclast formation (Boyle et al., 2003; Lapierre et al., 2010; Panupinthu et al., 2008). LPA also showed a possible ability of suppressing osteoclast apoptosis and inducing morphology changes in mature osteoclasts (Lapierre et al., 2010). In addition, osteoblasts are great producers of PTHrP, IL-1β, IL-6, IL-11, TNF-α, oncostatin M, and leukemia inhibitory factor. All of these paracrine factors, along with M-CSF and RANKL, trigger osteoclastogenesis in both physiologic and pathologic conditions. However, they also produce IL-3, IL-12, IL-18, which are antiosteoclastogenic factors, along with OPG and GM-CSF (Teitelbaum, 2005, 2007; Teti, 2013; Walsh & Gravallese, 2010). Such a specific, powerful, and finely regulated signaling system that osteoblast-lineage cells use to influence osteoclast-lineage cells, draws the attention to the existence of a reverse signaling system from osteoclasts to osteoblasts within the BMU (Karsdal et al., 2007; Martin & Sims, 2005).

2.3.2 Effects of osteoclasts on osteoblasts Both active and inactive osteoclasts promote bone formation by stimulating preosteoblast recruitment and differentiation (Martin & Sims, 2005), due to osteoclast-derived coupling factors: S1P, BMP-6, Wnt10b (Pederson et al., 2008), CT1 (Walker et al., 2008), Cthrc1 (Takeshita et al., 2013), CC3a (Matsuoka et al., 2014), TRAcP, phrins n K, and hepatocyte growth factor (Kiviranta et al., 2001; Lotinun et al., 2013; Teti, 2013). For instance, CT1 was detected in active osteoclasts and found to reduce SCL expression, acting thereby on osteocytes located near the resorption lacuna by entering the lacunar-canalicular network. If SCL expression remains suppressed in the resorptive site when mature osteoblasts reach the bone surface, the formation phase occurs in this area (Karsdal et al., 2007; Martin & Sims, 2005) (Sims & Martin, 2015). Besides, LRP5 acts on osteocytes and may act on late-stage osteoblasts, allowing to modulate bone mass through canonical Wnt signaling (Cui et al., 2011; Gong et al., 2001). In addition, BMP-6 and Wnt10b are two important anabolic agents highly expressed by osteoclasts (Baron & Rawadi, 2007; Vukicevic & Grgurevic, 2009). Both of these agents enhance bone formation rate (Pederson et al., 2008). However, these coupling factors are not all

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exclusively produced by osteoclasts, but they are also produced by other cell lineages in the BMU vicinity (Karsdal et al., 2008). For this reason, anti-resorptive factors inhibiting osteoclast activity, such as cathepsin K inhibitors, may reduce bone resorption without reducing its formation, which leads to potential anabolic effects (Sims & Ng, 2014). Owing to the time delay between the resorption and the formation activities, these factors probably exist in an unstable form throughout the reversal phase and affect osteoblast-lineage cells (Pederson et al., 2008; Walker et al., 2008). Currently considered as an important bone formation mediator, S1P is highly expressed by osteoclasts and may have both inhibitory and stimulatory effects on osteoblasts, depending on their differentiation stage and on the preosteoblast source (Pederson et al., 2008; Quint et al., 2013; Ryu et al., 2006). Preosteoclasts egress from the vasculature is stimulated by chemotactic factors, such as S1P, for which the required process is stimulated by 1,25(OH)2D3 (Kikuta et al., 2013). S1P is also expressed by other cells in the vasculature and interacts with its receptor expressed in preosteoclasts (Ishii et al., 2009). It was found to limit the resorption activity by promoting chemotaxis and facilitating preosteoclast migration from bone to blood, through its action on its S1PR1 receptor (Ishii et al., 2010), whereas its S1PR2 receptor mediates the chemorepulsion reverse effect, causing a change in preosteoclast direction from blood to bone (Kikuta et al., 2013). However, S1PR2 production is suppressed by vitamin D, which causes the inhibition of osteoclast generation and their resorptive activity (Kikuta et al., 2013). These S1P-related actions are all the more intriguing, because S1P represents one the many osteoclast-derived factors that contribute to the formation-to-resorption coupling mechanism (Sims & Martin, 2014). Despite the suggestive S1P role in the coupling mechanism within the BMU, further exploration of its actions should be performed (Alvarez et al., 2007; Sims & Ng, 2014). In the adult skeleton, Cthrc1, which is an osteogenesis stimulatory protein, is only produced by mature osteoclasts and was suggested to be a coupling factor that positively acts on bone formation (Takeshita et al., 2013). Cthrc1 could be a further actor in local events contributing to the overall remodeling process (Sims & Ng, 2014). Indeed, it enhances chemotaxis, osteoblast differentiation and matrix mineralization, increases osteoblast-specific gene expression, and accelerates osteoblast proliferation. Moreover, it is associated with the Wnt family signaling and is a downstream target of BMP-2 (Yamamoto et al., 2008; Zhao et al., 2006). Osteoblast differentiation was also found to be stimulated by the CC3 bioactive fragment 3a expressed by osteoclasts, with its receptor CC3aR being expressed in primary calvarial osteoblasts, as well as in stromal cell lines. In addition, it was suggested that CC3a in osteoclast-derived CM may enhance osteoblast-derived Alp activity, which may be increased by the presence of CC3aR agonist (Matsuoka et al., 2014). Indeed, the resorption-to-formation coupling may be mediated by CC3a in a high turnover model. Yet, CC3 effects on osteoblast-lineage gene expression is still not well-known (X. Chen et al., 2018). Owing to its anabolic properties, osteoclast-derived TRAcP may promote preosteoblast differentiation (Sheu et al., 2003; Sheu et al., 2002), which makes it a potential molecule in the coupling mechanism. TRAcP converts into an ATPase by enzymatic cleavage by cathepsin or trypsin and the TRIP-1 is one of its substrates (Miti´c et al., 2005; Sheu et al., 2003). However, the way these factors affect the remodeling phases has not yet been elucidated. Osteoblast function may be suppressed under the action of osteoclast-secreted sclerostin, an antagonist of the Wnt pathway (Kusu et al., 2003). Plus, BMPR1 signal-transduction pathway may contribute to negative regulation of bone formation by osteoclasts (Okamoto et al., 2011),

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highlighting the need for balanced stimulation/inhibition cycles of osteoblast activity to provide a controlled dynamic interaction between osteoblasts and osteoclasts (Teti, 2013). PDGF-BB is another osteoclast-induced factor that regulates bone formation by exhibiting complex activities on osteoblast-lineage cells (Kubota et al., 2002; Matsuo & Irie, 2008; O’Sullivan et al., 2007; Sanchez-Fernandez et al., 2008), but more work is still needed to fully elucidate the event cascade in which PDGF-BB is involved. Osteoblast-lineage cell proliferation is enhanced by the action of osteoclast-secreted HGF through AP-1, c-Src, AKT, and PI3K pathways, which induce osteopontin, a SIBLING extracellular matrix protein family member, and which are promoted by HGF canonical c-Met receptor (Chen et al., 2012). Interestingly, the osteoclast-derived HGF induces both osteoclast and osteoblast proliferation and motility, acting thereby as an autocrine-paracrine growth factor (Tamma & Zallone, 2012). It should also be noted that bone remodeling and osteoclastogenesis processes involve the interaction between integrin-mediated preosteoclasts and type I collagen, and that the expression of OSCAR by preosteoclasts stimulates osteoclastogenesis (Barrow et al., 2011; Bernhardt et al., 2010; Nemeth et al., 2011). Osteoclasts can also produce exosomal miR-214
3p that exerts negative actions on osteoblast efficiency in forming bone, and its presence is associated with the decrease in the formation rate (Li et al., 2016). They can also produce miRNA-enriched exosomes that use ephrinA2/EphA2 to recognize osteoblasts and inhibit their activity by transferring miR-214 into them (Sun et al., 2016). Furthermore, osteoclasts highly express Atp6v0d2, the functional importance of which is still not well-known yet (Rho et al., 2002). On one hand, a decrease in Atp6v0d2 is associated with an increase in osteoblast number and in bone mass. On the other hand, a decrease in Atp6v0d2 affects osteoclast maturation, but not their differentiation. Besides, Atp6v0d2 is linked to cell-cell fusion and mature giant osteoclast formation decreases in the absence of Atp6v0d2 (Lee et al., 2006). Notably, osteoblast-osteoclast crosstalk may also be established a through bidirectional signaling, where osteoclasts generate a forward signaling to directly act on osteoblasts, and osteoblasts respond by generating a reverse signaling that directly acts on osteoclasts.

2.3.3 Bidirectional regulations between osteoblasts and osteoclasts Direct osteoblast-osteoclast communication is also mediated by bidirectional signals, involving the interaction of the Eph receptor/ligand pathways (Matsuo & Irie, 2008). The Eph family of receptor tyrosine kinases and their membrane-bound ligands (ephrins) represent another class of axon guiding molecules (Sims & Ng, 2014) that exert relevant functions in skeletal development and bone remodeling (Sims, 2010). When an ephrin interacts with its corresponding Eph, both become activated and generate a bidirectional signaling (Murai & Pasquale, 2003). Giving the fact that both the receptor and the ligand are able to induce intracellular signaling, the distinction between them is made based on their structure instead of their function. Indeed, because Ephs mediate a forward signaling that stimulates osteoblast differentiation by blocking the small GTPase and RhoA, promoting thereby bone formation. In turn, ephrins initiate a reverse signaling that inhibits osteoclast formation by down-regulating NFATc1 and c-Fos expressions. However, ephrins and Ephs are subdivided into two subclasses, A and B, according to sequence conservation and to their affinities for each other. Type A Ephs preferentially bind the GPI-linked type A ephrins and type B Ephs preferentially bind to type B transmembrane ephrins. Eph/ephrinA signaling promotes osteoclast

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formation and inhibits osteoblast differentiation, whereas Eph/ephrinB signaling exerts the reverse effect on both cell populations (Tamma & Zallone, 2012). Nevertheless, exceptions should be noted, for instance in the case of ephrinA5 that binds to and activates EphB2 (Himanen et al., 2004; Murai & Pasquale, 2003), as well as ephrinB1 that activates EphB4 (Holmberg et al., 2005). Ephs and ephrins can be expressed by bone cells, as well as by their precursors. Particularly, osteoclasts express ephrinB2, linked to RANKL-induced c-Fos/NFATc1 transcriptional cascade during osteoclast differentiation (Zhao et al., 2006), whereas preosteoblasts display EphB4, known to induce osteogenic regulatory factors, such as Dlx5, Osx, and Runx2 (Chen et al., 2018; Irie et al., 2009), and this contact-dependent mechanism simultaneously promotes osteoblast differentiation and suppresses preosteoclast formation (Zhao et al., 2006). Therefore, ephrinB2/EphB4 complex affects both of the cell lineages and its inhibition reduces late osteoblast differentiation marker expression (Tamma & Zallone, 2012). Both ephrinB2 mRNA and protein are upregulated in response to both PTH/PTHrP and ephrinB2, through its action on EphB4. These data reveal a paracrine-autocrine action of ephrinB2 on EphB4 or EphB2, regulated by PTH or PTHrP in osteoblasts, and contributing as a local event to PTH or PTHrP anabolic actions (Allan et al., 2008). However, the ephrinB2/Eph4 bidirectional signal seem to be counterbalanced by the ephrinA2/ EphA2 pathway that regulates the remodeling process in the initiation phase. EphrinA2, expressed by osteoclast-lineage cells, promote osteoblast differentiation, whereas EphA2, expressed by preosteoblasts, exerts antiosteoblastogenic signals that inhibit bone formation (Kang & Kumanogoh, 2013). The ephrin/Eph bidirectional signaling allowed to quickly explain the coupling mechanism. Yet, the formation of ephrin/Eph complex requires direct contact between active bone-resorbing osteoclasts and osteoblast-lineage cells that are able to progress through differentiation to bone formation. However, a direct osteoblast-osteoclast contact within the BMU in vivo is likely rare to happen. Such cell-cell interaction mechanisms may rather occur in the bone marrow space between preosteoblasts and osteoclasts, or in the remodeling canopy (Kristensen et al., 2014; Kristensen et al., 2013). Besides, ephrinB2-induced inhibition of osteoclast formation probably requires contact between osteoblasts and osteoclast progenitors, rather than being restricted to a contact between osteoblasts and mature active osteoclasts. This has led to consider that osteoclast-derived ephrinB2 does not significantly contribute to the coupling mechanism (Sims & Martin, 2014). Further, EphB4 transgenic over-expression in osteoblastic cells provided unconvincing evidence of an increase in bone formation (Zhao et al., 2006). Interestingly, it was found that osteoblast-lineage cells, including osteocytes, are able to produce ephrinB2 (Allan et al., 2008; Irie et al., 2009; Zhao et al., 2006), and that ephrinB2/EphB4 signaling within osteoblast-lineage cells plays an important role in osteoblast differentiation process. However, the receptor blockade of this signaling pathway improved osteoclast formation, which is probably partly caused by the interruption of ephrinB2 reverse signaling in osteoclast progenitors, which inhibits osteoclast differentiation (Zhao et al., 2006). Semaphorins, which are axonal growth cone guidance molecules, are also involved in the osteoblast-osteoclast communication through Semaphorins/Plexins pathways (Negishi-Koga et al., 2011). Osteoblast-lineage cells produce Sema3A that acts on stromal-lineage cells to stimulate osteoblast differentiation and function, while acting upon the hemopoietic-lineage cells to inhibit osteoclast formation (Hayashi et al., 2012). Indeed, Sema3A interaction with the membrane protein neuropilin-1 (Nrp1), expressed on mesenchymal precursors, exerts an antiosteoclastic effect. It

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blocks the RANKL-induced osteoclast differentiation, which inhibits RhoA and ITAM signaling. In contrast, it activates the Wnt/β-catenin signal in osteoblasts. Sema3A activity is mediated through the binding of Sema3A/neuropilin-1 complex to the Plexin-A transmembrane protein, which prevents the binding of the complex to the ITAM-associated immune receptors in osteoclasts. It also recruits FARP2 in osteoblasts, which induces the Rac-GTP/β-catenin signal. Importantly, Sema3A is antagonized by Sema6C and Sema6D in osteoclasts through recruiting Plexin-A and preventing its binding to neuropilin-1 (Hayashi et al., 2012; Teti, 2013). Notably, other studies reported no effect of Sema3A on osteoclast formation (Fukuda et al., 2013; Takegahara et al., 2006), and indicated that bone remodeling is regulated by Sema3A produced in neurons by modulating the sensory nerve development, but not by directly acting on osteoblasts (Fukuda et al., 2013). Moreover, Sema4D is highly expressed by osteoclasts (Negishi-Koga et al., 2011) and uses its receptor PlexinB1 expressed by osteoblasts to significantly inhibit osteoblast differentiation. However, Sema4D effects on osteoblasts were found to likely be partially related to the IGF-1 signaling attenuation and were suggested to probably involve other receptors than Plexin-B1. Indeed, Plexin-B1 is highly expressed by osteoblasts during their differentiation and forms a receptor complex with ErbB2. The latter is phosphorylated when Sema4D binds to Plexin-B1, affecting kinase in osteoblasts. The binding of Sema4D to Plexin-B1-ErbB2 receptor complex may activate RhoA, which mediates IRS-1 phosphorylation, and through which Sema4D induces osteoblast motility. Sema4D also affects osteoblast localization to a proper site (Negishi-Koga et al., 2011). A soluble semaphorin, called Sema3B, is produced by osteoblasts and its production rate significantly increases by the presence of 1,25(OH)2D3. Sema3B enhances RANKL action, playing the role of an osteoclast formation promoter (Sutton et al., 2008), same as TGFβ (Quinn et al., 2001) and Wnt5a (Maeda et al., 2012), with different mechanisms operating in each case. Indeed, the isolated actions of semaphorin family members cannot be easily into the overall remodeling perspective, because of the complexity of their involvement in the bone cell activities. Still, their action should be mentioned to avoid an unrealistic consideration of the coupling molecular controls in the remodeling process by isolating pathways (Sims & Ng, 2014). Furthermore, a reverse signaling through RANKL was recently revealed, which provides another possible coupling pathway. Indeed, bone formation is promoted by inhibiting osteoclast formation under the action of W9, which is a TNFα-receptor antagonist peptide that blocks the binding of RANKL to its RANK. The latter was found to drive reverse signaling in osteoblast-lineage cells through RANKL, which might be in cooperation with other paracrine factors (Furuya et al., 2013; Sims & Martin, 2014). This third bidirectional signaling pathway represents another mechanism requiring an effective direct cell-cell contact.

2.3.4 Osteocyte contribution to the osteoblasts and osteoclasts Osteocytes were found to participate in the direct control of osteoblast and osteoclast differentiation and activity. However, their contribution in the regulation of osteoblast behavior under physiological conditions is, actually, controversial and still not fully identified. On one hand, it was reported that osteocytes, subjected to mechanical strains, activate osteoblasts by sending anabolic signals to rapidly release NO and PGE, as well as other small molecules, such as ATP (Hao et al., 2017). Besides, the mechanical disruption caused by bone resorption activates osteocytes and stimulates them to promote bone formation on the same resorbed surface. On the other hand, it was indicated

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that osteocytes negatively affect osteoblast differentiation, that their density negatively correlates with bone formation, and that their apoptosis or their network disruption increases bone formation rate (Bivi et al., 2012; Moriishi et al., 2012). It was demonstrated that bone metabolism and remodeling may also be controlled by osteocyte markers, such as SOST, sclerostin, MEPE, and DMP1 (Harris et al., 2007; Winkler et al., 2003). Indeed, the osteocyte response to mechanical stimuli is mediated through a pathway centered on the SOST glycoprotein. SOST is specifically expressed in osteocytes and antagonizes the canonical Wnt pathway, which inhibits osteoblast differentiation and activity (Van Bezooijen et al., 2004; Winkler et al., 2003) and exerts thereby anti-anabolic effects on bone formation. Besides, sclerostin expression significantly decreases under mechanical loading and increases throughout unloading (Sims & Martin, 2015). Furthermore, osteoclast formation starts with preosteoclast recruitment to the BRC by osteocytes. Being also a major source of RANKL, osteocytes regulate osteoclastogenesis (Hao et al., 2017), and apoptotic osteocytes express higher levels of osteoclastogenic-promoting factors, such as IL-6, IL-11, and TNF-α, along with RANKL, than normal osteocytes (Al-Dujaili et al., 2011; Kogianni et al., 2008; Shandala et al., 2012). Therefore, some pathological conditions that increase osteocyte apoptosis rate, such as microcracks and menopause, are accompanied with a colocalized osteoclast invasion and a significant increase in bone resorption rate (Colopy et al., 2004; Komori, 2013; Noble et al., 2003). In fact, osteocytes form a system that conducts information from mature osteoclasts to osteoblasts on bone surface (Sims & Martin, 2015), and the osteocyte-secreted IL-6 may tightly contribute to controlling the remodeling biomechanics, as a new mechano-sensitive cytokine (Chen et al., 2010; Sanchez et al., 2009), by exerting a dual effect on cell proliferation and apoptosis, as well as on osteoblast and osteoclast differentiation (Chipoy et al., 2004; Duplomb et al., 2008; Heymann & Rousselle, 2000; Kaneshiro et al., 2014; Palmqvist et al., 2002; Steeve et al., 2004; Yeh et al., 2002; Yoshitake et al., 2008).

2.3.5 Reversal cell contribution to the osteoblast-osteoclast interplay The separation in time and space of active osteoclasts from mature osteoblasts within the BMUs has drawn attention to the contribution of the osteoblastic reversal cells located at the direct vicinity of osteoclasts and osteoblasts in the osteoblast-osteoclast coupling mechanism. (Abdelgawad et al., 2016; Andersen et al., 2013; Jensen et al., 2015). This physical intimacy spearheaded the existence of communication bridges formed by the reversal cells between osteoblasts and osteoclasts. Indeed, these early reversal cells appear to be tightly linked to their neighboring osteoclasts, forming a direct cell-cell contact with them via short cytoplasmic extensions, or communicating with them through osteoclast product uptake (Delaisse, 2014; Henriksen et al., 2014; Karsdal et al., 2007; Matsuo & Otaki, 2012; Pederson et al., 2008; Sims & Martin, 2015). In contrast, the late reversal cells morphologically, ultrastructurally and immunohistochemically resemble to bone-forming osteoblasts, which suggests that they are actually late preosteoblasts (Abdelgawad et al., 2016). Interestingly, catabolic/collagenolytic functions have been assigned to the reversal cells (Delaiss´e et al., 2003; Everts et al., 2002; Mulari et al., 2004) and the direct communication between them and the osteoclasts has been suggested to regulate reversal cell function and differentiation. In turn, the reversal cells may generate a reverse signal to act on osteoclasts, which establishes a bidirectional regulation mechanism. The latter may involve the Eph-ephrin signals,

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explained above (Irie et al., 2009; Matsuo & Otaki, 2012; Zhao et al., 2006). Besides, the binding of osteoclastic Sema4D to osteoblastic Plexin-B1 is also likely to inhibit the reversal cell differentiation (Negishi-Koga et al., 2011). Furthermore, it was indicated that osteoclast-secreted coupling factors, such as TRAcP, are taken up by the early reversal cells. The latter react to these coupling factors and send the necessary signals to preosteoblasts when moving onto the bone surface. On the other hand, the demineralized collagen fibrils on the resorption lacunae are degraded and endocytosed into the reversal cells through clathrin-coated endocytic vesicles (Abdelgawad et al., 2016). Collagenases of the MMP family are involved in these extracellular collagenolytic activities. Notably, the early reversal cells showed a more abundant quantities of one of these collagenases, known as MMP-13, compared with the late reversal cells on the eroded surface near the osteoid. MMP-13 immunostaining was also observed within the lacunae resorbed by the neighboring osteoclasts, which suggests that MMP-13 produced by the early reversal cells may be used by osteoclasts. It was reported that osteoclasts may actually indirectly modulate MMP-13 through matrixderived growth factor liberation, and activated by the osteoclastic MT1-MMP (Andersen et al., 2004; Delaiss´e et al., 2003). Abundantly present in the early reversal cells, the endocytic collagen receptor uPARAP/Endo180 is likely to be involved in collagen endocytosis by the reversal cells (Abdelgawad et al., 2014). uPARAP belongs to the mannose receptor family, which may bind to collagen type I C-terminal region and be an important actor in collagenase-cleaved collagen nonphagocytic internalization and degradation. Instead of intact collagen, uPARAP preferentially internalizes collagenase-cleaved collagen, which implies the need for collagen fibrils to be partially degraded by collagenases, in order to become internalized and to be likely further degraded into the reversal cells (Abdelgawad et al., 2016; Madsen et al., 2007, 2011; Thomas et al., 2005).

2.3.6 Lining cell contribution to the osteoblast-osteoclast interplay The coupling factors may also target the bone lining cells (Delaisse, 2014). The latter lift from the bone surface when the resorption phase is initiated and form an anatomical structure, known as bone canopy, above the BMU, between osteoblasts and osteoclasts (Andersen et al., 2009; Kristensen et al., 2014). It was reported that biopsies from postmenopausal woman and GIOP patients exhibit incomplete canopies at the reversal phase arrest sites. Accordingly, it was suggested that the reversal phase completion requires the complete formation of the remodeling canopy (Andersen et al., 2014; Jensen et al., 2015). The canopy might also provide a controlled region, in which osteoclast- and osteoblast-lineage cells, as well as other implicated marrow cells, can exchange influence precursors and factors generated by the associated vasculature (Kristensen et al., 2014). In addition, these lifted bone lining cells may play a role in maintaining sufficiently high concentrations of the local coupling factors, which allows to recruit MSCs and to stimulate bone formation phase, or reduce cellular contributions to the coupling mechanisms (Sims & Martin, 2015).

2.3.7 Bone matrix contribution to the osteoblast-osteoclast interplay Bone matrix stores a plethora of latent growth factors, such as IGFs, PDGF, BMPs, and TGFβ, contributing to the resorption-to-formation coupling (Henriksen et al., 2014; Karsdal et al., 2007). All of these factors are deposited by osteoblasts during the matrix synthesis, and released and activated

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by osteoclasts during the resorption phase of the subsequent remodeling cycle, as well as via plasminogen activators and MMPs. Once released, these factors mainly act as stimulators of osteoblast progenitors, including their recruitment, migration, and differentiation (Abdelgawad et al., 2014; Dirckx et al., 2013; Teti, 2013). Furthermore, the exposed demineralized matrix left behind the active osteoclasts was found to interact with the early reversal cells (Abdelgawad et al., 2014; Everts et al., 2002; Mulari et al., 2004). Notably, conditions promoting the debris accumulation in the demineralized matrix coincide with an increase in the reversal cell densities, with a shorter reversal phase, and with an enhanced formation-to-resorption coupling (Jensen et al., 2014). The stored latent TGFβ is activated when released from the matrix, and becomes one of the key coupling factors that promote the formation phase at the previous resorption sites (Teti, 2013). TGFβ induces the activation of preosteoblasts recruited for the following formation phase and their migration to prior resorptive sites (Tamma & Zallone, 2012; Tang et al., 2009). These actions may be performed both directly and through the stimulation of osteoclast-released Wnt10b (Ota et al., 2013). It was, also, indicated that released TGFβ and IGF-1 induce bone MSC migration to the sites to be resorbed, and favor their recruitment by activating the mTOR (Tang et al., 2009; Weivoda et al., 2016; Xian et al., 2012). Furthermore, TGFβ and IGF-1 may also be produced by osteoblastlineage cells, but in latent complex forms that are activated by plasminogen activators generating plasim. The activity of these plasminogen activators is specifically enhanced by PTH and 1,25 (OH)2D3 (Sims & Martin, 2014). BMPs share the intracellular SMAD/MAP kinase pathways with TGFβ and also exert important effects on bone formation and tissue repair (Dean et al., 2009). However, it was reported that these matrix-derive growth factors are not likely to remain within the bone microenvironment during the reversal phase to affect mature osteoblasts when they arrive to the eroded area (Sims & Martin, 2015). Table 2.1 summarizes the influence of the main factors implicated in the osteoblast-osteoclast interplay and Fig. 2.5 illustrates an overall image of bone cell interactions.

2.3.8 Signals to and from other marrow components Osteoblasts and osteoclasts do not only regulate bone structure, but also HSC development. Osteoclast-induced regulation is performed owing to the high calcium levels they release during their resorption activity, which acts on the stem cell differentiation by interacting with their calcium receptors (Scadden, 2006), whereas osteoblast-induced regulation is performed by osteoblastlineage cells at early differentiation stages, which is required for a normal development of the HSCs into several lineages (Panaroni & Wu, 2013; Visnjic et al., 2004; Zhu et al., 2007). Since HSC niche contains an osteoblast progenitor population, it was suggested that these stem cells are, in turn, involved in maintaining osteoblast progenitors, and this was evidenced by the so-called osteal macrophages that control osteoblast differentiation. However, their relative contribution is yet to be identified (Allan et al., 2008; Sims & Martin, 2014). OSM cytokine is one of the macrophage-secreted factors and an OSM-neutralizing antibody was found to block the macrophage stimulatory effect on osteoblast differentiation (Guihard et al., 2012; Nicolaidou et al., 2012). Indeed, OSM is produced at all osteoblast differentiation stages, including osteocytes, and it directly interacts with osteoblasts and osteoclasts, promoting their activity (Walker et al., 2010). However, these findings need to be more investigated.

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Table 2.1 Secreted and membrane-bound and matrix derived factors in bone cell communication. Factor

Origin

Function

DMP1 Dkk1

Stimulates phosphate metabolism, mineralization Inhibits bone formation

SCL RANKL M-CSF

Early and mature osteocytes Osteoblasts and early and mature osteocytes Late osteocytes Osteocytes, other osteoblastic cells Osteoblasts and osteocytes

OPG CT-1

Osteoblasts and osteocytes Osteoclasts

BMP6

Osteoclasts, MSCs and HSCs

Wnt10b

Osteoclasts and T cells

S1P

Osteoclasts and vasculature

CTHRC1

Osteoclasts, MSCs, Osteoblasts and osteocytes Osteoclasts

CC3a Oncostatin M

Osteoclasts, macrophages, osteoblasts, osteocytes and Tlymphocytes

Sema4D

Osteoclasts and T-lymphocytes

EphrinB2

Osteoclasts, osteoblasts and osteocytes

RANKL/RANK reverse signal IGF-1, IGF-2 PDGF-BB BMP2 TGF-β

RANK on osteoclasts and RANKL from preosteoblasts and osteocytes Matrix, osteoblasts and macrophages Matrix, osteoclasts, osteoblasts and endothelial cells Matrix, osteoblasts and macrophages Matrix, osteoblasts, T-lymphocytes and macrophages

Inhibits bone formation Stimulates osteoclast differentiation and survival Stimulates preosteoclast and osteoclast proliferation and survival Inhibits osteoclast differentiation Stimulates bone formation, stimulates osteoblast, commitment, Suppresses sclerostin Expression, Stimulates, osteoclastogenesis Stimulates osteoblast, Differentiation, Stimulates, osteoclastogenesis from, human marrow cells Stimulates osteoblast, differentiation, Stimulates osteoclast, activity Promotes osteoblast, precursor recruitment Promotes osteoblast, migration and survival Stimulates osteoclast, recruitment and precursor chemotaxis, Inhibits osteoclastogenesis Stimulates osteoblast, differentiation and bone formation Inhibits osteoclast, formation and activity Stimulates osteoblast differentiation Promotes osteoclast recruitment Promotes osteoblast, commitment

Stimulates bone formation, Synergizes with BMP2, Stimulates, osteoclastogenesis Inhibits bone formation, and gene deletion increases bone formation, Stimulates, osteoclastogenesis Promotes osteoblast, differentiation Suppresses osteoblast, apoptosis Promotes late stage, osteoblast differentiation Inhibits osteoclastogenesis, Inhibits RANKL, production by osteoblasts Promotes bone formation Stimulates osteoblast, progenitor expansion Stimulates, osteoclastogenesis Promotes preosteoblast replication, migration, and differentiation, Stimulates bone formation Stimulates osteoblast, progenitor expansion, migration, and differentiation, Stimulates osteoclast, activity Stimulates osteoblast, progenitor expansion, migration, and differentiation, stimulates bone formation, Acts on preosteoclasts to stimulate osteoclastogenesis, Stimulates SCL, expression by osteocytes

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FIGURE 2.5 Intercellular communication pathways within the BMU whereby the remodeling process takes place. (1) Mechanical stimulus affecting OCY (osteocytes). (2) Stimulatory effects from OCY to Act OB (active osteoblasts). (3) Bone matrix signals to Act OB. (4) Signaling within osteoblast-lineage cells. (5) Stimulatory and inhibitory signaling from Act OB to OCP (osteoclast precursors), OC (osteoclasts), and Act OC (activated osteoclasts). (6) Bidirectional signaling between Act OB and Act OC. (7) Stimulatory and inhibitory signals from OCP to OBP (osteoblast precursors). (8) Stimulatory signals from late RvCs (reversal cells) to Act OB. (9) Stimulatory signals from early RvCs to Act OC.

Moreover, T-cells were suggested to provide a major RANKL source in physiologic and pathologic remodeling events, and their RANKL production is stimulated by the dendritic cells in the BMU vicinity (Gillespie, 2007; So¨derstro¨m et al., 2010; Weitzmann et al., 2001; Wythe et al., 2014). Since T-cell activation is controlled by VDR, vitamin D metabolites may act on the activated T-cells to regulate osteoclastogenesis. The latter is inhibited by several T-cell-derived factors, such as IL-4, IL-12, IL-18, and IL-23 (Allan et al., 2008; Horwood et al., 2001; Mirosavljevic et al., 2003). T-cells also produce Sema4D that has an inhibitory effect on osteoblast differentiation (Sims & Ng, 2014), and participate in PTH anabolic action through Wnt10b production (Bedi et al., 2012; Pacifici, 2010). Indeed, PTH downregulates SOST expression in osteocytes that negatively affects osteoblast differentiation and function (Rhee et al., 2011), and is also associated with both anabolic and catabolic processes in bone, according to its release and concentration (Tamma & Zallone, 2012). In addition, the immune B-cells were found to promote bone formation by producing Wnt1 in the marrow (Laine et al., 2013). Yet, much remains to elucidate regarding the importance and actions of T-cells, B-cells, and B-lymphocytes on osteoblasts and osteoclasts, as well as on the crosstalk between the two cell lineages (Sims & Ng, 2014).

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2.4 Factors influencing bone from a biological point of view 2.4.1 Age1 The bone mineral density changing by age was studied by many investigators. According to Currey (1969), over the range of the observed bone mineralization, the mineral amount increases, while mineral crystals join up end to end. (Cerroni et al., 2000) investigated bone disease metabolism and bone mineral density variation by age in both genders of free-ranging rhesus monkeys and found that bone mass acquisition is faster in males than in females, with a higher peak at an earlier age. To describe the human bone mineral evolution, Handschin and Stern (1995) developed a clear and precise work, during which 117 homogenized iliac crest biopsies of 0
95-year-old individuals were examined using X-ray diffraction analysis. This work revealed that mineral crystal perfection and size increased during the first 25
30 years and then decreased during the following years until slightly increasing again in oldest individuals. Meneghini et al. (2003) had recourse to measurements with micro- and high-quality XRD (X-ray diffraction) to study the evolution of bone mineral crystallographic structure during the early stages of bone formation in human embryonic vertebrae at different gestational ages. However, in some of these cases, trabecular and cortical bones were analyzed separately, without distinguishing gender or location in bone (Meneghini et al., 2003). The work made by Cho et al. (2003) highlighted the biochemical processes influencing bone mineral metabolism, by using a 2D solid-state method based on nuclear magnetic resonance (NMR) spectroscopy. Due to its ability to detect the bone crystal proton spectrum while removing the interfering matrix, this technique allows to eliminate specimen pretreatment needs, except cryogenic grinding. Henriksen et al. (2007) investigated the ability of bones to endogenously control osteoclastic resorption. The data revealed that bone resorption is an age-related process, with a significantly higher increase in osteoclast differentiation rate as well as resorption level in aged bones. Thereafter, the application of bone microspectroscopic imaging and Fourier transform infrared (FTIR) imaging (Boskey & Camacho, 2007; Carden & Morris, 2000) allowed to analyze and characterize bone state and even tissue imaging with chemical composition contrast that came with the imaging modalities development. Fuchs et al. (2008) also used FTIR microscopy to determine the time required for newly formed bone matrix to reach a physiological mineralization limit. The same technique was used by Gourion-Arsiquaud et al. (2009) to test whether some mineral and matrix bone properties can explain the fragility fracture risk or not.

2.4.2 Sex steroids Estrogens and androgens exert potent influences on the skeleton size and shape during growth and contribute to skeletal homeostasis during adulthood. The decrease in estrogen levels, usually associated with post-menopause, or in androgen levels, caused by the decrease levels of male estrogens derived from testosterone aromatization, increases bone remodeling, osteoblastogenesis, osteoclastogenesis, osteoblast and osteoclast numbers, as well as bone resorption and formation. However, the increase in these cells and processes is unbalanced, giving rise to a resorption rate that exceeds the formation one, which results in a net bone loss. Conversely, normal estrogen or androgen levels restrain the remodeling rate and maintain a focal balance between the resorption and the formation rates. Bone remodeling is attenuated owing to restrained sex steroid effects on osteoblast and

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osteoclast progenitor birth, in addition to an antiapoptotic effect on osteoblasts and osteocytes, and a proapoptotic effect on osteoclasts (Manolagas et al., 2013). In addition to inhibiting bone remodeling initiation by acting on osteocytes, estrogens inhibits bone resorption, by increase osteoclast apoptosis rate, blocking RANKL/M-CSF-induced activator protein1-dependent transcription through c-Jun activity reduction, and suppresses RANKL-induced osteoclast differentiation (Huber et al., 2001; Shevde et al., 2000; Srivastava et al., 2001). Indeed, estrogens also suppresses RANKL production by osteoblasts, T-cells and B-cells (Eghbali-Fatourechi et al., 2003) and increases OPG production (Khosla et al., 2001). IL-1 and TNF-α production was found to be modulated by estrogens. Moreover, estrogens inhibit the apoptosis and increase the lifespan of osteoblasts, due to the activation of the Src/Shc/ERK signaling pathway and the downregulation of JNK that alters the activity of a number of transcriptional factors, such as Elk-1, CCAAT enhancer binding protein b (C/EBPb), cAMP response element binding protein (CREB), and c-Jun/c-Fos. This results in the elevation of osteoblast functional capacity (Khosla et al., 2012). It was demonstrated that androgens promoted and suppressed the expression of a number of osteoblast markers, including collagen type 1 alpha 1, osteocalcin, and alkaline phosphatase. However, the evidence mainly suggested that androgens stimulate osteoblast differentiation. Osteoclast formation and survival are also regulated by androgens by acting on the RANK/ RANKL/OPG pathway. Estradiol was found to prevent osteocyte apoptosis and to enhance TGFα production, which inhibits osteoclast activity. Therefore, estrogens derived from testosterone may contribute to the osteocyte anabolic action (Mohamad et al., 2016).

2.4.3 Alcohol Alcohol effects on the adult skeleton depend on the age and drinking pattern of the individual. A number of conducted studies reported that moderate alcohol consumption is usually associated with a higher BMD and a lower bone fracture risk, but others detected no relationship between BMD and alcohol consumption (Ganry et al., 2000; Marrone et al., 2012; Mukamal et al., 2007; Rapuri et al., 2000; Sommer et al., 2013; Wosje & Kalkwarf, 2007). There is no adequate explanation for this variability, despite the focus of the negative studies on younger individuals at or near-peak BMD and at low fracture risk. These findings suggest that moderate alcohol does not increase peak bone mass but may slow age-related bone loss. In contrast, chronic heavy alcohol consumption is associated with a decrease in BMD and an increase in bone fracture risk (Gonz´alez-Reimers et al., 2011; Hyeon et al., 2016; Kim et al., 2003; Kouda et al., 2011; Malik et al., 2009; Santori et al., 2008), but there have been notable discrepancies. Differences may be linked to drinking pattern, magnitude, and duration, as well as to the evaluated skeletal sites in the conducted studies. Although no clear indication has been reported on the changes in nutrition with a moderate alcohol intake that would affect human bone metabolism, bone health is particularly damaged by acute weight loss and weight cycling, both being associated with binge drinking. Thus, inadequate energy availability may negatively affect bone metabolism and likely contributes to the low BMD, often observed in underweight chronic alcohol abusers. In addition, alcohol may affect the intake, absorption, metabolism, and excretion of micronutrients, such as calcium and vitamin D, which are critical to bone health. Besides, a wide range of defects in renal tubular handling of minerals are prevalent in alcoholics. The levels and/or signaling of several hormones that influence bone metabolism are also altered in alcohol consumers. This includes (1) vitamin D and PTH that regulate

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mineral homeostasis, (2) growth hormone (GH) that couples bone remodeling to energy metabolism, and (3) sex hormones that have been shown to greatly influence BMD (Gaddini et al., 2016).

2.4.4 Body size The skeleton develops and changes across the lifespan, responding to life experiences, ecological and environmental pressures, and individual physiology, which makes it an excellent topic to study using life history theory. Life history approaches to human biology suggest that physiology and phenotype result from tradeoffs in energy allocation between growth, maintenance, and reproduction. Recent work integrates life history traits with skeletal biology to show that some traits associated with women’s reproduction are linked to BMD and bone size (Lee et al., 2020). From a life history perspective, adult body size (height, weight, BMI), and body composition (body fat, lean mass) can be interpreted as cumulative signals of investment in body growth and maintenance (Lee et al., 2020), but they also reflect ongoing biomechanical demands, metabolic costs, and metabolic resources. Environmental pressures, developmental timing, and habitual behavior during development can affect longitudinal growth and robusticity of bones, even as height and frame size are under significant genetic influence (Kemper et al., 2000; Ryan & Shaw, 2015; Scheffler & Hermanussen, 2014). It was recently demonstrated that habitual use and overall body size are more strongly associated with frame size and cortical bone density than life history factors in this sample of healthy adults (Lee et al., 2020).

2.5 Concluding remarks The spatial and temporal arrangement of bone cells within the BMU is crucial to the remodeling process, ensuring its distinct and sequential phase coordination, under the control of several hormones, cytokines, and growth factors. The communication between bone cells is led through at least three modes: (1) a communication through a direct cell-cell contact, (2) a communication through gap junction formation, and (3) a communication through diffusible paracrine factors. Osteoblasts regulate osteoclast formation, differentiation, and maturation. In turn, osteoclasts exert positive and negative regulatory effects on osteoblast activity. Osteocytes, reversal cells, lining cells, bone matrix, macrophages, and T cells are all actors in the osteoblast-osteoclast crosstalk. The interaction between ephrins and Ephs generates the activation of both the receptor and its ligand, which results in a bidirectional signaling. Eph receptor/ligand pathways, Semaphorins/Plexins pathways, and RANKL/W9/RANK are all possible pathways of bidirectional signaling.

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Abbreviations AAP ACP ARHR ALP AP BMD BMI BTMs B2M CrP CT DEXA PHEX FGF23 FISH FRAX GIOP HypoPOM IFCC IFE IgH IJO IMiD IMWG IOF LDH LRP5 MBDs MM MRI NAI NICE N-OM NTX NFκB OI OM

American Academy of Pediatrics American College of Physicians Autosomal recessive hypophosphatemic rickets Alkaline phosphatase activity Alkaline phosphatase Bone mineral density Body mass index Biochemical bone turnover markers β2-microglobulin C-reactive protein Computed tomography Dual-energy X-ray absorptiometry Phosphate regulating endopeptidase homolog X-linked Fibroblast growth factor 23 Fluorescence in situ hybridization Fracture Risk Assessment Tool Glucocorticoid-induced osteoporosis Hypophosphatemic osteomalacia International Federation of Clinical Chemistry and Laboratory Medicine Immunofixation electrophoresis Immunoglobulin heavy chain Idiopathic juvenile osteoporosis Immune-modulatory imide drug International Myeloma Working Group International Osteoporosis Foundation Lactate dehydrogenase Low-density lipoprotein receptor-related protein 5 Metabolic bone diseases Multiple myeloma Magnetic resonance image Nonaccidental injury National Institute of Clinical Excellence Nutritional osteomalacia Urinary N-telopeptide Nuclear factor kappa beta Osteogenesis imperfecta Osteomalacia

Bone Remodeling Process. DOI: https://doi.org/10.1016/B978-0-323-88467-9.00006-0 © 2021 Elsevier Inc. All rights reserved.

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OP OPG PDB PEDF PET PTH RANK SERM s-PINP s-CTX TO VDDR VD-OM XLH 25(OH)D 1,25(OH)2D3

Osteoporosis Osteoprotegerin Paget’s Disease of Bone Pigment epithelium-derived factor Positron emission tomography Parathyroid hormone Receptor activator of NFκB Selective estrogen receptor modulator Serum procollagen type-I N-terminal propeptide Serum C-terminal telopeptide type-I collagen Transient osteoporosis Vitamin D-dependent rickets Vitamin D deficiency osteomalacia X-linked hypophosphatemia 25-hydroxyvitamin D 1,25-dihydroxy vitamin D

3.1 Metabolic bone diseases MBDs represent an umbrella term enveloping a wide spectrum of clinically different diseases, with a common condition of an aberrant bone chemical milieu that causes defects in bone and skeleton. MBDs are usually characterized by a dramatic clinical manifestation commonly reversible once the underlying cause is treated. Disruptions in bone mineralization lead to a group of diseases such as OM or rickets, whereas imbalances in bone remodeling process lead to the occurrence of other types of diseases, such as OP and PDB.

3.1.1 Osteoporosis An association between abnormal bones and fractures was first observed and commented by the British surgeon and anatomist, Sir Astley Paston Cooper, in 1822. In 1835, the term “osteoporosis” was used for the first time by the French surgeon and pathologist Jean Lobstein, to describe a condition with blue-gray sclera, which probably was OI type I. Then, Fuller Albright reported, in 1941, cases of vertebral fractures in women after losing ovarian function. The calcium balance was improved and the height loss was delayed after treating these women with estrogen intake. These findings established the relationship between OP and vertebral fractures and were the basis for defining postmenopausal OP. Afterwards, bone impaired quality and structural decay because of vertebral fractures have been demonstrated by several studies (Fig. 3.1). Indeed, vertebral fractures reflect OP severity and represent a strong fracture predictor, serving thereby as the hallmark of OP.

3.1.1.1 Clinical features of osteoporosis OP is a systemic skeletal disease characterized by a low BMD and an altered bone tissue microarchitecture, resulting from a bone resorption rate that exceeds its formation rate and leading to a decrease in bone mechanical strength and thereby to an increase in fragility fracture risk. OP clinical manifestations are fractures and their associated complications. Osteoporotic fractures mainly occur at the femoral head, spine, or wrest (Fig. 3.2). Particularly, one of the main consequences of

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FIGURE 3.1 Normal and osteoporotic vertebral bodies. Decreased structural strength is not only the result of reduced apparent bone density but also changes in the architecture of the trabecular bone (Bono & Einhorn, 2005).

FIGURE 3.2 Typical osteoporotic fractures at major sites. (A) Hip, (B) spine, (C) distal radius, and (D) proximal humerus (Yoo et al., 2015).

this kind of diseases is the appearance of microcracks in bone, which disturbs bone cell mechanosensing, a remodeling response crucial driver. Thus, microcracks induce osteoclastic resorption mechanism (Cardoso et al., 2009). Therefore, biological signals decrease over time, which negatively affects paracrine factor secretion governing osteoblast and osteoclast differentiations and activities (Lee et al., 2005) and contribute to the decrease in BMD and the degradation of bone microarchitecture. Bone mass is the main measurable determinant of osteoporotic fracture risk. Bone mass increases during childhood and adolescence, reaches its peak by the end of the second decade or the early third decade of life and remains at about the same level until the fifth decade, after which it constantly starts decreasing until the end of the lifecycle, with an approximate rate of 1% annually (Kaltsas et al., 2002). It is well-known that bone mass peak in men is higher than that in

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women, with a larger cross-sectional diameters in femoral necks and vertebrae, providing men with a greater bone strength compared to women. In spite of the similar volumetric bone mineral density between men and women during young adulthood, it was reported that structural and microarchitectural differences in bone between the two genders, provide men with a lower fragility fracture susceptibility than women, in addition to the higher bone loss rate in women during the 5 years following menopause, with an annual loss rate of about 3%-5% (Lambert et al., 2011). However, the peak bone mass magnitude, as well as the bone loss rate and duration determine the osteoporosis development likelihood. In spite of the existence of several risk factors, reduced BMD is the strongest fracture predictor (Kaltsas et al., 2002). Besides, sex hormones play a crucial role in bone growth and peak bone mass achievement. They are responsible for the skeleton sexual dimorphism that emerges throughout adolescence. The effects of estrogens on osteoblasts and osteoclasts and the effects of androgens on osteoblasts also reflect the difference in osteoporotic fracture risk between men and women and their role in the increase of osteoporosis prevalence with age (Compston, 2001). Indeed, a decrease in protein production with age was reported and a comparison of femoral neck trabecular bone between 18 to 37-year-old individuals with 51 to 79-year-old ones revealed that younger individuals have more extracellular bone matrix proteins and less bone matrix protein fragments than older individuals. This was also observed in preosteoblast cultures based on human trabecular bone from embryo to 60 years of age. Besides, cell proliferation rate is the highest within the 16th-18th gestation weeks, declines after birth, and remains to decrease with age, achieving 1/4 of its rate in a 30-year-old adult compared with that in a fetal sample; the total protein synthesis rates reflected the age-dependent changes in cell proliferation. Among the studied proteins, small proteoglycan content followed total protein content, but the cell-binding protein, osteonectin, increased until the onset of puberty and steadily decreased thereafter (Boskey & Coleman, 2010). Furthermore, cell lifespan is under the control of the replication cycle number, in addition to some external factors. Based on Hayflick limit regarding cell division, the latter arises with only a limited number decreasing with advancing age. Bone tissue aging is also associated with increased osteocyte apoptosis rate, contributing to bone weakening through at least two mechanisms; the micropetrosis zone formation, owing to empty lacunae mineralization, and the root canal system disruption, able to inhibit microcrack healing (Jilka et al., 2007; Manolagas & Parfitt, 2010).

3.1.1.2 Etiology of osteoporosis Today, OP is both a medical and a socio-economical problem and is one of the most prevalent bone diseases. It is a metabolic bone pathology that affects about 75 million people in the United States, Japan, and Europe, and causes approximately 9 million annual bone fractures over the world. The Chinese population aged 50 years and over was subjected to more than 2.3 million osteoporosis-related hip, wrist, and clinical vertebral bone fractures in 2010, and is expected to reach about 6 million bone osteoporotic fractures by 2050. From a socioeconomic perspective, financial burden of osteoporotic fractures is rapidly increasing. For instance, total annual financial costs of worldwide hip fractures are about 34.8 million dollars, and are estimated to reach 131.5 million dollars by 2050 (Kahla et al., 2018). Osteoporotic hip fracture incidence varies within populations of a given race, age, or sex. Particularly, white Scandinavia residents are subjected to higher age-related hip fracture incidence rates than comparable patients in Oceania or United States. The variation range among European

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countries is about 11-fold. Differences in physical activity levels, obesity, smoking, alcohol consumption or migration status cannot explain these geographic variations. Patients from Scandinavia have the highest vertebral deformity rates, with a threefold difference in prevalence between countries across Europe. Among European centers, the range is of 6.2%-20.7% for women and of 7.5%19.8% for men. However, the differences in vertebral deformity incidence are not as high as those in hip fracture in Europe and a number of these differences is associated with variations in physical activity and BMI (Harvey et al., 2010). Worldwide, fragility fractures are less common in men, but associated with a higher mortality than in women (Khosla et al., 2008). Osteoporosis manifestation and osteoporotic fracture risk may be assessed by a number of factors including hormonal, genetic, and nutritional factors, in addition to specific pharmacological therapies for inflammatory and immunological disorders (Mazziotti et al., 2012).

3.1.1.3 Diagnosis of osteoporosis BMD is considered as the basic standard and most frequent tool widely used in predicting fractures in clinical. It is mainly described as a T-score that reflects the number of SD by which the assessed BMD differs from the mean peak value in young adults. Osteoporosis is detected when T-score is lower than 2.5 SD (Kaltsas et al., 2002). BMD is frequently clinically assessed by DEXA that measures integrated cortical and trabecular areal 2D BMD at various bone locations. Bone quality refers to the non-BMD bone strength determinants that are less easily measured, such as bone microarchitecture, remodeling activity, mineralization degree and microdamage accumulation (Drake et al., 2015). Another diagnostic online or in print instrument is a risk-assessment tool called FRAX, which takes into account risk factors such as age, gender, race, BMI, smoking history, alcohol use, prior personal or parental fracture history, rheumatoid arthritis, femoral neck BMD measurements and glucocorticoid use, to predict a 10-year-fracture risk probability at the femur and other major fracture sites. Based on epidemiological data, it can also assess country-specific probabilities. FRAX can be combined with other diagnostic tools, such as DEXA, to determine appropriate patients for treatment. However, FRAX is not validated for use with total hip or lumbar spine BMD, for ages outside the range of 40-90 years, for patients on osteoporotic treatment, or for ethnic minorities. In addition, it does not include fall history as a risk factor, owing to the lack of a pharmaceutical evidence or a standardized metric in reducing fracture risk according to fall history (Tu et al., 2018). Since bone remodeling (or turnover) maintains mineral homeostasis and repairs bone fatigue damage and microcracks throughout life, BTMs may provide information on fracture risk independently of BMD and predict the rapidity of bone loss in untreated patients. BTMs include bone resorption markers, such as s-CTX and NTX, as well as bone formation markers, such as s-PINP. Therefore, the inclusion of these markers in assessment algorithms may enhance the fracture risk prediction. Further, BTMs can help predicting the response to treatments. A significant relationship was revealed between BMT reduction after antiresorptive therapy and fracture risk reduction in vertebral and nonvertebral locations. Generally, the greater the decrease in BTMs, larger is the reduction in fracture risk. Based on BMT assessment in fracture risk prediction and treatment monitoring performed by IOF and IFCC Working Group, s-PINP and s-CTX are recommended to be used as reference markers in observational and intervention studies (So¨zen et al., 2017).

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3.1.1.4 Management of osteoporosis Osteoporosis can be managed at early ages to prevent fragility fracture later in life. Three main categories of first-line measures can optimize bone health: nutrition, physical activity, and the underlying condition and associated comorbidity treatment. Calcium and vitamin D are the most well-described nutritional factors to maintain bone health. However, a number of other nutrients, including magnesium, potassium, protein, vitamins A, C, and K, iron, copper, zinc, and fluoride, also contribute to maintaining bone metabolism (Ward et al., 2016). Lifestyle measures to improve bone health also involve increasing physical activity levels, reducing alcohol intake, stopping smoking, and preventing falls (J. Compston et al., 2017). Bisphosphonates bind to bone active remodeling sites and suppress bone resorption by blocking osteoclast activity. These agents have made a significant contribution to osteoporosis management and are currently the most widely used antiresorptive therapies. Bisphosphonates reduce vertebral fracture risk in postmenopausal osteoporotic women, and nitrogen-containing bisphosphonates, such as alendronate, risedronate and zoledronate, reduce the hip and nonvertebral fracture risk (Chen & Sambrook, 2012). Indeed, Alendronate is approved for the prevention and treatment of postmenopausal osteoporosis, as well as for the treatment of osteoporotic men. Ibandronate is approved for the treatment of postmenopausal osteoporosis in women with increased fracture risk. Risedronate is approved for reducing vertebral fracture risk in postmenopausal osteoporosis, for reducing hip fracture risk in established postmenopausal osteoporosis, and for the treatment of osteoporotic in men at high fracture risk. Zoledronic acid is approved for the treatment of postmenopausal osteoporotic women and osteoporotic men at increased fracture risk, including those with a recent low trauma fracture (Compston et al., 2017). Denosumab represents the first biologic used in osteoporosis treatment. It is a fully human monoclonal RANKL antibody that prevents the binding of RANKL to its RANK, which inhibits osteoclast activation and function (see Chapter 2: Bone Remodeling Biology for more details). In the FREEDOM trial involving 7868 women with osteoporosis, subcutaneously administered denosumab significantly reduced vertebral, hip and nonvertebral fractures. No increase in infection risk was noticed on most phase 2 and 3 trials of denosumab, and in patients with rheumatoid arthritis. Moreover, no apparent short-term safety signals were detected when combining regimens of denosumab and biologics, in spite of the increase serious infection risk associated with combining other biologic agents, such as etanercept and anakinra. Nevertheless, a theoretical increase of infection risk stands up for combining denosumab with other biologic agents, and limited data are available on concurrent use of these combinations (Lim & Bolster, 2015). Raloxifene is the only SERM widely available to prevent and treat postmenopausal osteoporosis. It reduces vertebral fracture risk in postmenopausal osteoporotic women, but has no effect on nonvertebral fracture risk. Thus, it cannot be used as a first-line agent in the case of postmenopausal osteoporosis. Besides, the long-term raloxifene usage increases venous thromboembolic event risk. According to ACP, menopausal estrogen therapy or menopausal estrogen plus progestogen therapy or raloxifene are not recommended to treat osteoporosis in women (Akkawi & Zmerly, 2018). Human and salmon calcitonin are both worldwide approved for osteoporosis prevention and treatment. However, it is rarely used today as a preventive and treatment agent because of its limited efficacy in fracture prevention compared with other available agents and the increased cancer risk likelihood associated with its long-term usage (Khosla & Hofbauer, 2017). Although strontium

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is not approved in the United States, it has been in use for some time in Europe and elsewhere. It was associated with a 41% reduction in postmenopausal osteoporotic vertebral fractures, but no effect on nonvertebral fracture risk. Strontium usage was restricted in 2013 by the European Medicines Agency to the treatment of patients with severe osteoporosis because of safety concerns. Particularly, strontium usage has been associated with increased thromboembolic events and myocardial infarction risk, in addition to rare but serious skin reactions, such as DRESS syndrome (Khosla & Hofbauer, 2017). LRP5 nonfunctioning leads to a reduction in bone mass (Gong et al., 2001), and LRP5 up-regulation promotes bone density at a number of locations (Boyden et al., 2002). Since LRP5 is the main component of Wnt/β- catenin signaling pathway, the latter is, thus, of great importance in bone development process and in osteoporosis treatment (Ding et al., 2019).

3.1.2 Rickets Rickets is a common skeletal disorder among growing children, affecting their development, growth and health, and resulting in defective chondrocyte differentiation, defective osteoid mineralization, and defective epiphyseal growth plate mineralization. Rickets was first reported in the late 18th century and became endemic by the 20th century. Rickets is generally related to abnormal serum levels of calcium and/or phosphate that lead to different forms of rickets, such as nutritional rickets, caused by dietary deficiency of vitamin D, and/or calcium, and/or phosphate, vitamin Ddependent rickets, caused by vitamin D and/or calcium metabolism defects, and hypophosphatemic rickets, caused by resistance to vitamin D secondary to phosphate metabolism disruptions. Devastating consequences may be associated with rickets but are often poorly recognized. This disorder has lately been eradicated by fortifying food with vitamin D.

3.1.2.1 Clinical features of rickets Rickets involves both the epiphyseal cartilage and the newly formed cortical and trabecular bone. Widened epiphysal plates are the main clinical and radiological features of rickets (Fig. 3.3), with characteristic physical signs, including craniotabes, rachitic rosary and floppy muscles. Although florid rickets is rare in adolescents, long standing vitamin D deficiency can be associated with leg deformities, limb pain, tetany, muscle weakness, and cramps. For all forms of rickets, the underlying mechanism is low serum phosphate inducing a decrease in hypertrophic chondrocyte apoptosis rate at the growth plate and decrease in primary spongiosa mineralization rate at the new bone metaphysis (Tiosano & Hochberg, 2009). Besides, bone matrix formation and mineralization are delayed, which leads to unmineralized matrix accumulation on microscopic bone surfaces. Accordingly, the skeleton loses its stiffness and becomes severely deformed, which usually manifests as bowed legs and misshapen pelvis. Rickets is mainly associated with impaired growth velocity, limb and pelvic deformities, bone pain, muscle weakness, failure to thrive, and dental anomalies (World Health Organization, 2019). In phosphopenic/hypophosphatemic rickets, the disorder is generally by an increase in renal phosphate excretion. Urinary phosphate loss can be (i) a part of generalized tubular dysfunction as in Fanconi syndrome, (ii) secondary to increased synthesis or reduced catabolism of the FGF-23, or (iii) inactivating mutations in genes encoding for sodium-dependent phosphate transporters in the proximal renal tubule. In turn, calcipenic rickets, as its name suggests, is primarily caused by a lack of calcium, most commonly owing to a severe nutritional vitamin D deficiency, inability to

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FIGURE 3.3 Radiographic changes associated with rickets. Radiograph of the wrist of a child with widening of the epiphyseal plates, with associated defective mineralization, “fraying,” and cupping of the metaphyses (Berry et al., 2002).

form 25(OH)D or 1,25(OH)2D3, or owing to end-organ resistance to 1,25(OH)2D3. Therefore calcium absorption in the gut decreases and PTH secretion by the parathyroid gland subsequently increases. For both calcipenic and phosphopenic rickets forms, reduced phosphate concentration represents the common pathway in rickets manifestation (Chanchlani et al., 2020).

3.1.2.2 Etiology of rickets The peak incidence of rickets occurs among infants and young children of 6 months to 23 months of age, as well adolescents of 12 years to 15 years of age. Yet, it may also manifest in children aged between 2 years and 11 years. A reported rickets prevalence of upto 72% in Mongolia has led to suggest a rickets resurgence. Moreover, low calcium intake has been reported as common worldwide, but only few countries reported data at the national level. Vitamin D deficiency is also highly prevalent worldwide, particularly in exclusively breastfed infants, but also in children, adolescents and pregnant women, especially women from the Middle East. This is mainly related to low vitamin D intake or lack of sun exposure (World Health Organization, 2019). For instance, the multiple nutritional rickets case reports in the United States have led the AAP to recommend a daily intake of vitamin D supplement during the first two months of age for all solely breastfed infants (Gartner & Greer, 2003).

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However, no clear diagnostic procedure has been defined for nutritional rickets, which is required to enable assessing and comparing prevalence rates among and between populations.

3.1.2.3 Diagnosis of rickets The diagnosis of rickets is performed by physical examination, medical history, biochemical testing and radiography. Owing to the different forms of rickets, a patient-specific diagnosis is of crucial importance to determine the rickets cause. Several techniques can be applied, such molecular characterization in case of vitamin-D-resistant rickets, or molecular genetic techniques in case of heritable rickets. This investigation allows to provide the appropriate information on prevention, prognosis and management. Medical history takes into account dietary calcium intake assessment, environmental risk factors for nutritional rickets, and family history to identify a possible inherited rickets (Carpenter et al., 2017). Radiographs have traditionally been considered to be the reference standard in diagnosing rickets. Wrist and knee radiographs allow to detect rickets that typically appear as fraying, cupping and lateral widening with growth plate expansion in the metaphyseal region. The high PTH level that generates bone demineralization in in calciopenic rickets may be seen as evidence of osteopenia in bones with metaphyseal abnormalities. However, XLH bones tend to be sclerotic by adulthood, and dense vertebrae can be a particular ARHR type 1 feature, even in childhood. In conjunction with osteopenic bone and typical metaphyseal changes, long bone fractures may occasionally be associated with both calciopenic and phosphopenic (excluding XLH) forms of rickets, and severe cortical and trabecular bone loss may be seen on other forms of hypophosphatemic rickets (Carpenter et al., 2017). A differential diagnosis can be made using bone biopsy samples to distinguish XLH and ARHR type 1 from other forms of hypophosphatemia based on the presence or not of characteristic periosteocytic lesions (Carpenter et al., 2017). In the United States, rickets should be included in the differential diagnosis of children presenting with failure to thrive, developmental delay, and orthopedic abnormalities. Early diagnosis is essential because morbidity can be minimized if children are treated before eight months of age (Tomashek et al., 2001).

3.1.2.4 Management of rickets Management of the different types of rickets differs markedly. Treatment of vitamin D deficiencyinduced rickets usually requires an oral vitamin D preparation with calcium supplementation in children with poor dietary intake or evidence of hypocalcemia. A contentious issue arises regarding the choice of vitamin D preparation, calciferol form and dose regimen (Elder & Bishop, 2014). Hypophosphatemic rickets associated with raised serum FGF23 is treated by phosphate replacement alongside with either 1α-calcidiol or calcitriol. Bone metabolism should be regularly reviewed to monitor bony deformity, growth, and rickets- and treatment-associated complications, such as nephrocalcinosis, craniosynostosis, root abscesses, and parathyroid gland hyperplasia. Mainly during rapid growth periods, balancing phosphate intake with 1α-calcidiol is challenging, and some severe bowing deformities may require surgical intervention when the disorder is under control (Elder & Bishop, 2014).

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3.1.3 Osteomalacia Originally, the term was meant for and limited to the generalized bone softening and crippling deformities. In the 19th century, the German pathologist Pommer was the first to establish the histologic differentiation of OM from OP and osteitis fibrosa, based on cadaveric bone examination. The examination was later performed by Fuller Albright, but the most appropriate description was presumably provided by the restatement of Parfitt (1998), based on the current bone remodeling concepts; In a physiologic bone remodeling process, resorbed bone amount is replaced by the same normal lamellar bone amount in healthy subjects, by a lower normal lamellar bone amount in agerelated OP, by a complex woven bone and fibrous tissue mixture in osteitis fibrosa, and by unmineralized bone matrix in OM. However, the discovery of vitamin D made obvious the association of its deficiency with all bone softening conditions, which led to consider OM as a synonymous with any condition that could be cured by vitamin D but not necessarily caused by its deficiency. When a bone disorder does not respond to vitamin D usual treatment doses, it was classified as vitamin D dependent or resistant rickets and OM, and are currently known owing to vitamin D action or metabolism abnormalities (Bhan et al., 2018).

3.1.3.1 Clinical features of osteomalacia OM refers to a defective bone mineralization during the remodeling process, often caused by vitamin D or phosphate metabolism disorders, and ubiquitously occurs in adults or adolescents, and generally results in low BMD. In growing children, OM is always associated with rickets and is thereby the main cause of long bone bowing deformities and fractures in children with rickets, since bone stiffness decreases under poor mineralization. Low calcium intake and/or low vitamin D, particularly from lack of sunshine exposure, are the leading causes of body calcium deprivation worldwide and their combined deficiency accelerates bone demineralization (Uday & Ho¨gler, 2017). Indeed, OM and rickets both manifest through the same pathological process and have in common an absent or delayed mineralization of the growth cartilage and the newly formed bone collagen. Furthermore, OM can manifest in several forms, each one having its characteristic relationships of osteoid thickness with its surface and the adjusted mineral apposition rate (Fig. 3.4). Strictly speaking, an increase in only the thickness or the surface is not necessarily associated with OM and excess osteoid accumulation can occur in several conditions (Bhan et al., 2018). OM clinical hallmarks include vague and diffuse bone pain, proximal muscular weakness and/or polyarthralgias, and difficulty in maintaining wadding gait while walking. Although nonspecific, bone pain in OM particularly affects lower back, pelvic girdle, rib cage, and shoulders. However, symptoms can be confused with several other conditions, mainly OP. Less commonly, diffuse leg pain with apparently normal radiographs may reflect OM manifestation in elderly and confined patients (Reginato & Coquia, 2003). Biochemical and radiological alterations in OM are well described, but not totally specific and can differ according to the manifested form of OM. Whereas in VD-OM, vitamin D deficiency is the major factor associated with OM development, in the case of HypoPOM, phosphatonins, particularly FGF23, are likely to be the primary causative factor. Increased FGF23 serum values have indeed been associated with several HypoPOM-related conditions. Although hereditary forms of HypoPOM result from mutations in FGF32 gene or in PHEX, oncogenic OM is caused by a tumor-induced FGF32 overexpression (Gifre et al., 2011). Bone deformities such as leg

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FIGURE 3.4 (A and B): Diagrammatic depiction showing the relationship of osteoid thickness with fractional osteoid surface on the left (A) and with adjusted appositional rate on the right (B). There is no relationship between osteoid thickness and surface in normal subjects or in patients with 2 HPT, HVO-i and LTO until the osteoid surface is .70% (straight horizontal lines), after which the relationship is hyperbolic (interrupted curvilinear lines). On the right (B), there is a positive relationship between osteoid thickness and adjusted mineral apposition rate (straight interrupted lines), in normal subjects, and in patients with 2 HPT, HVO-i and LTO. The oblique interrupted line indicates the reversal of this relationship in patients with more severe osteomalacia (HVO-ii and iii), a cardinal feature of osteomalacia unlike all other conditions. The solid straight line represents a mineralization lag time of 100 days that separates patients with and without osteomalacia. Location of each category of osteomalacia is diagrammatically shown for clarity and simplicity. Note significant overlap of 2 HPT, HVO-i and LTO. AOM, atypical osteomalacia; FOM, focal osteomalacia; 2 HPT, secondary hyperparathyroidism; HVO-i,ii,iii, hypovitaminosis D osteopathy stages; LTO, low turnover osteoporosis (Bhan et al., 2018).

bowing, protrussio acetabuli, scoliosis and kyphosis occur very late in the course of OM after many years of noncharacteristic bone pain.

3.1.3.2 Epidemiology of osteomalacia Similarly, to rickets, OM is still endemic in some regions of the world because of the lack of solar exposure, which is the case in Asian countries, Middle East, and Patagonia. This results from limited seasonal sunlight or traditional outfits. N-OM is extremely uncommon in the white United Kingdom population, and presumably confined to elderly infirm individuals. However, Asian populations are relatively more commonly subjected to N-OM owing to the limited exposure to sun and to suboptimal dietary supply of vitamin D (Berry et al., 2002). In the United States, more than 25% of the elderly urban population may be subjected to hypovitaminosis D, which is particularly the case in undernourished, those confined to an environment with insufficient sunlight, or those

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ingesting inadequate dairy products. Moreover, intestinal vitamin D absorption tends to decrease with ageing, but also with dark complexion, such as African American populations (Reginato & Coquia, 2003).

3.1.3.3 Diagnosis of osteomalacia OM diagnosis have to take into account its variable and nonspecific features, alongside with its different forms. The diagnostic causes may include low serum calcium/phosphorus nutriments with an osteoid volume greater than 10% on bone biopsy (Fig. 3.5) assessed by double tetracycline labeling (Reginato & Coquia, 2003). In the case of suspected OM, a calcium phosphate test may be prescribed to assess calcium, phosphorus, and albumin deficiencies, followed by calciuria assessment. Painful bones are examined with DEXA and the presence of a slightly dirty opaque appearance and the characteristic

FIGURE 3.5 Bone biopsy of patient with osteomalacia. (A) Von Kossa, hematoxylin-eosin (H&E) stain for calcium and osteoid at 25 3 resolution. (B) Von Kossa, H&E stain for calcium and osteoid at 100 3 resolution. (C) Unstained, fluorescent for tetracycline at 100 3 resolution. (D) Von Kossa, H&E stain and fluorescent for osteoid at 100 3 resolution (Lewiecki et al., 2017).

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Looser-Milkman stripes are important for OM diagnosis. Besides, vertebrae structure is examined with CT and demineralized bone and increased osteoblast activity are determined using bone biopsy. In OM patient, serum vitamin D biological levels are low and PTH levels are high. Still, OM diagnosis is histological and not biological. Moreover, OM is associated with hypocalcemia and hypophosphatemia, but, phosphatase is usually elevated (Mendoza Massott et al., 2019). Radiologically, the bones show a diffusely decalcified appearance, which makes the long bones appear radiolucent in the intracortical area and the edges imprecise due to the increase in osteoid. The most frequent and characteristic radiological signs of the disease are the biconcave vertebrae and the Looser Milkman striae. The vertebrae have a fish-like appearance, with areas below the vertebral plateaus that become thickened (excess intraosseous cancellous bone) (Mendoza Massott et al., 2019). Differential diagnosis of several forms of OM, such as hypophosphatasia-associated OMs, can easily be misdiagnosed as OP, mainly in adults. In such cases, the diagnosis may only rely on a decrease in total AP (Gifre et al., 2011). Distinguishing OM from OP may be based on the manifestation of hip and shoulder pain, in addition to diffuse rib cage tenderness. Nevertheless, osteoporotic bone stress fractures may mimic pseudofractures, and OM may present with only diffuse demineralization without pseudofractures.

3.1.3.4 Management of osteomalacia Unlike other bone disorders, OM is treatable, and even curable, particularly if the underlying causes of OM, mineralization defect and vitamin D deficiency are well identified and appropriately managed. This can be achieved with simple measures, such as following adequate diets and ensuring enough exposure to the sun. The unmineralized bone matrix gets mineralized when treated with adequate vitamin D and calcium, which leads to a significant increase in BMD. Notably, most patients respond remarkably well, with gratifying biochemical, clinical and radiological recovery. The musculoskeletal symptoms disappear, the calcium, phosphorus and AP serum levels disruptions are reversed and the pseudofractures heal. Nevertheless, these parameters may not be sufficient for assessing the therapy endpoints, since the time course and ultimate extent of recovery in bone mineral deficits at different skeletal sites is not completely understood (Bhambri et al., 2006; Walker, 2014).

3.1.4 Paget disease of bone PDB was first called osteitis deformans and described in 1877 by Sir James Paget in a paper illustrating its clinical features (Paget, 1877). PDB is a common metabolic chronic disorder of the adult skeleton.

3.1.4.1 Clinical features of Paget disease of bone PDB is usually asymptomatic and is characterized by focal areas of aggressive osteoclastic bone resorption followed by imperfect osteoblastic bone formation. This disorder begins as a wedge of destructive osteoclasts at one bone end that slowly but relentlessly advance to disrupt the whole bone structure. The resulting deranged remodeling process causes bone expansion and structural weakness, sometimes accompanied with pain and deformity (Whyte, 2006), in addition to a possible number of other complications, such as secondary osteoarthritis and pathological fractures

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(Van Staa et al., 2002). Preferentially, it targets the axial skeleton, particularly the pelvis in 70% of the cases, the femur in 55%, the lumbar spine in 53%, the skull in 42%, and the tibia in 32% (Ralston, 2013). Fig. 3.6 shows PDB radiographic features in three different locations.

3.1.4.2 Etiology of Paget disease of bone PDB etiology remains a subject of debate. Owing to its particular geographic distribution, PDB is an unusual disorder that presumably involves genetic and environmental factors to occur. Indeed, PDB commonly occurs in the United Kingdom, Germany, France, New Zealand, Australia, and North America. However, it is uncommon in southern Europe, Ireland, Scandinavia and

FIGURE 3.6 (A) Paget’s disease of the tibia, with a flame shaped lytic wedge (arrowhead) and a pathological fracture (arrow). (B) Longstanding Paget’s disease of the femur, with bone expansion, trabecular thickening, mixed lytic and sclerotic areas, and fissure fractures (arrows). (C) Active Paget’s disease of the skull, with marked cortical thickening and an area of osteoporosis circumscripta (arrows) (Walsh, 2004).

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Switzerland, and rare in in Africa and throughout Asia, including India, China, and the Middle East. Elderly people are the most vulnerable to this disorder. For instance, PDB occurs in 1.5%3.0% of people over 60 years of age in the United States and seems to be less common in blacks in the northeastern United States, but equally affects men and women. The overall prevalence in Great Britain is of 3%-4% of people of more than 50 years of age. A geographic variation in prevalence has been observed in Britain, with rates ranging from 4.6% in southern areas to 8.3% in a number of regions in northwest England (Lyles et al., 2001). Genetic factors play a significant role in PDB, with 15%-40% of patients have a positive family PDB history. Three gene mutations have been identified in familial PDB and related syndromes: RANK, a member of the TNF receptor superfamily involved in osteoclast activity regulation, OPG, an antagonist receptor for RANK, and sequestosome 1, a protein involved in NFκB signaling regulation (Langston & Ralston, 2004). Postulated environmental triggers for PDB include intranuclear inclusion bodies resembling paramyxovirus nucleocapsids observed in pagetic osteoclasts have led to propose infection as a potential trigger of PDB. Although the identity of these structures is unclear, they may represent abnormal protein aggregates caused by autophagy pathway defects. Furthermore, dietary calcium intake during childhood, and repetitive mechanical loading also contribute PDB manifestation. Notably, PDB incidence and severity have declined over recent years, which may be linked to changes in environmental factors that presumably mitigate its predisposition, such as improved nutrition, reduced exposure to infections, and a more sedentary lifestyle resulting in reducing bone mechanical loading and a number of skeletal injuries (Ralston, 2013).

3.1.4.3 Diagnosis Paget disease of bone PDB is characterized by distinctive bone radiographs that typically show a mixed sclerosis and lysis image, with a deformity and an enlargement at the affected bones, a presumable cortex densification and increase in thickness, in addition to osteoporosis circumscripta. Predominant sclerotic lesions usually occur in late PDB. The skeletal involvement extent may be assessed using bone scintigraphy and quantified either as the total affected bone number or the involved skeleton proportion (Cundy, 2018). PDB can also be detected by a significant increase in bone resorption and formation biochemical markers in patients with extensive disease, although the marker level may remain within the reference range in approximately 10% of patients with limited bone involvement. Serum ALP activity tends to have its highest values in patients with skull localizations and total serum ALP activity represents an adequate marker to assess PDB biochemical activity. However, peptides of the cross-linking collagen type I domains, such as NTX or CTX, and serum P1NP are the most sensitive biochemical markers for bone resorption and formation, respectively. PDB is also associated with significant changes in calcium turnover, which can double even with 10% skeletal involvement, generally without affecting extracellular calcium homeostasis. Immobilized patients with extensive active disease or patients with PDB-related concurrent primary hyperparathyroidism may develop hypercalcemia. PDB is also frequently associated with renal stone disease and hypercalciuria (Appelman-Dijkstra & Papapoulos, 2018).

3.1.4.4 Management of Paget disease of bone Treatment aims to achieve clinical, biochemical, and radiological remissions, which respectively consist of relief of symptoms, return of plasma alkaline phosphatase level to the reference range, and filling in of osteolytic lesions (Walsh, 2004). The first effective treatments were performed in

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the 1980s by injection of salmon calcitonin or oral intake of etidronate disodium. These two medications have been able to suppress 50% of PDB biochemical parameters. More potent bisphosphonates, including alendronate, ibandronate, risedronate, and pamidronate have showed effectiveness in inhibiting PDB activity, but intravenous administration of zoledronic acid has been proven to represent the most effective therapeutic solution. A 15-minute-infusion suppresses biochemical activity into the normal range for upto 6.5 years, even in patients with considerably elevated bone resorption and formation parameters. A single infusion in patients with a median age of 76 years may provide a lasting remission for the rest of their life (Singer & Roodman, 2020). Disease activity is readily monitored by measuring plasma alkaline phosphatase level every 3 months after starting treatment. The treatment may be ceased when the reference level range is restored, or when no further reduction is observed on successive measurements. In the case of no increase in alkaline phosphatase level at baseline, or of liver disease, treatment response can be monitored by observing changes in alkaline phosphatase level within the reference range, measuring bone-specific alkaline phosphatase, measuring urine bone resorption markers, or performing repeat isotope bone scans (Walsh, 2004). The management of PDB-related complications frequently require surgical intervention. The latter is most commonly indicated in the case of joint replacement for osteoarthritis, but also osteotomy for deformity correction, surgery for fracture fixation or spinal stenosis correction, and prophylactic surgery for painful pseudofractures. However, Pagetic fracture fixation can be technically challenging, owing to bone deformity, enlargement, hardening, and increased vascularity. Moreover, orthopedic surgery might be required in the case of osteosarcoma development, but the prognosis is poor even with aggressive operative treatment, with an overall 5-year survival of about 6% (Ralston et al., 2008).

3.1.5 Osteogenesis imperfecta OI, a brittle bone syndrome, was described by Roger Smith, Martin Francis, and Gregory Houghton, in 1983, as a rare and heterogeneous class of heritable disorders called fragilitas ossium or OI and presumable primarily caused by an abnormal collagen biochemistry (R. Smith et al., 1983).

3.1.5.1 Clinical features of osteogenesis imperfecta OI is a heterogeneous genetic disorder of connective tissue, characterized by low bone mass, high bone fragility, skeletal deformities and short stature (Fig. 3.7). More than 80% of OI cases are caused by dominantly inherited mutations in Col1A1 or Col1A2, which are encoding genes of the α1(I) and α2(I) chains of collagen type I, the dominant protein in bone. OI severity ranges from perinatal lethal and severely deforming types to very mild forms with no deformities. Genetic heterogeneity of this condition is further complicated by extensive phenotypic variability of each genetic locus and different inheritance modes (Kang et al., 2017). Traditionally, these patients have been classified into four groups, going from OI I to OI IV, based on clinical criteria (Cheung & Glorieux, 2008). OI I is the mildest form of the disorder. It is characterized by frequent bone fractures during childhood and adolescence caused by minor trauma, but adults are less subjected to this kind of fractures. OI I is typically accompanied with a gray or blue tint to the sclera and may be associated with hearing loss in adulthood. The height of the affected subjects is usually normal

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FIGURE 3.7 Radiographic findings of the lower limbs. (A and B) Male patient with OI I showing minor bowing of the right femur and diaphyseal fracture of the left femur; (C) female patient with OI III showing severe bowing of the long bones; and (D) male patient with OI III showing significant diaphyseal fracture and osteoporosis (Brizola et al., 2017).

or near normal. However, OI II is the most severe form of the condition. During infancy, OI II is characterized by ben or crumpled bones that may fracture before birth, a narrow chest, with underdeveloped lungs and a very small rib cage, in addition to bowed arms and legs, outward hips, short height, dark blue sclerae, and usually thin and soft calvarial bones. Most infants with OI II are stillborn or die shortly after birth, usually because of respiratory failure. OI III is characterized by very fragile bones that may start fracturing before birth. In some cases, life-threatening breathing problems may result from rib fractures. Besides, bone abnormalities tend to worsen with age and frequently interfere with mobility. This third type is associated to very short stature and adults may have less than 3 ft. of height, sclerae are blue and lighten with age and adolescents start losing

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hearing. Moreover, a tooth development disorder, known as dentinogenesis imperfecta, usually occurs. In turn, OI IV is a moderate form of the condition where 25% of the affected subjects are born with bone fractures. The remaining subjects may not experience bone fractures until childhood or adulthood. Sclerae may be bluish in infancy but usually turns to white in adulthood. Additional characteristics of OI IV can involve short stature, hearing loss, and dentinogenesis imperfecta (Parker & Parker, 2007). Additional OI types have recently been distinguished and classified into OI V, VI and VII, but no collagen mutations have been identified. With progress in understanding the molecular mechanisms of this condition, further groups have been identified but not yet classified (Cheung & Glorieux, 2008).

3.1.5.2 Etiology of osteogenesis imperfecta Approximately, OI affects 6 to 7 per 100,000 people worldwide. OI I and IV are the most common forms of the disorder, with an estimated incidence of 3 to 4 per 100,000 people, whereas OI II and III are rarer, affecting 1 to 2 per 100,000 people (Parker & Parker, 2007). OI causes higher mortality than general population. In a recent cohort, people suffering from OI had higher death risk because of gastrointestinal and respiratory diseases and trauma. Moreover, they have low bone mass and experience age-related bone loss, making higher the fracture risk. Women undergo perimenopause loss and postmenopausal fracture rate in OI women is twice as high as that premenopausal OI women (Palomo et al., 2017).

3.1.5.3 Diagnosis of osteogenesis imperfecta Generally, family history, biochemical profile and clinical features are sufficient for diagnosing OI. When feasible, a differential diagnosis and specific form characterization are best established using a bone biopsy with histomorphometric analysis. Genetic testing is also useful in OI with gene mutations, but should not be used as the only diagnostic method, because mutations in Col1A1 and Col1A2 are may not be found (Glorieux & Rowe, 2012). Being a generalized tissue disorder, OI diagnosis is traditionally based on the presence of blue sclera and the manifestation of dentinogenesis imperfecta (Fig. 3.8). But this practice presents limitations, since bluish or dark sclerae are very common in healthy infants, which makes it not of much diagnostic use in this range of age. Dentinogenesis imperfecta is a more frequent clinical

FIGURE 3.8 Two eight-year-old boys with OI I, quantitative defects caused by a mutation in Col1a1 and no DGI. (A) In this individual, apically extended pulp chamber, taurodontism, in the right first permanent lower molar is seen. (B) Normal morphology of the corresponding tooth in the other boy (Andersson et al., 2017).

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evidence in primary than in permanent teeth and radiological or histological examinations often reveal bone abnormalities, even with normal teeth appearance. During the first two decades of life, clinically evident hearing impairment is uncommon, despite the subtle audiometric abnormalities that can be recorded in many children and adolescents suffering from OI. Hearing impairment is reported in about half of the affected adults with more than 50 years of age and in a higher proportions of those having clearly pathological audiometric findings (Rauch & Glorieux, 2004). Clinical and radiographic diagnosis are based on hallmark features that are long bones bowing deformities, fractures from mild trauma, joint hypermobility, and growth deficiency. According to age and OI severity, skeletal features can involve triangular facies and flat midface, chest wall deformities such as pectus excavatum or carinatum, barrel chest, and kyphosis or scoliosis. Radiography can also show generalized osteopenia, in addition to undertubulation and metaphyseal flaring, vertebral compressions, narrow thoracic apex, and gracile ribs. Since OI I to IV are caused by collagen mutations, diagnosis with bone histomorphometry shows low bone volume and trabecular number, with high turnover kinetics. Histology is distinctive in OI V to VI where no collagen defect is detected. This invasive test has been superseded by molecular testing for all types, and PEDF serum concentration for OI VI (Forlino & Marini, 2016). In addition to the signs outlined above, nonskeletal OI manifestations include muscle hypotonia, and cardiovascular abnormalities (Kang et al., 2017). NAI is one of the most challenging OI differential diagnoses, despite the contribution of social history and the relationship between certain signs and NAI, such as acromial fractures, outer end clavicle fractures, hand fractures in nonambulant children, and metaphyseal, posterior rib, and spinal fractures. Children with OI may be subjected to metaphyseal fractures, but this is presumably only the case when these children have obvious bone disease with radiologically abnormal bones. The fact that OI and NAI may coexist in children may complicates the diagnosis, mainly since NAI has no pathognomonic radiological signs. Clinically, hypophosphatasia can resemble severe OI, but the diagnosis can be performed based on low serum ALP levels and characteristic growth plate alteration. Differential diagnoses also involve Cushing’s disease, GIOP, lysinuric protein intolerance, congenital indifference to pain, homocystinuria, glycogen storage disease, calcium deficiency, immobilization, malabsorption, acute lymphoblastic leukemia and anticonvulsant therapy. Another challenging differential diagnosis is IJO, which is an acquired osteoporosis form. Disability, ensuing scoliosis and vertebral compressions are the main IJO symptoms, but they are mild, the diagnosis is hardly performed in the absence of long bone fractures. Differential IJO and OI diagnosis may be based on histomorphometry, because of a twofold decrease in trabecular bone formation rate in IJO compared with that in OI, with no evidence of bone resorption increasing rate. Nevertheless, the condition seems restricted to trabecular bone with hardly affected cortical bone, which explains the nonfrequent long bone fractures (Glorieux & Rowe, 2012).

3.1.5.4 Management of osteogenesis imperfecta Physical rehabilitation may help maximizing the gross motor function and daily life competencies. For children, physical rehabilitation actively promotes increased mobility and strength. The results have been best documented for the Dutch pediatric OI population. A 4-year-follow-up of 5 to 19year-old subjects showed that self-care and social function were enhanced over time, but mobility level plateaued in OI III and IV. A significant decrease over time of the joint range of motion in OI I patients, mainly in the lower extremities, whereas OI III and IV patients, severe motion

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limitations did not change with time. OI I children had no cardiac or pulmonary failures at rest, but fatigue during daily life activities remained in OI III or VI children (Forlino et al., 2011). In OI I and IV children, muscle force and aerobic capacity are enhanced, and fatigue levels are reduced when using a supervised training program. However, results showed that exercise regimen should be continued to maintain muscle force and physical capacity improvement (Van Brussel et al., 2008). When four motor-impaired OI III and IV children and adolescents were subjected to wholebody vibration using a tilt table, two of them achieved upright sitting and the other two were able to walk with minimal support, which they had not achieved with several years of bisphosphonate therapy (Semler et al., 2007). Progressive long bone deformity associated with recurrent fractures or obstructing motor development or function may be managed with surgical intervention, to allow extremity alignment and stability. The concept of multiple osteotomies and intramedullary fixation has been widely used to realign and stabilize long bones in children with OI, and intraoperative fluoroscopy may provide assistive guidance for less invasive osteotomy techniques. The mainstay of pathologic bone surgical fixation is intramedullary to avoid stress risers generated by a stand-alone plate and screw design. Nevertheless, the poor bone quality in OI setting makes surgical fixation challenging. The most common complication was rod migration. The number of necessary revisions owing to growth may be diminished with telescopic rods. Still, the rod size is controversial, because too large rods cause long bone stress shielding, whereas too small rods may bend and break (Olvera et al., 2018). In OI, bisphosphonate therapy increases BMD, particularly in growing children. In the presence of ongoing growth, intravenous bisphosphonate treatment helps improving vertebral compression fractures throughout bone modeling. Thus, the longer the treatment/growth period, the better the vertebral body dimensions. Scoliosis incidence seems to be not be altered with bisphosphonate use, but its progression may be delayed in severe OI forms. Although no improvements in vertebral body morphology have been associated with oral bisphosphonate treatment, but the latter has shown comparable fracture reduction in children as intravenous therapy. Therefore, its usage may be limited to mild OI or maintenance of moderate OI in the absence of compression fractures (Biggin & Munns, 2017). Studies have shown that long bone fracture rate decreases by 20% to 60% in children with OI when treated with bisphosphonates (Bishop et al., 2013; Lindahl et al., 2016; Palomo et al., 2015; Sakkers et al., 2004; Shi et al., 2016), while another showed a nonsignificant trend to reduction (Hald et al., 2015). Still, the high baseline fracture rate associated with OI points to long bone fracture occurrence despite bisphosphonate treatment. However, bisphosphonates have shown an ability to improve mobility, especially when started early in life. According to long-term follow-ups, children with OI IV become able to walk independently, which is not the case for children with OI III (Tauer et al., 2019). Nevertheless, bisphosphonates are an imperfect treatment for OI, since they do not address the underlying bone quality issue (Biggin & Munns, 2017). Besides, they have also shown adverse effects, including a frequent delayed healing of osteotomy sites in children with OI who present intramedullary rodding procedures. The risk of this complication seems to increase when using intravenous bisphosphonate therapy. Osteotomy site healing delay appears to decrease when avoiding bisphosphonate treatment in the 4 months following surgery. Osteonecrosis of the jaw is also a potential adverse effect related to bisphosphonate, but its occurrence with OI has not been confirmed in systematic reviews (Tauer et al., 2019). Although adequate calcium intake and vitamin D are considered of major importance in patients with metabolic bone disease, there are limited data from randomized trials about the optimal dose

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and target levels for both calcium and vitamin D in patients with OI. Cross-sectional studies indicate that 25(OH)D levels are positively associated with LS aBMD in patients with OI (Edouard et al., 2011), while combined calcium and vitamin D supplementation is associated with fracture prevention in adults with osteoporosis [60]. Moreover, it is accepted that BPs might be less effective or even result in adverse effects in cases of inadequate calcium intake and or vitamin D deficiency (Carmel et al., 2012; Peris et al., 2012). A recent randomized trial in children and adolescents with OI tested two daily doses of vitamin D3 (400 IU vs 2000 IU) for one year, with LS aBMD z-score as an endpoint [63]. Although the high dose vitamin D group attained higher levels of 25(OH)D, there were no significant between group differences in terms of BMD. However, subgroup analysis indicated that in patients with 25(OH)D levels below 20 ng/mL, high dose vitamin D was associated with marginally better BMD response. Thus, it seems that, at least in short term, patients with low 25(OH)D levels might benefit from higher doses. In general, guidelines advocate that daily calcium and vitamin D intake upto 1300 mg and 600
800IU per day respectively is sufficient, at least in most cases. Given the significant interindividual variability in attained 25(OH)D levels following vitamin D supplementation, the safety of the higher doses (upto 2000IU or more), the possible positive effects in muscle function and the limited data in OI, it is sensible to target for 25(OH) D levels upto 30 ng/mL using higher doses on a case by case basis (Tournis & Dede, 2018). Anabolic therapies are currently being investigated in OI setting. In adults with OI I, a randomized controlled trial on teriparatide showed an increase in BMD, but no improvement was recorded in more OI severe forms. Moreover, the sclerostin inhibitory effect decreases with antisclerostin antibodies, which increases BMD and effects are promising in adults suffering from OI, with positive preliminary results in the case of moderate OI (Palomo et al., 2017). It has been found that sclerostin antibody combined with low-dose bisphosphonates may have a synergistic effect (Olvera et al., 2018). However, more investigation is required to assess efficacy and safety in this population.

3.2 Multiple myeloma Plasma cells are a type of white blood cells making immunoglobulins that serve as a barrier against infections. In the case of a monoclonal neoplastic plasma cell proliferation in the bone marrow, these plasma cells turn into myeloma cells that can form a solitary bone tumor called plasmacytoma. When several plasmacytomas take place in the bone, the disease is called MM. Thus, MM is a cancer that initiates in plasma cells, but its pathogenesis is partially understood.

3.2.1 Clinical features of multiple myeloma MM is characterized by uncontrolled monoclonal plasma cell proliferation in the bone marrow, which most commonly leads to monoclonal immunoglobulin heavy chain (M protein) secretion, less commonly to light-chain-only secretion and rarely is a nonsecretory myeloma (Kumar et al., 2017). Accumulation of these immunoglobulins and interaction of the aberrant myeloma cells with other cells in the marrow induce several complications, such as such as bone lesions, infections,

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and pain. Besides, the imbalance the body mineral content leads to hypercalcemia and renal failure, whereas the lower-than-usual number of red blood cells because of myeloma cells leads to anemia and fatigue (Gerecke et al., 2016). MM leads to bone destruction and marrow failure. Approximatively 40% of cases harbor chromosome translocations causing overexpression of genes, such as MAFB, MAF, CCND1, CCND3, FGFR3, and WHSC1, also called MMSET, via their juxtaposition to IgH locus. Other cases exhibit hyperdiploidy. Nevertheless, these abnormalities are presumably insufficient for malignant transformation since they are also observed in the premalignant syndrome known as monoclonal gammopathy of uncertain significance. Malignant progression events involve KRAS, NRAS, FGFR3, and MYC activation, in addition to NFκB pathway activation. Besides, loss-of-function mutations in the histone demethylase UTX, also called KDM6A, have also been reported (Annunziata et al., 2007; Bergsagel & Kuehl, 2005; Chapman et al., 2011; Keats et al., 2007; Van Haaften et al., 2009).

3.2.2 Etiology of multiple myeloma The MM estimated incidence is about 2 per 100,000 people worldwide (Cowan et al., 2018) and about 6 per 100,000 in Europe (Sant et al., 2010; Smith et al., 2011). In the United States, MM represents the second most common hematologic malignancy, with an estimated incidence of 12,960 deaths and 32,110 new cases (Siegel et al., 2019). Although MM etiology remains unknown, an increased risk among first degree-relatives of patients with MM has been identified, which points to the role of a genetic component in MM manifestation (Altieri et al., 2006; Landgren et al., 2009; Vachon et al., 2009). Whether the spike in prevalence among relatives results from genetic factors or from shared environmental factors remains unclear. Age is an important risk factor for disease development. A 2012 study based on data from the United States National Cancer Institute register revealed that the median age of patients with MM at diagnosis is about 70 years, which suggests that MM is, in fact, a disease of the elderly (Kaya et al., 2012). These findings are in accordance with European multicenter studies that reported 6080 years of median patient age at diagnosis (Kristinsson et al., 2007; Lin et al., 2019; Raab et al., 2016; Remes et al., 2018). The risk of developing MM is more uncommon under 45 years of age and the median age at diagnosis is 65 years, with an observed 5-year-survival expectancy of about 56.49% (Gerecke et al., 2016; National Cancer Institute, 2016; Naymagon & Abdul-Hay, 2016). Interestingly, autologous stem cell transplantation, which is commonly used as a treatment approach in developed nations, has shown promising results even in patients above 75 years of age (Bashir et al., 2019; Cowan et al., 2018).

3.2.3 Diagnosis of multiple myeloma Unlike other malignancies, MM definition is clinicopathological; the diagnosis cannot be made unless when clinical manifestations of serious end-organ damage, such as osteolytic bone lesions and renal failure, are overt. This conundrum has prevented patients from receiving early therapy to avoid organ damage, and has prevented any attempts to treat cancer at its most susceptible microenvironmentdependent stage. These criteria were acceptable in an era of restricted treatment options that had substantial toxic effects with no apparent clinical benefits from early intervention. However, this

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definition can no longer be justified because treatment options have greatly improved, and data show early intervention in high-risk asymptomatic patients can extend survival. Moreover, advances in laboratory and imaging techniques call for an update on the specific variables that should be regarded as meeting the criteria for CRAB features. Some revisions to the monoclonal protein and bone marrow plasma cell requirements are also needed (Rajkumar et al., 2014). The diagnostic work-up for MM includes laboratory analyses, urine analyses, bone marrow biopsy, and radiologic evaluation. Laboratory analyses consist of a complete blood cell count with differential and platelet count, comprehensive chemistry count, LDH, B2M, serum FLCs, and serum protein electrophoresis with immunofixation and M protein quantitation. Urine analyses consist of a 24-hour urine for total protein and serum protein electrophoresis with immunofixation. Bone marrow biopsy is an important indicator for the diagnostic work-up and consists of immunohistochemistry and/or flow cytometry, cytogenetics, and FISH analysis (Brigle & Rogers, 2017) (Fig. 3.9).

FIGURE 3.9 Diffuse and multifocal myeloma by PET/CT. (A) Maximum intensity projection image of newly diagnosed patient with multiple myeloma demonstrating diffusely heterogeneous marrow activity involving the axial skeleton as well as extending into the marrow space of bilateral humeri and femora consistent with extensive diffuse disease. (B) Coronal MRI image in the same patient demonstrating diffuse infiltration of the marrow with abnormal STIR signal. (C) Coronal fused PET/CT image at the same level as the earlier MRI image demonstrating diffuse marrow uptake correlating with extensive osteolytic lesions consistent with extensive disease (Koppula et al., 2013).

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Upon imaging, MM-associated skeletal lesions can be divided into four types: (i) plasmacytoma, referring to a solitary lesion, (ii) myelomatous, referring to a diffuse skeletal involvement, (iii) diffuse skeletal osteopenia, and (iv) sclerosing myeloma (Amos et al., 2016). At initial diagnosis, DEXA has historically been used to detect myeloma bone disease as a punched-out osteolytic appearance, but, MM lesions can only be detected when at least 50% of the involved trabecular bone is destroyed. CT scans are more accurate than DEXA and are able to reveal lesions with less than 5% destruction of trabecular bone. Besides, they allow assessing the surrounding soft tissue involvement. A full-body MRI is very useful in detecting both bone lesions and soft tissue involvement, and its use in MM has been recommended by the IMWG (Dimopoulos et al., 2015). However, full-body MRI is not widely available and as such, PET/CT scans are gaining more widespread use, due to their ability to detect extramedullary disease that may not be revealed by other imaging techniques (Amos et al., 2016). The focal lesion number identified by MRI and their metabolic activity as determined by PET/CT are linked to a high-risk disease as defined by gene expression profiling (Fig. 3.10). In the axial skeleton, the existence of 8 or more focal lesions and their degree of uptake is associated with a lower event-free survival but not a lower overall survival (Waheed et al., 2013).

3.2.4 Management of multiple myeloma Major progress in treating MM has been achieved over the last twenty years, resulting in improved overall survival. Typically, patients with MM undergo a cycle of induction chemotherapy followed by autologous stem cell transplantation, inducing a remission phase of variable duration. This phase is usually followed by disease relapse, leading to a second line therapy and a subsequent treatmentfree remission phase. This cycle generally continues, with each remission phase progressively shortening until the disease stops progressing (Yong et al., 2016). Bisphosphonates are often used

FIGURE 3.10 Radiographic examination of the 37-year-old female patient. (A) S-shaped scoliosis and small bilateral scapula. (B) Multiplex old fractures. (C) Bent femoral shafts and expanded epiphysis, with low bone mass (Lu et al., 2014).

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in addition to anti-MM treatments to reduce the risk of multiple myeloma skeletal-related events, patients are often treated with bisphosphonates in addition to their antimyeloma treatments (DiazdelCastillo et al., 2020). In the United Kingdom and Europe, induction therapy in the form of triplet regimens is becoming the norm for newly diagnosed patients. These regimens typically contain a proteasome inhibitor, such as velcade or bortezomib, an IMiD, such as thalidomide, and a corticosteroid, mainly dexamethasone. This VTD regimen commonly involves 21-day-cycles, with typically 4-6 given cycles (Moreau et al., 2016). When the patient is ineligible for autologous stem cell transplantation, whether because of comorbidity or because of fragility, induction chemotherapy triplets are favored, owing to their slightly gentler intensity. These triplets typically contain velcade, the alkylating agent melphalan and prednisolone (VMP), or the alkylator cyclophosphamide, thalidomide and dexamethasone-attenuated regimen (CTDa) (Mateos et al., 2016; Mateos & San-Miguel, 2011). On evidence of relapse, second line therapy is offered and generally contains re-induction with a regimen, such as CTD, when a second autologous stem cell transplantation is considered. A potential long term reinduction program was provided by a regimen combining daratumumab with velcade and dexamethasone (DVd) and approved by NICE (Zhang et al., 2018). Third line therapy in the United Kingdom and frequently in Europe, often consists of using dexamethasone and IMiD lenalidamide (Revlimid, Celgene), plus or minus the oral proteasome inhibitor ixazomib (Mateos et al., 2017). This regimen is given indefinitely until relapse, and it is well tolerated and commonly suppresses the disease for several years (Diaz-delCastillo et al., 2020). Fourth line therapy and subsequent therapy lines contain thalidomide analog pomalidamide and dexamethasone (Dimopoulos et al., 2014), daratumumab monotherapy (Khagi & Mark, 2014), and retreatment using velcade and dexamethasone with the addition of the HDAC inhibitor panobinostat (San-Miguel et al., 2016). Purine analog bendamustine, dual alkylator, thalidomide, and dexamethasone are also used as a more hard hitting triplet regimen, if the patient is robust enough to tolerate them (Cheson et al., 2016). Using these fourth and subsequent line therapies is, in part, related to patient response to previous therapy lines and his/her robustness in facing progressive disease, in addition to whether the organ function declines or not. Although multiple novel therapies are being introduced, often trialed for the first time during these latter disease. Eventually, most of the patients succumb, despite the introduction of multiple novel therapies, often trialed for the first at these latter disease stages. Yet, a number of patients suffer from MM for 20 years or more, tolerate multiple treatment lines, sometimes enjoying prolonged remission phases, and may eventually die of other pathologies. At present, allogeneic stem cell transplantation is considered as the only therapy able to completely eliminate MM, but associated with a high mortality rate currently quoted around 15%-20%. It is thereby reserved for high risk patients with aggressive disease (Ikeda et al., 2019).

3.3 Recent rare case reports Mijaˇcika and Dubravka (2019) reported a TO of a 39-year-old pregnant woman with a first pregnancy and suffering from pain in both knees, but more severe on the right one. Symptoms

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developed progressively. The patient was healthy but had received infertility treatments. After delivery, the patient was in a wheelchair, complaining of pain in both knees and denying general symptoms. The dominant clinical appearance was the difficulty of mobility. The X-ray images revealed reduced mineralization of femur and tibia metaphysis, both with slightly reduced joint space of both median intercondylar hinges without reactive changes, in addition to a symmetrically thickened para-articular soft tissue. Physical therapy was started 5 weeks after childbirth and allowed to reduce pain, upgraded knee movement, improved mobility, and allowed the patient to walk the aid of one crutch. After five months of the disease onset, MRI of the right knee showed a massive stain bone-marrow edema at the femur distal metaphysis and tibia and fibula proximal metaphysis with consequent trabecular fractures of condyes with periosteal response, which are typical TO diagnosis. Six months from the condition onset, the intra articular effusion signs disappeared and with a preserved joint movement. Knee MRI one year after the symptom onset showed almost complete regression of the earlier present massive bone-marrow edema at the femur distal metaphysis and the tibia and fibula proximal metaphysis with only some mild edema residual zones. In the same period, the patient showed no subjective problems and no knee pathology signs. This case report indicated the importance of suspecting TO in pregnant women during the third pregnancy trimester, which occurs with a sudden onset of pain in one joint, as well as the noncorrelation of the clinical finding with the pain severity. An early diagnosis helps avoiding unnecessary invasive treatment approaches. Lu et al. (2014) reported a case report of a 37-year-old woman with OI and complete tooth loss, with a relatively low body weight and short stature, blue sclerae, high blood cholesterol levels, a history of high blood pressure, impaired hearing starting from the age of 29 years, poor sight, bending deformity in the bilateral lower limbs, pigeon chest, and moderate scoliosis, in addition to more other symptoms. The patient is a child of nonconsanguineous parents, but with a family history of OI. The father started losing teeth at the age of 40 years and one tooth remained by the age of 60 years. The mother and niece presented blue sclerae and the brother complained of knee pain. Biochemical tests revealed normal serum AP levels, with a low serum phosphorous concentration, a low high-density lipoprotein concentration, and high triglyceride levels, as well as normal urea biochemistry results, four blood coagulation indices, and D-dimer measurements. X-rays radiographs showed an S-shaped scoliosis, a smaller than average bilateral scapulae (Fig. 3.10), osteoporotic bilateral lower limbs, and bent bilateral femoral shafts, with evidence of previous multiplex fractures and a large epiphyses expansion (Fig. 3.10). An increase in the thickness of the right fibula middle portion and an irregular increase in the thickness of the right fibula cortical bone were also noticed. Based on the human collagen mutation database, genetic variations were analyzed and revealed a mutation in the Col1a2 gene that was once detected in a patient found to suffer from a moderate OI IV. The mutation disease-causing effect was later demonstrated. Van Zyl et al. (2014) reported a rare PDB complication in a 60-year-old woman who presented a 6 to 12-month-history of progressive increase of pain in the left pelvic and hip, the severity of which increased at night and at rest. Pelvic radiographs showed typical PDB features, involving the left pelvic and iliac bone. However, a radiological evidence of progressive left superior pubic ramus destruction, an elevated erythrocyte sedimentation rate, and a significant weight loss suggested the need for further investigation. Biochemical analysis revealed a moderate ALP elevation, but more sensitive bone resorption and formation biomarkers were not elevated. Skeletal scintigraphy showed an active monostotic PDB, with the presence of an unusual photopenic area at the left

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iliac bone. This phenomenon was earlier described as the “doughnut sign” that significantly supported the eventual diagnosis. MRI revealed the hallmarks of fluid-fluid levels, in accordance with the final histopathological diagnosis (Fig. 3.11). Bone biopsy allowed to describe the macroscopic features of a hemorrhagic tumor and the obtained microscopic sections confirmed the diagnosis of PDB-associated telangiectatic osteosarcoma. The tumor consisted of atypical cells with pleomorphic nuclei and producing osteoids, a moderate cytoplasm amount and an increase in mitotic figures. Moreover, multinucleated giant cells diffusely scattered throughout the tumor and atypical cells lined large telangiectatic spaces filled with red blood cells. Vupperla et al. (2018) reported the case of a 4-year-old boy with hair loss on the scalp and body that was first noticed after 1 month of birth. At the age of 2 years, the patient suffered from difficulty in walking. The abnormality did not occur among parents and elder sibling, despite second-degree consanguinity among parents. Clinical examination revealed typical VDDR type II features associated with alopecia, including hair loss on the eyelids, scalp, and whole body, except for few terminal hairs on the upper eyelids and over the vertex. The manifested rickets features included widened wrist, bowing legs, rachitic rosary and frontal bossing. The patient also presented nonclosed anterior fontanel, as well as hypoplastic anterior teeth and evidence of pulp exposure. Hypocalcemia and high AP levels were observed, the renal function test was within the normal range, but 1,25(OH)2D and PTH level measurements were not performed. Anteroposterior X-ray of the bilateral wrist indicated metaphyseal fraying, flaying, and cupping of the distal radius and ulna

FIGURE 3.11 (Left) Skeletal scintigraphy. Note the central photopenic area in the left iliac bone (arrow). This “doughnut sign” is pathognomonic of telangiectatic osteosarcoma, and represents cystic hemorrhagic components surrounded by increased uptake in the septa and peripheral solid areas. (Middle) MRI T1 postgadolinium (coronal view). Large soft tissue mass in left hemipelvis originating from pelvic and iliac bone, and displacing adjacent structures. (Right) MRI T2 (axial view). Characteristic radiological feature of telangiectatic osteosarcoma histological variant. Mass with different-sized multicystic spaces within it, containing fluid-fluid levels (arrow) (Van Zyl et al., 2014).

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(Fig. 3.12). Skin biopsy showed a decrease in follicle number and an increase in miniaturized follicle number throughout mid-dermis, with no inflammatory cell infiltration, in addition to a lack of hair shafts in the hair follicles. The treatment consisted of the administration of high calcium and vitamin D doses, due to which the biochemical parameters and X-rays of the distal radial and ulnar metaphyses improved. Yet, no improvements were recorded in alopecia. Arai et al. (2017) reported the case of a 39-year-old male suffering from a low back pain with no particular cause, following chest, right hip and bilateral foot pain. One year from the onset of the symptoms, an enlargement of elastic soft masses were noticed at the plantar side of the right hallux. No family history of remarkable MBDs were recorded. Laboratory analyses showed normal calcium levels, low phosphorus levels, high AP levels, and significantly high serum FGF23 levels. However, urine testing indicated a high phosphorus concentration with a low tubular phosphate reabsorption rate. Radiographs revealed a cystic radiolucent shadow in in right pubis, left third and fourth metatarsal bone, and right fourth metatarsal bone (Fig. 3.13). An increase in the uptake in the left third and fourth metatarsal bone, right fourth metatarsal bone, bilateral tarsus, right pubis, and bilateral rib were identified by bone scanning, and three soft tissue tumors in the right flexor hallucis longus muscle tendon and one tumor in the right first distal phalanx were identified using enhanced MRI (Fig. 3.13). After conducting a systemic venous sampling to measure FGF23, the tumors in right hallux were found to be responsible for the OM. Thereafter, the flexor tendon tumors and the distal phalanx tumors found in adhesion section of flexor tendon were resected. Histological examination showed that the three flexor tendon tumors comprised oval-shaped mesenchymal cells densely populated in fibrous background. Histiocytes and osteoclast-like giant cells were sparsely found in these tumors associated with multifocal hemorrhage and hemosiderin deposition. Necrosis and mitotic activities were absent. Furthermore, the tissue excised from distal phalanx consisted of hyaline cartilage and bone tissue showed no tumor. One hour after the surgery,

FIGURE 3.12 Metaphyseal fraying, flaying, and cupping of the distal radius and ulna (Vupperla et al., 2018).

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FIGURE 3.13 (Up-left) Radiographic observations. (A) AP radiograph shows cystic radiolucent shadow in right fourth metatarsal bone (arrows) and left third and fourth metatarsal bone (arrows). (B) AP radiograph shows cystic radiolucent shadow in right pubis (arrow). (Down-left) Magnetic resonance imaging. Gadolinium-enhanced T2 weighted magnetic resonance imaging shows three soft tissue tumor presented along right flexor hallucis longus muscle (arrow) and one tumor in right first distal phalanx (arrowhead). (Right) bone scan observation. Image shows an increased uptake in the bilateral right pubis, bilateral tarsus, right fourth metatarsal bone, left third and fourth metatarsal bone (Arai et al., 2017).

FGF23 serum levels significantly decreased and phosphorus levels regained normal levels. FGF23 serum concentration further decreased one day after surgery, and systematic pain progressively decreased and disappeared two months after surgery.

3.4 Concluding remarks




Despite the importance of appropriate BMD screening and treatment, OP is preventable with proper diet and lifestyle, and fall prevention. Investigating defective bone remodeling in PDB may provide a better solution to identify the osteoclast coupling factors and enhance new bone formation. Rickets is a disorder of growing children that arises from defective mineralization of the growth plate.

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OM is a histologic diagnosis and bone histomorphometry is essential to establish a definitive diagnosis. OI is a collagen-related disorder causing low bone mass and strength and high bone fragility. MRI and FDG-PET/CT imaging techniques provided a more sensitive tool to detect and stage the disease. TO diagnosis is usually delayed and treatment is often inadequate. Continuous treatment with large vitamin D doses is valuable in treating VDDR type II associated with alopecia. Surgical tumor resection may result in a rapid resolution of the metabolic defect.

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CHAPTER

Bone remodeling mathematical models

4

Abbreviations ARF ASCT BCPM BDG BMU BMD BMP BVF CBEB CDM c-Fms FE M-CSF NO OPG OI PTH PGE2 PDB PK/PD RANK RANKL SED SCLR TGF-β 2D 3D

activation
resorption
formation autologous stem cell transplant bidirectional communications and power module bone density gain bone multicellular unit bone mineral density bone morphogenetic protein bone volume fraction 2-chlorobenzoate 1,2-dioxygenase, beta subunit gene continuum damage mechanics colony stimulating factor 1 receptor gene finite element macrophage colony stimulating factor nitric oxide osteoprotegerin osteogenesis imperfecta parathyroid hormone prostaglandin E2 Paget’s disease of bone pharmacokinetic/pharmacodynamic receptor activator of nuclear factor-kappa beta receptor activator of nuclear factor-kappa beta ligand strain energy density sclerostin transforming growth factor beta bidimensional tridimensional

4.1 Bone remodeling in vitro Bone remodeling is a biological event that occurs in order to regenerate the bone matrix. Therefore it is considered as an important phenomenon allowing the maintainance of bone architecture, strength, and calcium homeostasis. Within this process, several bone cells are recruited to remove and rebuild the bone matrix. In the interest of understanding the process Frost (1969) has suggested an operator that englobes the different actions occurring during one remodeling cycle and called it a BMU. Many experimental studies have been realized to comprehend the biological interactions Bone Remodeling Process. DOI: https://doi.org/10.1016/B978-0-323-88467-9.00001-1 © 2021 Elsevier Inc. All rights reserved.

125

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Chapter 4 Bone remodeling mathematical models

within this BMU and explain the variation of bone volume throughout the process (Jilka, 2003). Researches have decomposed the whole bone remodeling process into four main phases according to the events occurring each period of time (Ait Oumghar et al., 2020). The first phase is called activation. It consists on the stimulation of cellular activity by biochemical or mechanical factors. The biochemical one could be an imbalanced production of certain hormones like the PTH, while the mechanical one is mediated by bone cells’ sensitivity of loads. Indeed, external loads are sensed by a special type of bone cells which are embedded in the bone matrix called osteocytes; these cells, thanks to their mechanotransduction ability, can recruit the other bone cells to contribute to bone remodeling by secreting numerous substances such as PGE2, NO, and SCLR (Ait Oumghar et al., 2020; Cao et al., 2020). The second phase is called resorption. Due to biochemical and mechanical stimulus, resorbing cells called osteoclasts and forming cells called osteoblasts adhere to the BMU. Osteoblasts release the main receptors permitting to bind osteoclast and stimulate their differentiation and activation, which are M-CSF and RANKL (Yamashita, Takahashi, & Udagawa, 2012). These ligands attach to c-FMS and RANK expressed by osteoclasts and enhance their function of resorption. Thereafter, the activity of resorption is slowed due to osteoblasts release of the soluble decoy of RANKL called OPG. This protein blocks RANK/RANKL binding and slows osteoclast activity consequently (Kohli & Kohli, 2011). The resorption step persists for 30
40 days. The third phase is called formation. After osteoclasts apoptosis, osteoblasts join bone lacunae and release the osteoid. The functioning of these cells is mainly controlled by the substances released in the bone microenvironment during bone dissociation such like TGF-β and BMP (Wu et al., 2016). Then, the last phase is called mineralization where bone matrix gets gradually mineralized. Giving its complexity, in some cases researchers find it difficult to extract all the information about this biological phenomenon in vivo. Thus in vitro bone studies seemed to be a way to resolve this problem. However, the development of in vitro bone remodeling mimicking is also considered as one of the most challenging type of studies in bone biology because of many reasons among which the long duration of bone cell culturing. Despite the limitations, some in vitro bone remodeling mimicking has been the subject of many research articles. In the work of Nugraha et al. (2018), authors have analyzed osteogenic differentiation of Gingival mesenchymal stem cells by culturing them in a platelet-rich fibrin that contains the most important growth factors stimulating their proliferation and differentiation. This in vitro study permit to analyze these cells ability of enhancing bone formation during a remodeling process. The obtained results have shown the importance of stimulating some substances expression during the osteogenic differentiation as they highly accelerate in vitro bone remodeling. Additionally we mention the work of Krishnan et al. (2014), in which the authors aimed to investigate breast cancer colony effect on bone. They employed a method permitting to quantify the 3D mineralization of bone tissue within breast cancer colonization using a bioreactor. This study permitted to understand how breast cancer cells degrade osteoblastic functioning by stimulating the osteoclastic one through the secretion of different proteins. To analyze the direct effect of glucose-loading and insulin on osteoblast functioning in women in in vitro, a study has been elaborated. Levinger et al. (2016) have cultured human osteoblasts to assess their viability and apoptosis using Cell Titer Blue. Thr study results showed that elevated levels of glucose cause decreased osteoblast viability and increased osteoblast apoptosis. Concurrently, assessing insulin treatment effect on osteoblasts in vitro, authors have found that this treatment rescued the destructive impact of glucose on osteoblasts.

4.2 Mathematical modeling in bone remodeling

127

Bone remodeling in vitro has proven its potential in studying numerous phenomena that could not be observed in vivo. Nevertheless, this type of analysis assays faces a lot of problems in terms of mimicking the remodeling and healing process (Kohli et al., 2018).

4.2 Mathematical modeling in bone remodeling 4.2.1 Mechanical models 4.2.1.1 Isotropic models The theory of adaptive elasticity (Cowin & Hegedus, 1976) probably represents the first complete consistent model of bone remodeling process, considering that trabecular bone apparent density evolution is governed by mechanical macroscopic variables, including strains, and that local elastic isotropic constants only depend on this apparent density. Indeed, Cowin and Hegedus (1976) formulated a conceptual model that consisted of a thermomechanical continuum theory, clarifying and predicting the strain-associated bone remodeling properties. Bone matrix was considered as a porous elastic solid with a fluid filling its pores. The bone adaptation properties were represented by a strain-controlled chemical reaction that transfers momentum, entropy, energy, and mass to and from the porous elastic solid. The addition of mass to the porous solid generates a change in its porosity. Particular representations for the balance of linear momentum, entropy inequality, energy and mass were assumed. Strain, porosity, temperature, and temperature gradient were related to the reaction rate through constitutive assumptions. At any point in the material, strain, and porosity represented two independent variables. The balance of momentum, energy, and mass, as well as the reduced entropy inequality were represented, respectively, by the following field equations: γν υ_ i 5 Tij;j 1 γνbi 1 pi

(4.1)

γν ε_ 5 Tij Lij 1 γνr 2 qi;i 1 h   r 1 h qi 1 γν η_ $ γν 2 θ θ θ ;i

(4.2)

1 2γνψ 2 γνηθ_ 1 Tij Lij 2 qi θ;i 1 h $ 0 θ

(4.3) (4.4)

This reduced entropy inequality was then used to restrict constitutive assumptions. In accordance with Wollf’s law, Huiskes et al. (1987) developed and tested computersimulation methods (Fig. 4.1) to predict stress-associated adaptation of bone remodeling. The models were based on the FE method combined with numerical formulations of adaptive remodeling theories, applied on a 2D proximal femur model. To determine the bone density or shape adaptations to alternative functional requirements, the actual SED, denoted U, was used as a feedback control variable and the distribution of the homeostatic equilibrium SED, denoted Un , was assumed as the remodeling objective. SED was denoted U and expressed as follows: 1 U 5 εij σij 2

(4.5)

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Chapter 4 Bone remodeling mathematical models

FIGURE 4.1 Schematic representation of the adaptive remodeling program, integrated with the finite element method (FEM) code.

where εij denotes the strain tensor and σij the local stress tensor. The difference between U and a site-specific Un was supposed to be the driving force for adaptive activity. Yet choosing SED as the feedback control variable for adaptive remodeling was arbitrary, the used theories are (quasi) static, where the effects of loading rates, inertia and viscoelasticity were not taken into account. Although changes in static loading are unlikely to result in adaptive bone reactions, the philosophy was to consider SED amplitudes as general representations of the actual recent loading history. Carter et al. (1989) applied the stress history formulation for predicting bone density distribution to a multiple-loading iterative remodeling of a 2D proximal femur FE model, and introduced a loading history-based technique to predict the bone trabecular alignment distribution. The study was conducted while assuming that the remodeling process is performed towards a state in which the mechanical stimulus subjected to bone tissue is independent of its anatomical position within the bone, and is determined by the cumulative loading cycles and differently oriented loads. A linear stimulus superposition for each loading case was then used to calculate the total stimulus to bone maintenance, and the calculated values were in turn used to determine the changes in bone apparent density and material properties. The stress solutions were determined according to these changes. This iterative technique allowed to predict the bone apparent density and orientation characteristics. For each simulated case, the calculated remodeling patterns revealed that bone density tended to progressively increase in some areas and decrease in others, independently of the modulus selected for the initial homogeneous model. The obtained density distributions were reasonable for about the first three iterations, but unreasonable for the seventh iterations that generated a much greater density and material property gradients than the observed gradients in the proximal femur. Beaupr´e et al. (1990) presented a time-dependent approach for bone modeling and remodeling in response to daily loading history (Fig. 4.2), based on the unifying approach of Hart (1989). The theory presented by Beaupr´e et al. (1990) took into account the bone surface area on which bone-

4.2 Mathematical modeling in bone remodeling

129

FIGURE 4.2 ´ bone remodeling model: (A) Block diagram representation of bone remodeling having multiple Beaupre’s feedback loops and (B) hypothetical curves for three bone regions showing the rate of surface remodeling as a function of the tissue level stress stimulus. ´ G. S., Orr, T. E., & Carter, D. R. (1990). An approach for time-dependent bone modeling and remodeling— Adapted from Beaupre, theoretical development. Journal of Orthopaedic Research, 8(5), 651
661.

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Chapter 4 Bone remodeling mathematical models

resorbing osteoclasts and bone-forming osteoblasts act, which thereby treated the remodeling process as a surface-mediated phenomenon. They postulated that bone cannot identify the appropriate mechanical stimulus level required for its maintenance from any intrinsic knowledge of its 3D spatial location. The appropriate level is rather set by local biochemical and systemic influences from adjacent tissues, and the difference between the actual and the appropriate levels of daily stimulus regulate the speed and impetus of bone modeling or remodeling. External changes in form or size associated with modeling or remodeling processes were directly calculated from the linear bone resorption and formation rates on periosteal surfaces, whereas internal remodeling was associated with the linear bone resorption and formation on internal surfaces. The rate of the linear remodeling is linked to the rate of the bone apparent density variation through the density of the local bone surface area. An empirically derived relation for the surface area density was used for both cortical and trabecular bone covering the whole apparent density range. For either internal or external remodeling, the time-dependent rate of bone resorption or formation on external bone surfaces was calculated using the following formulation:
 c1 ψb
2 ψbAS 1 ðc1 2 c2 Þw1 ðψb 2 ψbAS , 2 w1 Þ ð2 w1 # ψb 2 ψbAS , 0Þ c2
ψb 2 ψbAS  r_ 5 ð0 # ψb 2 ψbAS # 1 w2 Þ
c3 ψb 2 ψbAS ðψb 2 ψbAS . 1 w2 Þ c4 ψb 2 ψbAS 1 ðc3 2 c4 Þw2

(4.6)

where ci denotes an empirical rate constant, ψb the tissue level stress stimulus, ψbAS the attractor state stress stimulus, and wi the width of the central normal activity region. Beaupr´e et al. (1990) also established a relationship between the stress at the tissue level and that at the continuum level, following a standard homogenization technique and validated by experimental findings. However, the developed approach was based on a number of assumptions. For instance, the stress stimulus at the bone tissue was considered to tend towards a uniform value, the load history approach used to determine the local stress stimulus is a simplification of the actual loading history the bone is subjected to, the developed bone remodeling theory did not take into account the initial resorption phase prior to the remodeling changes in cortical bone, and the bone was considered as an isotropic material.

4.2.1.2 Anisotropic models Cowin (1986) defined trabecular bone tissue anisotropy using a second-order tensor that defines the bone mass distribution directions and principal values, called the fabric tensor. An elastic constitutive relation for trabecular tissue, involving the stress, strain and fabric tensors was developed and led to the first mathematical formulation of Wolff’s law at remodeling equilibrium. The fabric tensor referred to a quantitative stereological measure of the microstructural arrangement of trabeculae and pores of the trabecular bone and represents the inverse square root of the mean intercept length tensor that was introduced by Harrigan and Mann (1984). In his paper, Cowin (1986) gave a description of a local trabecular bone fabric tensor and elastic constants, and discussed the fabric tensor and its experimental determination. The developed mathematical formation depends on the concepts of the bone remodeling equilibrium, the fabric tensor and the principal stress directions. The remodeling equilibrium refers to the set of conditions under which trabecular bone tissue is not subjected to any trabecular architecture realignment or to net resorption and formation processes. Wolff’s law of trabecular architecture states that the principal stress axes coincide with the

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principal trabecular directions in the trabecular bone remodeling equilibrium. This implies the mandatory coincidence of the stress principal axes with the fabric principal axes, which requires a commutative matrix multiplication of the stress and the fabric tensors. The relation between the stress tensor and remodeling equilibrium, and between the strain tensor and the remodeling equilibrium was expressed as:     T11 5 C1111 ðν  ; H ÞE11 1 C1122 ðν  ; H ÞE22 1 C1133 ðν  ; H ÞE33     T22 5 C1122 ðν  ; H ÞE11 1 C2222 ðν  ; H ÞE22 1 C2233 ðν  ; H ÞE33     T33 5 C1133 ðν  ; H ÞE11 1 C2233 ðν  ; H ÞE22 1 C3333 ðν  ; H ÞE33

Tij

(4.7)

Eij

where denotes the remodeling equilibrium stress, the remodeling equilibrium strain, Cijkm the elasticity tensor that completely characterizes the linear elastic mechanical behavior of the trabecular bone tissue, ν  the remodeling equilibrium volume fraction, and H the remodeling equilibrium fabric tensor. The work provided an attempt to lay out predictive model general framework computation model for trabecular bone architecture and bulk density remodeling equilibrium owing to stress adaptation. One of the main conclusions of the work is that the principle directions of the fabric tensor coincide with the principal orthotropic directions of the elasticity tensor. However, it was developed based on an initial condition assuming that the volume fraction depends on the strain and on the fabric tensors. Jacobs et al. (1997) proposed that bone adaptive response is performed to provide a globally effective or efficient mechanical structure, and suggested a CDM-based specific mathematical formulation. The global efficiency assumption implied a local regulation process and led to a local regulation formation that accommodated the applied loading through a fully anisotropic response, without requiring any material symmetry. The notion of optimal bone adaptation was used to derive a general functional form that described the local behavior of the anisotropic stiffness tensor. The assumed optimally effective remodeling process at the global level led to a specific anisotropic remodeling at the local level. The developed algorithm was in the form if the following expressions: ρðt 1 ΔtÞ 5 ρðtÞ 1 Δtρ_ ðtÞ

(4.8)

If ρ_ . 0 then, Cðt 1 ΔtÞ 5 CðtÞ 1 Δt

β ρ_ ðtÞ σ  σ ρ σ∶ε

(4.9)

If ρ_ , 0 then, DðtÞ 5 C21 ðtÞ Dðt 1 ΔtÞ 1 DðtÞ 1 Δt

β ρ_ ðtÞ ε  ε ρ σ∶ε

Cðt 1 ΔtÞ 5 D21 ðt 1 ΔtÞ

(4.10) (4.11) (4.12)

where ρ denotes the bone density, ρ_ the apparent bone density, t time C the stiffness tensor, D the compliance tensor, σ the stress field, ε the strain field, and β a piecewise constant.

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Chapter 4 Bone remodeling mathematical models

The remodeling formulation behavior was assessed using a 2D proximal femur FE model, and the simulation outcomes were in a qualitative agreement with the observed trabecular alignment patterns. However, an infinitesimal strain field was assumed and the density variation resulting from physical deformation that manifests in the absence of a biological adaptive mechanism was ignored. Doblar´e and Garcıa (2002) proposed an internal bone remodeling model, based on a combined damage-repair theory, and grounded in the CDM theory. They considered that the evolution of bone microstructure internal variables and incidence on the variation of the elastic constitutive parameters can be expressed according to the exact CDM principles, with no reference to actual internal damage. Bone resorption was considered as a cumulative damage process, the internal variables comprised the apparent density and the fabric tensor, the remodeling evolution law was chosen while considering an associative model, using a damage criterion and a mechanical stimulus to accommodate experimental findings, such as the alignment of the fabric tensor principal directions with the elasticity tensor principle directions, the tendency of these principal directions to align with the stress tensor principle directions (Wolff’s law) or the ratio between the elasticity tensor principal values. The mechanical stimulus was then expressed in terms of the stress at the continuum level as: ψt 5

N X i51

"   # 1 ρ^ 2 nmi ̅σ i ρ

(4.13)

where ψt denotes the mechanical stimulus, i the load case, N the number of different load cases, ni the average number of load cycles per time step for each load case, m an experimental parameter, and ̅σ i the stress at the continuum level. The damage referred to a measure of the void volume within the bone tissue and the undamaged material was considered as the ideal bone state, perfectly isotropic with null porosity. The model identified bone voids with the microcracks or cavities of other material damage models, but adapted the standard assumptions in this theory to match the specific living material requirements. Therefore unlike the standard case assuming a consistently positive evolution of the damage as a direct corollary of the second law of thermodynamics, the damage-repair theory considers an additional negative evolution of the damage during bone repair owing to the provided metabolic energy not taken into account in a purely mechanical model. The damage tensor includes not only the bone structure microdirectionality through the fabric tensor, but also the porosity through the apparent density. Both variables were assumed to be independent owing to the used fabric tensor normalization condition. The internal variable of the model comprised a remodeling tensor directly linked to the damage tensor and included both the fabric tensor and the apparent density. The effective stress expression led thereby to a constitutive tensor with orthotropy directions that coincide with those of the damage tensor principal axes. The introduced anisotropic model was simulated and the results showed an overall density distribution close to reality and to previous models. Representing the anisotropic behavior by the stress surfaces showed a cortical layer anisotropy close to experimental findings. The model of Doblar´e and Garcıa (2002) also proved a number of important model properties, such as the fulfillment of the principle of minimum mechanical dissipation in bone resorption and formation for an associated law and convex damage criteria. The model also established a limit density value for the hardening exponent. The fabric tensor was aligned with the elasticity tensor, and the material tended to align its principal directions with those of the stress tensor, achieving a directional equilibrium when the fabric and the stress tensors are aligned, while the density value

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remained able to change. Moreover, bone resorption was suggested to lead to a faster evolution of the constitutive tensor anisotropic character than bone formation.

4.2.2 Biological models Komarova et al. (2003) developed a first mathematical model for the interaction between osteoblasts and osteoclasts. In this model, a mathematical description of the temporal osteoblast and osteoclast population dynamics and the associated changes in bone mass at a single BMU, was constructed (Fig. 4.3). The originality of this work was the incorporation of autocrine and paracrine interactions among osteoblasts and osteoclasts, allowing to investigate the cooperative roles of both of these regulation mechanisms in bone remodeling control. The cell population dynamics were described using the following system of differential equations: dx1 5 α1 xg111 xg221 2 β 1 x1 dt dx2 5 α2 xg112 xg222 2 β 2 x2 dt

(4.14) (4.15)

FIGURE 4.3 Komarova’s bone remodeling model: (A) Schematic representation of interactions between osteoclasts and osteoblasts included in the model, (B) Changes with time in the number of osteoclasts (OC, dashed line) and osteoblasts (OB, solid line) calculated from the model and (C) consequent changes in bone mass are calculated as a percentage of initial bone mass (100%). The pattern of a single remodeling cycle is similar to that observed in vivo and attributed to targeted bone remodeling. Adapted from Komarova, S. V., Smith, R. J., Dixon, S. J., Sims, S. M., & Wahl, L. M. (2003). Mathematical model predicts a critical role for osteoclast autocrine regulation in the control of bone remodeling. Bone, 33(2), 206
215.

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where 1 and 2 denote the osteoclasts and osteoblasts, respectively, xi the cell number, αi the cell production activity, β i the cell removal activity, and gij the net effectiveness of osteoclast- or osteoblast-derived autocrine or paracrine factors. The changes in bone mass was determined using the following equation: dz 5 2 k1 y1 1 k2 y2 dt

(4.16)

where z denotes the total bone mass, ki the normalized resorption and formation activities, and yi the active cell numbers, which is calculated according to the following conditions, with ̅x i being the cell number at steady state:  yi 5

xi 2 x i 0

if if

xi . x i xi # x i

(4.17)

The model allowed to predict different behavior modes. Two stable behavior modes of the remodeling process were defined, a first one corresponding to a targeted single remodeling cycle initiated in response to external stimulus, and a series of random remodeling cycles internally initiated. Then a third behavior mode corresponding to unstable oscillatory changes in osteoblast and osteoclast numbers and bone mass with increasing amplitude, similar to the remodeling process in pathologies such as Paget’s disease, was predicted. The findings revealed that the remodeling dynamic behavior mode mainly depends on osteoclast autocrine regulation parameter and the model suggests that preosteoblast availability may be a limiting factor in bone formation under certain conditions. This study revealed that modeling the simultaneous processes of osteoblast and osteoclast regulations and interactions, even in a simplistic form, results in a highly complex nonlinear behavior, and that the intrinsic properties of the osteoblast
osteoclast system can generate complex remodeling modes observed in vivo. Afterwards, Komarova et al. (2003) extended their model of osteoblast and osteoclast interactions within a single BMU to include changes in bone cell numbers and bone following PTH administration (Komarova, 2005), because the remodeling process is involved in PTH anabolic, as well as catabolic effects on bone. The model developed by Komarova (2005) aimed to examine the effect of RANKL/OPG increasing duration on the overall remodeling balance for a single cycle. Using the same system of differential equations describing the cell population dynamics [Eq. (4.14) and Eq. (4.15)], the same equation describing the changes in bone mass [Eq. (4.16)], as well as the same conditions for the active cell numbers [Eq. (4.17)], PTH effect was, at first, considered to only generate the increase of the RANKL/OPG ratio, and was modeled as a step increase in the parameter expressing osteoblast-derived osteoclast regulation, noted g21 . Then, PTH was also considered to promote the response of osteoblasts to stimulatory factors, and was modeled as a step increase in osteoblast autocrine regulation, noted g22 , or to promote osteoblast formation rate, and was modeled as a step increase in osteoblast production activity, noted α2 , or also to promote osteoblast survival, and was modeled as a step decrease in osteoblast removal activity, noted β 2 . The following equation was included in the previous system of differential equations: g21 5 f ðPTH Þ 5 stepðt0 ; d Þ

(4.18)

where g21 denotes the osteoblast-derived osteoclast regulation, t0 the time of PTH application, and d the duration of PTH-induced changes in RANKL/OPG, while assuming that PTH application was started at t0 5 1d.

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The model used PTH as a proresorptive agent, and predicted that bone
cell interactions are performed in such a way that the duration of applying PTH may result in qualitatively different outcomes, without having to assume that bone
cell response depend on whether PTH application is intermittent or continuous. The model suggested that PTH complex actions on the remodeling process may result from a strong coupling between osteoblasts and osteoclasts. However, it was considerably simplified, since only two cell types were taken into account, local autocrine and paracrine factors were supposed to only regulate osteoblast and osteoclast formation, and the parameters describing the autocrine and paracrine regulation effectiveness included actions of several factors. The work conducted by Lemaire et al. (2004) aimed to develop a theoretical framework able to explain bone biology experimental observations. In their paper, a mathematical model of bone remodeling cellular control was proposed to particularly examine the biochemical control network failures leading to bone diseases, such as osteoporosis. The model consists of a synthetic system including the cellular and biomechanical feedback mechanisms that spearhead bone turnover regulation, taking into account the PTH action in the remodeling process. The originality of this model was the incorporation of the RANK
RANKL
OPG pathway, representing an essential regulation mechanism of osteoclast formation (Fig. 4.4).

FIGURE 4.4 Diagrammatic representation of the basic structure of the model. The ovals represent cell compartments. The solid arrows represent flows of the pointed element. The solid arrows with a (1) (or (_) sign) next to them indicate a stimulatory (or inhibitory) action. The zigzag arrows represent cellular signaling pathways leading to an increasing (or a diminishing) production of the indicated agent. The small arrows pointing at an “X” indicate an elimination flow. The double dashed arrows represent receptor/ligand binding. The thin squared frames indicate types of cells which are not included in the model (Lemaire et al., 2004).

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Chapter 4 Bone remodeling mathematical models

The reaction scheme of PTH binding with its receptor was formulated as follows, without taking osteoblastic interactions into account: pP k5 k P 1 Pr " Pr}P k k6 dP

(4.19)

where P denotes PTH, Pr the PTH receptor, pP and dP are the PTH production and dissociation fluxes, respectively, and Pr}P is the complex formed by PTH and its receptor. The reaction schemes of the bindings of RANKL with RANK and of OPG with RANKL were giving by [Eqs. (4.20) and (4.21)], respectively: pL k3 k L 1 K " K}L k k4 dL

(4.20)

pO pL k k k1 O 1 L " O}L k k2 k dL dO

(4.21)

where K denotes the RANK receptor, L, the RANKL cytokine, O the OPG protein, K}L the RANK
RANKL complex, and O}L the OPG
RANKL complex. The equations describing the cell number evolution were formulated as simply balance equations. Without including a TGF-β compartment in the model, the TGF-β releasing rate per active osteoclast was supposed to be constant, and their concentration was supposed to be proportional to that of active osteoclasts. Based on the fact that osteoblast-lineage cells are supplied from a large uncommitted progenitor populations, that these progenitors express a specific TGF-β receptor, the activation of which leads to the differentiation of the progenitors into responsive osteoblasts, and that active osteoclasts mediate the TGF-β-induced effects on the progenitors, the progenitor response to TGF-β binding, governing the entering flow into the responsive osteoblast compartment, was expressed in terms of a proportionality relationship with the TGF-β receptor occupancy, πC : DR ∙πC 5 DR ∙

C 1 C0 C 1 Cs

(4.22)

where DR denotes a proportionality factor, C the active osteoclast concentration, C0 the basal osteoclast concentration, and Cs the dissociation coefficient of the binding of TGF-β with its receptor. The outgoing flow of the responsive osteoblast compartment is also the feeding flow to the active osteoblast compartment, and the binding of TGF-β acts by inhibiting the responsive osteoblast differentiation, which results in an inverse proportionality of cell response to πC : DB C 1 Cs ∙R 5 DB ∙ ∙R πC C 1 C0

(4.23)

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where DB denotes a proportionality factor. The apoptosis rate of active osteoblasts that do not differentiate into lining cells, nor into osteocytes, was expressed as a first-order degradation process equal to kB ∙B. On the other hand, the differentiation of preosteoclasts into active osteoclasts is promoted by RANK
RANKL binding, and is proportional to the RANK occupancy ratio, which, in this model, was defined as πL 5 K}L=K. The flow of the differentiation precursors entering the active osteoclast compartment was given by DC ∙K}L=K, where DC is the preosteoclast differentiation rate. Based on previous histological evidences, the bone formation and resorption rates were considered constant during the model time scale. Thus the total formed or resorbed bone amount within the BMU mainly depends on the ratio of active osteoclasts to active osteoblasts, noted C=B. The model was able to simulate the coupling mechanism between osteoblasts and osteoclasts, the catabolic effect related to PTH continuous administration, the RANKL catabolic action and the OPG anticatabolic action, in addition to metabolic bone diseases, such as glucocorticoid excess, senescence, vitamin D deficiency, and estrogen deficiency. The model also confirmed that bone formation therapies yielded better results that antiresorptive therapies in restoring bone loss, and that combining anabolic and antiresorptive therapies may provide better benefits than monotherapy. The model developed by Pivonka et al. (2008) aimed to investigate and incorporate an optimal model structure for RANKL and OPG expression on osteoblast lineage at different maturation stages. Afterwards, the investigation dealt with optimal changes in differentiation rates able to provide effective functional control within an active BMU (Fig. 4.5). The cell population model proposed in this study was mainly based on that of Lemaire et al. (2004), but incorporating a rate equation describing changes in bone volume, a rate equation describing TGF-β concentration in terms of the resorbed bone volume, RANKL and OPG expressions on osteoblast-lineage cells at different maturation stages, as well as activator/repressor functions based on enzyme kinetics. The model does not refer to a single BMU. It includes spatial averages of cell numbers over a finite bone volume that contains many BMUs. But, it may be contrasted in the case of studying a single BMU, since temporal and spatial sequences define the type of the present bone cells. The cell population dynamics were described by the following cell balance equations: dOBp TGF2β 5 DOBu ∙πTGF2β act;OBu 2 DOBp ∙OBp ∙πact;OBp dt dOBa 5 DOBp ∙OBp ∙πTGF2β rep;OBp 2 AOBa ∙OBa dt dOCa TGF2β 5 DOCp ∙OCp ∙πRANKL act;OC p 2 AOCa ∙OCa ∙πact;OCp dt

(4.24) (4.25) (4.26)

where OBu denotes the uncommitted osteoblast progenitors, OBp the preosteoblast cells, OC p the preosteoclast cells, OBa , the active osteoblasts, OC a the active osteoblasts, Di the cell differentiaTGF2β TGF2β TGF2β tion rate, Ai the cell apoptosis rate, πact;OB , πrep;OB , and πact;OC the activator/repressor functions u p p related to the binding of TGF-β to its receptors on osteoblasts and osteoclasts, and πRANKL act;OC p the activator function related to the binding of RANKL to its RANK on preosteoclasts. The above cell balance equations represent the changes in each cell population owing to the addition and removal of the respective cell lineage. Several activator and repressor function regulate the differentiation and apoptosis rates. For instance, the binding of TGF-β on its receptors expressed on uncommitted

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Chapter 4 Bone remodeling mathematical models

FIGURE 4.5 Schematic illustration of bone
cell population model: (A) cells interaction (B) Biologically observed expression of OPG and RANKL on osteoblastic cells and derived extreme cases for four models structures and (C, D) Normalized plots of RANKL and bone
cell concentration versus time (days) for model structures 1
4 for an increase of osteoclast differentiation rate. Adapted from Pivonka, P., Zimak, J., Smith, D. W., Gardiner, B. S., Dunstan, C. R., Sims, N. A., Martin, T. J., & Mundy, G. R. (2008). Model structure and control of bone remodeling: A theoretical study. Bone, 43(2), 249
263.

osteoblast progenitors promotes their differentiation, whereas its binding on its receptors expressed on preosteoblasts inhibits their differentiation. The evolution, over time, of bone volume, BV, was formulated as follows: dBV f a 1 kform OB fa 5 2 kres OC dt

(4.27)

where BV here denotes the percentage of normalized bone volume, kres the relative bone B resorption rate, and kform the relative bone formation rate, with OC a 5 OC a ðtÞ 2 OC a ðt0 Þ and f a 5 OBa ðtÞ 2 OBa ðt0 Þ, where OCa ðt0 Þ and OC a ðt0 Þ denote the numbers of active osteoclasts and OB osteoblasts at the initial state, t_0. This formulation allows to link the evolution of cell numbers in Eq. (4.24), Eq. (4.25), and Eq. (4.26) to the changes in bone volume.

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The RANK
RANKL
OPG pathway was also included in the model, coupled with TGF-β action on bone cells, since this forms the basic remodeling regulatory network. Based on a number of simplifications and assuming a quasi-steady state, the concentrations of OPG and free RANKL were expressed as follows:


 β 1;OPG ∙OBp 1 β 2;OPG ∙OBa ∙πPTH rep;OB 1 POPG;d ðt Þ OPG 5 ðβ1;OPG ∙OBp 1 β2;OPG ∙OBa Þ∙πPTH rep;OB eOPG 1D OPGmax RANKLeff RANKL 5 1 1 KA1;RANKL OPG 1 KA2;RANKL RANK

β RANKL;1 1 PRANKL;d eRANKL RANKLeff β RANKL 1 D

(4.28) ! (4.29)

where β 1;OPG denotes the preosteoblast-induced OPG production rate, β 2;OPG the active osteoblastinduced OPG production rate, RANKLeff the RANKL effective carrying capacity on osteoblast surfaces that represents the maximum RANKL concentration, KA1;RANKL the RANKL to OPG association binding constant, KA2;RANKL the RANKL to RANK association binding constant, RANK the eRANKL the RANKL degradation fixed RANK concentration, β RANKL the RANKL production rate, D rate, and PRANKL;d the external RANKL dosing rate. One key difference between the formulations used in the model of Pivonka et al. (2008) and those in the model of Lemaire et al. (2004) is in the investigation of the cell type that expresses RANKL and OPG. In Pivonka et al. (2008), both RANKL and OPG were assumed to be expressed by preosteoblasts and active osteoblasts. The outcomes of this study suggested that RANKL expression profile provides BMUs with a best functional responsiveness, and that TGF-β is included in the upregulation of osteoblast progenitor differentiation rate, in the downregulation of preosteoblast differentiation rate, and in the upregulation of active osteoclast apoptosis rate, which partially explains the particular suitability of TGF-β physiological actions in bone.

4.2.3 Biomechanical models Huiskes et al. (2000) presented a computational model of bone metabolic process confirming that the coupling mechanism throughout bone remodeling is governed by feedback from mechanical load transfer (Hu & Qin, 2020). The study aimed to explain the maintenance of trabecular architecture emerge as an optimal mechanical structure, and the association between the adaptation of trabecular architecture and external loads. Fig. 4.6 shows the proposed regulatory process that was based on a number of assumptions. First, as produced by a recent loading history, a typical SED rate in the mineralized tissue represents the mechanical variable triggering feedback from the external forces to bone metabolism. Second, SED rate generates a loading in the local environments of osteocytes that react by producing an amount of a biochemical messenger proportional to this rate. Third, the biochemical messenger induces signals that dissipate through the osteocytic network towards the bone surface and recruit osteoblasts for the remodeling process. Fourth, to mimic bone resorption in the model, the probability of osteoclast activation per surface site is regulated either by disuse or by microcrack occurrence within the bone matrix. In their model, Huiskes et al. (2000) directly linked the SED rate per osteocyte to the bone formation stimulus at the surface, taking into account the osteocyte mechanosensitivity and the

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Chapter 4 Bone remodeling mathematical models

FIGURE 4.6 The proposed regulatory process. Both enhanced external load intensity (amplitude and frequency) and resorption cavities provoke bone formation. Reductions in loading reduce bone mainly through unbalanced resorption (Huiskes et al., 2000).

distance-associated attenuation. Osteoblast recruitment stimulus was derived from Eq. (4.30) and the local variation of relative bone density was expressed as in Eq. (4.31). Pðx; tÞ 5

n X

fi ðxÞμi Rti ðtÞ

(4.30)

i51

  dm 5 τ Pðx; tÞ 2 ktr 2 roc for Pðx; tÞ . ktr dt dm 5 2 roc for Pðx; tÞ # ktr dt

(4.31)

where Pðx; tÞ denotes the osteoblast recruitment stimulus at a surface location x as a function of the time t, n the osteocyte number in the vicinity of the considered location, i the osteocyte, fi an exponential decay function that describes the attenuation of bone formation stimulus between the osteocyte and the surface location, μi the osteocyte mechanosensitivity, Rti ðtÞ the SED rate at the osteocyte location, m the relative bone density, τ a proportionality constant, ktr the threshold level of the osteoblast recruitment stimulus, and roc the relative resorbed mineral amount. Hazelwood et al. (2001) investigated the dynamic behavior of a new bone remodeling algorithm that included biological and metabolic effects on bone adaptation. The algorithm assumed that bone remodeling is lunched as a response to either disuse or microdamage and combined concepts from models simulating the remodeling process with those simulating the influence of mechanical factors on bone density. The work attempted to provide a more faithful reproduction of remodeling microstructural effects, by including BMU activity and analyzing the influence of a number of biological factors directly related to it, such as focal bone balance, mineralization period and activation frequency. On one hand, transient oscillatory responses were thought to occur throughout bone adaptation to disuse, but most of histomorphometric studies were inconclusive regarding this issue.

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FIGURE 4.7 Hazelwood’s bone remodeling mathematical model: (A) Schematic representation of the bone remodeling algorithm and (B) porosity (top), BMU activation frequency (bottom), and damage (inset, bottom) responses over time for the model in disuse situations. Porosity of the model increased as it was placed further in disuse. After initial increases, activation frequency returned to near normal conditions. Adapted from Hazelwood, S. J., Bruce Martin, R., Rashid, M. M., & Rodrigo, J. J. (2001). A mechanistic model for internal bone remodeling exhibits different dynamic responses in disuse and overload. Journal of Biomechanics, 34(3), 299
308.

Hazelwood et al. (2001) obtained oscillations in the BMU activation frequency in disuse simulations (Fig. 4.7), but no clear experimental data supported these findings. On the other hand, damage accumulation was quantified as the difference between damage growth and repair. The model predicted the BMU adjustment ability to overloads by increasing the remodeling rate to cope with the increase in damage formation, but with definite limits. Excessive loading, BMUs precipitously enter a “runaway remodeling” mode in which strain, damage, activation frequency, and porosity rapidly increase. This transition was also affected by small changes in loading or in the model parameters. However, the algorithm assumed that BMU activation frequency is related to damage and disuse through dose
response functions, and used the same mechanical stimulus function to determine the degree of disuse when strain is low as is used to determine the local damage. Hernandez et al. (2001) evaluated the potential
 for predicting bone mechanical properties with two-parameter power law functions of BVF BV TV and ash fraction ðαÞ, using an equation of the form:  b BV y5a αc TV

(4.32)

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Chapter 4 Bone remodeling mathematical models

where y denotes either the elastic modulus or the ultimate strength, and a, b, and c empirical constants. This formulation was used to determine the relative effects of BVF and ash fraction on the elastic modulus and ultimate strength of cortical and trabecular human bone, with a large ash fraction variation. This relied on determining or analyzing the values of b and c. In order to derive the two-parameter power law model used in this study, the above formulation was linearized, based on a logarithmic transform, and the constants a, b, and c were determined by performing two-parameter multiple linear regression analyses. The compressive ultimate strength and the elastic modulus were then respectively expressed as follows, with the exponents being given as mean plus or minus SE:  1:92 6 0:02 BV σULT 5 749:33 α2:79 6 0:09 TV  2:58 6 0:02 BV α2:74 6 0:13 E 5 84:37 TV

(4.33) (4.34)

These expressions clearly show the association of both the elastic modulus and the ultimate strength with the BVF and as fraction, and suggested, in addition to the significant influence of a change in ash fraction on both of the parameters. Unlike former studies, a poor relationship was found between BFV and ash fraction. However, the work provided by Hernandez et al. (2001) was based on a linear model and on assuming that the ash fraction and the true tissue density were related to each other in a simple linear fashion. Aspects of osteonal and trabecular orientation and architecture that affect mechanical properties were not taken into account and aspects of testing methods, such as analyzing data obtained from compression tests of bone placed directly between metal platens that are associated with an underestimation of elastic modulus, were not considered. Taylor et al. (2004) studied the theoretical prediction of stress fractures in bone during intensive physical activity, after developing a theoretical model based on the fatigue failure concepts and the Weibull approach (Taylor & Kuiper, 2001). In their paper, Taylor et al. (2004) improved this model by including adaptation and repair representations, to determine the way these two mechanisms reduced the failure probability, and to provide a more realistic prediction of the failure probability evolution with time. The approach was then applied to the case of human metatarsal, which frequently experiences stress fractures (Fig. 4.5). The repair process was represented as a probability density function Qr that did not change with the stress level [Eq. (4.35)] and the adaptation was considered as bone deposition that reduces the equivalent stress range Δσeq [Eq. (4.36)], which referred to a weighted average of all the stresses occurring throughout a given time period, thus, if deposition occurred, the stress value would continuously decrease. Qr 5

 ðr21Þ  r

υ t t 5 exp 2 tr tr tr 0 t 11n ðT 1 Δσeq 5 @ Δσn dtA tT

(4.35)

(4.36)

0

However, the model of Taylor et al. (2004) treated all people alike, without taking into account the individual variations in bone, it only considered short-time behavior, it neglected a number of

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complexities of the remodeling process, and it assumed that the damage, remodeling and adaptation processes occurred immediately of the increase in the applied stress.

4.2.4 Mechanobiological models Garcı´a-Aznar et al. (2005) formulated a continuum damage theory to assess damage growth and the generated bone elastic modulus degradation under cyclic loading. They proposed a bone remodeling continuous model to explore and simulate the coupling effect between the fatigue damage accumulation and removal, and the biological events occurring throughout the remodeling process. This allowed to assess the remodeling process and predict the stress fracture occurrence. From a biological perspective, the remodeling process consisted of mathematical description of the BMU activity. This model took into account the microstructural damage accumulation by fatigue. The subsequent BMU activation allowed to remodel the damaged tissue, but could also be activated to resorb the disused one under low mechanical stimuli. Besides, BMU activation was considered to be associated with a number of biological aspects and the amount of free surface available for such activation. This available surface is linked to porosity that changes with the BMU progression taking place in as an ARF sequence. The BMU progression rate and the duration of the phases of its sequence may vary with physiologic and metabolic factors and defines bone adaptation velocity. The deposited osteoid is initially organic and progressively undergoes the mineralization process. Therefore bone tissue mechanical properties depend on the matrix mineral content, porosity, and damage level, and they affect the stresses and strains the bone is subjected to, which closes the whole process. The algorithm scheme summarizing the model is illustrated in Fig. 4.8. The proposed model could simulate the temporal changes in bone apparent density, mineral content, elastic modulus and damage level, in addition to resorption rate generated by a fast damage accumulation under very high loads. However, the model of Garcı´a-Aznar et al. (2005) was used to simulate bone adaptation within the tissue, and did not take into account that, in cortical bone, most of the process is produced by periosteal or endosteal remodeling. Moreover, the spatial pore distribution, as well as bone mineralization and damage were assumed to be isotropic, despite the well-known anisotropic behavior of both the cortical and the trabecular bone. Martı´nez-Reina et al. (2009) introduced an extension to the anisotropic case of the isotropic model developed by Garcı´a-Aznar et al. (2005), and attempted to explain the changes in bone anisotropy associated with the changes in BMU progressing direction. The work aimed to simulate the real-time bone structure adaptation to changes in the mechanobiological environment and the proposed model was the first mechanobiological model that considers bone anisotropy. Besides changing bone porosity, BMUs were also considered to change the pore shape and orientation according to the direction of their progression, which determines the directional dependence of bone mechanical properties. Based on the strains the bone matrix is subjected to, and the orientation of the resultant cracks, an orientation was also assigned to damage. Moreover, pores and damage orientation were considered to affect the bone anisotropy, and together with the porosity and mineral content, provided the mechanical properties assumed in the model. The latter was then implemented to assess the mechanical properties and the anisotropic behavior of the femur proximal head (Fig. 4.9). Fig. 4.10 shows the distribution of bone volume fraction (vb ) at the beginning and the end of the simulation. According the obtained results, the fabric tensor was aligned with the strain tensor and so it happened with the elasticity tensor, the stiffest direction came to be the maximum load

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Chapter 4 Bone remodeling mathematical models

FIGURE 4.8 (A) Schematic representation of the proposed bone remodeling algorithm. (B) Influence of the consideration or not of the elastic modulus degradation in function of the damage level: (a) evolution of the bone volume fraction for cortical bone under a high overload of constant stress (b) evolution of damage level under the same loading conditions. Adapted from Garcı´a-Aznar, J. M., Ru¨berg, T., & Doblare, M. (2005). A bone remodelling model coupling microdamage growth and repair by 3D BMU-activity. Biomechanics and Modeling in Mechanobiology, 4(2
3), 147
167.

direction, and it distribution minimized the SED absorbed by bone. The model outcomes were then compared with the experimental mechanical properties found by former models. The alignment was in accordance with Wolff’s law (Wo¨lf, 1986). Among the highlighted conceptual differences was the possibility of simulating actual temporal changes in the directional structure. A single element was subjected to one of these changes caused by a load rotation, in order to examine the bone structure tendency to align with external loads, which was previously investigated by other authors. One of the model limitations is the assumption of a local spatial BMU progression instead of a global progression, in addition to the nonconsideration of other factors affecting bone mechanical properties, such as collagen fibril orientations and lamellar dimensions. A spatiotemporal diffusion model of bone remodeling model has been proposed in the work of Ayati et al. (2010) based on Komarova’s model (Komarova et al., 2003) where several biological stimuli affecting the autocrine and paracrine signaling pathways of bone cells are incorporated (Fig. 4.11). The inclusion of a spatial dimension has been mediated by developing a diffusion model defined in a spatial domain noted Ω. The main variables of the model are cell density of osteoclasts

FIGURE 4.9 Martı´nez-Reina’s bone remodeling model: (A) Algorithm of the isotropic internal bone remodeling model based on the BMU activity, (B) Evolution of bone volume in the three cases simulated, and (C) Evolution of the Young modulus in the principal stress directions in the tow load cases. ´ M. (2009). A bone remodelling model including the Adapted from Martı´nez-Reina, J., Garcı´a-Aznar, J. M., Dominguez, J., & Doblare, directional activity of BMUs. Biomechanics and Modeling in Mechanobiology, 8(2), 111
127.

FIGURE 4.10 Distribution of the bone volume fraction at the beginning and the end of the simulation (Martı´nez-Reina et al., 2009).

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Chapter 4 Bone remodeling mathematical models

FIGURE 4.11 (A) Schematic representation of the effects of myeloma on the autocrine and paracrine signaling in the osteoclast and osteoblast cell populations in the presence of tumor. (B) Graphs of the solutions C(t, x) and B (t, x) of the bone model without myeloma with an additional spatial dimension (Ayati et al., 2010).

Cðt; xÞ, cell density of osteoblasts Bðt; xÞ, and bone’s mass zðt; xÞ. Each one of these variables are defined for an integration point (x) and time instant (t), as presented in the following expressions: dCðt; xÞ @2 Cðt; xÞ 1 α1 Cðt; xÞg11 Bðt; xÞg21 2 β 1 Cðt; xÞ 5 σ1 dt dx2 dBðt; xÞ @2 Bðt; xÞ 1 α2 Cðt; xÞg12 Bðt; xÞg22 2 β 2 Bðt; xÞ 5 σ2 dt dx2   dzðt; xÞ @2 zðt; xÞ 5 σ3 2 k1 ðxÞmax 0; Cðt; xÞ 2 CðxÞ 1 k2 ðxÞmax 0; Bðt; xÞ 2 BðxÞ 2 dt dx

(4.37) (4.38) (4.39)

In Eqs. (4.37
4.39), σ1 , σ2 , and σ3 represent, respectively, the spatial diffusion parameters of osteoclasts, osteoblasts, and bone mass, while αi gij , β i , and ki production activity, autocrine and

4.2 Mathematical modeling in bone remodeling

147

FIGURE 4.12 Scheiner’s bone remodeling modeling: (A) Sketch of the bone
cell population model and involved differentiation. (B) Micromechanical representation of cortical bone and (C) mechanoregulatory feedback: the concentrations of active osteoblasts and active osteoclasts.

paracrine parameters, bone cells apoptosis rates, and normalized resorption and formation activities as defined in the Section 4.2.2. Scheiner et al. (2013) have raised the issue of multiscale property in their research paper. They proposed a mechanobiological mathematical model of bone remodeling coupling the biological behavior of bone cells (Fig. 4.12A) with multiscale mechanics (Fig. 4.12B). Based on the work of Pivonka et al. (2008) the biological part describing bone cells dynamics has been constructed. Concerning the mechanical modeling, authors have introduced a mechanical activation function that will represent strains’ effect on preosteoblast proliferation as osteoblasts could also have a mechanosensory ability. The formulation of this activation function is based on experimental observation showing straining intensity effect on the proliferation rate of osteoblasts (Jones et al., 1991; Kaspar et al., 2002). Accordingly, it depends on strain energy density as expressed in the following equation: _

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