Design and Simulation in Biomedical Mechanics (Advanced Structured Materials, 146) 3030659828, 9783030659820

Table of contents :
Contents
1 Comparative Study of Interferometry and Finite Element Analysis in Maxillofacial Applications (Hemimandibulectomy Type IVc)
1.1 Statement of the Problem
1.2 Introduction
1.3 Case Study
1.4 Materials and Methodology
1.4.1 Manual Modeling
1.4.2 Modeling Digitization
1.4.3 Finite Element Simulations
1.5 Results and Discussion
1.5.1 Digitization
1.5.2 Digital Modeling
1.5.3 Finite Element Analysis (FEA)
1.5.4 Discussion
1.6 Conclusions
References
2 Experimental and Numerical Evaluation of an Orthognathic Implant with Facial Asymmetry and Skeletal Class III
2.1 Introduction
2.2 Clinical Case
2.3 Objectives
2.4 Materials and Methods
2.4.1 Cephalometric Analysis
2.4.2 Experimental Testing
2.4.3 Numerical Analysis
2.5 Results
2.5.1 Experimental Photo-Elastic Test
2.5.2 Image Correlation Test
2.5.3 Finite Element Analysis (FEA)
2.6 Discussion
2.7 Conclusions
References
3 Biomechanical Evaluation of Sharped Fractures in Human Jaws Using Plates Articulated by the Champy Method
3.1 Introduction
3.1.1 Statement of the Problem
3.1.2 Osteosynthesis
3.1.3 Conventional Miniplate
3.1.4 Lambda Plate
3.2 Materials and Methods
3.2.1 Selection of Tests and Parameters for Simulation
3.2.2 Mandibular Kinematics
3.2.3 Material Selection
3.3 Experimental Tests
3.3.1 Duplicates on the Cadaveric Jaw
3.3.2 Instrumentation of the Cadaveric Jaw for Mechanical Experimentation Purposes
3.3.3 Joint Motion Simulation
3.3.4 Software Testing Preparation
3.3.5 CAD Modeling of Plates and Screws
3.3.6 Plate CAD Segmentation and Modeling (with Deformation)
3.4 Scanning of Bended Plates
3.4.1 Digitization Process
3.4.2 Assessment of Digitization
3.4.3 Finite Element Simulation
3.5 Discussion of Results
3.5.1 Assessment of Results
3.6 Analysis of Results
3.7 Study Using GOM Correlate to a 3D Printing of the Champy Method
3.7.1 Clarification
3.7.2 Process
3.7.3 Preparation
3.7.4 Experimental Procedure
3.7.5 GOM Correlate
3.7.6 Results
3.7.7 Analysis of Results
3.8 Conclusions
References
4 Comparative Study of Stress and Strain of Orthopaedic Implants for the Hip with Photoelastic and Image Correlation Techniques
4.1 Introduction
4.2 Clinical Case
4.3 Methodology
4.4 Materials and Methods
4.4.1 Design and Characterization of the Specimens for Experimental Evaluation
4.4.2 Experimental Study (Healthy and Abnormal Hip, and Prothesic Models)
4.5 Results
4.5.1 Results of the Photoelastic Test
4.5.2 Results of the Image Correlation Test
4.6 Discussion
4.7 Conclusion
References
5 Numerical–Experimental Study for the Determination of the Structural Mechanical Behavior of the Wall of the Cranial Vault Using Finite Element Method and Image Correlation
5.1 Introduction
5.2 Methodology
5.3 Materials and Methods
5.3.1 Design and Generation of the Three-Dimensional Model
5.3.2 Model Preparation for the Photoelasticity Test
5.3.3 Model Preparation for Image Correlation Analysis
5.4 Photoelastic Study
5.5 Image Correlation Study
5.6 Finite Element Analysis
5.7 Results
5.7.1 Photoelastic Test Results
5.7.2 Image Correlation Test
5.7.3 Numerical Results
5.8 Discussion
5.9 Conclusions
References
6 Numerical Simulation of Cranial Distractor Components Using Passive and Generative Design
6.1 Introduction
6.1.1 Fundamentals of the Generative Design
6.2 Materials and Methods
6.3 Original Piece Analysis
6.4 Simulation Results from the Generative Design
6.4.1 Results
6.4.2 Results from Study 6
6.4.3 Results from Study 7
6.4.4 Results from Study 8
6.5 Conclusions
References
7 Tridimensional Design and Printing Techniques to Obtain Personalized Prosthetic Components for Specific Cases Involving Bone Defects
7.1 Introduction
7.2 Materials and Methods
7.2.1 DICOM Images
7.2.2 Segmentation
7.2.3 3D Models
7.2.4 Printing the 3D Models
7.2.5 Design and Printing of the Implant Prototype
7.2.6 Production of the Definitive Implants
7.2.7 Mechanical Testing of the Implants
7.3 Results
7.4 Conclusions
References
8 Numerical–Experimental Study of 3D Printed Ortheses for Rehabilitation of Patients with Musculoskeletal Lesions
8.1 Introduction
8.2 Materials and Methods
8.2.1 Digitization
8.2.2 Model and Printing
8.2.3 Numerical Analysis
8.2.4 Interferometry
8.3 Results
8.4 Conclusions
References
9 Design of an Auxiliary Mechanical System for the Diagnosis of Lordosis and Scoliosis
9.1 Introduction
9.1.1 Anatomy of the Vertebral Column
9.1.2 Biomechanics of the Human Vertebral Column
9.1.3 Deformations of the Vertebral Column
9.1.4 Alternative Measurement Procedures for Vertebral Column’s Deformations
9.1.5 Lenke’s Classification
9.1.6 Definition of the Lumbar Column’s Modifier
9.1.7 Definition of the Thoracic, Sagittal Column’s Modifier
9.2 Case of Study and Methodology
9.3 Tomographic Data Segmentation
9.3.1 3D Printing of the Vertebral Column
9.3.2 Application of QFD Methodology Design
9.3.3 Manufacture of the Device
9.4 System Instrumentation
9.5 Data Acquisition
9.6 Tests
9.7 Analysis of Results
References

Citation preview

Advanced Structured Materials

Juan Alfonso Beltrán-Fernández Andreas Öchsner   Editors

Design and Simulation in Biomedical Mechanics

Advanced Structured Materials Volume 146

Series Editors Andreas Öchsner, Faculty of Mechanical Engineering, Esslingen University of Applied Sciences, Esslingen, Germany Lucas F. M. da Silva, Department of Mechanical Engineering, Faculty of Engineering, University of Porto, Porto, Portugal Holm Altenbach , Faculty of Mechanical Engineering, Otto von Guericke University Magdeburg, Magdeburg, Sachsen-Anhalt, Germany

Common engineering materials reach in many applications their limits and new developments are required to fulfil increasing demands on engineering materials. The performance of materials can be increased by combining different materials to achieve better properties than a single constituent or by shaping the material or constituents in a specific structure. The interaction between material and structure may arise on different length scales, such as micro-, meso- or macroscale, and offers possible applications in quite diverse fields. This book series addresses the fundamental relationship between materials and their structure on the overall properties (e.g. mechanical, thermal, chemical or magnetic etc.) and applications. The topics of Advanced Structured Materials include but are not limited to • classical fibre-reinforced composites (e.g. glass, carbon or Aramid reinforced plastics) • metal matrix composites (MMCs) • micro porous composites • micro channel materials • multilayered materials • cellular materials (e.g., metallic or polymer foams, sponges, hollow sphere structures) • porous materials • truss structures • nanocomposite materials • biomaterials • nanoporous metals • concrete • coated materials • smart materials Advanced Structured Materials is indexed in Google Scholar and Scopus.

More information about this series at http://www.springer.com/series/8611

Juan Alfonso Beltrán-Fernández · Andreas Öchsner Editors

Design and Simulation in Biomedical Mechanics

Editors Juan Alfonso Beltrán-Fernández Escuela Superior de Ingeniería Mecánica y Eléctrica, Unidad Zacatenco Instituto Politécnico Nacional Unidad Profesional Adolfo López Mateos, Mexico City, Mexico

Andreas Öchsner Faculty of Mechanical Engineering Esslingen University of Applied Sciences Esslingen, Baden-Württemberg, Germany

ISSN 1869-8433 ISSN 1869-8441 (electronic) Advanced Structured Materials ISBN 978-3-030-65982-0 ISBN 978-3-030-65983-7 (eBook) https://doi.org/10.1007/978-3-030-65983-7 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Contents

1 Comparative Study of Interferometry and Finite Element Analysis in Maxillofacial Applications (Hemimandibulectomy Type IVc) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Juan Alfonso Beltrán-Fernández, Kevin Brandon Chávez Landeros, Juan Carlos Hermida Ochoa, Luis Héctor Hernández-Gómez, José Enrique Rodríguez-Miramar, Edgar Alfonso Figueroa-Rodríguez, and Pablo Moreno-Garibaldi 1.1 Statement of the Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Materials and Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.1 Manual Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.2 Modeling Digitization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.3 Finite Element Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5.1 Digitization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5.2 Digital Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5.3 Finite Element Analysis (FEA) . . . . . . . . . . . . . . . . . . . . . . . . . 1.5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Experimental and Numerical Evaluation of an Orthognathic Implant with Facial Asymmetry and Skeletal Class III . . . . . . . . . . . . . Juan Alfonso Beltrán-Fernández, José Enrique Rodríguez-Miramar, Erick Omar Alvarado-Alcántara, Juan Carlos Hermida-Ochoa, Alejandro David González-Peña, Edgar Alfonso Figueroa-Rodríguez, and Luis Héctor Hernández-Gómez 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Clinical Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

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2.4 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1 Cephalometric Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2 Experimental Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.3 Numerical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.1 Experimental Photo-Elastic Test . . . . . . . . . . . . . . . . . . . . . . . . 2.5.2 Image Correlation Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.3 Finite Element Analysis (FEA) . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Biomechanical Evaluation of Sharped Fractures in Human Jaws Using Plates Articulated by the Champy Method . . . . . . . . . . . . . Juan Alfonso Beltrán-Fernández, Héctor Gallardo-Ayala, Michelle Chagoya-López, Cesar Antonio Trujillo-Perez, Mauricio González-Rebattú y González, Marco Antonio Maturano-García, Juan Carlos Hermida-Ochoa, Luis Héctor Hernández-Gómez, Juan Luis Cuevas-Andrade, Alejandro David González-Peña, and Pablo Moreno-Garibaldi 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 Statement of the Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 Osteosynthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.3 Conventional Miniplate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.4 Lambda Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Selection of Tests and Parameters for Simulation . . . . . . . . . 3.2.2 Mandibular Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3 Material Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Experimental Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Duplicates on the Cadaveric Jaw . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Instrumentation of the Cadaveric Jaw for Mechanical Experimentation Purposes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.3 Joint Motion Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.4 Software Testing Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.5 CAD Modeling of Plates and Screws . . . . . . . . . . . . . . . . . . . . 3.3.6 Plate CAD Segmentation and Modeling (with Deformation) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Scanning of Bended Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Digitization Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2 Assessment of Digitization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.3 Finite Element Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Discussion of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.1 Assessment of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Analysis of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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3.7 Study Using GOM Correlate to a 3D Printing of the Champy Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7.1 Clarification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7.2 Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7.3 Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7.4 Experimental Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7.5 GOM Correlate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7.6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7.7 Analysis of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Comparative Study of Stress and Strain of Orthopaedic Implants for the Hip with Photoelastic and Image Correlation Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Edgar Alfonso Figueroa-Rodríguez, Juan Alfonso Beltrán-Fernández, Juan Carlos Hermida-Ochoa, Brayan Leonardo Pérez-Escobar, Juan Luis Cuevas-Andrade, Erik Omar Alvarado-Alcántara, Alejandro David González-Peña, José Enrique Rodríguez-Miramar, and Luis Héctor Hernández-Gómez 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Clinical Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.1 Design and Characterization of the Specimens for Experimental Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.2 Experimental Study (Healthy and Abnormal Hip, and Prothesic Models) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.1 Results of the Photoelastic Test . . . . . . . . . . . . . . . . . . . . . . . . 4.5.2 Results of the Image Correlation Test . . . . . . . . . . . . . . . . . . . 4.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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5 Numerical–Experimental Study for the Determination of the Structural Mechanical Behavior of the Wall of the Cranial Vault Using Finite Element Method and Image Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 Juan Alfonso Beltrán-Fernández, Alejandro David González-Peña, Juan Carlos Hermida-Ochoa, José Enrique Rodríguez-Miramar, Edgar Alfonso Figueroa-Rodríguez, Erick Omar Alvarado-Alcántara, Luis Héctor Hernández-Gómez, and Juan Luis Cuevas-Andrade 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 5.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

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5.3 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 Design and Generation of the Three-Dimensional Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.2 Model Preparation for the Photoelasticity Test . . . . . . . . . . . . 5.3.3 Model Preparation for Image Correlation Analysis . . . . . . . . 5.4 Photoelastic Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Image Correlation Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6 Finite Element Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7.1 Photoelastic Test Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7.2 Image Correlation Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7.3 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.8 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Numerical Simulation of Cranial Distractor Components Using Passive and Generative Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Juan Alfonso Beltrán-Fernández, Erik Omar Alvarado-Alcántara, Juan Carlos Hermida-Ochoa, Edgar Alfonso Figueroa-Rodríguez, Alejandro David González-Peña, José Enrique Rodríguez-Miramar, Luis Héctor Hernández-Gómez, Pablo Moreno-Garibaldi, and Juan Luis Cuevas Andrade 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.1 Fundamentals of the Generative Design . . . . . . . . . . . . . . . . . 6.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Original Piece Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Simulation Results from the Generative Design . . . . . . . . . . . . . . . . . 6.4.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.2 Results from Study 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.3 Results from Study 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.4 Results from Study 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Tridimensional Design and Printing Techniques to Obtain Personalized Prosthetic Components for Specific Cases Involving Bone Defects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Juan Carlos Hermida-Ochoa, Juan Alfonso Beltrán-Fernández, Juan Luis Cuevas Andrade, Luis Héctor Hernández-Gómez, Teresa Berenice Uribe-Cortés, and Pablo Moreno-Garibaldi 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.1 DICOM Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.2 Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.3 3D Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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7.2.4 Printing the 3D Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.5 Design and Printing of the Implant Prototype . . . . . . . . . . . . 7.2.6 Production of the Definitive Implants . . . . . . . . . . . . . . . . . . . 7.2.7 Mechanical Testing of the Implants . . . . . . . . . . . . . . . . . . . . . 7.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Numerical–Experimental Study of 3D Printed Ortheses for Rehabilitation of Patients with Musculoskeletal Lesions . . . . . . . . Juan Alfonso Beltrán-Fernández, Juan Luis Cuevas Andrade, Juan Carlos Hermida Ochoa, Luis Héctor Hernández Gómez, Teresa Berenice Uribe-Cortés, and Pablo Moreno Garibaldi 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.1 Digitization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.2 Model and Printing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.3 Numerical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.4 Interferometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Design of an Auxiliary Mechanical System for the Diagnosis of Lordosis and Scoliosis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Juan Alfonso Beltrán-Fernández, Juan Carlos Hermida-Ochoa, Luis Héctor Hernández-Gómez, Carolina Alvarado-Moreno, Itzel Bantle-Chávez, Pablo Moreno-Garibaldi, and Erik Omar Alvarado-Alcántara 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1.1 Anatomy of the Vertebral Column . . . . . . . . . . . . . . . . . . . . . . 9.1.2 Biomechanics of the Human Vertebral Column . . . . . . . . . . . 9.1.3 Deformations of the Vertebral Column . . . . . . . . . . . . . . . . . . 9.1.4 Alternative Measurement Procedures for Vertebral Column’s Deformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1.5 Lenke’s Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1.6 Definition of the Lumbar Column’s Modifier . . . . . . . . . . . . . 9.1.7 Definition of the Thoracic, Sagittal Column’s Modifier . . . . 9.2 Case of Study and Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3 Tomographic Data Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.1 3D Printing of the Vertebral Column . . . . . . . . . . . . . . . . . . . . 9.3.2 Application of QFD Methodology Design . . . . . . . . . . . . . . . 9.3.3 Manufacture of the Device . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4 System Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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9.5 Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.6 Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.7 Analysis of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 1

Comparative Study of Interferometry and Finite Element Analysis in Maxillofacial Applications (Hemimandibulectomy Type IVc) Juan Alfonso Beltrán-Fernández, Kevin Brandon Chávez Landeros, Juan Carlos Hermida Ochoa, Luis Héctor Hernández-Gómez, José Enrique Rodríguez-Miramar, Edgar Alfonso Figueroa-Rodríguez, and Pablo Moreno-Garibaldi Abstract Human bone tumors, severe trauma, and infection are the main causes of large bone defects. Currently, these defects are repaired using reconstruction plates that connect remaining bone, without any bone grafting. This study focuses on two aspects: the first, experimental testings using digital image correlation and secondly numerical testing studies in order to evaluate the influencing factors in the design of a custom prosthesis and maxillofacial applications. In this work, it is proposed to design and characterize a prototype mandibular prosthesis for hemimandibulectomy recovery class IVc to a patient with bone cancer. For the design and prototype, the physical and morphological characteristics of the patient as well as the strength J. A. Beltrán-Fernández (B) · K. B. C. Landeros · L. H. Hernández-Gómez · J. E. Rodríguez-Miramar · E. A. Figueroa-Rodríguez · P. Moreno-Garibaldi Instituto Politécnico Nacional - Escuela Superior de Ingeniería Mecánica y Eléctrica - Sección de Estudios de Posgrado e Investigación Unidad Profesional “Adolfo López Mateos”, Edificio 5, 3º Piso, Colonia Lindavista. Gustavo A. Madero, 07738 México D.F., México e-mail: [email protected] K. B. C. Landeros e-mail: [email protected] L. H. Hernández-Gómez e-mail: [email protected] J. E. Rodríguez-Miramar e-mail: [email protected] E. A. Figueroa-Rodríguez e-mail: [email protected] P. Moreno-Garibaldi e-mail: [email protected] J. C. H. Ochoa Centro de Investigación y Laboratorio Biomecánico - Carmen, #18, Chimalistac San Ángel, 01070 Ciudad de México, México e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 J. A. Beltrán-Fernández et al. (eds.), Design and Simulation in Biomedical Mechanics, Advanced Structured Materials 146, https://doi.org/10.1007/978-3-030-65983-7_1

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properties of the used material are necessary. The mandibular prosthesis prototype design will be created based on the 3D reconstruction of the mandible of tomographic studies, which were obtained using the ScanIP software. Subsequently, the 3D models were exported to a CAD software in order to fix the necessary adaptations to the bone. The 3D models were printed in acrylonitrile butadiene styrene, and a digital image correlation was used in order to evaluate the residual stress and strain differences which can be observed in all the cases, also in the case of implants and the remaining healthy bone, caused by masticatory forces.

1.1 Statement of the Problem Mandibulectomy is a surgical technique that involves the removal of the jaw bone [1] (Fig. 1.1). It is usually used for the treatment of cancer in the lower jaw. However, it is also used to treat diseases such as osteomyelitis (inflammation of the bone caused by an infection), osteoradionecrosis (death of the bone from radiation), or in ameloblastoma (benign tumor) [2]. There are three types of mandibulectomy, which are • Marginal mandibulectomy: The basilar edge is maintained, and only part of the jaw is removed [1]. In this case, resection is performed up to the mylohyoid line (marked by the red box, see Fig. 1.2), with no affecting the lower cortical. Fig. 1.1 Basilar edge [3]. Reprinted with permission from Springer Nature publishers

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Fig. 1.2 Marginal mandibulectomy [3]. Reprinted with permission from Springer Nature publishers

Fig. 1.3 Segmentary mandibulectomy [3]. Reprinted with permission from Springer Nature publishers

Marginal mandibulectomy is used when the jaw has a normal appearance and there is no indication that the cancer has spread along the bone [4]. • Segmental mandibulectomy: The entire sector of the jaw is removed, losing the continuity of the jaw [1].

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This type of procedure involves for the patient a loss of facial contour, phonation, and swallowing disorders, as well as aesthetic defect. Historically, apart 1970 in Japan [5], it began to replace that section of the jaw with a part of bone from another part of the body, with the fibula being the most common, as it is the smallest of the lower bones [4] (Fig. 1.3). However, experience and time have shown that the main disadvantages are the time required to perform such a technique, as well as the cost involved and the high rate of complications [5]. Considering a study from the public hospital “IMSS Siglo XXI”, where 60 patients who experienced a mandibulectomy and reconstructed with microvascularized fibula, shown that 10 patients reported non severe complications. The most common experienced exposure of osteosynthesis material (union of fragments of a bone). Finally, 50 patients reported double anastomosis venous (connection surgical between two structures) due to the lack of an adequate vessel and technical difficulties. • Our Hemimandibulectomy: The procedure by which one half of the jaw is removed, as shown in Fig. 1.4 [6]. In this type of technique, where a larger section of the jaw is removed, it is restored in a similar way to segmental mandibulectomy. There are mainly two procedures: • Iliac Crest Flap: provides an appropriate thickness for implant application where an anatomical correction must be achieved with its curvature. However, limitations are available to mold it due to thickness, and therefore, this feature prevents the exact shape of its contour and achieves the ideal occlusion on the healthy side of the jaw [7]. • Bula flap: based on this, titanium prostheses emerge to provide an alternative in fields of application such as dentistry, where they have shown good results due to extraordinary biocompatibility [8]. Thus, titanium prostheses result in a simplified surgical procedure by reducing surgical time and avoiding a second procedure for obtaining a graft. In addition, modeling minimizes the risk of contamination of the receiving site, reducing its morbidity [9]. It is important to mention that all osteosynthesis plaque must meet properties of: Resistance: to provide stability. Ductility: to allow anatomical molding. Biocompatibility: to not produce local or systemic adverse effects [8]. Therefore, the materials that are frequently used for prosthetics are as follows: • Stainless steel: although it has some anticorrosive potential by interaction between different metal components of the implant. • Cobalt–chromium–molybdenum alloys. • Pure titanium or alloy: is the most used given its extreme chemical passivity and excellent biocompatibility, as well as for gathering physical properties suitable for excellent biomechanical behavior over time. In addition, titanium density allows implants to weigh 45% less than steel and cobalt implants. The low module of elasticity is another advantage of titanium as it minimizes pressure protection, which

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Fig. 1.4 Hemimandibulectomy [6]. Reprinted with permission from Springer Nature publishers

is transferred to the bone (the relative importance of pressure protection increases as the size of the implant increases). Finally, titanium shows good performance at high temperatures, as well as a high corrosion resistance [8]. In conclusion, mandibular osteosynthesis with titanium implants following cancer procedures is a perfectly systematized technique that allows the bridging of bone defects after hemimandibulectomy [8], which represents a great option for the patient to be treated.

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1.2 Introduction Biomodeling is a technique for jaw rehabilitation that allows the conversion of twodimensional (2D) images obtained from a computed tomography (CT) scan to a threedimensional (3D) image through professional software, where correct and accurate performance has been shown during the process when reconstructing the patient’s anatomy, ensuring proper implementation during and after surgery [2]. On the other hand, 3D printing is part of the process for carrying out the above-mentioned technique, as it has allowed the transformation of digital models to physical structures that allow proper analysis. Thus, in everyday life, 3D printing has countless applications and different types of materials to print. For example, the acrylonitrile butadiene styrene (ABS) is a thermoplast which has the characteristic of being flexible and resistant to shocks [1]. Therefore, ABS is used due to its high strength, and it is possible to obtain a polished and reusable surface [3]. The purpose of this work is to show the 3D construction of a CT scan to know the affected area of the patient with bone cancer in the lower jaw and thus identify the necessary requirements of prosthetic design for the second stage of the project. Similarly, 3D printing of the computerized axial tomography (CAT) is presented to delimit the replacement zone. Molding and modeling techniques are an important element in prosthetic prototyping processes, as they offer the possibility to study and compare the structure being analyzed from the beginning to the end of the process [1]. Thus, models become necessary when working on bone structures [1]. For example, to carry out the construction of models from plaster, the following stages are carried out • • • • •

Drying the print. Plaster selection. Measurement of dust/water ratios. Mixing the components. Emptying the plaster in the impression [1].

Similarly, sanding must be carried out to obtain the thickness of the desired bone structure. It is also necessary to be precise when sanding, since the plaster tends to be quite fragile when a force is applied to it, making it easy to break the mold. However, there are other materials, such as acrylic, with which this process of molding and modeling can be carried out. This material is moldable, sand proof, and has the necessary mechanical properties, such as • • • •

Chemical resistance. Impact resistance. Weatherproof. Properties related to its cold molding [2].

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Fig. 1.5 Simulation of prosthetics with bone structure [10].nn Reprinted with permission from Springer Nature publishers

Properties that will be important since force tests will be carried out and for which it is necessary to have the appropriate material to simulate these forces. Thus, the exact replicas of the bone structures allow to make the necessary adaptations at the receiving site so that the implants are not exposed to unnecessary defects or modifications. Advantage is that allows surgeons to perform the necessary surgical technique for each situation [3]. Where, the application of different surgical techniques based on biomodels provides a great advantage in surgical planning since one can design and manufacture an implant that correctly restores the lost bone structure. Figure 1.5 shows a 3D simulation with the healthy region of the bone structure [10]. On the other hand, the use of bicortical screws of inverted thread for fixation in the mandibular branch has been of great use for stabilization in the limitation of muscle forces, which are the cause of bone displacements, and in the same way has been shown to shorten the recovery period by healing and primary fixation [11]. While these screws have been used in sagittal osteotomies, it is important to mention that the variety of reports in the literature has given credibility to internal rigid fixation systems. Since, the placement of 3 screws type “lag screw”, allow to stabilize jaw bone structures, a superior intermaxillary fixation has been reported against the bicortical screw fixing systems [11]. Thus, screw assembly through a bracket that provides greater fixation, as shown in Fig. 1.6, allows an adaptation of the geometric body to the body of the maxilla where it will be assembled [7]. The advantage of this assembly method lies in the creation of surfaces, having the opportunity to manipulate the region to assemble and meet the structural requirements that the patient demands. Undoubtedly, the fixation by adapting to the jaw body as a hug allows to create a high fixation point. It is important to state the goals and objectives of this work: Particular Goals • Reproduce a Biomodel from the affected area of the patient creating a threedimensional model using a CT scan CAT.

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Fig. 1.6 Prosthetic support with screw assembly [7] Reprinted with permission from Springer Nature publishers

• Generate alternative material prosthesis prototypes under design criteria using molding techniques. • Mechanically evaluate the prototype of the selected prosthesis by applying experimental techniques and corroborating them with a simulator. Objectives 1. Reconstruction of the preoperative CAT through the ScanIP program, to study the affected area and thus identify the necessary requirements of prosthetic design. 2. 3D CT printing for replacement zone delimitation. 3. Perform under molding and modeling techniques (gypsum, acrylic replica) prosthetic designs. 4. Clinically endorse the proposal by the surgeon. 5. Digitize the proposal endorsed with professional digitization systems. 6. The deliverables for this stage are at least one of the prototype prosthetics. 7. 3D printing and mechanical characterization (Programs: Creo Parametric, SolidWorks, GOM-Correlate, Atos-Scanning System).

1.3 Case Study The subject of our study is a 70-year-old male patient who has lower jaw cancer. The protocol was approved by the committee of the Instituto Politécnico Nacional and ISSSTE. The patient also consented to receive surgical treatment.

1.4 Materials and Methodology The methodology used in this work considers three important stages. 1. Design and printing of the reconstruction of the preoperative clinical case. 2. Modeling of prosthetic design proposals.

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3. The prosthetic proposal will withstand the forces contained during the chewing process. Once the last stages were discussed, a biomodeling technique is applied, since the conversion of two-dimensional images obtained from a CT to a three-dimensional image through the biomodeling has shown during the process a correct and precise performance when reconstructing the patient’s anatomy, ensuring the correct implementation during and after surgery. Finally, the segmentation of the images, which is characterized by the separation of the structures to be represented in the biomodeling, will provide a greater detail in the construction of the biomodeling [1, 2]. Thus, the biomodeling reduces morbidity and surgery time, avoiding complications during and after surgery due to precise modeling of the area to be rehabilitated. In addition, a good relationship has been shown between the patient’s anatomy and the biomodeling at the time of attaching the prosthesis to the bone, avoiding a malfunction [1, 12]. This work will use the ScanIP program, which is a software specialized in 3D image processing that allows you to view, analyze, quantify, segment, and export 3D image data. Such software has an algorithm that allows to search for pixels similar and close to those that are being selected, this in order to create a 3D model as close to the patient. ScanIP also has an interface that allows one to export segmented images to the STL format. Because of this, this software is used to generate high-quality 3D models from image data, which have a myriad of applications in different branches of science. It is necessary to emphasize that ScanIP has different masks, useful when it is necessary to make two or more pieces of the same structure. In this study, two masks were made in order to analyze in detail the structure of the jaw for the creation of the proposals to be presented in the second stage of the project. The masks that were created were 1.Skull. 2.Jaw. Figure 1.7 shows the skull mask in red, while the jaw mask is shown in the color blue. ScanIP’s methodology consists of the following steps: Step 1: Select layer by layer the areas of interest of the CAT, which will be converted to 3D, as shown in Fig. 1.8, this selection is made using a red pencil. The white area is the person’s skull, and there are 450 layers of the skull to be able to model the entire area. As an example, Fig. 1.9 shows another layer of the skull, where the blue part corresponds to what one want to convert to 3D. At this stage, it is necessary to emphasize that ScanIP has a tool which allows to modify the brightness and contrast, which favors a better resolution of the image.

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Fig. 1.7 Skull mask (red) and jaw (blue)

Fig. 1.8 User selected with red pencil zone to be converted in 3D

The team decided to work with the brightness level by default and to increase the contrast level by 25%. Figures 1.10 and 1.11 show the differences between the two images that have 0 and 25% brightness. As in Fig. 1.11 can be seen, the clipping of the edge of the bone is more clearly compared to Fig. 1.10, and therefore, a better segmentation is modeled, also in 3D.

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Fig. 1.9 User selected with blue pencil zone to convert in 3D

Fig. 1.10 Contrast to 0%

On the other hand, another tool that ScanIP has is the CAT view on different axes as shown in Fig. 1.12. The views of Fig. 1.12 are very useful because according to the area of the skull being selected, it is necessary to go to other views to create a better stroke.

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Fig. 1.11 Contrast to 25%

Fig. 1.12 View on different axes (axial, sagittal and coronal) of the CAT

For example, in the dental area, it is difficult to distinguish the lower and upper jaw in the axial plane. However, in the sagittal plane, the structures are well defined.

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Fig. 1.13 3D view of the bounded area

Step 2: Once the 450 layers have been delimited, it was proceeded to perform a “render”, in order to perform a 3D model of the mask. Figure 1.13 shows the 3D mask after the area that has been delimited. Step 3: Export the ScanIP file to the STL format for the 3D printing system. Step 4: 3D printing was carried out with the material acrylonitrile butadiene styrene (ABS). ABS is a thermoplastic which contains a base of polybutadiene elastomers which makes it more flexible and shock resistant [4]. In addition, due to its high strength, it is possible to obtain a polished and reusable surface [11]. Thus, ABS has the following properties: • • • •

Rigidity Stability at high temperatures Hardness Mechanical resistance [11].

So, it is indicated in 3D printing when looking to perform force tests and also when the material will be exposed to high temperatures [4]. Figure 1.14 shows the preview once the file has been converted to the STL format. Once the parts have been printed, it is necessary to remove extra material due to some overlap error in the masks.

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Fig. 1.14 Preview of the STL format

Fig. 1.15 Manual modeling

1.4.1 Manual Modeling To make different proposals of prostheses, manual modeling was carried out using moldable and malleable materials, and the materials that were used were gypsum and acrylic. The first step was to remove the mold from the patient’s preoperative print. This was achieved by taking the negative out of the patient’s preoperative impression using

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Fig. 1.16 Alginate mold

a mixture of alginate and water. In a container where the impression of the jaw was loose, three portions of water and one portion of alginate were mixed continuously for 30 s. Then, the impression of the jaw was placed, to which oil and wax were added to prevent it from sticking to the alginate, the mixture was allowed to dry for 10 min until hard, and the mold was created. Importantly, the alginate solidified in a very short time, i.e., 1 or 2 min, so it was necessary to perform this procedure until a functional mold was obtained. Once the mold dried, it was removed from the container, and a cross section was made to remove the jaw (Fig. 1.14). After removing the jaw, the mold was rebuilt and sealed with a little more water mixture and alginate (Fig. 1.15). Subsequently, the mixture of water and plaster was made in the ratio of two portions of plaster for one portion of water, poured into the mold, and with the help of a plaster vibrator, the mold was filled, and the bubbles were removed (Fig. 1.16). The acrylic used includes liquid acrylic and its MDC Dental brand Nic Tone powder monomer. For the molding of the proposals, it was decided to use the acrylic because the plaster broke easily and the acrylic is much more resistant and moldable, with very good mechanical properties which will be useful later for the simulation of the bite in the press. Some mechanical properties are • • • • •

High impact resistance Rockwell hardness M: 100 Compression resistance: 1020 kg/m2 Light Density: 1180 kg/m3 .

To perform the acrylic replica, the same procedure was carried out as for the plaster replica, only a little more care was needed because the acrylic has a significant thermal reaction and because when mixing the monomer and acrylic could become corrosive if the correct measurements were not used (Fig. 1.17). In the end, three plaster replicas and two acrylic replicas were obtained.

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Fig. 1.17 Mixing

In addition, sanding was performed with a Dremel © tool, high-speed motor, and a stone mounted in order to reduce the thickness of the replicas of the jaw that anatomically have variations due to cancer. Thus, the reduction was worked on with the acrylic replicas since they were subsequently the ones that were digitized. In Fig. 1.18, the jaws with a lower thickness after the reduction process and the jaw in acrylic without reduction are shown.

1.4.2 Modeling Digitization Also, the 3D scanner used allowed to guarantee quality and production to reduce time and costs. It is important to mention that the main application of such a system is 3D digitization. Figures 1.19, 1.20, 1.21 and 1.22 show the sensor used to digitize the model jaw. The software used by this sensor is the ATOS Core, which allows to perform the scanning process and has the necessary features, such as • • • • •

Editing polygon meshes. Inspection. Reporting. Teaching doing. Selective projection.

Thus, these hardware and software tools allowed to carry out the scanning process effectively. Also, the format of the file that is exported from ATOS Core is of the STL type, which can be imported into any CAD program.

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Fig. 1.18 Jaw with reduction (left-hand side). Jaw without reduction (right-hand side)

Fig. 1.19 GOM optical measuring system

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Fig. 1.20 GOM optical measuring system stored in a box

Fig. 1.21 Sensor, tripod, and laptop with ATOS Core system

For this process, it was necessary to calibrate the sensor, and a three-axis rotary table must be counted, as shown in Fig. 1.23. Thus, the software asks to place the sensor at different heights and scans the object over the rotary table and asks to tilt the table to scan from another angle. This process is performed successively, every 25° on the x-axis and 90° on the y-axis, as shown in Fig. 1.23. Once the scanning area has been delimited, as shown in Fig. 1.24, the jaw must be placed within that area so that it can be recognized by the software.

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Fig. 1.22 Sensor, tripod, laptop with ATOS Core software and jaw to digitize

Fig. 1.23 Three-axis scanner and rotary table

The green dots serve as a reference for scanning, and these are attached to the platform where it is scanned. Three marks are then placed on the jaw as a reference for the scanner. Figures 1.25 and 1.26 show the jaw with three reference points. It is important to mention that the software recognizes such benchmarks without having to be scanned during the calibration process. Similarly, it is not necessary to put reference points on the inside of the jaw, since the software recognizes the position of the points on the outside. Figure 1.27 shows the jaw on the inside. To start digitizing the jaw, it was necessary to create a new project and perform successively every 45°. Thus, it is verified that the entire jaw was scanned. The way to verify that the process is correct is by the absence of gaps within the structure of the digital image.

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Fig. 1.24 Software-delimited scanning area

Fig. 1.25 Reference points in jaw marked red

Then, in Fig. 1.28, the result of scanning the first view of the jaw is shown, and thus, the part is rotated every 45° to perform the scanning process again. Once the entire jaw is scanned from the top, it is necessary to scan it on the reverse side, as shown in Fig. 1.29. This is done in order to obtain a complete picture in terms of actual jaw thickness and dimensions. In the same way, the scan is performed every 45°.

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Fig. 1.26 Three reference points in the jaw marked by red circle

Fig. 1.27 Inner part of the jaw

Once scanned on both sides, the two structures are merged to create one through the traverse tool. Figure 1.30 shows the merging of both parts. Once done, the analysis and filling of gaps in the structure are carried out, since although it is scanned on both sides, there are areas which are difficult to be scanned. However, the software can recognize these areas and re-seal them so that our piece is one piece and, above all, solid. This is achieved through the tool to close holes.

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Fig. 1.28 Result first scan view

Fig. 1.29 Reverse side jaw scanning

Then, in Fig. 1.31, a gap is shown in the structure. On the other hand, in Fig. 1.32, the structure has been re-sealed. To continue, it was necessary to define the number of meshes. This part of the process is key, since the greater the number of elements, the piece will have a greater definition. However, this will make our file heavier and harder to process. So, through the fine mesh tool, we decided to have 250,000 elements which provide adequate quality, and in the same way, the file size is not as heavy so that we can process the image in any CAD program. It is shown in the figure.

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Fig. 1.30 Fusion of both pieces

Fig. 1.31 Gap in the structure

It can be observed that the part has some porosity, which must be removed through the tool repair mesh in order to have a smooth surface (Fig. 1.33). Figure 1.34 shows the smooth surface. It is important to mention that the effect of smoothing the surface means a greater number of elements. This increases the number of mesh elements again. So once this process is finished, it is necessary to reduce the number of mesh elements again through the fine mesh tool.

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Fig. 1.32 Filled structure

Fig. 1.33 Mesh with 250,000 elements

Finally, to homogenize the number of elements in the mesh, the mesh smooth tool is used. Figure 1.35 shows the jaw mesh. The file is exported in the STL format for processing in a CAD software. Once in PTC Creo Parametric ©, i.e., the CAD software, the file is converted from STL format to shrink-wrap, as shown in Fig. 1.36, which is a format to convert our mesh into a solid piece. It is worth mentioning that the quality of the jaw was

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Fig. 1.34 Smooth surface

decreased, but the conversion time to a solid piece with this format compared to the IGES or STEP format was shorter. Once the solid model was created, it is necessary to create a slice over the jaw, 3/4 of it, which is where the healthy part of it begins for mandibular prostheses as shown in Fig. 1.37. This process was performed with the sketching and extrusion tools, where a top view of the jaw was used, and from it, a box of the branch area

Fig. 1.35 Mesh with fewer elements

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to be removed or extruded was created, to generate the result exposed in the figure already mentioned. To continue adjusting the model prosthesis, a slit was performed in the form of the same jaw, this for greater stability and fixation of the support plate to the prosthesis, and in turn, the plate will be in contact with the healthy branch of the patient, as in Fig. 1.38 is shown. Figure 1.39 presents an outline of the patient’s healthy branch, in which it will contact the support plate. The support board was made in a PRT file, generated by Creo Parametric, with different tools such as sketching, extrusion, rounding, plane, and chamfer. The plate was started with a regular, rectangular shape, as shown in the outline of the plate in Fig. 1.40.

Fig. 1.36 Conversion from STL format to a solid

Fig. 1.37 Prosthesis with cut to 3/4 jaw

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Fig. 1.38 Prosthesis with 3/4 jaw cut with slit for support plate

Fig. 1.39 Branch cut

Once the sketch was created, an extrusion of 4 mm was performed, to generate a solid part as shown in Fig. 1.41. Next, the chamfer tools were used twice and round once over the part for more ergonomics and anatomical functionality. Figure 1.42 shows the strokes. The next step was the creation of the holes shown in Fig. 1.43, these are useful as the anchor areas to both the bones and muscles. For the creation of these holes, the sketching and extrude tools were used. By the top line, the circles are at 6.25 mm; while on the bottom line are separated 6 mm between each center, and with a diameter

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Fig. 1.40 Plate from the base boundary

Fig. 1.41 Extrusion of the base boundary

of 2.5 mm all circles, as shown in Fig. 1.43. Finally, these circles were extruded for 4 mm. Next, it was to create an elliptic shape to the top of the part with an elliptical extrusion, as shown in Fig. 1.44. The sketching and extrude tools were reused. For the next step, five rounds were applied as shown in Fig. 1.45, this is in order to not generate injury and discomfort to the patient and generate more similar forms to anatomical ones. Only the rounding tool was used here.

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Fig. 1.42 Implementation of the chamfer and rounding tools on our part

Fig. 1.43 Creation of the anchor holes on the support plate

Almost to finish, an extension was added to the same piece, as shown in Fig. 1.46 with a thickness of 4 mm, equal to that of the part. This was done so that the piece is close to that of the prosthesis. Sketching and extrusion tools were used. Finally, a rounding was generated to the outline of the piece to soften the plate, Fig. 1.47, and leave it ready for assembly with the prosthesis, see Fig. 1.48. The assembly was imported in STL format for 3D printing as shown in the results.

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Fig. 1.44 Elliptical extrusion

Fig. 1.45 Fillets around the part for ergonomics, green contours

1.4.3 Finite Element Simulations Once the jaw was scanned, and in STL format available, PTC Creo Parametric was used to convert the part, by exporting the wrap-type level 10, to a solid piece. The solid part is shown in Fig. 1.49. Thus, with a solid piece, the healthy part (branch and right condyle) was cut to start generating our prosthesis, and a plaque was added for the binding to the healthy

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Fig. 1.46 Extension of the part in green outline

Fig. 1.47 Rounding of the contours of the plate

branch that will remain to the patient after removing the part with original cancer. Figure 1.50 shows the bond with the board. Once this was done, it was re-exported to STL format, this to print the part as a single piece. Figure 1.51 shows the 3D printing process. Since the prosthetic proposal was printed, all teeth were removed manually, and the result was as shown in Fig. 1.52.

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Fig. 1.48 Plate and prosthetic assembly

Fig. 1.49 Solid piece

This prosthesis proposal was rescanned and obtained in STL format, it was converted with the tool wrapped in SolidWorks (c), in which STEP conversion was used, which is also a solid part format (Fig. 1.53).

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Fig. 1.50 Mandible model assembled with the plate

Fig. 1.51 3D printing process

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Fig. 1.52 Toothless prosthesis

This was done as an alternative to the Creo Parametric wrapping tool since it generated noise, and simulation was not produced with this format, but with the help of SolidWorks and export to STEP format. A manipulated part was generated in the simulation application called: Simulate. Different errors as node or face splice can be seen in Fig. 1.54.

Fig. 1.53 Solid piece

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Once with the STEP part, it was imported into Creo Parametric to be converted to the PRT format, which is the part format used by this software, this was done to be able to manipulate its appearance and generate some holes Fig. 1.55 to apply muscle representative forces to the piece to hold it and keep it in place. Once the total of holes were drawn, it was used to Creo Simulate program to apply forces (see Fig. 1.56), restrictions, and materials, such as the Ti-6Al-4V, 316L stainless steel, and cortical bone.

Fig. 1.54 Simulation errors

Fig. 1.55 Hole generation for muscle insertion

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The forces (orange arrows) were added depending on the direction of the jaw, because of their original geometry 100 N on each of its components were considered, and the resulting component was 170 N. All forces were added to the upper face of the jaw, supplying the teeth (see Fig. 1.57), but also within some of the holes of the plate. On the other hand, constraints are areas where the part is not moved. In this case, they were added to it on specific faces of the jaw base, as is shown in Fig. 1.58. Finally, three new materials were added within the simulations, the ones already mentioned above.

Fig. 1.56 Forces applied to the jaw

Fig. 1.57 Applied forces

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Table 1.1 shows the different properties of the materials. Each simulation (one per material) used the material of the Table 1.1 to obtain the desired and concordant results, as shown in Figs. 1.59, 1.60 and 1.61. It is important to mention that stress analysis (MPa) refers to the mechanical behavior that the prosthesis will have when applying the load. Also, the displacement (mm) shows where the largest displacement is made and its results. It can be seen in the plots that the condylar part is the section with important displacements. On the other hand, a maximum shear stress analysis (MPa) shows how the prosthesis is working under fragile behavior. Finally, the stress analysis (MPa) provides information on how the chewing force acts on the prosthesis.

1.5 Results and Discussion The use of biomodeling in this study allowed to reconstruct the CT scan precisely, which offers accuracy to the work and a modeling for the prototype to be created for the patient. In Figs. 1.62, 1.63, 1.64, 1.65, and 1.66, the mask that was created for the jaw and some of the layers is shown, respectively. In Figs. 1.67, 1.68, 1.69, 1.70 and 1.71, the mask that was created for the skull and some of the layers is shown, respectively. It can be seen from the previous figures that the objective of this work was carried out successfully, since the biomodeling was built from a CAT and printed the model. This will be a fundamental part of the project to carry out the design of the prototype of the mandibular prosthesis. Similarly, image processing through biomodeling is a technique that allows necessary details to ensure that the prosthesis fully encompasses the affected surface. In the same way, it helps to define the characteristics of the prosthesis, since it allows to see the requirements of functionality of the area and make morphometric measurements of the patient for future dental requirements. Also, the ABS material will allow us in the next stages of the project to carry out force tests to the prototype of mandibular prostheses, where a force performed on titanium can be simulated on a scale and thus carry out an analysis with both mechanical and experimental characterization.

1.5.1 Digitization Through the scanning process through professional systems, it is possible to optimize time and costs, but above all, the accuracy of the prototype of prostheses is guaranteed. This part of the process plays an important role as it is through this that one manages to accomplish something that for decades had not been done. Then, in Fig. 1.72, the jaw is observed after the scanning process is complete. Thus, a process that has been practiced in this area of science proposes as innovative digitization through professional programs to ensure that the prototype of

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Fig. 1.58 Constrains

Fig. 1.59 Simulation with cortical bone

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Fig. 1.60 Simulation with Ti-6Al-4V

Fig. 1.61 Simulation with stainless steel 316-L

prostheses does not just meet the highest quality standards, but adapts exactly to the patient’s anatomy.

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Fig. 1.62 Front view jaw

Fig. 1.63 Side view jaw

1.5.2 Digital Modeling The results obtained at the end of the assembly of the support plate and the prosthesis were 3D printing as shown in Figs. 1.73 and 1.74. Based on this 3D printing, as future work, it will be necessary to sand and fill, properly the missing gaps to give better quality and presentation to the prosthesis.

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Fig. 1.64 Previous view jaw

Fig. 1.65 Layer 94 jaw

This process is important in order to generate a new model to be scanned and finally to obtain an STL format. A second conversion into a solid piece (IGES, shrink-wrap, STEP) is necessary to perform an stress analysis on the study on the prosthesis, and obtain the data of a bite simulation of the patient.

1.5.3 Finite Element Analysis (FEA) In the simulation process, force loading processes were carried out with different materials in order to analyze how the jaw responds to these forces. Figures 1.75 and 1.76 show a comparison between the different materials.

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Fig. 1.66 Layer 63 jaw

Fig. 1.67 Front view of the skull

The titanium alloy shows better results compared to stainless steel, and 316-L maximum shear (Figs. 1.78, 1.77, 1.79 and 1.80). On the other hand, it is observed that the values we obtained are very similar to each other, where the cortical bone shows a slight inferiority in this property.

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Fig. 1.68 Side view of the skull

Fig. 1.69 Lower view of the skull

However, in displacement, it can then be observed as in the same way the cortical bone undergoes a greater displacement compared to titanium alloy and stainless steel.

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Fig. 1.70 Layer 338 of the skull

Fig. 1.71 Layer 221 of the skull

1.5.4 Discussion Once the computer simulation was obtained, an experimental test was carried out with different weights were applied to the jaw to observe the deformation that it suffers. The weights that were applied are shown in Table 1.2.

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Fig. 1.72 Result of the scanning process

Fig. 1.73 Printing the supports for the prosthesis

Thus, the jaw behavior was optimal, because the deformation did not fracture the jaw model. The total force applied was 19.6 N, while the force applied to the Y-axis was 10.6 N.

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Fig. 1.74 3D printing of the prosthesis

Fig. 1.75 Cortical bone Ti-6Al-4V, stainless steel, and 316-L von Mises stress (MPa)

1.6 Conclusions In this study, a biomechanical model from CT and CAD software was analyzed. As conclusion of this work, it was able to observe that biomodelling is an activity that requires a lot of details in each layer of the CT. However, these details are of great importance as they are the basis for creating an excellent prototype of mandibular prostheses. It allows to build biomodels from segmentation techniques that provide reliable and adequate results in surgical planning as well as in the treatment of patients [7, 9, 10, 13–15].

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Fig. 1.76 Cortical bone Ti-6Al-4V, stainless steel, and 316-L maximum shear stress (MPa)

Fig. 1.77 Cortical bone Ti-6Al-4V, stainless steel, and 316-L maximums displacements (mm)

For the second stage, manual modeling is a very accessible and quick technique to do. However, it requires practice due to the reactions of the different materials that are used. It is a technique that allows to shape the proposal of prostheses from the characteristics into real measures of the patient, allowing to eliminate and correct deformations without modifications of the functional characteristics of the patient.

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Fig. 1.78 Experimental analysis using image correlation

Fig. 1.79 Strain in experimental analysis

Also, through the scanning process, it is possible an optimization of costs and time. However, that is in terms of the manufacturing process, as accuracy in the prototype of prostheses is also guaranteed when implementing it in the patient. Similarly, the digital modeling of the proposed assembly to attach the prosthesis to the healthy branch of the jaw allows to create exactly the assembly that the patient requires according to the anatomical characteristics. Finally, it is considered that,

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Fig. 1.80 Percentage of deformation in experimental analysis

Table 1.2 Weight for correlate study

Weight #

g

1

0

2

100

3

400

4

900

5

1400

6

2000

despite being a slow and very detailed process, the results that were achieved were those proposed at the beginning of this second installment. Also, for the last delivery, the prototype prosthesis will be subjected to forces to verify that the chewing and speech process can be carried without problem. Finally, it was possible to design and simulate the prototype of prostheses using different materials and observing how each of these behaves due to the variation of its properties. Also, this work was very detailed, and so there were quite a few complications throughout the process. However, in the end, the design of the prototype prosthesis was achieved. The main purpose of this work is to use the tools to create solutions that generate a high value to the quality of life of people. Finally, it is very well known that in orthopedics and prosthetic design there is a challenge to create more economical and faster processes. For the second stage, manual modeling is a very accessible and quick technique to do. However, it requires practice due to the reactions of the different materials that are used. It is a technique that allows to mold the proposal of prostheses from

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the characteristics into real measurements of the patient, allowing to eliminate and correct the deformations without altering the functional characteristics of the patient. Also, through the scanning process, we can guarantee an optimization of costs and time. However, that is in terms of the manufacturing process, as accuracy in the prototype of prostheses is also guaranteed when implementing it in the patient.

References 1. Ferraz, E.G., Andrade, L.C., Safira Dos Santos, A.R., Torregrossa, V.R., Rubira-bullen, I., Sarmento, V.A.: Application of two segmentation protocols during the processing of virtual images in rapid prototyping: ex vivo study with human dry mandibles. Clin. Oral Invest. 17(9), 2113–2118 (2013). https://doi.org/10.1007/s00784-013-0921-7 2. Ciocca, L., Mazzoni, S., Fantini, M., Persiani, F., Baldissara, P., Marchetti, C., Scotti, R.: A CAD/CAM-prototyped anatomical condylar prosthesis connected to a custom-made bone plate to support a fibula free flap. Med. Biol. Eng. Compu. 50(7), 743–749 (2012). https://doi.org/ 10.1007/s11517-012-0898-4 3. Cordeiro P.G.: Classification system for mandibulectomy defects. In: De Santis, G., Cordeiro, P., Chiarini, L. (eds.), Atlas of mandibular and maxillary reconstruction with the fibula flap. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-10684-3_1 4. Escobar, C.: ABS Printing Material and its Features, from 3D Printers (2013). https://imp resoras3d.com/blogs/noticias/102832135-the-material-of-impression-abs-and-your-features. Accessed on 22 May 2017 5. Ayala, J.: Clinical Manual of Orthodontics (2009). Accessed on 23 May 2017 6. Shaw, R.J., O’Connell, J.E., Bajwa, M.: Basic surgical principles and techniques. In: Warnakulasuriya, S., Greenspan, J. (eds.), Textbook of Oral Cancer. Textbooks in Contemporary Dentistry. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-32316-5_20 7. Beltrán-Fernández, J.A., Romo-Escalante, E., López-Saucedo, F., Moreno-Garibaldi, P., Hernández-Gómez, L.H., Urriolagoitia-Calderón, G., Camacho-Tapía, N.: Biomechanical assembled prosthesis of a temporo mandibular joint disorder using biocompatible materials. Springer Int. (2014). https://doi.org/10.1007/978-3-319-07383-5_11 8. AcmePlastics: Properties of Acrylic Acrylic and Polycarbonate Acrylic. AcmePlastics (2012). https://www.acmeplastics.com/acrylic-vs-polycarbonate#:~:text=Polycarbonate%20offers% 20much%20more%20resilience,polycarbonate%20is%20easier%20to%20scratch. Accessed on 23 May 2020 9. Beltrán-Fernández, J.A., González Rebatú, M., Hernández-Gómez, L.H., González Rebatú, A., Urriolagoitia-Calderón, G.: Biomechanical prosthesis design of an orbicular cranial cavity. Springer Int. (2013). https://doi.org/10.1007/978-3-319-00479-2_7 10. Kirke, D.N., Owen, R.P., Carrao, V., et al.: Using 3D computer planning for complex reconstruction of mandibular defects. Cancers Head Neck 1, 17 (2016). https://doi.org/10.1186/s41 199-016-0019-4 11. Plastics Technology: ABS, from Technology of Plastics. https://tecnologiadelosplasticos.blo gspot.mx/2011/06/abs.html. Accessed on 22 May 2020 12. Konstantinovi´c, L., Todorovi´c, A., Lazi´c, P.: Possibilities of reconstruction andimplantprosthetic rehabilitation following mandible resection. ProQuest (2013). https://www.cun. es/diccionario-medico/terminos/mandibulectomia, https://image.slidesharecdn.com/anatom iaradiogrficamaxilarymandbulaussrx-140214172028-phpapp01/95/anatomia-radiogrfica-max ilar-y-mandbula-uss-rx-78-638.jpg?cb=1392398511, https://thelancet.com/cms/attachment/ 2045960722/2057173283/gr2_lrg.jpg. Accessed on 23 May 2020 13. Beltrán-Fernández, J.A., et al.: Numerical and Experimental Analysis of a Personalized Prosthesis for a Patient with Unilateral Hip Osteoarthritis. Springer, Cham (2020). https://doi.org/ 10.1007/978-3-030-20801-1_21

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14. Moreno-Garibaldi, P., Beltrán-Fernández, J.A., Yescas-Hernandez, J.A., González-Rebattu, M., Carrera-Espinoza, R., Hernández-Gómez, L.H., López-Liévano, D.R., Pava-Chipol, N.D., Pava-Chipol, J.F., Urriolagoitia-Calderon, G.M.: Identification of stress fields in a customized mandibular reconstruction based on a photoelastic model. J. Craniofacial Surg. (2019). https:// doi.org/10.1097/SCS.0000000000005901 15. Beltrán-Fernández, J.A., Hernández, I.A., Bantle-Chávez, I., Alvarado-Moreno, C., Hernández, L.H., Moreno, P., et al.: Manufacturing of a Human’s Hand Prosthesis with Electronic Movable Phalanges Based on a CT Image: An Amputation Case, Cham, Springer International, pp. 355– 396 (2020). https://doi.org/10.1007/978-3-030-20801-1_26

Chapter 2

Experimental and Numerical Evaluation of an Orthognathic Implant with Facial Asymmetry and Skeletal Class III Juan Alfonso Beltrán-Fernández, José Enrique Rodríguez-Miramar, Erick Omar Alvarado-Alcántara, Juan Carlos Hermida-Ochoa, Alejandro David González-Peña, Edgar Alfonso Figueroa-Rodríguez, and Luis Héctor Hernández-Gómez Abstract A numerical evaluation of an orthognathic prosthesis used in patients with facial asymmetry and mandibular prognathism was performed for this study. Mechanical testing was also performed by using axial tomography (computed tomography scan), and experimental methods such as photo-stress and image correlation were included. Our clinical case was a patient diagnosed with prominent mandible and abnormal size; atypical morphology, abnormal mastication and sense of smell, and difficulty talking as a consequence of the bone deformity; bad alignment of the mandible and upper maxilla, atypical movement of the tongue and deficiency for the occlusion process (closing of the mouth). This study aimed mainly to characterize the mechanical stress and structural behavior of numerical models obtained by the patient’s clinical and morphological profile through a computational approach based on the finite element method.

J. A. Beltrán-Fernández (B) · J. E. Rodríguez-Miramar · E. O. Alvarado-Alcántara · A. D. González-Peña · E. A. Figueroa-Rodríguez · L. H. Hernández-Gómez Instituto Politécnico Nacional - Escuela Superior de Ingeniería Mecánica y Eléctrica - Sección de Estudios de Posgrado E Investigación Unidad Profesional “Adolfo López Mateos” Edificio 5, 3º Piso, Colonia Lindavista. Gustavo A. Madero., 07738 México D.F., México e-mail: [email protected] E. O. Alvarado-Alcántara e-mail: [email protected] A. D. González-Peña e-mail: [email protected] L. H. Hernández-Gómez e-mail: [email protected] J. C. Hermida-Ochoa Centro de Investigación y Laboratorio Biomecánico - Carmen, #18, Chimalistac San Ángel, 01070 Ciudad de México, México © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 J. A. Beltrán-Fernández et al. (eds.), Design and Simulation in Biomedical Mechanics, Advanced Structured Materials 146, https://doi.org/10.1007/978-3-030-65983-7_2

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2.1 Introduction The principal purpose for the use of an orthognathic implant in patients suffering dentofacial deformity is to improve mastication and facial aesthetics. In the early 1900, Angle [1], known as the father of modern orthodontics, described three types of dental malocclusion as Categories I, II, and III. Category III comprises the mesiobucal cusp of the first superior molar occluding between the first and second molar of the mandible. In other words, the mandible and maxilla (upper jaw bone) are misaligned, a condition also known as mandibular prognathism (MP). In cases of PM, the mandible is excessively developed in relation to the maxilla. A gold key standard treatment for this pathology includes orthognathic surgery often related to dental treatment which includes the section of a portion of the mandibular body and placement of an implant to join the segmented parts through fixation with screws. In this study, the 64 years old patient suffered from bone loss of the mandible and severe mandibular atrophy. Our study proposed the development of personalized orthognathic implants with perforations. Implants were generated using a computer-aided design software (CAD) and based on the patient’s inferior maxilla geometry. A model of the mandible geometry was obtained by segmentation of CT scan images, and a cephalometric clinical analysis was also performed. Sagittal mandibular osteotomy (Obwegeser osteotomy) was performed preoperatively to shorten the length of the mandible thus correcting the grade IIII malocclusion. Four digital designs were 3D printed and their digital models were numerically analyzed to corroborate which one could optimal for the patient deformity.

2.2 Clinical Case Our clinical case consisted of a patient that granted a written consent for the use of his clinical data for the study. The subject had a diagnosis of osteonecrosis (bone loss of mandible and maxilla) which causes problems for eating and talking. This case also poses a challenge for bone perforation in the attempt to place a dental implant due to the bone loss through necrosis. The diagnosis of MP was considered to develop a personalized prognathic implant taking into account the dimensional modification required at the mandible and superior maxilla; planning required the assistance of a maxillofacial surgeon and review of orthodontic techniques aiming at the correction of all dento-cranial and maxillofacial problems and facial aesthetics.

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2.3 Objectives The objectives of the present study were discussed and planned by a team comprised of a maxillofacial surgeon, an orthodontist surgeon, and a biomedical engineer advisor and were as follows: • Understanding of the maxillary occlusion, physiology, and dental deformity. • Analysis of the cephalometric study and diagnosis. • Creation of the cranial model (including the superior and inferior maxillary bones) by the use of a CT scan from the patient and segmented in the Simpleware Scan IP© software. • Design and evaluation of the inferior implant using SolidWorks ©, PTC-CREO Parametric©, and ANSYS Workbench ©. • Manufacture a personalized prototype through fused deposition modeling (FDM) technique with ABS (3D printer).

2.4 Materials and Methods 2.4.1 Cephalometric Analysis Cephalometric analysis was chosen for this particular study due to its fundamental value for the diagnosis of dentofacial and skeletal anomalies; it also determines the occlusal vertical dimension (OVD). The use of Ricketts’ criteria established that the lower facial height (LFH) corresponds to the OVD [2]. Figure 2.1 shows that the LFH is comprised of two lines connecting the following cephalometric points: (i) the central point of the ascending mandibular ramus (Xi), the anterior nasal spine (ANS) and (ii) Xi and the point where the symphysis of the mandible changes from convex to concave (Pb). The height determines the distance between the maxilla and the mandible when the teeth are in contact. In this case, the patient is edentulous, that is, total absence of teeth in both maxilla and mandible. In addition of knowing the OVD, the diagnosis of Class III PM was established. The maxillofacial surgeon recommended surgical intervention using upward bilateral bone osteotomy in order to correct the mandibular prognathism. DICOM images from the patient’s CT scan were imported into Simpleware ScanIP (Synopsys inc.) to facilitate visualization in the axial, sagittal, and coronal planes of the region of interest. The model’s volume was generated through the creation of masks according to different anatomical planes and to effectively draw the profiles of the bone regions, see Fig. 2.2. The volume of the models was generated using layers of 3 mm resolution; each mask (blue and purple) represented the skull and the jaw, respectively. Boolean operations were performed to obtain three-dimensional models based on the profile masks. The resulting archive was a NURBS model (non-uniform rational basis spline) which was exported as a stereolithography (STL) file to be processed in a CAD model

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Fig. 2.1 Lower cephalometric facial height [2]. Reprinted with permission from Springer Nature publishers

Fig. 2.2 Mask generation in Simpleware ScanIP© software a transversal visualization, b coronal visualization, c sagittal plane viewing and d obtaining a 3D visualization of the masks generated from the anatomical planes

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Fig. 2.3 Mandible model printed in PLA

software. SolidWorks was used to convert our models into solids. Importantly, both types of bone natural densities (trabecular and cortical) that include different material modulus were characterized during segmentation of the models in ScanIP. A model of the mandible was 3D printing based on the fuse deposition modeling technique (FDM) in polylactic acid (PLA) and used later during our experimental tests, see Fig. 2.3.

2.4.2 Experimental Testing 2.4.2.1

Photo-Elastic Test

In order to analyze the stress distribution in our geometrical model, a photo-elastic transmission technique was utilized. For this purpose, a photo-elastic resin model was casted in a rubber mold based on our segmented bone geometry. The obtained photo-elastic model was subjected to loads by using a round polariscope SMMAJ, 060 series, capable of delivering 2500 N load (Interface brand), see Fig. 2.4a. Several pictures of the model were taken and analyzed to account for any residual stress previous to the test. The loading test was recorded on video to analyze the structural mechanical behavior of the model, see Fig. 2.4b.

2.4.2.2

Digital Image Correlation

To reinforce the data from the photo-elastic test, a DIC was performed on the PLA maxillary models. Figure 2.5 shows the mounting position of the models to simulate the human bite by placing a rigid steel plaque between the cranial model and a tubular metallic piece in the mandible, allowing a uniform distribution of the applied load, and avoiding abnormal stress concentration.

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a

b

Fig. 2.4 a Polariscope model SMM-AJ. b Unloaded photo-elastic model

Fig. 2.5 Printed mottled model simulating the human bite

The load was applied manually by the SSM-AJ polariscope frame until the model was damaged. Preliminarily, a stochastic pattern (mottling) was applied to both cranial and mandible models to measure the percentage of deformity through the DIC technique by the use of the GOM correlate V2.0.1 software. The test was recorded on video to obtain either MPEG or AVI formats with a Web camera (Logitech C920 Pro) with a resolution of 1080p/30 fps–720/30 fps, respectively. The video camera was placed at a fixed distance during the test. The model surface was analyzed by the video software and a measurement scale was defined automatically. These scales allowed the program to create a trapezoid or working area which later measured displacement through their axis.

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2.4.3 Numerical Analysis 2.4.3.1

Finite Element Analysis

The mandible digital model obtained by segmentation of the patient’s CT scan DICOM files was exported to SolidWorks (Dassault Systemes) to be processed as a neutral file (IGS, STEP, and SAT). The model mesh was cleaned and corrected by the use of ANSYS SpaceClaim (Ansys inc.) and was then processed to finite element analysis (FEA) by the ANSYS Workbench module. Finite element analysis (FEA) used was tetrahedral; the corresponding amounts of elements and nodes are shown in Table 2.1. Mechanical properties assigned to the FEA models were taken from the literature [3–5] and are displayed on Table 2.2. A maximal Young© modulus of 14.7 GPa was used and the Poisson© ratio was 0.33 [5]. The boundary conditions were assigned as follows: at the mandible, the inferior portion of the body was fixed and tension and compression forces were prescribed at 300 N and 500 N, respectively [6]. Load at 300 N represents both internal and external pterygoid muscles with a value of 228–225 N on the ramus (see Fig. 2.6); the compression load of 500 N represents the masseter and temporal muscles with a value of 408–468 N on the mandible body. In two analyzed conditions (with and without implants), both mentioned values were applied. Table 2.1 3D model finite element features Model

Elements

Nodes

Mandible

185,949

314,826

Sagittal mandibular osteotomy

367,833

623,725

Sagittal mandibular osteotomy—first implant (moldable—3 screws)

268,584

456,928

Sagittal mandibular osteotomy—second implant (moldable—4 screws)

276,073

471,169

Sagittal mandibular osteotomy—third implant (bar)

266,588

452,699

Table 2.2 Material properties used for the numerical orthognathic implant and bone assembly

Compression test Tension test

Resistance

167–213 MPa

Young© modulus

14.7–34.3 GPa

Resistance

107–170 MPa

Young© modulus

11.4–29.2 GPa

Bending test

Resistance

103–238 MPa

Young© modulus

9.8–15.7 GPa

Torsion test

Resistance

65–71 MPa

Young© modulus

3.1–3.7 GPa

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Fig. 2.6 Variables of the mandible in the analysis with workbench

Table 2.3 Material properties used for the numerical orthognathic implant and bone assembly

Property

Bone

Titanium

E (GPa)

Cortical 14

Trabecular 1.37

µ

0.3

0.34

S u (MPa)

965

We assigned for the implant the material properties of the Ti6I4V titanium alloy, because of its wide use in orthopedic and maxillofacial devices [7], and good osteointegration [8]. The material properties used in the orthognathic implant and bone assembly are shown in Table 2.3 and were taken from similar studies [6]. Four orthognathic prototype implants were presented to the surgeon, see Fig. 2.7. The first one (a) comprised fixation with screws alone; the second one (b) comprised a moldable plate screw fixation with three screws fixed in the area just next to the masseter; the third one (c) included a moldable longitudinal plate with four screws; and the fourth (d) was a support arch around the whole mandible anterior edge and fixed through four screws.

2.5 Results 2.5.1 Experimental Photo-Elastic Test The mounted mandible specimen was subjected to a linear load as shown in Fig. 2.8a and resulting reaction forces were collected. The maximum stress concentration was at the mandible body, specifically at the area of bone reabsorption next to the

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c

b

d

a

Maximal Stress(MPa)

Fig. 2.7 Mandibular osteotomy fixated with four orthognathic implant prototypes; a fixation through M 2.5 × 8 mm screws alone; b T-shaped moldable implant fixed with 3 M 2.5 × 6 mm screws; c longitudinal moldable implant M 2.5 × 6 mm; d arch-shaped implant fitting the anteroinferior edge of the mandible with two orifices for screw fixation of M 2.5 × 6 mm size, two on each edge of the plate

b

80 60 40 20 0

0

5

10

15

Force (N)

Fig. 2.8 a Photo-elastic test without implant; b linear load and maximal stress on a specific anatomical point

ramus and distally. A crack appeared during the test during the maximum stress concentration just prior to the fracture of the model as seen in Fig. 2.8b.

2.5.2 Image Correlation Test Surface displacement points were obtained by GOM and compared with those of the actual experimental photo-elastic test. Interestingly, the maximum displacement

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Fig. 2.9 Vertical displacement obtained by GOM correlate

occurred at the point of bone reabsorption, just where the fracture of the model was produced, see Fig. 2.9. Figure 2.10 shows the graph of time versus deformation percentage and the most critical point yields a maximum value of 14.402% in respect of the Y-axis.

2.5.3 Finite Element Analysis (FEA) The FEA of the mandible reported a maximum stress at the mandible ramus, see Fig. 2.11, and the maximum von Mises stress occurred mainly at the condylar area of the mandibular ramus. At the mandibular osteotomy, see Fig. 2.12, the stress concentration occurred in areas of decreased bone geometry, and also in nearby areas to the simulated bone cut. In reference to the generated stresses with the traditional fixation without implant, and those with fixed screws to the sagittal osteotomy, there was higher stress at the more distant screw to the mandible ramus, localized at the mandibular body where the mandible thickness is significantly reduced, see Fig. 2.13. Stress distribution of implants with three and four screws fixation showed very similar behavior at their central part and in contact with the mandible body (see Figs. 2.14 and 2.15) whereas the other two conditions had a higher stress concentration at the distal fixation screws. Finally, the arch-shaped implant showed a maximum stress distribution at the ramus condyles bilaterally, whereas the minimal stress was observed at the osteotomy

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Fig. 2.10 Time versus deformity percentage of four specific points taken (Condyle, angle, body, and maximal bone reabsorption) obtained in GOM correlate

Fig. 2.11 Distribution of the maximum principal stress from the mandible FEA test

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Fig. 2.12 Right sagittal mandibular osteotomy; top and left isometric views

Fig. 2.13 Maximum principal stress at the mandible with severe bone reabsorption

area suggesting that the arch-shaped implant yield a better distribution of stress through the numerical model, see Fig. 2.15.

2.6 Discussion In the last years, maxillofacial surgeons have adapted a so-called hybrid technique for fixation at the mandible structures. The main rationale for this is due to a better mechanical resistance that implants fixated with screws can provide, and the combination of bicortical or monocortical fixation, with and without the use of an implant. Bicortical fixation with screws was first introduced by Spiessl and popularized afterward by Paulus and Steinhauser [9]. Simultaneously, Michelet proposed fixation of

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Fig. 2.14 Maximum principal stress distribution with the implant and four fixation screws

Fig. 2.15 Maximum principal stress distribution with the arch-shaped implant

the segment after an osteotomy by using sagittal sections and implants with monocortical screws [9]. Sagittal mandibular osteotomy is currently being used to correct mandibular prognathism, or type III malocclusion. Fixation systems have to maximize stability in order to achieve an ideal distribution of loads between the bone segments; its mechanical behavior can be compared to a beam comprised of large transversal sections, only using bone and a thin transversal section where the implant is connected.

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According to some publications, implants are less resistant compared to fixation with bicortical screws alone [9]. Some implants were created for healthy patients that still had teeth. For this reason, our study does not apply the same treatment technique for people with severe mandibular bone reabsorption and without teeth, since bicortical screws will not yield good support with a compromised bone density and fractures are likely to occur. However, our study showed that implants with three or four monocortical screws allow better distribution of stress at the implant middle zone which is where our experimental test shown that bone failure is most likely to occur. Experimental tests allowed us to locate the areas of maximal stress and deformation. Our implants did not affect the function and yielded excellent mechanical resistance in all conditions. Our arch-shaped implant with the use of monocortical screws reduced stress by 10% in the area where mechanical failure was expected to occur and therefore, we could conclude that it can potentially reduce the incidence of other fractures, however, it requires a more invasive surgery for implantation and its heavier when compared with the previous three proposed prototypes. In spite of this, an arch-shaped implant can potentially be a solution for future dental implants.

2.7 Conclusions The present study performed experimental and numerical testing on personalized orthognathic implants to treat a case of bone reabsorption. The analysis of our results can comprehensively conclude that in experimental tests without implant, a fixation with small screws is needed in order to avoid detrimental effects on the mandible bone structure. However, a hybrid technique which requires the insertion of a bicortical screw in conjunction with a system comprised of an implant and monocortical screws increases resistance and better stress distribution. However, the load capacity of the system was lower when compared to bicortical screws alone. An optimal implant should yield resistance and stress distribution, particularly at their fixation points. Based on our results, our proposed implants could be beneficial in the treatment of some maxillofacial pathologies, especially those in which the bone quality has been highly compromised.

References 1. Angle: Treatment of malocclusion of the teeth: Angle’s system. Phila SS White Dental Manuf. Co 610, 5–59 (1907) 2. Jayakumar, J., Jayakumar, N., John, B., et al.: Quantitative prediction of change in chin position in Le Fort I impaction. J. Maxillofac. Oral Surg. 19, 438–442 (2020). https://doi.org/10.1007/ s12663-019-01298-7https://doi.org/10.1007/s12663-019-01298-7

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3. Caeiro, J.R., González, P., Guede, D.: Biomechanics and bone (& II): trials in different hierarchical levels of bone and alternative tools for the determination of bone strength. Rev. Osteoporos Metab. Min. (2013). https://doi.org/10.4321/s1889-836x2013000200007https://doi.org/ 10.4321/s1889-836x2013000200007 4. Hunt, K.D., O’Loughlin, V.D., Fitting, D.W., et al.: Ultrasonic determination of the elastic modulus of human cortical bone. Med. Biol. Eng. Comput. (1998). https://doi.org/10.1007/bf0 2522857https://doi.org/10.1007/bf02522857 5. Oyen, M.L., Ferguson, V.L., Bembey, A.K., et al.: Composite bounds on the elastic modulus of bone. J. Biomech. (2008). https://doi.org/10.1016/j.jbiomech.2008.05.018https://doi.org/10. 1016/j.jbiomech.2008.05.018 6. Beltrán-Fernández, J.A., et al.: Design and characterization of a mandibular prosthesis prototype by hemimandibulectomy. In: Öchsner, A., Altenbach, H. (eds.), Engineering Design Applications. Advanced Structured Materials, vol. 92. Springer, Cham (2019) 7. Barrère, F., van der Valk, C.M., Meijer, G., et al.: Osteointegration of biomimetic apatite coating applied onto dense and porous metal implants in femurs of goats. J. Biomed. Mater. Res. Part B Appl. Biomater. (2003). https://doi.org/10.1002/jbm.b.10057https://doi.org/10.1002/jbm.b. 10057 8. Havelin, L.I., Engesaeter, L.B., Espehaug, B., et al.: The Norwegian arthroplasty register: 11 years and 73,000 arthroplasties. Acta Orthop. Scand. (2000). https://doi.org/10.1080/000164 700317393321https://doi.org/10.1080/000164700317393321 9. Sato, F.R.L., Asprino, L., Consani, S., et al.: A comparative evaluation of the hybrid technique for fixation of the sagittal split ramus osteotomy in mandibular advancement by mechanical, photoelastic, and finite element analysis. Oral Surg. Oral Med. Oral Pathol. Oral Radiol. (2012). https://doi.org/10.1016/j.tripleo.2011.08.027https://doi.org/10.1016/j.tripleo.2011.08.027

Chapter 3

Biomechanical Evaluation of Sharped Fractures in Human Jaws Using Plates Articulated by the Champy Method Juan Alfonso Beltrán-Fernández, Héctor Gallardo-Ayala, Michelle Chagoya-López, Cesar Antonio Trujillo-Perez, Mauricio González-Rebattú y González, Marco Antonio Maturano-García, Juan Carlos Hermida-Ochoa, Luis Héctor Hernández-Gómez, Juan Luis Cuevas-Andrade, Alejandro David González-Peña, and Pablo Moreno-Garibaldi Abstract This work details the study of the effectiveness in the use of plates, as a treatment support during the fracture of a mandibular angle. It also analyzes the mechanical operation of the fissure repair plates on the jawbone using methods like finite element simulation and image correlation experimentation. With the purpose to evaluate the mechanical capacities of a new prototype plate compared to one of J. A. Beltrán-Fernández (B) · H. Gallardo-Ayala · M. Chagoya-López · C. A. Trujillo-Perez · L. H. Hernández-Gómez · J. L. Cuevas-Andrade · A. D. González-Peña · P. Moreno-Garibaldi Instituto Politécnico Nacional - Escuela Superior de Ingeniería Mecánica y Eléctrica - Sección de Estudios de Posgrado e Investigación Edificio 5, 2do Piso, Unidad Profesional Adolfo López Mateos “Zacatenco” Col. Lindavista, 07738 Ciudad de México, México e-mail: [email protected] H. Gallardo-Ayala e-mail: [email protected] M. Chagoya-López e-mail: [email protected] C. A. Trujillo-Perez e-mail: [email protected] L. H. Hernández-Gómez e-mail: [email protected] J. L. Cuevas-Andrade e-mail: [email protected] A. D. González-Peña e-mail: [email protected] P. Moreno-Garibaldi e-mail: [email protected] M. González-Rebattú y González · M. A. Maturano-García Hospital Regional 1 de Octubre ISSSTE, Cirugía Maxilofacial, Av Instituto Politécnico Nacional 1669, Gustavo A. Madero, 07300 Ciudad de México, CDMX, Mexico e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 J. A. Beltrán-Fernández et al. (eds.), Design and Simulation in Biomedical Mechanics, Advanced Structured Materials 146, https://doi.org/10.1007/978-3-030-65983-7_3

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the commonly used namesakes, since the mechanical capacities of the new model are unknown. Keywords Biomodeling · Champy plates · Three-dimensional printing · Masks · Computed axial tomography, digital image correlation · 3D printing models · Mandibular prosthesis · Mandibular reconstructions · Shaped fractures

3.1 Introduction 3.1.1 Statement of the Problem According to the Mexican Institute of Social Security, a mandibular fracture refers to the lack of bone continuity that occurs in any anatomical area of the jaw. The jaw is the only moving bone on the skull; it forms the lower third of the size of the face and plays an important role in the development of language, swallowing, and breathing; it also occupies a prominent esthetic area giving each individual a unique facial feature. Due to its prominent anatomical position, the jaw is a vulnerable point to injuries caused by trauma or accidents; for this reason on a frequency ratio, jaw fractures are ranked second within facial fractures and tenth among fractures throughout the body. They represent 36% of all fractures of the maxillofacial complex [1]. The jaw is subjected to the action of the chewing muscles, whose joint action will determine if the fracture strokes are favorable, whether they tend to approximate them, or unfavorable, when they tend to separate them [2] (Fig. 3.1). For the oral and maxillofacial surgeon, who is dedicated to find the most common anatomical patterns within these fractures, it is vital to know the mechanical behavior of the jaw set and its interactions with different forces before and during the healing of a fracture. For any surgical procedure, there is an analysis of success rate, infection, regeneration, among other parameters, based on experience or statistical analysis. Since most interventions are emergency and more so, it is not possible to experiment with patients. For this reason, it is vitally important to analyze surgical intervention procedures thoroughly, by means of computer simulations, as well as by physical tests. This way by the results obtained, the current work seeks to improve the process of surgery and treatment, relying on finite element analysis, in the proposal of new solutions. M. A. Maturano-García e-mail: [email protected] J. C. Hermida-Ochoa Centro de Investigación y Laboratorio Biomecánico, Carmen #18, Chimalistac San Ángel, 01070 Ciudad de México, CDMX, Mexico e-mail: [email protected]

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Finally, from these simulations and tests, it is desired to evaluate the mechanical capacities of a newly proposed plate by the beneficiary, which is similarly fixed (in the oblique line) as the traditionally used ones, but its mechanical capacity is yet to be known. Once the information has been obtained, the data resulting from all simulations and operations will be compared to determine whether the use of the plate proposed by the beneficiary is feasible and desirable.

3.1.2 Osteosynthesis It consists of surgery exposing directly to the fracture, which tries to return the bone to its original position by implementing a fixation device (miniplate) to the fractured segments of the bone. osteosynthesis with plates can be single-loaded or shared [3]. In those using single-loaded plates, the rigid plate moves forces to the fracture site. While for those using shared loaded plates, the force is divided between the fixation plate and the bone involved. These miniplates are low-profile fixed with monocortical screws [3, 4]. Four main objectives are followed for treatment: • • • •

Return to the anatomical position of the fracture. Restore occlusion. Fix booth segments of bone until complete healing. Avoid complications [3].

Rigid fixing plates must be aligned with the outer oblique line, as it represents a neutral zone between stress and compression stresses to achieve stable fixation (see Fig. 3.2). The jaw angle is one of the areas with the highest number of fractures in the jaw area. Fractures in the jaw angle are the most problematic in the facial region due to the high frequency of complications and difficult access to the surgical site. Some traditional methods of fixing the jaw angle fracture may include wire osteosynthesis and maxillomandibular fixation. Currently, these fractures are treated by plate/screw osteosynthesis where the bone segments are secured by fixing a plate, a two-plate fixation or a single-rigid plate. However, the discussion about the ideal type of fixation for jaw angle fractures continues. The fixation of the jaw angle fractures is mechanically complex because the increased stress load of the jaw is interrupted in this area. Finite element analysis (FEA) is a numerical analysis technique that can determine displacements, stresses, and deformations on an irregular solid body, given the complex behavior of the material and the load conditions imposed on that body. Stress analysis obtained from FEA modeling of maxillofacial bone structures can provide information on the interactions between hardware and bone during normal patient operation [5]. Previous studies have shown the usefulness of finite element modeling to capture the unique and complex biomechanics of mandibular fracture deformation. Some

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Fig. 3.1 Anatomical location of jaw fractures [2]. Reprinted with permission from Springer Nature publishers

Fig. 3.2 External oblique line [4]. Reprinted with permission from Springer Nature publishers

of which are set out in this paper in order to serve as a reference for the tests and measurements that will be carried out for this project. The results obtained from various clinical and biomechanical studies will be analyzed for the following fixing plate geometries: • Conventional 4-hole miniplate • Lambda plate (conventional position).

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3.1.3 Conventional Miniplate This kind of low-profile plates are fixed with monocortical screws (screws 2.0 mm in diameter and 6 or 8 mm in length) on a neutral position to prevent injury to the dental apex and lower dentary nerve. (see Fig. 3.3) The plates must be precisely modeled to ensure the correct reduction of the fracture and its maintenance in an appropriate position. A slight over-bent achieves a greater reduction in the lingual face of the fracture (Fig. 3.3). These kinds of plates are placed at the level of the external mandibular oblique line or in the upper oral cortical, in the ideal lines of osteosynthesis described by Michelet and Champy [6]. For a conventional four-hole miniplate, the following previously conducted test data for jaw angle fractures were gathered (Fig. 3.4). Fig. 3.3 4 hole miniplate [6]. Reprinted with permission from Springer Nature publishers

Fig. 3.4 Jaw forces (Study 1) [7]. Reprinted with permission from Springer Nature publishers

74 Table 3.1 Results of study 1

J. A. Beltrán-Fernández et al. Type of fixation

Stress in the plate (MPa)

Displacement (mm)

Screw stress (MPa)

Conventional miniplate

17.935

0.53–0.49

22.352

In the study “Evaluation of the postoperative stability of a counter-clockwise rotation technique for skeletal class II patients by using a novel three-dimensional position-posture method” [7] (for simulation), the mandibular loads were determined as shown in Fig. 3.4. In this study, a displacement between bone fragments, a von Mises stress tests on the plate, and stress tests on the plate fixing screws, were tested, with a total strength of 200 N. The results of the study are expressed in the following Table 3.1. In the study “A customized fixation plate with novel structure designed by topological optimization for mandibular angle fracture based on finite element analysis” [8] (for simulation), mandibular loads were determined as expressed in Fig. 3.5. This study performed von Mises stress tests on the plate and screws (as a whole) and the displacement between the bone fragments, with a total force of 250 N placed in the area of the second right molar. The results of the study are expressed in Table 3.2. Fig. 3.5 Jaw forces (Study 2) [8]. Reprinted with permission from Springer Nature publishers

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Fig. 3.6 Lambda plate [9]. Reprinted with permission from Springer Nature publishers

Table 3.2 Results of study 2

Type of fixation Stress in the plate (MPa)

Displacement (mm)

Conventional miniplate

0.635

394

3.1.4 Lambda Plate The lambda plate comes in left and right versions. It emulates a two-plate technique, with its specific shape and seven-hole design, with the width of a single plate in the upper segment, allowing the surgeon to raise the lambda plate to the narrowest area of the condyle neck just below the head (condylar). The fixing arms are mounted on the jaw canal to avoid the risk of injury. The lambda plate can be placed using surgical approaches retro-jaws. For positioning, the straight segment of five holes has to be placed parallel to the back edge of the branch (condylar) aligned with the line head. The anterior arm may be bent to fit the bone surface below the sigmoid notch [9] (Fig. 3.6). The lambda plate is normally used for the treatment of fractures in the condylar area, mainly due to its thin double-fixation structure. No previous test recompilation was performed for this geometry as it will be used in a completely different position than its conventional one. Said that; the finite element analysis performed on this plate has been developed in the proposed configuration and the comparison has been made with the conventional plates used in the Champy technique for jaw angle fracture.

3.2 Materials and Methods To carry out this work, the methodology has been structured as follows:

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• Stage 1: – Association to the biomechanical concepts of the jaw and other theoretical concepts that require to address the subject. – State-of-the-art research. – Learning to take data by the usage of Scan-IP and tomography software and specialists and also the learning of various techniques such as (modeling, simulation, measurement, and depending on the specific case, even considering the help of specialists). – Establishment the methodology. – Presentation of the protocol. • Stage 2 – – – – –

Visit with the maxillofacial surgeon (obtaining skulls from the bone bank). Handling of RX plates and CT scans of healthy patients and cases. Segmentation of tomographic data and segmentation of radiological studies. Simulation of 3D models from CT scans. First partial conclusion.

• Stage 3 – Surgical solution instrumentation modeling. – 3D printing of pre-surgical models. – Evaluation of stresses and deformations on plates and bone material (of the instrumented and digitized model). – Adjustments. – Testing: Experimental tests on physical instrumented models and numerical tests on digitized models. – Comparison of conditions between models (result comparison). – Discussion of results (medical and engineering guarantee). – Final conclusion.

3.2.1 Selection of Tests and Parameters for Simulation Based on the information above, it was concluded that osteosynthesis is one of the most discussed topics in the clinical literature. The segments must be fixed to achieve the rigidity and stability needed to speed up the healing period and provide rapid recovery. If these fixing methods are not well performed, they may cause serious complications while in treatment. As a result, surgerists have increased interest in investigating which method of osteosynthesis is most appropriate. Clinically, the biomechanical functions of rigid fixation systems depend on the interaction between the three components, plate, screws, and bone. A conventional system of bone plate screws requires precise adaptation of the plate to the underlying bone. Without this intimate contact, the tightening of the screws pulls the bone

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segment to the plate and results in alterations of the segment position and occlusal ratio [4]. This is why von Mises stress tests were performed for the simulations for both the plate and the fixing screws (as a whole); this aiming to compare the proposed new method with the lambda plate in angular fractures by verifying its load distribution. Similarly, bone fragment displacement tests were performed to verify whether the fixation of bone fragments would be adequate and stable with this method. The geometry of a conventional Champy miniplate was selected to have a comparison point of the proposal performance (lambda plate) in this study. Specifically, it has been simulated with a four-hole Champy plate placed on the inner oblique line, as it is the mostly used plate for this method.

3.2.2 Mandibular Kinematics In order to develop the simulation, it is also important to consider anatomical data and mandibular kinematics for realistic and reliable simulation. With the help of the Kinovea software, measurements of the mandibular kinematics were made in order to identify which are the moving and fixed parts of this system. The selection of fixed and movable parts is essential for proper finite element analysis. Fixed segments were declared as “constraint” in the software simulation, and for movable sections, the force vectors were applied. Within the Kinovea software, two videos of jaw movements were analyzed, the first sideways, in which three reference points were chosen to be able to visualize the oral opening movement and identify which part of the jaw is involved in this movement. Moderate opening movements and maximum opening movements were performed. Similarly, the analysis of a frontal intake of the oral opening movement has been performed in order to verify the separation that occurs by this movement. This analysis has been performed for moderate opening movement and subsequently for maximum tightening movement. The analysis demonstrates that the parts involved in the opening movement are: the inframeniscal area, which can have a separation up to 2 cm in a moderate opening motion and up to 6 cm is a maximum opening motion, and the condylar center of rotation, which takes the function of axis rotation of the movement (Fig. 3.7). For a moderate aperture, the movement is considered as pure horizontal rotation, since the line area functions as a hinge axis and does not move from its position [10] (Fig. 3.8). On a maximum opening, the ligaments are tightened resulting in a translation of the condyles, making a small forward movement resulting in a forward-down-up movement [10] (3.9). Initially, the analysis verified the separation of the different types of aperture, with the help of the front view of the movement, obtaining the following results (Fig. 3.10): See the details for moderate opening in Table 3.3.

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Fig. 3.7 Kinovea © study (side view)

Fig. 3.8 Moderate opening movement [10]. Reprinted with permission from Springer Nature publishers

Table 3.3 Separation for moderate opening

Initial separation (cm)

Final separation (cm)

 separation (cm)

2.02

3.27

1.25

1.96

2.90

0.94

1.96

2.81

0.85

2.02

3.00

Average  separation

0.98 1.00

See the details for maximum opening in Table 3.4. The results obtained for both moderate and maximum opening correspond to the parameters obtained in the literature. Subsequently, the opening angle for both moderate and maximum has been found and checked for the following results (Fig. 3.9). The angles for moderate opening are summarized in Table 3.5. The angles for maximum opening are summarized in Table 3.6.

3 Biomechanical Evaluation of Sharped Fractures … Table 3.4 Separation for maximum opening

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Initial separation (cm)

Final separation (cm)

 separation (cm)

2.02

5.15

3.13

2.04

4.90

2.86

2.06

4.99

2.93

2.11

4.80

2.69

Average  separation

2.90

Fig. 3.9 Maximum opening movement [10]. Reprinted with permission from Springer Nature publishers Fig. 3.10 Kinovea (front view)

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Table 3.5 Angle for moderate opening

Initial angle

Angle  angle

Final angle

112°

115°

3°

112°

114°

2°

111°

114°

3°

111°

113°

2°

Average  angle

Table 3.6 Angle for maximum opening

2.5°

Initial angle

Final angle

Angle  angle

111°

121°

10°

112°

117°

5°

111°

118°

7°

110°

116°

5°

Average  angle

6.75°

Subsequently, the behavior of these movements has been found experimentally; for this, the center of the analysis video has been taken as the coordinate (0, 0), so the mandibular movement on the axis “x” and axis “y” could be plotted as shown in Fig. 3.11. In the condylar movement, it can be verified that, for moderate opening, the condyles did not have a movement of great relevance, but when switching to maximum aperture, they had a positive movement in the x-axis (translation), as explained in the literature of jaw kinematics. The same procedure has been performed for the inframeniscal area obtaining the following graph in Fig. 3.12.

-4

-3

-2

0

-0.46

-0.68

Movement in x axis (cm)

Fig. 3.11 Condyle movement

-1 -0.24

Movement in y axis (cm)

-5

-0.9

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-5

Movement in y axis (cm)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

-5.8

-6.6

-7.4

-8.2

Movement in x axis (cm)

Fig. 3.12 Inframeniscal movement

It can be observed that there are more significant movements in the inframeniscal area, since it is in this area where the greatest displacement takes place to perform an oral opening. The previous jaw kinematics analysis defines, that, for the simulation, the condylar area must be taken as a fixed point, and the inframeniscal area considered as movable, as Kinovea’s motion analyses suggest, the movements in the condylar area are very small for normal jaw functions (moderate opening) and only represent a significant movement in the maximum opening. With the moving and fixed areas of the simulation defined, the next step in the process is to analyze the anatomical behavior of the jaw in order to simulate the forces. The force produced during chewing is generated by multiple muscles working simultaneously and together on the surface of the lower jaw. To determine the influence of each muscle during the production of a given force, an anatomical model is used for stress distribution analysis. For the jaw-plate-screw system simulations, the forces exerted by the reported jaw muscles were applied based on the study “resistance and stress finite element analysis of different types of fixation for mandibular orthognathic surgery” [8], the mandibular loads were determined as shown in Table 3.7.

3.2.3 Material Selection In order to perform the post-surgical case simulations, the selection of materials has been assigned and justified in the Creo Parametric Software as described in the following: • Plates and screws

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Table 3.7 Normal muscle forces for structural static analysis

Muscle

Muscle area in cross section (cm2 )

Force (N)

Right masseter (C)

3.4

151

Middle right pterigodium (D)

1.9

145

Right temporary muscle (E)

3.9

235

Left masseter (F)

3.4

151

Middle left pterigodium (G)

1.9

145

Left temporary muscle (H)

3.9

235

Table 3.8 Comparison table—mechanical properties—PVC versus bone Material

Young’s module (MPa)

Elastic limit (MPa)

Energy absorbed to performance (kJ/m3 )

Bone

310 (40–160)

3.3 (0.4–9.0)

21.8 (2–90)

PVC

123.2 ± 14.9

3.0 ± 0.1

41.2 ± 11.4

All osteosynthesis plates are required for minimal properties, mainly adequate strength (to provide stability), enough ductility (to allow anatomical molding), and biocompatibility (not to produce local or systemic adverse effects). The materials with which the implants are manufactured for osteosynthesis are varied; stainless steel, cobalt-chromium-molybdenum alloys, and titanium are mainly used, pure or alloyed. Titanium was assigned as a material for the simulation of plates and screws, since as a biomaterial, it is mainly used for osteosynthesis in the skull-maxilo-facial territory. This due to its extreme chemical passivity (and therefore excellent biocompatibility), as well as for gathering the appropriate physical properties for good biomechanical behavior in the long term. Its density makes implants weigh about 45% less than steel and cobalt implants, an important factor in patient comfort especially in long bindings. Its low module of elasticity is another advantage, as it minimizes pressure and it is transferred to the bone; the relative importance of pressure protection increases as the size of the implant increases [11]. Similarly, this material is covered by ISO 5832:2014, which provides the standard to follow on metallic material implants for surgery [12]. • Jaw The bone has the characteristic of evolving by modifying its properties according to the loads to which it is subjected and regenerate in case of damage or altering its mechanical properties before pathological processes or simply with age.

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The bone is a living tissue (its microscopic structure changes) that is in continuous growth process subject to biochemical, biophysical, and biological processes related to each other and with mechanical and geometric properties. In bone tissue, there are mainly two cases of material behavior, transverse isotropy and orthotropy. Cross isotropy has equal elastic characteristics in two perpendicular directions, but different in the third, orthotropy has different elastic characteristics in three perpendicular directions. [13] Taking this into account, the Creo Parametric Software does not present a material that resembles 100% to the isotropic and orthotropic mechanical properties presented by human bones, so a material that does resemble the isotropic properties of a human bone, in this case is PVC. Previous medical articles used different methods to study possible substitute materials for human bone during in vitro biomechanical testing. Fresh animal and human bone do have viscoelastic properties that make its properties and behavior unique. PVC foams have also shown such properties, which could make them a better model material for bone (during in vitro biomechanical testing). According to Young’s module, the elastic limit and energy absorbed to performance represent the sponginess of the human bone structure better than other materials. Their viscoelastic and energy-absorbing properties also make them a more suitable material for bone modeling [14] (Table 3.8).

3.3 Experimental Tests 3.3.1 Duplicates on the Cadaveric Jaw Two real cadaveric jaws were used for physical testing; one of these is kept in one piece to associate it with the healthy (pre-fractured) jaw data while the other will be associated with the fractured jaw data. These pieces were rescued from the bone bank of the Hospital (ISSSTE 1° de Octubre) (Table 3.9). Plated The lambda plate originally intended for the repair of fractures in the condylar area is proposed in this work as an alternative to the use of conventional plates for the angle area. The plate is manipulated by means of tweezers and forceps as to fulfill its new function (Table 3.10). For the process of emulating the fracture, first the plate was fixed to the jaw by screws to the cadaveric jaw, before proceeding to fracture it in order to have a better control during cutting (Fig. 3.13). The screws to secure the plates to the bone use the “Matrix” 2.9 mm radio system, used for plates with 1.5 mm system in the same standard (Fig. 3.14).

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Table 3.9 a General views of the cadaveric jaws. b General views of the cadaveric jaws Jaw “healthy”

Jaw “fractured”

Frontal

Frontal

Left lateral

Left lateral

Table 3.10 Folding and scale of the plate proposal for implementation in jaw angle fracture Lambda-type plate. Front-facing view of the plate proposal

Proposal of usage

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Table 3.11 Views of the cadaveric jaw configured as analogous to the postoperative stage Left lateral

Frontal

Fig. 3.13 Recommended configuration of the plate, according to the profile of the area of mandibular interest (applied on the oblique line) [11]. Reprinted with permission from Springer Nature publishers

Fig. 3.14 Maxillofacial hardware screws data

3.3.2 Instrumentation of the Cadaveric Jaw for Mechanical Experimentation Purposes The instrumentation of the fracture was carried out by cutting with dental Dremel along the line shown in Fig. 3.15 (Table 3.11).

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Fig. 3.15 Fracture instrumentation

3.3.3 Joint Motion Simulation For the physical testing of the lambda plate, it was proposed to perform a joint motion simulation with the help of the LIVE system ™ of AMTI which is a specialized tool for the simulation of this type of testing. This system focuses on the kinetic realism of the simulation to provide the closest possible approach to real conditions (Fig. 3.16). This system was selected for its six degrees of freedom at full speed and full load (Fig. 3.17). For physical analysis, the parameters obtained from the mandibular kinematics analysis for moderate jaw opening were used (see Tables 3.3 and 3.5). For the applied force with the system, a resulting axial force was applied to incisors of a value of 145 and 250 N. The proposal of mounting the cadaveric jaw to the VIVO system is shown in Fig. 3.18. To carry out the simulation on the bony jaws, it was necessary to develop a base to hold the base of the jaw (by the chin bulge) and at the same time can be assembled to the machine guideline (Fig. 3.19). Similarly, a base was designed to hold the condyles fixed to the machine on the axis of rotation (Fig. 3.20). Once the bases were fixed on the simulation, the test started. Unlike static simulations in Creo, where a characteristic force is exerted for one second (simulating a hit), this dynamic test aims to discover the life cycle of the plate implemented by indefinite cycles. After six days for the completion of this test, attrition has been observed in the fixing of the plate.

3 Biomechanical Evaluation of Sharped Fractures … Fig. 3.16 VIVO system

Fig. 3.17 VIVO tool simulation camera

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Fig. 3.18 Clamping proposal diagram for the jaws in the VIVO machine, the goal is to keep the condyles fixed to the axis of rotation and to attach the base of the chin to the force leader while the rotation is established

Fig. 3.19 Base developed based on the user manual of the VIVO machine. Physical reproduction of the CAD model

3.3.4 Software Testing Preparation 3.3.4.1

Scanning Process for Patient-Like Models

Management and segmentation of tomographic data and radiological studies were developed. The management and segmentation of tomographic data and radiological studies of the patient and healthy cases were carried out, and the following digitized models were obtained (See Table 3.12).

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Fig. 3.20 Base developed to attach the condyles to the axis of rotation. Physical reproduction of the CAD model

Table 3.12 Patient-analog digitized models Model

Software Function

Healthy jaw

Scan-IP

Required for 3D printing playback for physical stress, deformation, and rupture testing

Pre-operative jaw (fractured) Radi-Ant Necessary to export to Creo and establish finite element analysis of the cadaveric jaw Required for 3D printing playback for physical stress, deformation and rupture testing Necessary for physical implementation with a Champy plate for further digitization Postoperative jaw

3.3.4.2

Radi-Ant Fracture status reference

Digitizing “Healthy” Jaw with Scan-IP

Scan-IP is a program that groups hand-drawn layers on a CT scan. The bone can be seen in contrast to the other elements as it has a white color with greater opacity, saturation, and brightness. The process goes by generating a mask and using the pen tool while drawing layer by layer the elements of the skull recovered from a “healthy” patient without any fracture. As shown in Figs. 3.21 and 3.22, the YX, YZ, and XZ planes of a full-body tomography, the lines that cross images on each plane, correspond to the area where another of the selected views crosses. Giving a 3D feel. When generating a STL model, all elements illustrated above the layer must be rendered to generate a 3D object.

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Fig. 3.21 Healthy jaw segmentation in Scan-IP software

Fig. 3.22 3D objects are created in “. STL” to import them later into Creo Parametric

3.3.4.3

Pre-operative Jaw Scanning with Radi-Ant

Radi-Ant DICOM viewer is an application for processing and displaying medical images in DICOM (digital imaging and communications in medicine) format [15]. It is not necessary for the project to generate models of the fractured jaw, since tests of any kind cannot be carried out with elements of “failure.” However, this model is necessary for instrumentation with the conventional Champy plate, so it was required to use a 3D print of this model (Table 3.13).

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Table 3.13 Pre-operative jaw scanning views with Radi-Ant Lower

3.3.4.4

Left side

Isometric

Digitization of the Postoperative Jaw with Radi-Ant

It is noteworthy to see that the implementation of a double plate on the right-hand side of the patient left a postoperative wound much larger than that on the left-hand side with the newly proposed configuration (Tables 3.14 and 3.15).

3.3.5 CAD Modeling of Plates and Screws CAD modeling of selected plates was performed for studies to document their original dimensions and geometry (before implementation). • Conventional four-hole Champy plate (Table 3.16): • Lambda type plate (Table 3.17): • Lambda-type plate trimmed similarly to the postoperative implementation (Table 3.18): • Treadles screw (4 × 8 mm) Table 3.14 Digitalization views of the postoperative jaw with Radi-Ant Frontal

Left-hand side

Isometric

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Table 3.15 Postoperative views of base patient Frontal

Left lateral

To develop the correct assembly for simulation of finite elements via a commercial software, the tread of the screws was not designed in order to simplify the joining and fixation within the Creo Parametric program (Table 3.16), since in this way, the software considers the element to be fully fixed between surfaces, and the assemblies corresponding to the previous plates were made for documentation (Tables 3.19, 3.20, 3.21 and 3.22).

3.3.6 Plate CAD Segmentation and Modeling (with Deformation) Lambda-type plate segmentation with proposed configuration. The Champy lambda-type junction plate corresponding to the actual implementation was modeled at 1:1 scale using the Radi-Ant software (Fig. 3.23).

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Table 3.16 CAD modeling conventional Champy junction plate Isometric view

Front view

Side view

Isometric view of the plate with 0.3 mm fillets

Front view of the plate with 0.3 mm fillets

Side view of the plate with 0.3 mm fillets

Table 3.17 Cad modeling lambda-type plate Isometric view

Front view

Side view

Isometric view of the plate with 0.3 mm fillets

Front view of the plate with 0.3 mm fillets

Side view of the plate with 0.3 mm fillets

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Table 3.18 CAD modeling Champy-type lambda joining plate trimmed similar to postoperative implementation Isometric view

Front view

Side view

Isometric view of the plate with 0.3 mm fillets

Front view of the plate with 0.3 mm fillets

Side view of the plate with 0.3 mm fillets

Table 3.19 Cad screw modeling 4 × 8 mm Isometric view

Front view

Side view

To separate the plate from the organic structures, the highest density (corresponding to metals) has been selected. And so, everything other than the plate was removed using the brush tool. It was necessary to make several cuts from different angle views in order to eliminate as much bone as possible (Fig. 3.24). Importing files from Radi-Ant to Creo requires saving the files in “STL” format from Radi-Ant, and then import it into Creo. It is possible to edit the geometry as a facet and then edit its surface as a cloud; in this way, the model had been cleaned up from any remnants around the desired geometry (which could not be visualized by Radi-Ant) (Table 3.23).

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Table 3.20 Conventional Champy plate assembly with screws Isometric view

Front view

Side view

Table 3.21 Lambda plate assembly with screws Isometric view

Front view

Side view

Table 3.22 Lambda type plate assembly analogous to postoperative implementation with screws Isometric view

Front view

Side view

Once saving as a. wrap/envelop type with properties of a level 10 faceted solid, it was possible to edit the geometry as with any.prt object (extrude, round, cut or make planes) (Fig. 3.25).

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Fig. 3.23 Postoperative resonance front view and zoom in to the proposed plate implemented

Fig. 3.24 Lambda plate segmentation

3.4 Scanning of Bended Plates 3D printing of the pre-operative jaw was performed, in order to model in addition with the regular Champy plate. This print was made with conventional PLA filament as shown in Fig. 3.26.

3 Biomechanical Evaluation of Sharped Fractures … Table 3.23 Lambda-type junction plate from postoperative tomography Right-hand side view

Fig. 3.25 Segmented lambda tomography plate Fig. 3.26 Pre-operative jaw 3D printing

Front view

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The 3D printing was performed aiming to perform the instrumentation of these with every kind of plate used in this work and being able to digitize every plate with the reformation that is necessary to assemble them in the oblique line of the jaw.

3.4.1 Digitization Process The scanning process was based in ATOS Core, which is a three-dimensional measurement system of components up to 500 mm in size. The sensor forms the basis for a wide range of measurement tasks, from simple 3D scanning to fully automated measurement and inspection processes (Fig. 3.27). ATOS Core uses a stereoscopic camera that is based on the principle of triangulation. The sensor projects different light patterns onto the object’s surface. The two cameras record these patterns and form a mesh based on the distribution of the light projected. And then the device translates it to the GOM correlate software in order to generate a 3D surface. ATOS Core uses multiple phase changes and fuses the heterodyne to achieve high accuracy at the subpixel level. Separate 3D coordinates Fig. 3.27 ATOS core system [1]

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with optical transformation equations are automatically calculated for each camera pixel [1]. Reference stamps were positioned at points recognizable by the program, aiming to establish the joints between scan layers. This process is illustrated in Fig. 3.28. The ATOS system can perform the scan without these reference points as the scanner detects the geometries that the blue light system touches; however, as the piece to be scanned consists of two layers of scanning (relative to the upper and lower side of the jaw respectively), these points will indicate the joints between the two surfaces when full scanning is obtained. First the top of the jaw has to be scanned and named “Side 1.” This process is an attempt to cover as much volume as possible in each shot to make the process effective. The process is illustrated in Fig. 3.29. Since the light of the ATOS system fails to detect the part that is in contact with the base, the same procedure has to be performed for the lower jaw or side 2 (Fig. 3.30). The second part of the digitization is then performed. The result of scanning is the generation of a shell resembling the jaw, but this piece is generated hollow. Also, these attempts of digitization produced parts that presented gaps, resulting from the lack of reflection of the system light at these points; these gaps in most cases are translated as defects. In Fig. 3.31, a side with a major defect is shown: Represented in blue is shown the shell seen from the outside. In red, the shell seen from within. And in gray the correctly generated shell. Therefore, it is required to perform the scan in order to obtain as few gaps as possible. In the final piece, the remaining defects were filled with the Inspector Software. Once the full shell has been obtained, the last step is to fill in the remaining defects and to generate the final solid (Table 3.24). Fig. 3.28 Placement of landmarks

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Fig. 3.29 Scan side 1 (top)

Fig. 3.30 Scanning of side 2 (bottom)

3.4.2 Assessment of Digitization Table 3.24 shows an assessment of different digitization grades obtained for the model of jaw and Champy plate along the development of this work.

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Fig. 3.31 Final process scanning

3.4.3 Finite Element Simulation 3.4.3.1

Assembly

Using the pre-operative jaw and the digitized plates, an assembly has been created in order to be simulated. The fractured jaw and each plate were assembled, and the holes were generated in the jaw perpendicularly to the planes in order to keep their alignment (Fig. 3.32). The screws were assembled as shown in Fig. 3.33. This procedure was performed for each plate configuration along with the fractured cadaveric jaw.

3.4.3.2

Static Analysis

In accordance with the methodology, simulations were made for the lambda plate in its new configuration and for the conventional Champy plate in screw-plate assembly and jaw plate screws. For each of the simulations, the condylar area was considered as a fixed point, based on the jaw kinematics study presented in the mandibular kinematics section.

Radi-Ant

Refined

Scan-IP

ATOS Core

Jaws

(continued)

Table 3.24 a Comparison of deferent digitization results. b Comparison of deferent digitization results. c Comparison of deferent digitization results

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Radi-Ant

Plates

Final simulation quality

Jaws

Table 3.24 (continued)

ATOS core

(continued)

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Refined

Jaws

Table 3.24 (continued) Final simulation quality

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Fig. 3.32 Assembly of jaw plate

Fig. 3.33 Assembly of jaw plate screws

The studies conducted using the Creo Parametric Software were: “displacement,” “maximum shear stress,” and “von Mises stress” tests. Such studies are based on a static simulation.

3.4.3.3

Static Analysis for Screw-Plate Assembly

Single simulations of the plates were performed with their respective screw assembly, in order to have mechanical behavior considering the forces interacting with all components. Two vectors, 151 N in Z plane and 235 N in plane X, were determined as the most significant muscle forces near the plate based on the information raised in the section of mandibular kinematics (Fig. 3.34). Under these conditions, the results presented in Table 3.25 were obtained. Note that the tension in the plate is much lower for the lambda plate than for the conventional miniplate. This is important because the screws do not exert as much tension in the lambda configuration which is convenient at the time of treatment of

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Fig. 3.34 Forces for plate-screw simulation

Table 3.25 Simulation results on assembly plate screw

Plate Lambda Conventional

von Mises stress (MPa) 67.5317 147.494

Displacement (mm) 0.02637 0.02395

an angular fracture, since at this point, it is desired to have the least possible tension in the plate to achieve a more efficient treatment. On the other hand, it can be observed that the displacement is smaller in the conventional plate, but, likewise it could be observed that when comparing the area where the displacement is exerted, it is much larger on the conventional plate than on the lambda plate, which tells us that the conventional plate tends to have a greater displacement area compared to the lambda plate (Fig. 3.35).

3.4.3.4

Static Analysis for Jaw-Plate-Screw Assembly

For the jaw-plate-screw system simulations, the forces exerted by the jaw muscles reported in the mandibular kinematics section were placed similarly to those presented in Fig. 3.36. Simulation 1: static jaw simulation with lambda-type plate under normal mandibular forces This simulation suggests that the tension distributed in the arms of the plate as the displacement is less. It can also be observed that the compression stresses are much larger than those presented on the plate (Figs. 3.37 and 3.38).

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Fig. 3.35 Displacement in screw-plate simulation

Fig. 3.36 Muscle forces applied to the jaw

Simulation 2: static jaw simulation with Champy (conventional) plate under normal mandibular forces For this simulation, the condyles were adjusted to be fixed points. Fixed points were also placed at the bottom of the two screws that contact the rear jaw, and the muscle forces described above to emulate the usual behavior of the jaw. The other two screws were declared only as contacts and not as dots (Fig. 3.39). Table 3.26 expresses the results found on the simulations performed (Fig. 3.40).

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Fig. 3.37 Assignment of forces for simulation 1

Fig. 3.38 Simulation results 1, from left to right: von Mises stress test, displacement test, and maximum cut stress test

3.5 Discussion of Results As seen in Table 3.26, the von Mises stress presented on the lambda plate is lower than that presented on the conventional Champy plate. This is important, because it means that the lambda plate distributes better the forces across its geometry generating less stress along itself and the screws that fix it. This characteristic is convenient for the treatment of an angular fracture. In accordance to the displacement analysis, it can be observed that the lambda plate serves as a joint that allows the homogeneous movement of the mandibular structure. This can be verified looking at the displacement, a displacement close to

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Fig. 3.39 Assignment of forces for simulation 2

Table 3.26 Results of simulations with muscle forces applied to the jaw

Case of study

Lambda plate

Champy plate

Von Mises stress (MPa)

451.897

675.076

Displacement (mm) Maximum shear stress (MPa)

0.57504 393.380

1.61328 432.815

Fig. 3.40 Simulation results case 2, from left to right: von Mises stress, displacement and maximum shear stress

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0 mm (Fig. 3.41), in contrast to the Champy plate which has a greater displacement in the chin area of up to 10 times the displacement in the condylar area. It is also important to emphasize that the lambda plate had a significant displacement in the last screw of the system (Fig. 3.42), which represents that this element will have the tendency to move from its site. Such behavior is common in the treatment of fractures by means of osteosynthesis with plates, but it is equally of the utmost importance to anticipate such situations to avoid future complications for the patient. It is important to mention that the simulation is a static test, and it represents that the displacement presented by the screw should not be expected to occur in this way unless the jaw (in question), receives a firm blow/hit similarly to that of the simulation. On the other hand, note how on the Champy plate (conventional), there is a detachment of the plate in the area of the upper jaw, indicating that this plate will have the tendency to fail in this area, detaching from the jaw. This behavior did not occur in the lambda plate, indicating that this geometry presents greater resistance and stability in the case of impacts. Finally, the maximum shear stress is higher for the Champy plate (conventional) which has a value of 837,476 MPa. This value is close to the limit of the mechanical Fig. 3.41 Screw offset. Lambda plate

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Fig. 3.42 Displacement and maximum von Mises stress on the Champy plate

tensile strength for titanium, which could represent an elastic deformation of the material or, failing that, a break of the material.

3.5.1 Assessment of Results To support the results obtained during the simulations, a comparison has been made with those obtained in the study “resistance and stress finite element analysis of different types of fixation for mandibular orthognathic surgery” [5] presented in Table 3.27. As Table 3.27 shows, the results obtained during the simulations of this work are within the range of those obtained in this study, indicating that the simulations have reliable results for the analysis of jaw plates. Differences in the magnitudes of the results may be due to the non-allocation of forces, since it was obtained from a consensus of the studies consulted throughout the project, in advice from the medical body that advises this work. Similarly, the geometry and volume of the jaw is not strictly equivalent to that of the study in question, since that geometry depends directly on the patient. Table 3.27 Final results “resistance and stress finite element analysis of different types of fixation for mandibular orthognathic surgery” Type of fixation

Plate von Misses stress (MPa)

Displacement (mm)

Conventional miniplate

394

0.635

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3.6 Analysis of Results It is notorious that there is an apparent inconsistency between the applied loads, and the percentages of displacement. However, this phenomenon can be explained due to the relaxation existing in the material from which the tested jaw is made, which is PLA. When applying a load, it is applied suddenly, considerably increasing the deformation; however, in a short period of time, the applied load is distributed, the part recovers a portion of its original position, and the deformation decreases. It is noteworthy that the latest loading applications maintain high percentages of deformation, especially the last portion, which makes the difference between deformation in initial stages of loading, and final stages. When carefully examining the distribution of deformations in the part, it can be seen that the highest percentage of deformation is around the plate, in the posterior section of the angle, which is consistent, since the jaw physically presents a discontinuity in that area, making it more prone to warping than the rest of the piece.

3.7 Study Using GOM Correlate to a 3D Printing of the Champy Method 3.7.1 Clarification In this study, the jaw in question is imprinted with the integrated plate, which means that the plate is, like the rest of the jaw, made of PLA. The existence of the plate in the printed jaw serves the only function of having a more adequate geometric representation of a cadaveric jaw instrumented with a titanium plate.

3.7.2 Process To carry out this study, there is a printed model of the instrumented jaw, which was obtained by digitizing the original jaw using the ATOS CORE system. There are also modeled clamps to hold the jaw; these were modeled using SolidWorks and ZbrushCore2018, performing Boolean operations to generate a negative of the contour of the condyles. The objective of these restraints is to keep the jaw fixed, and to allow the easy application of load on the condylar area, leading to the mandibular branch, and the angular area of the jaw, where it is instrumented (Fig. 3.43).

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Fig. 3.43 Clamp model completed

3.7.3 Preparation To carry out the correlation study by points in GOM correlate, it is necessary that the object to study is mottled with a contrasting pattern, consisting of a white background with black dots. The printed jaw is painted with white spray paint, and later mottled using a black sharpie (Fig. 3.44). Once the jaw is mottled, it is mounted on the clamping set (Fig. 3.45).

Fig. 3.44 Mottled imprinted jaw

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Fig. 3.45 Jaw mounted with clamps

3.7.4 Experimental Procedure With the jaw mounted with its clamps, weight is added to the rectangular profile of the clamp. In this specific case, 3D printing filaments were used, each with a different weight, which was noted before performing the test. Six coils of filament were used, which weigh 200, 400, 550, 550, 650, and 1200 g respectively, which, at the end, will provide a total load of 3.5 kg (Fig. 3.46). The test is recorded in real time with a camera. At the end of the trial, the video stops and it is uploaded to a computer.

Fig. 3.46 Application and transmission of loads

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Fig. 3.47 Polygon and section view in the manipulation of GOM correlate

3.7.5 GOM Correlate In the GOM correlate interface, the video of the piece tested is imported, and it is subsequently verified that the program properly detects the mottled pattern on the piece. Once the video has been successfully imported, a calibration procedure is performed, so that the program can accurately identify the travel distances. Then, a polygon is traced and delimits the area to be analyzed, in this case is the area surrounding the plate applied via the Champy method. In order for GOM correlate to give a satisfactory result, it is necessary to further specify in which zone it should perform a displacement check. For this effect, a line is drawn in the “construct section in viewing direction” option that crosses the surface whose deformation is of interest for the test and specifies that the deformation to be measured is in the X-axis (Fig. 3.47).

3.7.6 Results Once GOM correlate finishes computing the entered information, a report is generated, showing the relationship between the test time and the percentage of displacement that the tested object has through a graph. The test time is directly linked to the application of load on the jaw (Fig. 3.48 and Table 3.28).

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Fig. 3.48 Time-displacement graph of the test to the printed jaw

Table 3.28 Summary of the times, loads, and displacements of this study

Time (s)

Load (g)

Displacement (%)

0

0

0.00

1

200

0.55

8

600

0.90

12

1150

0.65

21

1700

0.95

28

2350

0.80

34

3550

1.05

3.7.7 Analysis of Results It is notorious that there is an apparent inconsistency between the applied loads, and the percentages of displacement. However, this phenomenon can be explained due to the relaxation existing in the material from which the tested jaw is made, which is PLA. When applying weight, it is applied suddenly, considerably increasing the deformation; however, in a short period of time, the applied load is distributed, the piece recovers a portion of its original position, and the deformation decreases. It is noteworthy that the latest loading applications maintain high percentages of deformation, especially the last portion, which makes the difference between deformation in initial stages of loading, and final stages. When carefully examining the distribution of deformations in the piece, it can be seen that the highest percentage of deformation is around the plate, in the posterior section of the angle, which is consistent, since the jaw physically presents a discontinuity in that area, making it more prone to warping than the rest of the piece.

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3.8 Conclusions Based on the concept that bone segments must be correctly fixed during the osteosynthesis process, achieving the rigidity and stability necessary to speed up the healing period and provide rapid recovery of the patient, it can be defined that the lambda plate mounted on the oblique line has the correct mechanical qualities and geometry to be considered an alternative for the treatment of jaw angle fractures. Also, compared to the conventional Champy plate, mounted (equally) on the mandibular oblique line, the lambda plate is a better alternative for the treatment of this type of fracture, since it has a lower von Mises stress, less overall displacement and its maximum stress to cut is not close to the limit of mechanical tensile strength of titanium. Clinically, the biomechanical functions of rigid fixation systems depend on the interaction between the three components, plate, screws, and bone. A conventional system for bone plate requires precise adaptation of the plate to the underlying bone. Without this intimate contact, the tightening of the screws draws the bone segment to the plate, as seen in the Champy (conventional) plate simulation and results in alterations in the position of the segment. As for the simulation process it is concluded that it should be taken into account that the scanning processes creates parts made up of thousands of triangles that can complicate the conversion and manipulation of the files and, as a result, computers with a higher processing capacity and a RAM of at least 32 GB have to be used. Another possible solution is the use of multiple computers connected to each other to use the capacity of the combined cores in parallel.

References 1. Gómez Roselló, E., Quiles Granado, A.M., Artajona Garcia, M., et al.: Facial fractures: classification and highlights for a useful report. Insights Imag. 11, 49 (2020). https://doi.org/10. 1186/s13244-020-00847-whttps://doi.org/10.1186/s13244-020-00847-w 2. Alba by Pablo García-Cuenca: Ostentesynthesis with a miniplate versus two miniplates. Oral Maxillofacial Surg. Serv. 1, 1–68 (2011). https://ddd.uab.cat/pub/trerecpro/2011/hdl_2072_1 71750/TR_DePabloGarcia-Cuenca.pdf 3. Victor, L.A.: Mandibular fracture type Champy-Michelet. Clin. Update J. 28, 1390–1394. https://www.revistasbolivianas.org.bo/pdf/raci/v28/v28_a06.pdf 4. von Arx, T., Lozanoff, S.: Posterior mandible. In: Clinical Oral Anatomy. Springer, Cham (2017) https://doi.org/10.1007/978-3-319-41993-0_14 5. Atik, F., Ataç, M.S., Özkan, A., Kılınç, Y., Arslan, M.: Biomechanical analysis of titanium fixation plates and screws in mandibular angle fractures. Nigerian J. Clin. Pract. 19, 386–390 (2016) 6. Elsayed, S.A., Elsayed, E.H., Altaweel, A.A.: Stabilization of anterior mandibular fracture using different osteosynthesis devices: perioperative clinical notes. Oral Maxillofac. Surg. (2020). https://doi.org/10.1007/s10006-020-00917-9https://doi.org/10.1007/s10006-020-009 17-9

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7. Wan, Z., Shen, S.G., Gui, H., et al.: Evaluation of the postoperative stability of a counterclockwise rotation technique for skeletal class II patients by using a novel three-dimensional position-posture method. Sci. Rep. 9, 13196 (2019). https://doi.org/10.1038/s41598-019-493 35-2https://doi.org/10.1038/s41598-019-49335-2 8. Liu, Y., Fan, Y., Jiang, X.: Bio. Med. Eng. (2017). de Springer Link Sitio web: https://link.spr inger.com/article/10.1186/s12938-017-0422-z. Accessed on 08 Oct 2019 9. Bhadauria Fernandes, T., Dhupar, V., Akkara, F., et al.: Efficiency of the 2-mm titanium lambda plate for open reduction and internal fixation of subcondylar fractures of the mandible: a prospective clinical study. J. Maxillofac. Oral Surg. (2020). https://doi.org/10.1007/s12663020-01435-7https://doi.org/10.1007/s12663-020-01435-7 10. Ozkan, Y.K.: Movements and mechanics of mandible occlusion concepts and laws of articulation. In: Özkan, Y. (eds.), Complete Denture Prosthodontics. Springer, Cham (2018). https:// doi.org/10.1007/978-3-319-69032-2_8 11. Perry, M., Holmes, S.: Mandibular fractures. In: Perry, M., Holmes, S. (eds.), Atlas of Operative Maxillofacial Trauma Surgery. Springer, London (2014). https://doi.org/10.1007/978-1-44712855-7_6 12. ISO: Implants for surgery—metallic materials—part 11: wrought titanium 6-aluminium 7niobium alloy (2014). de ISO Sitio web: https://www.iso.org/standard/64615.html. Accessed on 12 Jan 2019 13. Rentería, M.Á.F.: The mechanics of the bone a review of the models of bone remodeling. 31-dic19, Research Professor of the Higher School of Ciudad Sahagún of the Bachelor of Mechanical Engineering Autonomous University of the State of Hidalgo Website: https://www.uaeh.edu. mx/investigacion/productos/7851/6_la_mecanica_del_hueso.pdf 14. Oroszlány, Á., Nagy, P., Kovács, J.G.: Compressive properties of commercially available PVC foams intended for use as mechanical models for human cancellous bone. 30-dic-19, vol. 12, No. 2 (2015). de Acta Polytechnica Hungarica Sitio web: https://www.uni-obuda.hu/journal/ Oroszlany_Nagy_Kovacs_58.pdf 15. Welcome to RadiAnt DICOM Viewer. 30-dic-19, de Based on version 5.5.0 of RadiAnt DICOM Viewer. Last changed on Wednesday, November 20, 2019. Sitio web: https://www.radiantvi ewer.com/dicom-viewer-manual/

Chapter 4

Comparative Study of Stress and Strain of Orthopaedic Implants for the Hip with Photoelastic and Image Correlation Techniques Edgar Alfonso Figueroa-Rodríguez, Juan Alfonso Beltrán-Fernández, Juan Carlos Hermida-Ochoa, Brayan Leonardo Pérez-Escobar, Juan Luis Cuevas-Andrade, Erik Omar Alvarado-Alcántara, Alejandro David González-Peña, José Enrique Rodríguez-Miramar, and Luis Héctor Hernández-Gómez Abstract The present study comprises a comparative exercise to determine stress, strain, and amorphic structural state in a hip prosthesis with the use of the photoelastic and image correlation technique. Several photoelastic models, some of them with a stochastic finish were created by the use of a computed tomography scan, stereolithographic three-dimensional printing, and rapid prototyping. Ideally, our results E. A. Figueroa-Rodríguez (B) · J. A. Beltrán-Fernández · J. L. Cuevas-Andrade · E. O. Alvarado-Alcántara · A. D. González-Peña · J. E. Rodríguez-Miramar · L. H. Hernández-Gómez Instituto Politécnico Nacional, Escuela Superior de Ingeniería Mecánica y Eléctrica—Sección de Estudios de Posgrado e Investigación Edificio 5, Unidad Profesional Adolfo López Mateos “Zacatenco” Col. Lindavista, 2do Piso, 07738 Mexico City, Mexico e-mail: [email protected] J. A. Beltrán-Fernández e-mail: [email protected] J. L. Cuevas-Andrade e-mail: [email protected] E. O. Alvarado-Alcántara e-mail: [email protected] A. D. González-Peña e-mail: [email protected] J. E. Rodríguez-Miramar e-mail: [email protected] L. H. Hernández-Gómez e-mail: [email protected] J. C. Hermida-Ochoa Centro de Investigación y Laboratorio de Biomecánica, Carmen #18, Col. Chimalistac San Ángel, 01070 Mexico City, Mexico e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 J. A. Beltrán-Fernández et al. (eds.), Design and Simulation in Biomedical Mechanics, Advanced Structured Materials 146, https://doi.org/10.1007/978-3-030-65983-7_4

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could yield a significant time reduction of techniques aimed to evaluate stress and strain of surgical models either pre or postoperatively. Keywords Arthroplasty · Image correlation · Hip dysplasia · Photo elasticity · Orthopaedic implants

4.1 Introduction Coxofemoral pathology presents a high incidence in the Mexican population, representing the second more relevant joint pathology. This disease is more frequent in patients between 55 and 75 years of age; females are more affected than males (72.2% and 27.8%, respectively) according to the Instituto Nacional de Rehabilitación (INR) [1], of Mexico City. Surgical procedures, such as total hip arthroplasty (THA), are highly effective in which they provide pain relief and enhanced mobility of patients suffering with joint degeneration [2]. Even when the evolution of surgical techniques and design of new implants had been satisfactory, THA still represents a challenge of high complexity comprising a high index of mistakes and complications such as implant wear, migration, and patient negligence [3]. Arthroplasty treatments involve significant variables for their efficacy: Bone morphology and structure, biological loads (especially those involved at the coxofemoral region), and the particular characteristics of the prosthetic implant. However, there is no optimal solution for some cases, therefore, experimental tests are crucial. A comparative experimental test was performed on a healthy and a pathologic coxofemoral area, and a novel customized implant. Specimens were developed using photoelastic resin and digitized through digital image acquisition [4]. The geometry was obtained by 3D printing (FDM) [5] and applied to produce the mold used for the photoelastic test [6], and for the model used in the image correlation. The aim of the study was to register the stress and strain of the specimens subjected to loads and compare the resting versus the operational state of them. This allowed us to monitor the prosthetic behavior in a healthy hip and find an optimal anatomical position.

B. L. Pérez-Escobar Universidad Juárez Autónoma de Tabasco, Avenida Universidad S/N, Zona de la cultura, Col. Magisterial, 86040 Villahermosa, Centro, Tabasco, Mexico e-mail: [email protected]

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4.2 Clinical Case The patient selected for this study was 18 years old, a 45 kg weighed male with severe left hip destruction, secondary to bone cancer (Sarcoma) that subsided after radiotherapy. The residual hip lesion had gross bone loss and necrosis in the iliac region. Clinically the patient had pain and very limited mobility of the left hip with great detriment for his quality of life. The patient was subjected to a total hip arthroplasty (THA) in which all cartilage from the proximal hip was removed by precise bone cuts. Cartilage from the hip acetabulum was also removed by rasping the cartilage with a special rim, until subchondral bone was reached. In this particular case, the whole femoral head was cut and removed and remaining acetabular fossa was reshaped to yield a more cavitated bone region and allow the prosthetic femoral head to move naturally.

4.3 Methodology Figure 4.1 depicts the methodology used for comparison of stress and deformations in the orthopedic implants. Using the methodology described in Fig. 4.1 aids to design the prototype, materialize, evaluate and validate the mechanical behavior, and posteriorly obtain the medical validation and definitive manufacture of the prosthetic components.

4.4 Materials and Methods 4.4.1 Design and Characterization of the Specimens for Experimental Evaluation Based on digital acquisition of images from CT scan of the patient (Granted by the Centro de Investigación y Laboratorio de Biomecánica “CILAB”), a stereolithografic 3D model was obtained using the ScanIP© segmentation software. Specimens from the healthy and the abnormal hip and the hip component prototype were generated through this method. Scan IP allowed for visualization of the CT scan study in 3 planes (coronal, sagittal, and transversal). The contours of each image allowed to elaborate masks from the areas of interest and allowing the generation of tridimensional models in the form, or NURBS (non-uniform rational B-spline). The visual analysis of the obtained 3D virtual hip models allows for a better understanding of the patient study and its left hip pathology since it allows the inspection of the areas of bone loss and destruction and allows comparison with the contralateral normal hip. The NURBS model was exported into a stereolithographic file (STL) and then transformed into a

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Yes

Medical valida on

Yes

Problem approach with physician

Coxartrosis causes and sequelae

Clinical case knowledge

No

Digita on of the prototype for replicas

Prototype produc on by 3D prin ng

CT scan modeling through digital image aquisi on

Parametriza on of the affected area and proposed prosthesis

No

Produc on of rubber molds and resin models

Experimental analysis by photoelas city and image correla on

No

Yes Approval to produce the defini ve prosthesis

Analysis and discussion of results from mechanical behavior

Fig. 4.1 Flow chart which depicts the methodology used for the comparative study of stress and strain in orthopaedic implants

solid numerical model using a computer-aided design (CAD) software, as shown in Fig. 4.2. The model file represented the true anatomical geometry of the patient and it allowed for direct 3D-FDM impression. Characterization of the areas of interest was performed by 3D printing and parameters used are depicted in Table 4.1. These parameters may vary depending on the material used, most commonly PLA and ABS. Figure 4.3 shows the importing of the STL file into the printer platform and printing corresponding parameters. Figure 4.4 shows the 3D impression of models of PLA characterized by the segmentation program. Postprocessing of the PLA printed models was performed by sanding and acetone bath in order to enhance the geometric surface and obtain a better rubber-mold. The silicon-rubber was poured over the PLA models and demolding was initiated 2 h after the rubber cure process started (see Fig. 4.5). The molds were then used to cast models using two types of compounds: 1 Photoelastic resin (PL-1, micromeasurements Inc.) Poly methyl methacrylate (PMMA)

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Fig. 4.2 Hip reconstruction in different anatomical planes: a coronal, b transversal, c sagittal and d shows a virtual 3D reconstruction of the different hip components based on the masks defined in the segmentation process

Table 4.1 Assigned printing parameters

Parameter

Value

Layer height

0.2 mm

Printing speed

45 mm/s

Type of filling

Rectilinear

Density of filling

20%

Extrusion temperature

190 °C

Bed temperature

50 °C

Supports

Yes

(Eurofix), a polymer known for its biocompatibility, and used as bone cement (see Fig. 4.6). A polymer catalyzer was used to elaborate the photoelastic models from the healthy and abnormal hips. Since the photoelastic resin undergoes an exothermic reaction during curing, rubber molds were selected due to its capacity to resist changes of temperatures without altering the geometry details. Also, the replication of geometry with these molds yields a very high definition of detail (see Fig. 4.7).

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Fig. 4.3 STL files import into the 3D printer program: a parameters of processing, b cut process of the printing paths

Fig. 4.4 a Coronal view of anatomical areas of the healthy (right) and abnormal (left) hips, b sagittal view of the femoral head and acetabular components

Fig. 4.5 Creation of the silicon rubber mold: a bone structures of the hip, b acetabulum and femoral head prosthetic components

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Fig. 4.6 Model extraction from the 3D PLA printed models to cast the photoelastic resin and PMMA models

Fig. 4.7 a Models representing the healthy and abnormal hips made of photoelastic resin (PL-1), b acetabular and femoral head components

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The orthopaedic surgeon contribution was important during the whole study process; evaluation of the diseased area of the hip and planning of the preoperative process, and elaboration of the preliminary prothesic geometry (manually modeling the acetabular component) which could better fit the bone defect area (see Fig. 4.8). To follow the surgeon’s criteria, inverse engineering was performed through digitation of the manually modeled component as depicted in Fig. 4.9. Figure 4.10 shows digitization of the acetabular model through light incidence and a surface swept resulting in a cloud of points which was characterized as a shell through the digitizing software. Digitization of the acetabular model allowed to keep the original geometry. The resulting STL file was converted to a neutral format (IGS, SAT, STEP) to be able to process it in any CAD software (Figs. 4.3b and 4.4b).

Fig. 4.8 Proposed acetabular prototype elaborated according to the surgeon’s criteria

Fig. 4.9 a Digitizing Scanner calibration, b surface scanning of the manually made prosthetic component for the acetabulum

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Fig. 4.10 a Scanning of the proposed acetabular component through surface swept, and b digitization process of the acetabular component

A rubber mold was elaborated for the PMMA components just like in the case of the photoelastic resin as shown in Fig. 4.11.

Fig. 4.11 a Elaboration of rubber molds to cast the materials b PMMA casting mold and c acetabular components and femoral head

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4.4.2 Experimental Study (Healthy and Abnormal Hip, and Prothesic Models) To elaborate the experimental studies, normal conditions to which the patient is normal subjected, such as physiological loads were considered, since these would be acting upon the natural structures, but also on the prosthetic components. Photoelasticity was our selected technique to obtain the natural mechanics and structural behavior of photoelastic models, since it allowed to register the fields of produced stress. Complementary and through image correlation the percentage of deformation of the prosthesis prototypes were also obtained after these were subjected to load [8, 9].

4.4.2.1

Photoelastic Test

We analyzed the healthy and abnormal hip areas and the proposed prothesic prototype aiming to observe the fields of stress. The method used the following equations: σp =

P ×n t

σmax = KI =

N× f t σmax σp

(4.1) (4.2) (4.3)

P N t f

is the applied load through the polariscope is the stripe order is the specimen thickness is the photoelasticity constant of the resin given by the manufacturer 250,000 N/m σmax is the maximal stress is the nominal stress σp is the coefficient of stress concentration KI Determination of the stripe N order was based in document TN-702-2 from the photoelastic resin manufacturer and its values are displayed in Table 4.2 [10]. For the elasticity test we used specimens shown in Fig. 4.7. The specimens were subjected to load conditions using a mechanical press from an unloaded state. Mounting and fixing of the specimens is depicted in Fig. 4.12; all were subjected to gradual compressive load. The stripe pattern can be seen at the neck of the femoral head which we assume is the most compromised at the hip area. Red squares represent the thinnest areas of the specimens and therefore we assume they are mechanically more compromised (see Figs. 4.12 and 4.13).

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Table 4.2 Characteristic of isochromic stripe from micro-measurements resin PL-1

a)

b)

c)

Fig. 4.12 Photoelastic specimens a abnormal hip area b healthy hip area c proposed hip prothesis

4.4.2.2

Image Correlation Test

Image correlation test presents the deformation evaluation of the prosthesis component. The model was made of PMMA and load was applied gradually. Strain was calculated according to Hooke’s law on a PMMA specimen.

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a)

b)

c)

Fig. 4.13 Red squares depict the highest loads applied on the photoelastic models. The most critical high load areas will be determined

Our correlation image test also required a stochastic pattern applied to the model surface (mottling) by using a white primer with a flat finish, and the mottling was then applied on black paint with flat finish. The correlation software (GOM CORRELATE) used these patterns to account for deformation during the application of loads. The same frame of compression load applied on the photoelasticity test was used for image correlation test, just as shown in Fig. 4.14. A video of the whole load application on the prosthetic component was recorded on video to later be analyzed for gradual strain. Fig. 4.14 Mounted and fixed prosthetic model of the hip prosthesis, showing the surface mottling

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Fig. 4.15 a Importing of video to the correlation software, b segmentation of the video

The method for the image correlation is described as follows: After the compression of the model is performed, the video taken during the test was imported to the correlation software (Fig. 4.15). Adjustment of the software parameters was necessary for our analysis as shown in Fig. 4.16 and described below: 1. The surface component 2. The dimension of the surface component An axis following the desired direction for measurement has to be selected, in this case, the Y axis was chosen to measure the strain (Fig. 4.17). Afterwards the program can determine the deformations of the specimen with respect of time and applied loads. This yields a better understanding of the deformation behavior and references (Labels) are added in order to register the deviation (Fig. 4.18).

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b)

a)

Fig. 4.16 a Parameter modification, b selection of the surface component over the area of interest

b)

a)

c) Fig. 4.17 a Selection of the deformation component, b sizing of the area of interest and c sizing of the surface component where the correlation test was performed

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a)

b)

c) Fig. 4.18 a Deviation labels inserted on the surface component, b percentage of strain, c visualizing the surface component deformation

4.5 Results This section reports the results obtained from the experimental tests pertaining to photoelasticity and image correlation. In each of them, we achieved to observe the geometrical behavior of every specimen. This knowledge is essential to guide us in the necessary adjustments for the manufacturing of the definitive prosthesis.

4.5.1 Results of the Photoelastic Test Results of the prosthesic tests based on the healthy and abnormal areas of the hip are depicted in Tables 4.3, 4.4 and 4.5. In these tables, we observe the photoelastic

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Table 4.3 Photoelastic test on the abnormal left hip

σmax (kPa)

t (m)

σ p (kPa)

0

0.01

0

0

0

0

0.01

0

0

0

0.28

0.01

0.1

7000

127,421

2.94

0.8

0.01

0.2

20,000

84,947.3

3.92

0.9

0.01

0.4

22,500

63,710.5

4.91

1.08

0.01

0.5

27,000

50,968.4

t (m)

σ p (kPa)

σmax (kPa)

No.

P (N)

1

0

2

0.98

3

1.96

4 5 6

N

K1

Table 4.4 Photoelastic test on the normal hip

No.

P (N)

N

K1

1

0

0.28

0.01

0

5000

0

2

0.98

0.6

0.01

0.04

10,714.29

0

3

1.96

1.08

0.01

0.15

19,285.71

127,421

4

3.92

1.22

0.01

0.34

21,785.71

63,710.5

5

5.89

1.39

0.01

0.58

24,821.43

42,473.67

6

7.85

1.63

0.01

0.91

29,107.14

31,855.25

7

9.81

2

0.01

1.4

35,714.29

25,484.2

8

11.77

2.35

0.01

1.98

41,964.29

21,236.83

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Table 4.5 Photoelastic test on the proposed hip prosthesis

No.

P (N)

N

t (m)

σ p (kPa)

σmax (kPa)

K1

1

9.62

0

0.015

0

0

0

2

19.25

0

0.015

0

0

0

3

28.87

0.28

0.015

0.5

4666.7

8659.3

4

38.49

0.45

0.015

1.2

7500

6494.4

5

48.12

0.6

0.015

1.9

10,000

5195.6

6

57.74

0.8

0.015

3.1

13,333.3

4329.6

7

67.37

0.9

0.015

4

15,000

3711.1

8

76.99

1

0.015

5.1

16,666.7

3247.2

9

86.61

1.08

0.015

6.2

18,000

2886.4

10

96.24

1.22

0.015

7.8

20,333.3

2597.8

11

105.86

1.39

0.015

9.8

23,166.7

2361.6

12

115.48

1.39

0.015

10.7

23,166.7

2164.8

13

125.11

1.63

0.015

13.6

27,166.7

1998.3

14

134.73

1.63

0.015

14.6

27,166.7

1855.6

15

144.35

1.82

0.015

17.5

30,333.3

1731.9

16

153.98

1.82

0.015

18.7

303,33.3

1623.6

patterns and calculation of the stress distributed over the specimens. We highlight that the natural compression and tensile trabecular system of the human hip were used to make a comparison on our testing (Fig. 4.19).

4.5.2 Results of the Image Correlation Test It is important to note that the percentage of strain for the PMMA specimen included 5 points of interest where more geometric compromise was expected (Fig. 4.20 and Graph 4.1).

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Fig. 4.19 Natural compression and tensile trabecular system of the human hip [11]. Reprinted with permission from SpringerNature publishers

Figure 4.21 depicts a color pattern representing the grade strain; this data will drive the necessary adjustments to produce de definitive prosthetic component to be implanted in vivo. Graph 4.2 shows the gradual deformation over time at the five pints of interest for the PMMA model.

4.6 Discussion After the photoelastic test results were analyzed we conclude that mechanical behavior of the models was adequate. In those cases, with thinner geometrical

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Fig. 4.20 Maximal percentage of deformation considering five points of interest for the PMMA specimen due to the gradual load that was applied

sections, specifically the interface between the femoral head and the proximal diaphysis of the femur at the abnormal left hip, where maximal stress concentration occurred. Meanwhile the healthy right hip had a stress field expected and based in comparison with the analytical representation with distinction of the areas subjected to tension and compression. Moreover, the specimen representing the abnormal hip experimented a reduction of its structural capacity of 10% when compared to the healthy hip side. This would potentially compromise function in the real life for a patient with such structural abnormalities. The hip prosthesis specimen displayed an adequate mechanical behavior with values comparable or lower to those reported in the literature in generic hip implants. However, when compared with the specimen in the abnormal region, the structural behavior improved approximately 80%. This could potentially translate into better clinical outcomes for the real patient. Interest was focused on the PMMA mechanical behavior which is the material used to manufacture our hip prosthesis. Our experimental tests have shown a favorable deformation of only 0.3 to 0.45%.

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Graph 4.1 Percentage of deformation—time of the image correlation analysis test

4.7 Conclusion Our present study was focused on the evaluation of the mechanical behavior of a proposed hip prosthetic component customized for a case of hip destruction, with gross loss of bone and residual dysplasia of the hip joint. The design of the hip components was based on the patient hip defect geometry and our aim was to test its operational viability and minimize unnecessary surgical procedures [12]. It is desirable to offer novel implants to treat bone strain at the hip joint and improve the patient’s quality of life. We designed and tested a novel experimental hip prosthetic component using photoelastic and image correlation tests. We compared both abnormal and healthy hip sides in order to get familiarized with the normal natural mechanics of the hip and compare these findings for the testing on the abnormal side. This would make us more confident about the mechanical features needed for our customized implants [13]. To fabricate the models, we used CT scan studies and 3D printing. This allowed us to get familiarized with the patient’s hip geometry and lesion morphology. Our

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Percentage of deformation

Fig. 4.21 Resulting deformation of the model during the applied load

Time of the image correlation analysis test

Graph 4.2 Deformation—time of the test during the image correlation test on the prosthesis

technique was optimal and low-cost, and facilitated the implementation of changes in our designs [14, 15]. Engineering evaluation is strongly related to biomedical processes who are in search for better and personalized solutions, especially in those cases where generic commercial prosthesis cannot be implemented to a particular case.

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References 1. Ibarra, L.G., Segura, V.H., Chávez, D.D., et al.: Las enfermedades y traumatismos del sistema músculo esquelético. Un Análisis del Instituto Nacional de Rehabilitación de México, como base para su clasificación y prevención. Secretaría de Salud (2013) 2. Pastrián, D.M., Garabano, G., Sel, H.: Reemplazo total de cadera en pacientes con displasia luxante. Rev. Asoc. Argent Ortop. Traumatol. 82(3), 231–241 (2017) 3. Davalillo, C.T., Orbazo, F.G., Marco, F.R., Mejía, T.M., Mario, J., Álvarez, N.: Reconstrucción acetabular en la artroplastía de revisión. Estudio retrospectivo de 76 casos. Hospital Español de México 21(4), 182–188 (2007) 4. Sutton, M.A.: Digital image correlation for shape and deformation measurements. Springer Handbook of Experimental Solid Mechanics, pp. 565–600 (2008). https://doi.org/10.1007/ 978-0-387-30877-7_20 5. Pérez-Mañanes, R., Calvo-Haro, et al.: Nuestra experiencia con impresión 3D doméstica en Cirugía Ortopédica y Traumatología. Hazlo tú mismo. Rev. Latinoam. de Cir. Ortop. 1(2), 47–53 (2016). https://doi.org/10.1016/j.rslaot.2016.06.004 6. Valle Velasco, P.R.: Estudio comparativo de los métodos de elementos finitos y fotoelástico en la determinación de esfuerzos para mejorar el diseño mecánico de piezas. (2013) 7. Chu, T.C., Ranson, W.F., Sutton, M.A.: Applications of digital-image-correlation techniques to experimental mechanics. Exp. Mech. 25(3), 232–244 (1985). https://doi.org/10.1007/BF0 2325092 8. Francés, A., Claramunt, R., Cebrian, J.L., et al.: Biomechanical assays for the study of the effects of hip prostheses: Application to the reconstruction of bone defects with femoral allografts. Musculoskeletal Surg. 97(2), 123–130 (2013). https://doi.org/10.1007/s12306-012-0234-z 9. Pan, B., Yuan, J., Xia, Y.: Strain field denoising for digital image correlation using a regularized cost-function. Opt. Lasers Eng. 65, 9–17 (2015). https://doi.org/10.1016/j.optlaseng.2014. 03.016 10. Vishay Precision Group: Introduction to Stress Analysis by the PhotoStress® Method by TN702-2 the PhotoStress, pp. 1–14 (2005) 11. Konda, S.R.: Anatomy of the proximal femur. In: Egol, K., Leucht, P. (eds.) Proximal Femur Fractures. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-64904-7_1 12. Fadero, P.E., Shah, M.: Three dimensional (3D) modelling and surgical planning in trauma and orthopaedics. Surgeon 12(6), 328–333 (2014). https://doi.org/10.1016/j.surge.2014.03.008 13. Nordin, M., Frankel, V.H.: In: Hill, M.G. (ed.) Biomecánica Basica del Sistema Musculoesquelético, 3a edicion (2004) 14. Beltrán-Fernández, J.A., Ruiz-Muñoz, O.R., et al.: Numerical and experimental analysis of a personalized prosthesis for a patient with unilateral hip osteoarthritis. In: Advanced Structured Materials, vol. 113 (2020). https://doi.org/10.1007/978-3-030-20801-1_21 15. Ruiz-Muñoz, O.R.:. Diseño de prótesis personalizada de cadera para paciente con coxartrosis unilateral. Instituto Politécnico Nacional (2016)

Chapter 5

Numerical–Experimental Study for the Determination of the Structural Mechanical Behavior of the Wall of the Cranial Vault Using Finite Element Method and Image Correlation Juan Alfonso Beltrán-Fernández, Alejandro David González-Peña, Juan Carlos Hermida-Ochoa, José Enrique Rodríguez-Miramar, Edgar Alfonso Figueroa-Rodríguez, Erick Omar Alvarado-Alcántara, Luis Héctor Hernández-Gómez, and Juan Luis Cuevas-Andrade Abstract In the present work, the effect of trauma impacts on the cranium and the influence of cranial brain fluid on the walls of the cranial vault are analyzed. Using experimental methods (photoelasticity and image correlation), as well as numerical methods with ANSYS Mechanical APDL® , the results were studied in order J. A. Beltrán-Fernández (B) · A. D. González-Peña · J. E. Rodríguez-Miramar · E. A. Figueroa-Rodríguez · E. O. Alvarado-Alcántara · L. H. Hernández-Gómez · J. L. Cuevas-Andrade Instituto Politécnico Nacional, Escuela Superior de Ingeniería Mecánica y Eléctrica—Sección de Estudios de Posgrado e Investigación Edificio 5, Unidad Profesional Adolfo López Mateos “Zacatenco” Col. Lindavista, 2do Piso, 07738 Mexico City, Mexico e-mail: [email protected] A. D. González-Peña e-mail: [email protected] J. E. Rodríguez-Miramar e-mail: [email protected] E. A. Figueroa-Rodríguez e-mail: [email protected] E. O. Alvarado-Alcántara e-mail: [email protected] L. H. Hernández-Gómez e-mail: [email protected] J. L. Cuevas-Andrade e-mail: [email protected] J. C. Hermida-Ochoa Centro de Investigación y Laboratorio Biomecánico Carmen, #18, Chimalistac San Ángel, 01070 Mexico City, Mexico e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 J. A. Beltrán-Fernández et al. (eds.), Design and Simulation in Biomedical Mechanics, Advanced Structured Materials 146, https://doi.org/10.1007/978-3-030-65983-7_5

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to know the mechanical behavior in the surface of the cranial vault in which the cranial plates for replacement or reconstructive surgery for injuries by trauma (third degree) are required. Also, it would be considered as an economic and capable option for prosthesis which only considers titanium and stainless steel as material for the replacement.

5.1 Introduction The cranium is comprised of several bones, and two regions can be recognized: the neurocranium and the visceral cranium. The adult neurocranium is formed by eight bones: four odd aligned on the middle line (frontal, ethmoid, sphenoid, and occipital) and two pair series (temporal and parietal). The neurocranium has a vault-shaped top called calvaria (cranial vault) and a base. Flat bones (frontal, ethmoid, sphenoid, and occipital) comprise the calvaria. The cranial base is formed by the sphenoid and temporal bones [1]. The Monro-Kellie doctrine states that the inner cranium comprises three main components: blood, cerebrospinal fluid (CSF), and cerebral parenchyma. An increase in the volume of one or more components due to head trauma (HT) can increase the internal cranial pressure (ICP) and lead to intracranial hypertension (IH). This doctrine also states that cranial expansion is impossible after fontanelles fusion, see [2]. In other words, the cranium keeps a constant volume independent from its contents [3]. Normally, the cerebral parenchyma volume equals 1.100 ml, whereas blood and CSF equal 150 ml each [4]. Under physiological conditions, ICP is maintained at 10 ± 5 mm Hg [5]. An ICP increase between 20 and 30 mmHg represents mild IH; 30 to 40 mm Hg represents a moderate IH; and ICP higher than 40 mm Hg is considered severe IH. Trauma lesions represent the highest mortality in people under 40. Among these, head trauma is the main mortality cause in poly-trauma patients. Approximately two-thirds of all traumatic deaths are associated with head trauma and represent 20% of deaths occurring to patients of productive age [6]. In Mexico, head trauma is the fourth cause of death in accidents and violence-related injuries; mortality rates 38.8 per 100 thousand inhabitants. Males have a higher rate than females in a 3:1 ratio, and age ranges from 15 to 45 years old. Most common causes of head injury are traffic accidents (75%) and affect people under 25 y/o, motorcycle drivers, and drivers under the influence of alcohol [7]. Experimental tests were planned by using photoelastic techniques and image comparison. A photoelastic resin model was casted on a mold based on a 3Dprinted model (image acquisition and data segmenting techniques were used for this purpose). Experimental results were finally compared with numerical tests with the use of ANSYS Mechanical APDL® .

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5.2 Methodology Figure 5.1 shows the used methodology for the present study. Models used in our tests were elaborated at the biomechanics laboratory of the Instituto Politécnico Nacional with calibrated equipment listed as follows: • Polarizer SSM-AJ, 060 series • Image correlation system GOM ARAMIS—Correlate • 3D printer XYZ Da Vinci AiO Study case knowledge and information search about the subject

Photoelastic analysis of resin models to account for stress distribution

Image correlation test to account for model deformity

Study of head injury trauma and consequences

Photoelastic resin model elaboration and image correlation for experimental studies

Numerical model generation with a FEA program using a CAD repaired model

CT scan obtained from a patient

Rubber mold elaboration based on 3D printed models

Numerical model to analyze stress and deformation

Modeling based on CT scan segmentation

Prototype generation through 3D printing

Model cleaning and repair with a CAD software Fig. 5.1 Followed methodology in our study

Study comparisons

Results discussion

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5.3 Materials and Methods Procedures and techniques used in our study shown in Fig. 5.1 are described in the following section.

5.3.1 Design and Generation of the Three-Dimensional Model The experimental and numerical models were obtained through a computerized axial tomography scan, which was exported as DIACOM files (Provided by the Research Center and Biomechanical Lab “CILAB”). Then, the DIACOM files were used to generate a three-dimensional (3D) model through segmentation with the Simpleware Scan IP ©. The 3D model was created using images of all anatomical planes (coronal sagittal and transverse) as shown in Fig. 5.2. Masks were drawn on each layer of images of the bone structures of the cranium. Color was given to each layer to differentiate regions of the cranial structure. The tomography resolution was 1/16 mm between layers allowing to create a high-resolution model. All two-dimensional (2D) layers were stacked in anatomical sequence, and finally, a 3D model was obtained by a Boolean operation. The reconstructed model was exported as a stereolithographic file (STL) to be processed on a CAD, CAE, and 3D printing software. The CAD software subtracted

Fig. 5.2 Reconstruction of a cranium using all three anatomical planes: a transverse, b coronal, c sagittal and d 3D rendering view

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the bone material to produce a cut on the sagittal plane of the complete cranial structure. Closed meshing of surfaces was performed and extruded 3 mm to later be 3D printed (see Fig. 5.3). The resulting model was 3D printed with the use of polylactic acid (PLA) 1.7 mm filament through “Cura Ultimnaker 4.0” software. Figure 5.4 depicts parameters used for printing the model (printing speed was 45 mm/sec, 35% density, and layer height of 0.2 mm.). These parameters allowed a high-printing definition model.

Fig. 5.3 Preparation of the model using Solidworks® : a middle sagittal plane cut, b extruded surface from the cut, c repaired model

Fig. 5.4 Printing parameters for the model

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5.3.2 Model Preparation for the Photoelasticity Test Once the model was printed (Fig. 5.4), a PL-1 resin model (micromesurements) was casted in a silicone-rubber mold. Styrene barriers were used to optimize the mold and reduce the amount of material needed (Fig. 5.5). Our silicone-rubber mold was reinforced with the use of plaster of stone since the resin PL-1 undergoes an exothermic reaction at curing time, which could weaken the mold, see Fig. 5.6. Casting of the resin was performed gradually into the rubber mold to avoid air bubbles, which are detrimental for the photoelastic analysis, see Fig. 5.7. Two CNC cut acrylic pieces (6 mm thick) sealed the resin model. Both had the exact geometry of the cranial vault (Fig. 5.8a). Two bores were done in one of the pieces to introduce a connection through a hose connected to a compressor and a spike connection to a manometer. Care was taken to avoid leaks (Fig. 5.8b). The acrylic piece assembly sealed with silicon is shown in Fig. 5.9. The model assembly was reinforced with the use of screws and nuts as shown in Fig. 5.10.

Fig. 5.5 Construction of the silicone-rubber mold: a mold before optimization, b mold optimized with styrene, c rubber used for the mold, d casted rubber with optimized mold

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Fig. 5.6 Plaster base to protect the mold

Fig. 5.7 Resin PL-1 casting

5.3.3 Model Preparation for Image Correlation Analysis For the correlation analysis, the 3D printed model used for the mold creation was utilized (Fig. 5.4). A white coat of paint was applied on the PLA model, and mottling

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Fig. 5.8 a Cranial vault cut of a 6-mm acrylic piece, b acrylic piece showing the pneumatic connections

Fig. 5.9 Model assembly

was performed with black paint in a stochastic fashion to allow for maximal contrast and measure the deformation by image correlation as shown in Fig. 5.11. After mottling, the same procedure used on the resin model was performed to obtain the final model for the correlation image test (Figs. 5.12b and 5.13).

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Fig. 5.10 Reinforced model with screws

Fig. 5.11 3D printed model prepped with white paint coat and a black mottling

5.4 Photoelastic Study In order to elaborate on the experimental studies, normal pressures at the cranial vault have to be considered. Our tests did not include the meninges (dura, arachnoid, and pia) for simplification since these tissues are too small.

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Fig. 5.12 a Model shows the bores for the pneumatic connections. b Final assembly of the model for image correlation

Fig. 5.13 Final experimental models

This study analyzed the stress fields on the cranial vault after a ICP increase. Stress was visualized through isochromatic stripes; the stripe values depend on the light color issued through its pass of the polariscopic filters. Each stripe represents a constant stress as shown in Table 5.1. To calculate the intensity of stress factor, the following equations were used [8]:

5 Numerical—Experimental Study for the Determination … Table 5.1 Values of the stripe colors spectrum of stress

151

Fringe color

Fringe order

Black

0.00

Gray

0.28

White

0.45

Yellow

0.60

Orange

0.80

Red

0.90

Purple

1.00

Blue

1.08

Blue-Green

1.22

Green-Yellow

1.39

Orange

1.63

Pink-Red

1.82

Purple

2.00

Green

2.35

Green-Yellow

2.50

Red

2.65

Red-Green

3.00

Green

3.10

Pink

3.65

Pink-Green

4.00

Green

4.15

Nominal stress σp =

P×N t

(5.1)

Maximal stress through the stripe range σmax =

N× f t

(5.2)

Factor of stress intensity KI =

σmax σp

(5.3)

where P is the load, N is the stripe order, T is the specimen thickness, F is the photoelastic resin constant given by the manufacturer (250,000 N/m), σ max is the maximal stress, and σ p is the nominal stress.

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Fig. 5.14 Polariscope SSMAJ model

The experimental test used a circular polariscope model SSM.AJ, 060 series (Fig. 5.14). The piece was mounted on the lens center using a cable to avoid view obstruction. A manometer was placed on a polariscope profile to enhance visualization of the applied pressure as shown in Fig. 5.15.

5.5 Image Correlation Study Deformation of the model was measured by image correlation at the region of interest through the applied mottling. However, it was also important to obtain an image sequence or high-definition video to obtain adequate deformation values. Therefore, a video of the test was obtained through a webcam (Logitec C920 Pro) with a resolution of 1080p/30 fps or 720p/30 fps. The camera was placed over a base

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Fig. 5.15 Mounted specimen on the polariscope without applied pressure

Fig. 5.16 Video exported to image correlation software

Fig. 5.17 Surface components: a creation of component and b visualizing of the obtained surface

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to register the exact moment of pressure application; the video was then exported to GOM Correlate® (Fig. 5.16). A surface component was created on the model (Fig. 5.17). This component had values that were modified to obtain a precise reference value by taking the distance of the ordinate axis on the sagittal plane (Fig. 5.18). Finally, deviation labels were created to facilitate the reading of the deformation percentage at the highest affected areas due to the ICP elevation just as illustrated in Fig. 5.19.

Fig. 5.18 Parameter modification of the surface components

Fig. 5.19 Model with deviation labels

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5.6 Finite Element Analysis The surface obtained and shown in Fig. 5.3c was imported to make the numerical model with Autodesk Netfabb® (see Fig. 5.20). The surface geometry of the model was repaired in this software and was then imported to ANSYS Mechanical APDL® (Fig. 5.21). A linear, elastic, and isotropic model was used to characterize the cranial vault. Material properties used are depicted in Table 5.2 [9]. The loads and boundary conditions fixed the model on the external surface, and pressure was applied on the internal edges of the cranial vault as shown in Fig. 5.22. After mechanical properties and boundary restrictions were applied to the model, a fine mesh was applied as shown in Fig. 5.23. The amount of elements and nodes is shown in Table 5.3.

Fig. 5.20 Repaired model in Autodesk Netfabb®

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Fig. 5.21 Surface model imported to ANSYS mechanical APDL® Table 5.2 Mechanical properties for the cranium

Cortical bone Young’s modulus

1.5E + 04 MPa

Poisson’s ratio

0.21

Density

1.500 kg m−3

Fluence resistance

225 MPa

Fig. 5.22 Loads and boundary conditions applied to the model

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Fig. 5.23 Fine mesh on the model

Table 5.3 Number of elements and nodes of the numerical model

Model

Elements

Nodes

Cranial vault

7999

30,377

5.7 Results 5.7.1 Photoelastic Test Results After pressure application to the model, we observed areas of the cranial vault had more stress concentration than others. The parietal and occipital bones had a higher response with an equivalent pressure of 150 mm Hg. After this limit was exceeded, the whole structure experimented a change, although differentiation of the stripes was difficult, and therefore, we centered our analysis on the two mentioned bones as shown in Fig. 5.24. The frontal bone also presented reaction to induced pressure; however, the stripes were indistinguishable due to the small bone thickness compared to the parietal and occipital bones. The graph in Fig. 5.25 depicts calculated values of the maximal stresses to an applied pressure. The occipital bone had a calculated stress of 90 MPa, corresponding to the calculated pressure of 150 mm Hg. The occipital bone has half the stress compared to the parietal (41.686 MPa).

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Fig. 5.24 Photoelasticity test: a occipital bone and b parietal bone 152

MAXIMUM STRESS (MPA)

160

136

140

116

120 90

100 67

80

75

50.83 45.00 41.67 33.33 37.50 25.00

50

60 40

Parietal Bone

57.92

20

0.00 0

0 0

200

400 LOAD (N)

600

800

Fig. 5.25 Applied load graph—maximum stress

5.7.2 Image Correlation Test Both the occipital and frontal bones suffered a deformation when submitted to ICP elevation at the correlation image test; however, the fontal bone shows more deformation. Figure 5.27 depicts a graph showing the deformation of the element as a function of time. Importantly, the frontal bone had no drastic changes as shown with other bones. The cranial vault had no severe deformity at an equivalent pressure of 150 mm Hg as it could be assumed. The corresponding values for the frontal, parietal, and occipital were 1.469, 1.358, and 1.196, respectively (Fig. 5.26).

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Percentage of deformation

Fig. 5.26 Percentage of deformation under a 150 mm Hg pressure

Image correlation test time Fig. 5.27 Deformation percentage graph versus time. Black line (frontal bone), pink line (parietal bone), blue line (occipital bone)

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5.7.3 Numerical Results The numerical analysis of the cranial vault shows higher stress concentration on the frontal and occipital bones (Fig. 5.28). The von Mises value of the frontal bone under 155 mm Hg pressure is 114 MPa, while in the occipital bone the stress was 57 MPa. Under these load conditions, the cranial vault showed a maximum deformation of 0.3 mm between the frontal, sphenoidal, and occipital bones (Fig. 5.29).

Fig. 5.28 von Mises stress results for FEM test

Fig. 5.29 Generated deformation of the numerical model under an ICP of 150 mm Hg

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5.8 Discussion The photoelastic test has shown that the main field stress occurred on the occipital and parietal bone. However, the numerical model displayed a different behavior. The frontal and parietal areas were more affected under the applied pressure. Since the numerical model had a higher stress compared to the photoelastic model, we can establish that the area thickness at the frontal bone is lower compared to the parietal bone. The numerical model has shown deformity results due to flexion at the frontal bone area and due to extension at the occipital area. These results matched with the results obtained with the image correlation test. We could establish that the image correlation test includes the numerical and photoelastic results assuring that the maximal stress is located at the frontal bone, followed by the parietal bone.

5.9 Conclusions Through the knowledge of engineering and medicine, the present study focused on testing the mechanical behavior of the cranial vault under conditions of severe ICP. Research of the internal behavior of the cranial vault is crucial for the development of security devices and even cranial cap prosthesis. However, it was shown that to recreate intracranial conditions on numerical and experimental tests, it is essential to have knowledge of its components. This analysis yielded tools for the study of the idiopathic IH, a condition in which its cause is still unknown. We believe that this study could help the physician to understand furthermore which areas are compromised in such pathology. This methodology represents a good option since it is not invasive, and anatomical models were obtained through segmented images, using fast and efficient tools used in the developing of 3D prototype generation. Finally, it has been established that a team effort between engineering and medicine sciences is complementary and could yield the development of new devices or surgical techniques aimed to enhance the patient’s quality of life [10–15].

References 1. Moore, K.L., Dalley, A.F., Agur, A.M.R.: Anatomía con orientación clínica. Wolters Kluwer, Phila (2013) 2. Mascarenhas, S., Vilela, G.H.F., Carlotti, C., et al.: The new ICP minimally invasive method shows that the Monro Kellie doctrine is not valid. Intracranial Press Brain Monit XIV (2012). https://doi.org/10.1007/978-3-7091-0956-4_21

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3. Rodríguez, B.G., Rivero, G.M., Guitiérrez, G.R., et al.: Conceptos básicos sobre la fisiopatología cerebral y la monitorización de la presión intracraneal. Neurol (2015). https://doi.org/ 10.1016/j.nrl.2012.09.002 4. Gilo, A.F., Herrera, M.A., Anciones, B.: Hipertension intracraneal aguda. Neurol (2010). https://doi.org/10.1016/S0213-4853(10)70044-X 5. López, F.P., Lubillo, M.S.: Avances en el traumatismo craneoencefálico. Emerg 21, 433–440 (2009) 6. Instituto Mexicano del Seguro Social: Intervenciones de enfermería en la atención inicial de pacientes con traumatismo craneoencefálico grave en urgencias. Guias Pract. Clin. (2018). http://imss.gob.mx/profesionales-salud/gpc. Accessed 27 April 2019 7. Carrillo, E.R., Meza, M.J.M.: Trauma craneoencefálico. Mex Rev. Mex. Anest. 38(Suppl: 3), 433–434 (2015) 8. Dalley, J.W., Riley, W.F.: Experimental stress analysis. McGrraw Hill, N Y (2004) 9. Asgharpour, Z., Baumgartner, D., Willinger, R., et al.: The validation and application of a finite element human head model for frontal skull fracture analysis. J. Mech. Behav. Biomed. Mater. (2013). https://doi.org/10.1016/j.jmbbm.2013.02.010 10. Moreno, G.P., Beltrán, F.J.A., Yescas, H.J.A., et al.: Identification of stress fields in a customized mandibular reconstruction based on a photoelastic model. J. Craniofac. Surg. (2019). https:// doi.org/10.1097/SCS.0000000000005901 11. Beltrán, F.J.A., Hernandez, G.L.H., Cuevas, A.J.L., et al.: Design and manufacturing of a temporomandibular joint (TMJ) prosthesis for mandibular bone necrosis using the finite element method. Eng. Des. Appl. Adv. Struct. Mater. (2019). https://doi.org/10.1007/978-3319-79005-3_27 12. Beltrán, F.J.A., Picco, D.I., Bantle, C.I., et al.: Design and characterization of a mandibular prosthesis prototype by hemimandibulectomy. Eng. Des. Appl. Adv. Struct. Mater. (2019). https://doi.org/10.1007/978-3-319-79005-3_22 13. Moreno, G.P., Beltrán, F.J.A., Hernandez, G.L.H., et al.: Selección de material biocompatible de bajo costo para manufactura de prótesis maxilar personalizada. Dyna Ing. Ind. (2018). https:// doi.org/10.6036/8633 14. Moreno, G.P., Beltrán, F.J.A., Hernández, G.L.H., et al.: Uso de modelo fotoelástico para la detección de zonas estructurales críticas en el diseño de una prótesis maxilofacial personalizada. Dyna New Technol. (2017). https://doi.org/10.6036/NT8286 15. Camacho, T.N., Beltrán, F.J.A., González, R.M., et al.: Numerical study in biomodels of maxillofacial prosthesis (cancer and osteonecrosis cases). Des. Comput. Mod. Eng. Mater. Adv. Struct. Mater. (2014). https://doi.org/10.1007/978-3-319-07383-5_5

Chapter 6

Numerical Simulation of Cranial Distractor Components Using Passive and Generative Design Juan Alfonso Beltrán-Fernández, Erik Omar Alvarado-Alcántara, Juan Carlos Hermida-Ochoa, Edgar Alfonso Figueroa-Rodríguez, Alejandro David González-Peña, José Enrique Rodríguez-Miramar, Luis Héctor Hernández-Gómez, Pablo Moreno-Garibaldi, and Juan Luis Cuevas Andrade Abstract Today, assisted design software offers more capacity and iterations, and its methodology optimally solves geometries with enough rigidity and weight, keeping their specific characteristics desirable for some design objectives, and thus

J. A. Beltrán-Fernández (B) · E. O. Alvarado-Alcántara · E. A. Figueroa-Rodríguez · A. D. González-Peña · J. E. Rodríguez-Miramar · L. H. Hernández-Gómez · P. Moreno-Garibaldi · J. L. C. Andrade Instituto Politécnico Nacional, Escuela Superior de Ingeniería Mecánica y Eléctrica—Sección de Estudios de Posgrado e Investigación Edificio 5, Unidad Profesional Adolfo López Mateos “Zacatenco”, Col. Lindavista, 2do Piso, 07738 Ciudad de México, Mexico e-mail: [email protected] E. O. Alvarado-Alcántara e-mail: [email protected] E. A. Figueroa-Rodríguez e-mail: [email protected] A. D. González-Peña e-mail: [email protected] J. E. Rodríguez-Miramar e-mail: [email protected] L. H. Hernández-Gómez e-mail: [email protected] P. Moreno-Garibaldi e-mail: [email protected] J. L. C. Andrade e-mail: [email protected] J. C. Hermida-Ochoa Centro de Investigación y Laboratorio de Biomecánica, Carmen #18, Chimalistac, San Ángel, 01070 Ciudad de México, Mexico e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 J. A. Beltrán-Fernández et al. (eds.), Design and Simulation in Biomedical Mechanics, Advanced Structured Materials 146, https://doi.org/10.1007/978-3-030-65983-7_6

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achieving originality, affordable functionality and reproducibility through manufacturing systems such as three-dimensional manufacturing. For this reason, the present study uses a computerized generative design method to optimize the main components of a cranial distraction system aiming to perform a geometric optimization of the original components and preserving the actual mechanical performance in spite of reducing the weight of the distractor components. By the use of commercial software packages such as PTC Creo Parametric©, PTC Creo Simulate©, Frustum©, Autodesk fusion 360°©, and Solid edge©, several generative proposals were evaluated. These evaluations were performed under load and boundary in order to preserve the cranial distractor function and optimize the amount of material used by the additive manufacture technique. Keywords Generative design · Distractor · Cranial · Additive impression · Additive manufacturing · Optimization

6.1 Introduction Generative design has significantly impacted architecture and could mean a change in the paradigm of the design process and other disciplines. This is formally an exploration tool, however in other fields like computer-assisted manufacturing it yields the possibility of materialize prototypes, not only limited to this but also with the potential for other disciplines such as the medical field by the design of devices. In the present study, a generative design was applied on a cranial distractor device in order to enhance its manufacturing qualities like reduction of its weight, a better rigidity modulus, and generation of possible viable proposes for its production serving as a guide for its fabrication through additive or subtracting manufacturing technique, and also account for those models that cannot be effectively reproduced by any other method of inverse engineering.

6.1.1 Fundamentals of the Generative Design Generative design represents the evolution of the technological development of computers such as software. These agents are becoming more robust for the solving of complex problems and are tools that our study was based on. Generative design is the result of collaborative, inter, and multidisciplinary work [1] where the engineer and designer points of view converge aiming to solve a concrete problem, its origins emerge from theoretic basis that have been redefined through a few decades [2], It’s inspiration has been through the observation of nature, the evolution and adaptation of species, and the growth of plants [3]. The application of the conceptual enhancement of the species is reflected in the multiplicity of proposes that generative design yields thanks to the application of algorithms programmed for this purpose.

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Tedeschi [4] states the fact that the generative design cannot be defined by a computer-assisted design (CAD) software. Instead it actually belongs more to an epistemological reclassification known as algorithm assisted design (AAD) which allows either the engineer or designer to use this tool of design instead of using a tool to only document an idea or concept conceived as the author of any design could do by the use of a CAD software. Features that make the generative design unique are: (1) incorporated algorithms of the evolutive design and (2) topologic optimization, although not limited to this one [5]. Feature number 1 offers the generation of multiple proposals or iterations with high possibility to be transformed from a digital to a tangible state, therefore viable for their materialization through additive or subtractive manufacturing methods. From the start the algorithm has the capacity to specify at least a desired manufacturing process. Feature number 2 allows every proposal to be subjected to a formal optimization process assisting to reach the objective of a generative design study.

6.2 Materials and Methods In our study, we used a generative design module software, Autodesk® Fusion 360°® to perform the design process as illustrated in Fig. 6.1. To obtain results by generative design, limited and well-defined parameters are needed. User requirements have to be considered, in this case a medical surgeon. Parameters implied directly in the present redesign for the cranial distractor are shown in Table 6.1. The principles of the design dictate that the problem has to be structured and analyzed; also, functionality and characteristics of the object have to be defined [7]. The generative design method helps to integrate the object’s framework [8] and then it will be matched within the Autodesk® Fusion 360® software, see Fig. 6.2. Once the client’s requirements have been defined it is important to emphasize at which load the object will be subjected during normal usage conditions and also its

Fig. 6.1 Generative design process

166 Table 6.1 Design requirements by the surgeon [6]

J. A. Beltrán-Fernández et al. Requirements by the surgeon

Specifications

System stability

Deformation must be less to 1 mm

Controlled distraction

Distraction mechanism vector yields 1 mm daily

Light

Weight must be 800 g or less

Limited finish and sharp edges Rounded edges

Fig. 6.2 Generative design structure [8]. Reprinted with permission from Springer Nature publishers

desirable weight. A characteristic of the generative design is that it could emerge from an existing geometry obtained from a parametric or surface-based modeling software, or the geometry can be created from scratch. An important objective of this study is to generate the structure that acts like the seed or base on which a geometry will be constructed by algorithm generation. The present study will start from the model assembly of a cranial distractor, called “Arch support, propose 2” see Figs. 6.3 and 6.4. The generative method used in our study was the Fusion 360® approach since it offers good functionality for the generative design. There are other options for the same topographic optimization which can obtain similar results, but a substantial difference of the generative design is that more variables are taken into account including construction method, materials, etc. Furthermore, the generative method offers a wide range of iterations that ultimately helps to take decisions about the most optimal proposal, which is the main focus of our investigation. As a result of the topologic optimization only one proposed design was used. An organic type geometry resulted after the algorithms were applied to the original configuration. The functionality of the generative design was only active in two modes: (1) on a commercial version of 30 day-trial, and (2) on Autodesk accounts that have not been activated as educative versions. Account licenses can be as a monthly version or annual renewal. To start a new study of generative design we need to access the

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Fig. 6.3 Cranial distractor and arch-support [6]. Reprinted with permission from Springer Nature publishers

Fig. 6.4 Views and details from the arch-support

work space of Autodesk® Fusion 360® Generative Design which can be found on the upper-left corner of the window, see Fig. 6.5. At this point, the work flow is very similar to the design proposed by Krish [9] where the designer modifies the model features and the restrictions to generate the iterations, see Fig. 6.6. Once the program is in the environment frame, tools are activated and buttons will be selected from left to right, see Fig. 6.7. 1. A generative study is performed 2. Model editing: Strongly related to point 3; geometry is defined in this mode

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Fig. 6.5 Access to the generative design module Fig. 6.6 Generative design process proposed by Krish [9]. Reprinted with permission from Springer Nature publishers

Fig. 6.7 Tools from the work environment of the generative design in Autodesk® Fusion 360®

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Fig. 6.8 Localizing the critical structural points. Initial formal synthetization

Fig. 6.9 Red areas: areas where no geometry will be constructed. Purple areas: connection elements where material could be constructed

3. Define the construction or the areas where construction is or not possible [8]. It is defined as the construction of the model skeleton. The software requires at least two solid bodies, and these can be simple Euclidian bodies or any type of geometry, see Fig. 6.8. The arch-support, even when representing a well-defined geometry, required a partition in sections in the indicated areas to be able to process as a generative design (see Fig. 6.9): (a) Sections where the created surface has to be untouched due to the fact they interact with other modules or mechanisms, or spaces where the constructed geometry could interfere with other components. (b) Areas where morphogenesis starts, these could be two bodies of any shape that defines this is a genetic model [9]. 4. Structural fixation points of the piece are defined (fixed, axis, or sliding), in the arch-support propose 2 the elements or faces are defined as fixed, and an icon displaying a lock appears on the faces where the command was applied. 5. Loads are defined (see Figs. 6.10 and 6.11) on the geometry faces, direction, and magnitude. Also, the direction of gravity according to the orientation of the piece to be optimized was included. 6. The generative design study has two objectives: (a) The security factor is established when the mass is maximized. (b) When stiffness is maximized along with the security factor, the mass is also defined in the piece. The selection of these parameters gives meaning to the study, that is: Increasing the stiffness through

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Fig. 6.10 Types of structural loads

Fig. 6.11 Definition of structural loads

the formal exploration given by the algorithms yielded by the explained parameters and reduce the objects mass through the same algorithms that will form the connections between the green areas to be preserved, see Fig. 6.12. 7. Once the manufacturing methods are established it is important to highlight that the generative design it’s not only to be used with additive manufacturing since there are other methods such as subtractive numerical control with 2 to 3 axis in which parameters could be established for a cutter, see Fig. 6.13.

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Fig. 6.12 Objective selection for the generative design Fig. 6.13 Definition of manufacturing method

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It is important to mention that even when the program is designed to manufacture any purpose with computational methods, the generated iterations can be applied in other traditional methods and without the use of the numerical equipment. 8.

Define the possible materials to be used in manufacturing the object, more than one can be selected, see Fig. 6.14. 9. The program performs a pre-verification where we observe if the necessary information is complete or some adjustments are needed, see Fig. 6.15. 10. A previous visualization of the piece is generated, see Fig. 6.16. 11. Once the parameters have been established a fast test is run to generate the iterations. It is important to understand that the processing is made in the cloud and hence it has to be uploaded. Fig. 6.14 Definition of the material for the generative design study

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Fig. 6.15 Confirmation message stating that the parameters are completed for the study to be performed

Fig. 6.16 Formal pre-visualized piece

12. The status of the study has to be activated and the iterations can be in process, completed, or converged and the status will read “completed.” 13. Access to the different iterations resulted from the different tests previously defined are shown in Fig. 6.15 and comprise: miniature (1), properties (2) result dispersion graph (3), view in table (4); these types of display is very useful to choose which option is optimal, see Fig. 6.17. Fig. 6.17 Visualizing of results form a generative design study

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Fig. 6.18 Original piece previous to the study

6.3 Original Piece Analysis As we have previously mentioned, the design requirements were plotted in Table 6.1 by Martinez, and so the outcome of that is a tailored device (Fig. 6.18) which is subject of improvements that is why the aim of this paper is to find that the proposed piece (arch-support, proposal 2) would offer a well balance between its weight and structural stiffness. The distractor requires a left and right version of the above-mentioned piece, and both parts represent 40.33% of the total weight of the assembly, expressed in a mass with a Ti6A1-4 V alloy (403.7 gm, depicted in Table 6.2), this piece has the largest mass in respect with the other components and because of that, it is the component that will be processed in the generative design study. Another parameter to be considered is the distractor’s strength under normal conditions, the necessary force obtained for the arch-support proposal 2 used for the average medium stress was 37.7 N [6].

6.4 Simulation Results from the Generative Design Methodology of the generative design inside Fusion 360® establishes that one of the principal objectives is to reduce the mass and increase the stiffness and therefore the

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Table 6.2 Physical properties of the cranial distractor components Component

Mass (g)

Number of pieces

% mass

Component mass (g)

1

Arch-support, proposal 2

81.426

2

40.3

162.9

2

Vertical bar

26.721

2

13.2

53.4

3

Cranial fixing screw

11.578

4

11.5

46.3

4

Anchoring screw

22.809

2

11.3

45.6

5

Central bar

38.475

1

9.5

38.5

6

Horizontal tensional bar

9.993

2

5.0

20.0

7

Tensor support

6.736

2

3.3

13.5

8

Tensor mechanism

5.518

2

2.7

11.0

9

Screw ISO 4762 M3 × 6 hex

0.907

4

0.9

3.6

10

Tensor

1.623

2

0.8

3.2

11

Screw ISO 4026 M4 × 20 opresor

1.04

2

0.5

2.1

12

Tensor nut

0.714

2

0.4

1.4

13

Screw ISO 4026 M34 × 4 opresor

0.345

2

0.2

0.7

14

Screw ISO 4026 M4 × 4 opresor

0.345

2

0.2

0.7

15

Screw ISO 4027 M3 × 8 opresor

0.204

2

0.1

0.4

16

Screw ISO 4028 M4 × 5

0.193

2

0.1

0.4

Material: Titanium 6Al-4 V

Total: 403.7

Bold represents the piece with the highest percentage of mass compared to the other components

reduction of weight and increase in stiffness in the components have to be monitored through the iterations. Four test runs of generative studies generated 48 outcomes, all suitable for manufacturing through additive technique using materials like aluminum, titanium, and the titanium alloy 6A1-4 V. However, it is necessary to analyze each one and select the one that satisfies our proposed objectives. Peculiarly, iterations showed that in spite the general requirements for the components were well defined, some iterations failed in comparison with others and not necessarily in sequential order, that is, one can get a good result out of a bad or a good previous iteration and for this very reason several iterations are needed before we reach the optimal result. This is reflected in our results in which we show that study number 1 failed, but 2 was successful and generated 16 iterations. Studies 3,4, and 5 failed, but 6,7, and 8 generated 8, 12, and 12, respectively, see Fig. 6.19.

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Fig. 6.19 Formal results from study 2

Table 6.3 Numerical results from generative study 2

6.4.1 Results In the following, the results of the different generative design studies are presented using the parameters depicted in Table 6.1. In order to select a suitable propose, values obtained and depicted on the green cells need to be analyzed and compared with those depicted in the gray cells that represent Martinez optimized results. Results shown in red cells are those that did not accomplished the ideal optimization set by the desired parameters, while those in yellow represent the ones that are closer to the original values of the studied proposal, see Table 6.3. From the results of the first successful study (study 2) we see a prominence of red cells which indicates that the results are not optimal for the design purpose in terms of weight and rigidity.

6.4.2 Results from Study 6 Study 6 shows poor optimization of the components and values remain very similar to the original ones, also with is a reduction of stiffness in all proposals (Fig. 6.20; Table 6.4).

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Fig. 6.20 Formal results from study 6

Table 6.4 Numerical results from the generative study 6

6.4.3 Results from Study 7 Results shown in study 7 show an incipient optimization of parameters, specially related to stiffness, although the mass remains the same as that of the original proposal (Fig. 6.21; Table 6.5).

Fig. 6.21 Formal results from study

Table 6.5 Numerical results from study 7

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Fig. 6.22 Formal results from study 8

Table 6.6 Numerical results from study 8

6.4.4 Results from Study 8 Results from study 8 show optimized parameters related to mass, stress deformity, and the security factor; for this reason, iterations 2, 3, 6, 7, 10, and 11 are the best options for production (Fig. 6.22; Table 6.6).

6.5 Conclusions The generative design process is indeed a new way to obtain a useful design when diverse proposals are involved in the search for the final product to be produced. This is of special interest and utility when there are limitations in the manufacturing process. Although the generative process is not the only option to generate proposals for additive manufacturing, it could potentially help and guide any proposal to be produced in any type of traditional manufacturing method. The work flow of parametric design programs aids to understand the work flow of generative design inside Autodesk® Fusion® 360. However, this can confuse the designer without a solid foundation knowledge of the finite element process since it comprises familiarity with the iteration generation process needed for each proposal. Results obtained by this process also help to understand the best method to place the fixation points on the piece, load direction, and everything related to the finite element process that allows the designer to choose the best settings for the algorithm generation and optimal generation of proposals.

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The obtained proposal by this generative method could be manufactured and evaluated by a numerical validation process which is the traditional way to validate the viability of the piece to be produced. The main advantage of this novel design method is that it strengthens the weak points of those engineers and designers during their training period and in a real collaborative scheme of work. For the designer, this method helps to have validated and viable proposals, and for the engineer it allows to obtain esthetic proposals (visually attractive). In both cases, these proposals as susceptible to be manufactured in any traditional method but no limited to them. Three-dimensional impression and subtractive manufacturing are also an option once the generative design study has been effectively performed. Among other advantages to this generative method we mention the following: • • • •

Originality Reduced weight Increased stiffness Reduction of manufacturing costs (material saving through additive manufacturing process) • Generation of novel shapes • Variety of already validated proposals • Formal search (esthetic) of a design proposal The use of this method is a real application of Industry 4.0 concept since iterations use artificial intelligence as shown in studies 2, 6, 7, and 8. Also the use of 3D printers to obtain 3D objects reassert this concept.

References 1. Cortés, E., Cruz, A.: Generative design as tool for social innovation : a methodological approach. Back to Futur [ICDHS 10th + 1 Conf Proc B., 44–8 (2015) 2. Stiny, G.: Pictorial and Formal Aspects of Shape and Shape Grammars on Computer Generation of Aesthetics Objects. Springer Basel AG (1975), 419 p 3. Bentley, P., Corne, D.: Creative Evolutionary Systems. Creative Evolutionary Systems. Morgan Kaufmann (2002), 576 p 4. Tedeschi, A.: AAD Algorithms-Aided Design : Parametric Strategies Using Grasshopper. Le Penseur (2014), 15–30 p 5. Brown, K.N., McMahon, C.A., Sims Williams, J.H.: Features, aka the semantics of a formal language of manufacturing. Res. Eng. Des. 7(3), 151–172 (1995) 6. Beltrán-Fernández, J.A., Martínez-Paredes, J., González-Rebattú, M., Hernández-Gómez, L.H., Ruíz-Muñoz, O.: Customization and numerical simulation of a cranial distractor using computed axial tomography (CAT). In: Öchsner, A., Altenbach, H. (eds.) Properties and Characterization of Modern Materials. Advanced Structured Materials, vol. 33. Springer, Singapore (2017). https:// doi.org/10.1007/978-981-10-1602-8_30 7. Bagassi, S., Lucchi, F., De Crescenzio, F., Persiani, F.: Generative design: advanced design optimization processes for aeronautical applications. In: 30 Congress of the International Council of the A [Internet] (2016), p. 7. Available from: http://www.icas.org/ICAS_ARCHIVE/ICA S2016/data/papers/2016_0720_paper.pdf

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8. Li, H., Lachmayer, R.: Generative Design Approach for Modeling Creative Designs. In: IOP Conference Series: Materials Science and Engineering (2018), p. 7 9. Krish, S.: A practical generative design method. Comput. Des. 43, 88–100 (2011)

Chapter 7

Tridimensional Design and Printing Techniques to Obtain Personalized Prosthetic Components for Specific Cases Involving Bone Defects Juan Carlos Hermida-Ochoa, Juan Alfonso Beltrán-Fernández, Juan Luis Cuevas Andrade, Luis Héctor Hernández-Gómez, Teresa Berenice Uribe-Cortés, and Pablo Moreno-Garibaldi Abstract This work proposes and demonstrates the application of Biomechanics to make printed designs in 3D systems, in order to improve customized prosthetic components. The study provides solutions that benefit patients with orthopedic area defects. In addition, the publication of this work will increase the scientific production and international recognition of the National Polytechnic Institute. Keywords 3D printing · Bone · Stereolithographic models · Prosthesis · Orthopedic

J. C. Hermida-Ochoa (B) · T. B. Uribe-Cortés Centro de Investigación y Laboratorio de Biomecánica, Carmen # 18, Col. Chimalistac San Ángel, 01070 Mexico City, Mexico e-mail: [email protected] T. B. Uribe-Cortés e-mail: [email protected] J. A. Beltrán-Fernández · J. L. C. Andrade · L. H. Hernández-Gómez · P. Moreno-Garibaldi Instituto Politécnico Nacional—Escuela Superior de Ingeniería Mecánica y Eléctrica—Sección de Estudios de Posgrado e Investigación Edificio 5, Unidad Profesional Adolfo López Mateos “Zacatenco” Col. Lindavista, 2do Piso, 07738 Mexico City, Mexico e-mail: [email protected] J. L. C. Andrade e-mail: [email protected] L. H. Hernández-Gómez e-mail: [email protected] P. Moreno-Garibaldi e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 J. A. Beltrán-Fernández et al. (eds.), Design and Simulation in Biomedical Mechanics, Advanced Structured Materials 146, https://doi.org/10.1007/978-3-030-65983-7_7

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7.1 Introduction Orthopedic surgery often requires the use of implants to solve problems related to bone loss caused by accidents or pathologic conditions like malignant bone lesion or fractures. Generic implants are available worldwide to solve and treat these problems. However, they often cannot be fitted in disrupted bone in which its geometry has been compromised due to the complexity of a fracture or particular bone destruction and often represents a challenge since bone healing depends among other factors such as age and metabolic, but more importantly on the stability achieved after a particular lesion has been fixed with a particular system like plates and other devices [1–6]. Custom-made implants are available for joints like knee and hip and other joints and offer good treatment for fractures and other bone defects but many are not readily available worldwide and their cost are beyond reach of some patients. The use of tomographic studies allows to obtain precise three-dimensional geometries of the bones and their possible lesions by means of segmentation and reconstruction of a particular anatomical region that can be replicated virtually. Characterization of a particular region that has been damaged allows for a comprehensive understanding of the bone defect and allows the customization of novel implants that could conform to a certain geometrical defect whatever its cause. The advent of three-dimensional printing today offers a myriad of possibilities to obtain geometries only possible to obtain in the past by the use of CNC and other manufacturing techniques. A segmented and reconstructed area with damage at the bone tissue can be printed in order to have a perfect three-dimensional understanding of the often-complex pattern of fractures or tumoral areas. It is only logical to think that by the same means engineers and surgeons can make decisions about what type of implants might be ideal for a particular defect and also help in the design of new and customized geometries that can potentially be materialized as implants. Therefore, it is only desirable that a 3D printer can be used to produce implants that are tailored to a certain lesion. However, an important limitation is the few available printable materials which are suitable for implantation. Mainly most implants used today are made of metal allows like cobalt-chrome allows, and there are just a few industrial 3D printers capable to print them and the operational cost is very high. The other problem is that printed metals are often not certified to be implanted in a human body due to the lack of purity needed to assure acceptable biocompatibility and even optimal mechanical performance. In spite of this limitation, 3D printing could represent a good start in the path to design and develop a new range of customized implants to offer treatment options specially in complicated cases. Our Center of Investigation and biomechanics laboratory in conjunction with the Instituto Politécnico Nacional designed a method to design and produce geometrically viable implants tailored to a specific case of bone with the objective to demonstrate that 3D printing techniques can be used to customize devices aimed to treat bone defects. An implant tailored for a case of osteosarcoma in a 6-year-old child was produced by our method and then mechanically tested to account for its mechanical viability before implantation. Our implant was manufactured in PMMA, a polymer

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widely used today as a surgical bond for other metallic implants due to its ideal material properties and high biocompatibility [7–13].

7.2 Materials and Methods A clinical case of our population was selected for scanning, segmenting prototyping, and producing an implant aimed to surgically treat a patient. The selected patient was a 16-year-old boy with left hip osteosarcoma that has destroyed the bone at the superior portion of the acetabulum and the femoral head. The patient’s surgeon required our service to elaborate a viable implant to allow the patient to bear his own weight and walk during a period of 2 years previous the implantation of a definitive metal implant once he reached skeletal maturity at 18 years of age (Fig. 7.1).

7.2.1 DICOM Images The patient was subjected to a CT scan of the pelvis without contrast. The scan was performed at high resolution of 0.625. DICOM images, a universal format for medical images, were obtained from the scanning service and they were analyzed in the scan

Fig. 7.1 Sequential process of segmentation and printing of the models

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Fig. 7.2 Mask definition of each anatomical section to be reconstructed

viewer MicroDicom (open source) to account for resolution and to corroborate that the whole sequence was present.

7.2.2 Segmentation DICOM images in a sequential order typically represent a complete CT scan study of a particular anatomical area. Segmentation is the process where these images are stacked in a sequential order and processed by a special software to obtain a threedimensional image of the scanned area. Our team used the 3D slicer software (open source) to obtain a reconstructed image of the whole pelvis of our patient. Manual cleaning of the model is important due to the fact that artifacts can be present in the images; therefore, the operator needs to be familiar with the anatomy of the particular area. Images are masked with colored areas to define anatomical sections of interest and the software reconstruction is based on these slices (Fig. 7.2). The finished model of the hip was then exported in the stereolithographic format (STL).

7.2.3 3D Models The STL hip model was exported to a CAD software (Rhinoceros) where the model was cleaned of redundancies and noise artifacts. After these steps the model is ready for the 3D simulation and printing (Fig. 7.3).

7.2.4 Printing the 3D Models The cleaned hip models were imported into the zortrax z suite software and a simulation was completed. Proper supports and position were adjusted and the material

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Fig. 7.3 Reconstructed model from segmentation after it was exported to an STL format

Fig. 7.4 To the left, simulation of the acetabulum and a section of the proximal femur based on the STL segmented model ready to be printed. To the right printed models

selection followed. We selected Z-Ultrat from zortrax which is an ABS following the recommended settings for the used material the model was printed (Fig. 7.4).

7.2.5 Design and Printing of the Implant Prototype Based on the femur and acetabulum geometry of our 18-years old patient we designed two implant prototypes aiming first to replace the geometry of the femoral head with

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Fig. 7.5 CAD design of the femoral head and the acetabular roof components

Fig. 7.6 Printed components for femur and acetabulum

a spherical shape based on similar dimensions to the contralateral femur which was intact. Secondly, we designed a prototype based on the missing roof of the acetabulum in order to keep the femoral sphere prototype in place and allow mobility and weight bearing. Both designs were made in rhinoceros and posteriorly printed in our 3D printer using an ABS-based material (Figs. 7.5 and 7.6), respectively.

7.2.6 Production of the Definitive Implants Once the hip implants were printed these were embedded in silicon rubber (P-53) and left to cure to obtain molds of their geometry, see Fig. 7.7.

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Fig. 7.7 Silicon rubber molds were opened in half and a mixture of surgical PMMA was mixed according to the manufacturer instructions (Eurofix)

7.2.7 Mechanical Testing of the Implants Obtained PMMA models were mounted in a custom-made adapter and anatomically mounted in a multiaxial servo hydraulic joint simulator (VIVO AMTI). This machine can simulate virtually all movements and loads produced at different joints of the human body by the use of ISO waveforms. Implants were encapsulated in a chamber with bovine calf serum as lubricant at a 37 °C constant temperature, see Fig. 7.8. An ISO hip waveform was used to simulate human gait at 2 Hz and using an axial load of 460 N which matched the subject weight. A total of 106 cycles were completed and components retrieved from the simulator.

7.3 Results During the mechanical test, the behavior of the waveform feedback showed good conformity of the prescribed wave as compared with the feedback suggesting a good geometrical conformity of both implants when the joint movements took place gradually (Fig. 7.9). A linear penetration of the femoral head into the acetabular model of 0.17 mm was registered in the z-axis suggesting a linear wear five times lower compared to polyethylene acetabular cups which are gold standard implants in hip replacement (Fig. 7.10). Both head and acetabular articular surfaces showed a mirror like polishing finish, no visual pitting was observed after the test and structural integrity of both models was preserved (Fig. 7.11). After the mechanical test was concluded, both models were sterilized and surgically implanted in the patient satisfactorily.

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Fig. 7.8 Figure from left to right: the anatomical mounting of the hip components and posterior encapsulation of the mounted components for mechanical testing

Follow up of the patient to account for durability and function will be needed and subjected to a new study.

7.4 Conclusions Orthopedical surgery requires devices in order to treat some musculoskeletal conditions such as bone loss due to trauma or tumoral lesions. Patients of developing countries are typically under financial hardship and thus some devices are out of reach to complete their treatment. It is necessary to develop alternatives to the available medical devices often produced in other developed countries in order to offer accessible solutions for this kind of population. The advent of 3D printing represents a good tool to aid in the design and production of new devices that offer new alternatives to more expensive components. Our team in CILAB in collaboration with the IPN have created a system for the design and production of new implants that could potentially benefit our population of patients. Our technique offers engineers and clinicians the opportunity to create new geometries that can geometrically adapt

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Applied Load (Fz) 50 -50

Load N

-150 -250 -350 -450 -550

One gait cycle/1 Hz

Displacement (mm)

Fig. 7.9 Figure shows the curves during the mechanical test showing conformity of the joint surfaces

1.5 1 0.5 0 -0.5 -1 -1.5 -2 -2.5 -3

Z AXIS DISPLACEMENT – HEAD PENETRATION

One gait cycle/1 Hz

Fig. 7.10 Figure depicts the progressive penetration of the femoral head into the femoral component of around 0.3 mm (cold flow)

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Fig. 7.11 Mirror like finish of both surfaces after completion of the test where no noticeable pitting or gross wear was observed (from left to right acetabular and femoral head implants)

to bone lesions. The use of inexpensive and biocompatible materials such as surgical PMMA offers a good alternative for the construction of implants. We believe that our collaboration ignites a myriad of possibilities to create an internal design and production line of devices for orthopedic use. The fact that we have access to a state-of-the-art testing machine is also a remarkable tool to validate our devices and assure the mechanical and structural viability of those. More studies need to be done in order to standardize our system of design and production and yield a real benefit for our hospitals and institutions and help the patient to have access to treatments that will allow them a better quality of life without further stressing their economical hardship.

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References 1. Baker, C.E., Moore-Lotridge, S.N., Hysong, A.A., et al.: Bone fracture acute phase response—a unifying theory of fracture repair: clinical and scientific implications. Clinic Rev. Bone Miner. Metab. 16, 142–158 (2018). https://doi.org/10.1007/s12018-018-9256-x 2. Kostenuik, P., Mirza, F.M.: Fracture healing physiology and the quest for therapies for delayed healing and nonunion. J. Orthop. Res. 35, 213–223 (2017). Published online 2016 Dec 19. https://doi.org/10.1002/jor.23460 3. Loi, F., Córdova, L.A., Pajarinen, J., Lin, T.H., Yao, Z., Goodman, S.B.: Inflammation, fracture and bone repair. Bone 86, 119–130 (2016). Published online 2016 Mar 2. https://doi.org/10. 1016/j.bone.2016.02.020 4. Meling, T., Harboe, K., Enoksen, C.H., Aarflot, M., Arthursson, A.J., Søreide, K.: Reliable classification of children’s fractures according to the comprehensive classification of long bone fractures by Müller. Acta Orthop. 84, 207–212 (2013) 5. Tian, L., Tang, N., Ngai, T., Wu, C., Ruan, Y., Huang, L., Qin, L.: Hybrid fracture fixation systems developed for orthopaedic applications: a general review. J. Orthop. Translat. 16, 1–13 (2019). Published online 2018 Jul 21. https://doi.org/10.1016/j.jot.2018.06.006 6. Einhorn, T.A., Gerstenfeld, L.C.: Fracture healing: mechanisms and interventions. Nat. Rev. Rheumatol. 11, 45–54 (2015). Published online 2014 Sep 30. https://doi.org/10.1038/nrrheum. 2014.164 7. Yang, J., Zhang, K., Zhang, S., Fan, J., Guo, X., Dong, W., Wang, S., Chen, Y., Yu, B.: Preparation of calcium phosphate cement and polymethyl methacrylate for biological composite bone cements. Med. Sci. Monit. 21, 1162–1172 (2015). Published online 2015 Apr 23. https://doi. org/10.12659/msm.893845 8. Dall’Oca, C., Maluta, T., Cavani, F., Morbioli, G.P., Bernardi, P., Sbarbati, A., Degl’Innocenti, D., Magnan, B.: The biocompatibility of porous vs non-porous bone cements: a new methodological approach. Eur. J. Histochem. 58, 2255 (2014). Published online 2014 Jun 23. https:// doi.org/10.4081/ejh.2014.2255 9. Oonishi, H., Akiyama, H., Takemoto, M., Kawai, T., Yamamoto, K., Yamamuro, T., Oonishi, H., Nakamura, T.: The long-term in vivo behavior of polymethyl methacrylate bone cement in total hip arthroplasty. Acta Orthop. 82, 553–558 (2011) 10. Pauksch, L., Hartmann, S., Szalay, G., Alt, V., Lips, K.S.: In vitro assessment of nanosilverfunctionalized PMMA bone cement on primary human mesenchymal stem cells and osteoblasts. PLoS ONE 9(12), 0114740 (2014) 11. Dall’Oca, C., Maluta, T., Micheloni, G.M., Cengarle, M., Morbioli, G., Bernardi, P., Sbarbati, A., Degl’Innocenti, D., Lavini, F., Magnan, B.: The biocompatibility of bone cements: progress in methodological approach. Eur. J. Histochem. 61, 2673 (2017) 12. Lee, S.H., Tai, C.L., Chen, S.Y., Chang, C.H., Chang, Y.H., Hsieh, P.H.: Elution and mechanical strength of vancomycin-loaded bone cement: in vitro study of the influence of brand combination. PLoS One 11(11), e0166545 (2016) 13. Birkeland, Ø., Espehaug, B., Havelin, L.I., Furnes, O.: Bone cement product and failure in total knee arthroplasty: a follow-up study of 26,147 knee replacements between 1997 and 2013 in Norway. Acta Orthop. 88, 75–81 (2017)

Chapter 8

Numerical–Experimental Study of 3D Printed Ortheses for Rehabilitation of Patients with Musculoskeletal Lesions Juan Alfonso Beltrán-Fernández, Juan Luis Cuevas Andrade, Juan Carlos Hermida Ochoa, Luis Héctor Hernández Gómez, Teresa Berenice Uribe-Cortés, and Pablo Moreno Garibaldi Abstract Equinovarus foot or known as clubfoot is a frequent musculoskeletal deformity occurring at birth. It comprises a misalignment of the foot and shortened tendons and produces pain and serious physical limitations. It occurs mainly in patients with cerebral palsy, duchenne muscular dystrophy, residual clubfoot deformity, and spina bifida. The initial gold standard treatment for an equinovarus foot is the structural correction with the use of ortheses aimed to allow the patient to walk and perform rehabilitation exercises. These ortheses come mainly in the form of boots molded with plaster of Paris or fiberglass bandages. Premanufactured ortheses are also available and yield great resistance and support to the foot; however, they can be very costly and out of reach for some population. Recently, our research center of investigation and biomechanics laboratory (CILAB), with the assistance of the Instituto Politécnico Nacional (IPN) started printing three-dimensional personalized ortheses for diverse musculoskeletal problems, including clubfoot patients aiming to lower the costs of treatment for our pediatric patients. Our preset study analyzed the resistance of two 3D printed ortheses: one for a normal subject and another for a clubfoot patient through optical interferometry and numerical analysis. Our purpose J. A. Beltrán-Fernández (B) · J. L. C. Andrade · L. H. H. Gómez · P. M. Garibaldi Instituto Politécnico Nacional- Escuela Superior de Ingeniería Mecánica y Eléctrica- Sección de Estudios de Posgrado e Investigación Edificio 5, 2do Piso, Unidad Profesional Adolfo López Mateos “Zacatenco” Col. Lindavista, 07738 Ciudad de México, México e-mail: [email protected]; [email protected] J. L. C. Andrade e-mail: [email protected] L. H. H. Gómez e-mail: [email protected] J. C. H. Ochoa · T. B. Uribe-Cortés Centro de Investigación y Laboratorio de Biomecánica, Carmen #18, Co. Chimalistac San Ángel, 01070 Ciudad de México X, México e-mail: [email protected] T. B. Uribe-Cortés e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 J. A. Beltrán-Fernández et al. (eds.), Design and Simulation in Biomedical Mechanics, Advanced Structured Materials 146, https://doi.org/10.1007/978-3-030-65983-7_8

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was to anticipate failure of our personalized designs, especially in cases, where the foot gait is abnormal such as in the case of clubfoot patients. Keywords 3D printed · Ortheses · Equinovarus foot · Interferometry · Digitization

8.1 Introduction Musculoskeletal disorders in infants during birth should be property diagnosed so that the child has an adequate treatment according to his pathology, and the progression of the disorder can be prevented in the short or long term. There are different anomalies that can occur at the time of delivery or that can be observed in the process of pregnancy such as malformations (e.g., cleft lip), disruption (e.g., amniotic band syndrome), dysplasia (e.g., skeletal dysplasia), syndromes (e.g., turner syndrome), or deformations that are alterations in the shape, position, or structure of a part of the body that biomechanics effects of that part can compromise the whole organism such as the clubfoot which is part of this study. Clubfoot is a pathology from the foot and ankle, where the foot is in equine, supine, varus, and adduct to the forefoot. Clubfoot is one of the most frequent musculoskeletal pathologies reported worldwide between 1 and 4.5 per thousand born, and in Mexico, it represents about 2.3 per thousand born as reported in a study made at Centro Médico ABC in Mexico City, matching the world ranks [1]. Clubfoot is more frequent in boys than girls with a ration of 2:1 [2]. A preferred classification of clubfoot is the Dimeglio’s classification (see Fig. 8.1) which divides the condition in four levels: I. II. III. IV.

Level Moderate Severe Highly severe.

A standard treatment to help the correction of this pathology is with the use of ortheses. Ortheses are external devices that help the neuromusculoskeletal system to modify its function and structure. Ortheses are used in orthopedics and physiotherapy to help the correction during activity or displacement. Ortheses also help in the correction and alignment of deformities, to yield better function of the locomotor system and limiting or blocking a movement or articular range. Ortheses manufactured in Mexico can be expensive making them inaccessible to low-income people. Therefore, CILAB biomechanics laboratory as part of the Dr. Germán Días Lombardo Hospital in Mexico City, personalized 3D printed ortheses, for patients who require them, customized and at low costs. A comparison of the ortheses was performed by means of interferometry analysis and numerical analysis to demonstrate the resistance of the 3D printed ortheses made of Z-Ultat.

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Fig. 8.1 Dimeglio’s classification for clubfoot [2]. Reprinted with permission from SpringerNature publishers

8.2 Materials and Methods The analysis of our 3D printed ortheses was as follows; two ortheses (the clubfoot and the healthy foot) were printed for comparison as shown in Fig. 8.2.

Fig. 8.2 Methodology

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Fig. 8.3 Digitalizing the foot with 3D systems sense

8.2.1 Digitization A clubfoot and a normal foot were digitized, and dimensions were taken, Fig. 8.3. Digitizing of the model was obtained by using a 3D scanner (3D systems sense-RS) and was cleaned using the scanner software (3D systems sense) see Fig. 8.4. The program allows to save the file as a stereolithographic (STL) file that allows to be exported as a CAD model see Fig. 8.5. Digitization is ideal because the scanning yields the real dimensions, and it provides a precise model of the anatomical area.

8.2.2 Model and Printing 8.2.2.1

CAD Modeling

Once the digitization was completed, the modeling in a CAD software continued. First, the STL file is necessary to be imported in a CAD software see Fig. 8.6. For this purpose, the Rhinoceros 5 software was used. Second, an orthesis was previous digitized and imported to a CAD software and adapted to the foot. It was necessary to rotate the foot in many grades in order to have many views to help the ortheses model, see Fig. 8.7 and 8.8. To adjust the ortheses, it is necessary to create a cage as shown in Figs. 8.8 and 8.10. When the orthesis was finished, it was sent for printing. The orthesis was exported to an STL file in order to be printed as shown in Fig. 8.11.

8 Numerical–Experimental Study of 3D Printed Ortheses … Fig. 8.4 Scanning image as captured directly from the patient’s limb

Fig. 8.5 Completed digitized model

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Fig. 8.6 Foot digitalized and imported in CAD software

Fig. 8.7 Coronal plane, foot, and ortheses

8.2.2.2

3D Printing

Models were exported from Rhinoceros in a STL file and uploaded to a Z-suite printing software (Zortrax) see Fig. 8.12. This software allowed the model to be moved, resized, rotated, auto-arranged, splitted, rotated optimized, and created supports, layer thickness, density, print speed, material, dimensions, among other features see Fig. 8.13.

8 Numerical–Experimental Study of 3D Printed Ortheses … Fig. 8.8 Sagittal plane, foot, and ortheses

Fig. 8.9 Ortheses modified in the cage

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Fig. 8.11 Model cleaned and ready to be printed

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Fig. 8.12 Ortheses displayed in the printer software, Z-suite

Fig. 8.13 Dimensions of the model that the Z-suite gave

The software made an analysis in order to check the model viability as shown in Fig. 8.14. Fig. 8.14 Analysis for the model

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As shown in Fig. 8.14, the software defines in green the areas that are correct for the printer (see Fig. 8.15) and in red, the areas that are too thin which were very low and therefore did not represent a problem for the printer to print the ortheses (see Fig. 8.16). After modifying the settings, the software displays the model in the position that will be printed and the print time, material usage, among other features, see Figs. 8.17, 8.18, and 8.19. Fig. 8.15 Z-SUITE shows the correct areas, those ones that are not too thin

Fig. 8.16 In red, areas that are too thin

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Fig. 8.17 Z-suite shows the model ready to be printed

Fig. 8.18 Print time and material usage for the model

8.2.3 Numerical Analysis The models that were analyzed by the finite element method (FEM) were in a stereolithographic format (STL) because they were digitized. It was necessary to convert them to solid bodies and reduce the elements in order to allow less computational resources.

8.2.3.1

Mesh Arrangement and Conversion to Solids

Once the orthesis models were finished, they were exported to a STL format, and the elements were reduced so that when importing them into a CAD program, the computational time could be reduced. Solid CAD models allow them to be stored in a native file format such as IGS, STEP, SAT. The reduction of the elements was made in an Autodesk © program called Netfabb and solidification in SolidWorks. The process described above was applied on the two ortheses. The STL file was then imported in the Netfabb software, where the mesh was fixed, see Fig. 8.20. The software shows probable defects in the mesh such as closed meshes, surface orientation, edges, elements (triangles), among other features. The number of edges

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Fig. 8.19 Finished ortheses

Fig. 8.20 Netfabb platform

and triangles comprising our models could be seen after these were imported in the Netfabb for both, i.e., the normal and clubfoot cases, see Table 8.1. For the ortheses of the clubfoot (see Fig. 8.21) as well as the ortheses for the healthy foot (Fig. 8.22). After the mesh was fixed, the numbers of edges and elements were reduced in order to help the computational resources to facilitate the solidification and the numerical analysis. The mesh in Fig. 8.23 resulted in more elements when compared to mesh

8 Numerical–Experimental Study of 3D Printed Ortheses … Table 8.1 Edges and triangles from the ortheses

Clubfoot

205 Healthy foot

Edges

609,750

660,303

Triangles

406,500

440,202

Fig. 8.21 Clubfoot ortheses in Netfabb

Fig. 8.22 Healthy ortheses in Netfabb

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Fig. 8.23 Unfixed mesh

depicted in Fig. 8.24. This was applied for both models representing clubfoot and healthy foot. The numbers of edges and triangles are shown in Table 8.2, while the fixed meshes can be seen in Figs. 8.25 and 8.26 for the healthy foot and clubfoot, respectively. After the mesh was fixed, the STL file had to be made into a solid model in order to perform the numerical analysis. The files were made solid models using SolidWorks and then translated as a universal file like step, parasolid, IGES, and others. In this Fig. 8.24 Fixed mesh in Netfabb

Table 8.2 Edges and triangles after cleaning the model

Clubfoot

Healthy foot

Edges

48,489

55,086

Triangles

32,326

36,724

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Fig. 8.25 Ortheses from the healthy foot with the mesh arranged

Fig. 8.26 Ortheses from the clubfoot with the mesh arranged

case, a step file was used. To be certain that the file was a solid, it is important to see that the software interface displays “Imported Solid 1” on its interface menu as seen in Fig. 8.27.

8.2.3.2

Finite Element Method

The finite element method (FEA) is a numerical method aimed to solve related equations for variables approach of continuous data. A group of variable data is given in discrete points (nodes). The process consists in a separation of the system in

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Fig. 8.27 Successful solid model

individual components or elements in order to know their behavior and then rebuild the original system for its analysis. This represents a general approach method of discretization for continuous problems defined by mathematical expressions. In FEM as in our models, the term known as domain represents a “continuous system.” Also, there are the “boundary conditions” or “limits” which are ranges or conditions from a function that interacts in the continuous system and will be solved in the problem. The mesh generation is called “discretization,” where we generate the “elements” and “nodes.” An element is a part of the continues system that is separated from the continuous system, and its typical shapes are triangles, quadrilaterals, or tetrahedron. These elements are united in a point that is called “node” and often represent the vertex of many elements. The numerical analysis was made in the commercial simulation software ANSYS© with the following characteristics: The ortheses were printed in Z-Ultrat, a polymer based on ABS. Young’s Modulus was 1850 MPa and Poisson’s ratio of 0.35, and the model was loaded with 450 N that represents more load than the boys apply on the ortheses. A friction coefficient of 0.8 was assigned to obtain a friction force of 55.53 N. For the boundary conditions, we considered the three human gait phases as shown in Figs. 8.28 and in 8.29. The meshes were generated with 287,601 elements, 422,134 nodes, and 107,604 elements, 189,641 nodes for the orthesis of the clubfoot and the orthesis of the healthy foot, respectively, and the results are shown in the next pages. Figure 8.30 shows the generated meshes.

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Fig. 8.28 Three phases of the gait cycle

Heel strike

Stance

Push off

Fig. 8.29 Boundary conditions: where P = 450 N, F = fixed, F = 55.53 N for the human gait phases

Fig. 8.30 From left to right, the clubfoot orthesis and the healthy foot orthesis meshes are shown

8.2.4 Interferometry Interferometry is an experimental test that uses digital correlation of images that allowed to measure the displacement in 2D and 3D images. The technique consists

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in taking a series of pictures or video during the test from the initial to the final stage. For the preparation of the model, it is necessary to paint the surface of the model in white as shown in Fig. 8.31. Next, a mottled with black painting is made to generate a contrast that allowed the program run the simulation as shown in Fig. 8.32. If the program does not distinguish the mottled, then it is necessary to repeat the process of painting. In images like in video, the file is divided in virtual subsets called facets, and through an algorithm of correlation, a region or facet of the initial image is searched until the final image is obtained to determine the displacement vector in each set of facets. For this study, the mottled was performed in both ortheses. The experimental study was made in GOM correlate software using human gait phase’s videos in both ortheses, Fig. 8.33. File formats accepted by the software are MP4, MPEG, or AVI. In this study, an AVI file was used. Through a surface component, conditions like quantity of points, area selection were generated. The software identifies these parameters and performs the analysis, see Figs. 8.34, 8.35, and 8.36. Fig. 8.31 Orthesis painted in white color in preparation for the mottling

8 Numerical–Experimental Study of 3D Printed Ortheses … Fig. 8.32 Mottled orthesis

Fig. 8.33 Video for interferometry proof

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Fig. 8.34 Surface component calibration

Fig. 8.35 Calibration completed

8.3 Results Figures 8.37, 8.38, 8.39, and 8.40 show the distribution of the loads base on the FEM analyses. Tables 8.3 and 8.4 show the results of the FEM such as equivalent stress (von Mises), maximum principal stress, and total deformation for both ortheses.

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Fig. 8.36 Results

Fig. 8.37 Equivalent stress (von Mises). Distribution of loads in the lateral side of the healthy foot

The results shown in Tables 8.3 and 8.4 indicate that the ortheses, printed in 3D in CILAB, are adequate for the patient. The maximum principal stress in the ortheses doesn’t exceed the yield stress of the material which is equal to 30.70 MPa. This suggested that there is no plastic deformation that affects the ortheses. When the results of FEM and interferometry are compared, we observe the zones, where the results match. The displacements that were been registered in the interferometry

214 Fig. 8.38 Close up of image 36 where the concentration of the von Mises stress is shown

Fig. 8.39 Equivalent stress (von Mises). Distribution of loads in the lateral side of the clubfoot

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Fig. 8.40 Close up of image 38 where concentration of the von Mises stress is shown

Table 8.3 Results of the FEM analysis for the healthy ortheses Healthy orthesis Heel strike

Stance

Push off

von Mises (MPa)

3.0044

0.60759

1.3639

Maximum principal stress (MPa)

3.0883

0.49042

1.0764

Total deformation (m)

0.98616e−3

5.5201e−6

2.2596e−5

Table 8.4 Results of the FEM analysis for the clubfoot orthesis Clubfoot orthesis Heel strike

Stance

Push off

von Mises (MPa)

3.3637

1.4434

2.8586

Maximum principal stress (MPa)

3.625

0.80668

1.7727

Total deformation (m)

0.31761e−3

8.7771e−6

2.634e−5

analysis for the clubfoot and healthy foot were 1.392 mm and 1.276 mm, respectively. In Figs. 8.41 and 8.42, it is shown the matched zones of both analysis in the printed ortheses. Like in Figs. 8.41 and 8.42 zones that match in the deformation, in Figs. 8.43 and 8.44 the lateral side zones of deformation also matches. Another result observed in the FEM but not in the interferometry study is in the floor stand, where there is wear in the floor stand especially in the heel zone as it can be seen in Fig. 8.45.

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Fig. 8.41 Zones were the orthesis from the clubfoot showed deformation. Interferometry in figure (a) and FEM in figure (b)

Fig. 8.42 Zones were the orthesis from the healthy foot which tends to deform. FEM in figure (a) and interferometry in figure (b)

8.4 Conclusions Through 3D printing, it has been possible to develop ideas that previously remained in the drawing board to something tangible without the need of a machining center or through some manufacturing procedure that is not available to everyone. In addition

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Fig. 8.43 a Interferometry analysis and b the FEM. The red arrows show the matched zones. Orthesis for the clubfoot

Fig. 8.44 a Interferometry analysis and b the FEM. The red arrows shows the matched zones. Orthesis for the healthy foot

to 3D printing, there are technologies such as scanning process and CAD programs that help the design of 3D models through reverse engineering. Available ortheses for musculoskeletal conditions like clubfoot are generally costly. CILAB laboratory creates custom 3D printed orthoses that are accessible to their patients without a big impact, help on their economy, and correct the pathology they present.

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Fig. 8.45 Comparison of the 3D printed ortheses and the numerical analysis. The red arrow shows the wear in the 3D printed and above it, the FEM

Through the study of interferometry and FEM analysis, it is possible to visualize the areas, where the model tends to concentrate the stresses produced and if necessary make the necessary corrections to strengthen the design. As mentioned in the results, 3D printed orthotics support the loads of the patient who is going to use it. Three-dimensional printed prostheses under experimentation and numerical analysis yield certainty to achieve a better physical recovery for the patient. Collaboration between hospitals and research centers could potentially optimize resources to benefit more cases with musculoskeletal malformations such as clubfoot.

References 1. Torres-Gómez, A., Pérez-Salazar-Marina, D., Cassis-Zacarías, N.: Pie equino varo aducto congénito, prevalencia en una población mexicana. Rev Mex Ortop Ped. 12(1), 15–18 (2010) 2. Lampasi, M., Abati, C.N., Bettuzzi, C., et al.: Comparison of Dimeglio and Pirani score in predicting number of casts and need for tenotomy in clubfoot correction using the Ponseti method. Int. Orthopaedics (SICOT) 42, 2429–2436 (2018). https://doi.org/10.1007/s00264018-3873-3https://doi.org/10.1007/s00264-018-3873-3 3. Knöhr, A.O.: Resultados Clínicos a mediano plazo de la técnica Ponseti en pie equino varo aducto en pacientes con mielomeningocele. Programa de estudios de posgrado de la especialidad de ortopedia y traumatología para optar por el grado de especialista médico. Costa Rica. Ciudad Universitaria Rodrigo Facio San José (2015) 4. Romero, A.J.A.C., Martínez, U.N.: Tratamiento del pie equino varo aducto mediante la incisión tipo Cincinnati en el Hospital para el Niño Poblano. Acta Ortop Mex. 20(5), 201–205 (2006). https://www.medigraphic.com/cgi-bin/new/resumen.cgi?IDARTICULO=8936

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5. Rodríguez, R.E.I., Arredondo, R.R., López, M.N.: Nuevo enfoque terapéutico del metatarso varo congénito y residual de pie varo equino. Estudio de cinco años. Gaceta Médica Espirituana 16(2) (2014). https://www.medigraphic.com/cgi-bin/new/resumen.cgi?IDARTICULO=51874 6. Moret, J.: Anomalías músculo esqueléticas en el periodo neonatal. Para optar el título de especialidad en pediatría y puericultura. Universidad de Carabobo. Valencia. Hospital de niños “Dr. Jorge Lizarraga” (2015). https://hdl.handle.net/123456789/2290 7. Huertas, R., Rosselli, P.: Pie equinovaro congénito complejo: presentación de un caso. Acta Ortopédica Mexicana 27(3), 197–200 (2013). https://www.medigraphic.com/cgi-bin/new/res umenMainOrto.cgi?IDARTICULO=44166 8. Castellar, N.V., Jaime, V.A.: 24 de octubre del 2013. Resultados del tratamiento de pie equino varo congenito con el método de ponseti. Especialidad en ortopedia y traumatologia. Cartagena de indias D. T. H. Y C. Facultad de Medicina Universidad de Cartagena. https://hdl.handle.net/ 11227/5319 9. Gómez, M.: Mervyn Modelos teóricos de la causalidad de los trastornos musculoesqueléticos Ingeniería Industrial. Actualidad y Nuevas Tendencias, vol. IV, núm. 14, junio, pp. 85–102 (2015). https://www.redalyc.org/articulo.oa?id=215047422009 10. Gozar, H., Derzsi, Z., Chira, A., Nagy, Ö., Benedek, T.: Finite-element-based 3D computer modeling for personalized treatment planning in clubfoot deformity: case report with technique description. Medicine 97(24), e11021 (2018). https://doi.org/10.1097/MD.000000000 0011021https://doi.org/10.1097/MD.0000000000011021 11. Goldstein, R.Y., Seehausen, D.A., Chu, A., Sala, D.A., Lehman, W.B.: Predicting the need for surgical intervention in patients with idiopathic clubfoot. J. Pediatric Orthopaedics 35(4), 395–402 (2015). https://doi.org/10.1097/bpo.0000000000000282https://doi.org/10.1097/bpo. 0000000000000282 12. Shabtai, L., Segev, E., Yavor, A., Wientroub, S., Hemo, Y.: Prolonged use of foot abduction brace reduces the rate of surgery in Ponseti-treated idiopathic club feet. J. Children’s Orthopaedics 9, 177–182. (2015).https://doi.org/10.1007/s11832-015-0663-y 13. Balasankara, G., Luximonb, A., al-Jumailya, A.: Current conservative management and classification of club foot: a review. J. Pediatric Rehabil. Med. 9, 257–264 (2016). https://doi.org/ 10.3233/PRM-160394 14. Joshua, B., Holt, M.D., Oji, D.E., John Yack, M.D.H., Morcuende, J.A.: Long-term results of tibialis anterior tendon transfer for relapsed idiopathic clubfoot treated with the ponseti method. J. Bone Joint Surg. 97, 47–55. https://doi.org/10.2106/JBJS.N.00525 15. Lascano Freire, M.A.: Diciembre 2012. Estudio de Músculos Neumáticos y Determinación de Parámetros Funcionales Para Ser Aplicado en una Ortesis Dinámica de Pie Caído. Para obtener grado de licenciatura. Facultad de Ingeniería Civil y Mecánica.Ambato-Ecuador. https://reposi torio.uta.edu.ec/handle/123456789/3740 16. Li, R., Luo, T., Zha, H.: 3D digitization and its applications in cultural heritage. In: Ioannides, M., Fellner, D., Georgopoulos, A., Hadjimitsis, D.G. (eds.), Digital Heritage. EuroMed 2010. Lecture Notes in Computer Science, vol. 6436. Springer, Berlin, Heidelberg (2010). https:// doi.org/10.1007/978-3-642-16873-4_29

Chapter 9

Design of an Auxiliary Mechanical System for the Diagnosis of Lordosis and Scoliosis Juan Alfonso Beltrán-Fernández, Juan Carlos Hermida-Ochoa, Luis Héctor Hernández-Gómez, Carolina Alvarado-Moreno, Itzel Bantle-Chávez, Pablo Moreno-Garibaldi, and Erik Omar Alvarado-Alcántara Abstract Scoliosis and lordosis are medical conditions, which present an atypical curvature of the spine. These deformations can be easily diagnosed, altogether with the degree of their severity through orthopedic measurement processes and clinical reviews. However, the preformed studies which classify the severity of these deformations are, in their majority, empirical and present great opportunity for improvement. Therefore, they are based on radiographies that offer a clear image of the spine, but present the problem of a constant patient’s exposition to ionizing radiation and as a consequence an increment of potential hazards for health. This also means, results are subject to the physician’s interpretation and expertise. The present work intends to describe and analyze the design and function of a mechanical system that is capable of significantly reducing the radiological exposure of patients with scoliosis and J. A. Beltrán-Fernández (B) · L. H. Hernández-Gómez · C. Alvarado-Moreno · I. Bantle-Chávez · P. Moreno-Garibaldi · E. O. Alvarado-Alcántara Instituto Politécnico Nacional - Escuela Superior de Ingeniería Mecánica y Eléctrica - Sección de Estudios de Posgrado e Investigación Unidad Profesional “Adolfo López Mateos” Edificio 5, 3º Piso, Colonia Lindavista. Gustavo A. Madero, 07738 Ciudad de México, México e-mail: [email protected] L. H. Hernández-Gómez e-mail: [email protected] C. Alvarado-Moreno e-mail: [email protected] I. Bantle-Chávez e-mail: [email protected] P. Moreno-Garibaldi e-mail: [email protected] E. O. Alvarado-Alcántara e-mail: [email protected] J. C. Hermida-Ochoa Centro de Investigación y Laboratorio Biomecánico - Carmen, #18, Chimalistac San Ángel, 01070 Ciudad de México, México e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 J. A. Beltrán-Fernández et al. (eds.), Design and Simulation in Biomedical Mechanics, Advanced Structured Materials 146, https://doi.org/10.1007/978-3-030-65983-7_9

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lordosis. The main goal of this device is to diagnose both deformations by obtaining the angles of curvature of the patient’s spine, using a method that does not depend entirely on human interpretation.

9.1 Introduction In order to identify the main medical characteristics involved in both illnesses, four subsections of the anatomical and biomechanical function of the human spine, together with the angles of deformation that can be identified and the alternative measurement processes that are currently performed to obtain an accurate diagnosis, will be described hereafter.

9.1.1 Anatomy of the Vertebral Column The human vertebral column, also called spine, is composed of 33 bones called vertebrae, which are divided into regions, as shown in Fig. 9.1. The cervical region consists of seven vertebrae, the thoracic and dorsal regions have twelve vertebrae, and finally, five vertebrae can be found in the lumbar region, being also part of the sacrum and the coccyx [1]. The distribution presented by the spine and its natural curvatures enable vital functions such as movement and support of the body. A healthy vertebral column presents four physiological curves. From the sagittal point of view, which is the plane that divides the human body into the right-hand and left-hand side, the curves called cervical lordosis, lumbar lordosis, dorsal kyphosis and sacral kyphosis (shown in Fig. 9.2) can be identified. According to Pascale [3], the maximum points of each curve can be found in the following sections of the column: • • • •

Cervical curve: between vertebrae C6 and C7. Dorsal curve: between vertebrae D6 and D7. Lumbar curve: between vertebrae L4 and L3. Sacral curve: between vertebrae S4 and S3.

Each vertebra consists of two parts, the vertebral body and the vertebral arch, which also enclose the vertebral foramen that contains the spinal cord. Between the vertebrae, fibrocartilaginous joints called intervertebral discs can be found. These hydraulic systems separate the vertebrae from each other and provide optimal cushioning protection against repeated impacts, allowing the performance of the natural movements of each functional unit. An intervertebral disc is also formed of two parts (as shown in Fig. 9.3):

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Fig. 9.1 I: lateral view of the vertebral column: a cervical region (composed of 7 vertebrae), b thoracic region (composed of 12 vertebrae), c lumbar region (5 vertebrae), d sacrum, e coccyx [2]. Reprinted with permission from SpringerNature publishers

(a) an outer fibrous ring formed by several layers that cross one another, forming a mesh-like structure. The fibrous layers unite the vertebrae and protect the nucleous. (b) The central pulposus structure called the nucleous, composed of 80% of water, distributes the hydraulic pressures in all directions within each intervertebral disc under compressive loads. The combination of two vertebrae, together with the intervertebral disc is known as the vertebral column’s functional unit. A typical vertebra consists of two parts: the vertebral body and the vertebral arch. The superior and lateral view of a vertebra are represented in Fig. 9.4. Each vertebra consists of several processes, which allow one or more muscles to insert themselves into the joint of two vertebrae. The processes are categorized as followed: • Spinous processes: represent a major part of a vertebra, pointing dorsally from the junction of the laminae and serving to attach muscles and ligaments.

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Fig. 9.2 I: characteristic curves of the vertebral column. a Cervical curve, b thoracic curve, c lumbar curve, d sacral curve [4]. Reprinted with permission from SpringerNature publishers

Fig. 9.3 Schematic representations of the adult intervertebral disc: a midsagittal cross section showing anatomical regions. b Three-dimensional view illustrating AF lamellar structure [5]. Reprinted with permission from SpringerNature publishers

• Transverse processes: one on each side of the vertebral body, project from either side at the point where the lamina joins the pedicle, between the superior and inferior articular processes. They serve for the attachment of muscles and ligaments, in particular the intertransverse ligaments. A facet on each side of the thoracic vertebral body articulates with the head of the rib.

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Fig. 9.4 Superior and lateral view of a column’s vertebra [6]. From SpringerNature publishers Reprinted with permission

• Articular processes: superior and inferior on each side of the vertebra, which serve to restrict the range of possible movement.

9.1.2 Biomechanics of the Human Vertebral Column Biomechanics is defined as the science in charge of studying the internal and external forces, as well as their impact on the human body. The anatomical branch studies the form and localization of a structure. On the contrary, biomechanical studies intend to analyze and comprehend the causes and consequences of the exerted forces on the anatomical structures and its possible effects. The human vertebral column is a complex mechanical structure, which has been adapted to bipedalism, combining the stiffness of the vertebrae and the elastic effect of the intervertebral discs. This particular combination of properties allows the whole column to support considerable charges and loads, providing at the same time a broad, but controlled mobility. This equilibrium is achieved through the systems that interact in order to assure stability, protection, flexibility, elasticity and mobility [7]. The rigidity of the vertebrae gives stability to the skeletal posture, supporting the pressures on the vertebral areas and acting as a protective layer of the spinal cord, forming the medullar canal. The articular stability is in charge of the ligaments, which also act as first-grade stabilizers of joints. Muscles act as second-grade stabilizers and as third-grade stabilizers, the anatomical functions of the facet vertebra joint [8]. The vertebral body is able to resist the compression forces along its vertical axis due to the distribution of its trabeculae, being each one of them the tiny osseous protractions that together create an osseous mesh and confine the medullar cavities of the spongy tissue. The vertical ones join both intervertebral discs and the horizontal protrude from them and cross the pedicles, passing through the articular processes and the posterior arch. Between these three groups, a weak area can be found. It is made up a triangular, anterior basis. Therefore, the anterior portion of the vertebral

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body is less tough to compression loads in comparison to the posterior area of the vertebra [7]. The flexibility of the joints allows by themselves or as the sum of each component of the joint-vertebral set, a movement range of several amplitudes, making the flexion, extension and rotation movements possible (Fig. 9.5), altogether with the combined movements of flexion or extension with rotation [8]. Figure 9.6 illustrates the rotation center during the antero-posterior flexion–extension movement. It can be found in the inferior section of the vertebral body (A) and also a lateral movement, which the rotation center can be found in the superior section of the vertebral body [7].

Fig. 9.5 Column axis during rotation [9]. Reprinted with permission from SpringerNature publishers

Fig. 9.6 Rotation centers of the vertebral column [9]. Reprinted with permission from SpringerNature publishers

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9.1.3 Deformations of the Vertebral Column As mentioned before, the human spine consists of different areas in which any kind of alteration can provoke a deformation. These atypical forms could appear in form of the following curves: • Scoliosis • Kyphosis • Lordosis The main causes of these conditions are: • • • • •

Birth defects. Traumatisms (falls, blows, accidents). Wrong posture. Aftermaths of neuromuscular illnesses. Sometimes unknown causes, most probably genetics.

The natural curves of the column change over time, being classified as hyper or hipo, depending on the causes. Scoliosis is a deformity in which a lateral curvature is generated, in conjunction with a vertebral rotation that affects the vertebrae over the years. Scoliosis is among the many deformities of the vertebral column, the most common one and is considered a three-dimensional pathology (Fig. 9.7): • Sagittal: an intervertebral extension, which causes a scoliotic segment lordosis, is produced.

Fig. 9.7 a Radiography of a column with scoliosis. b Radiography of a healthy vertebral column [10]. Reprinted with permission from SpringerNature publishers

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• Frontal: a lateral inclination of the vertebra can be observed. • Axial: an abnormal rotation of the vertebrae is produced, • causing asymmetry of the pedicle’s position. Scoliosis If appreciated from an external point of view, the illness manifests itself as a clear asymmetry of the back and the rib cage, which can also be visually detected as a height difference of the shoulders, the auxiliary folds and the pelvic girdle. Furthermore, the scapulae present an asymmetric bony prominence in form of a rip hump at the level of the curve’s convexity, therefore, generating an increment or decrement of the thoracic kyphosis and the natural lordosis of the spine, as shown in Fig. 9.8. This particular deformity is usually caused due to scoliosis, but is not classified as a dangerous disease. However, it is related to life quality problems for teenagers regarding their social and psychological development. The visual perception of the deformity’s degree can be appreciated in Fig. 9.9 [11]. Fig. 9.8 Asymmetric back’s surface of a patient who suffers from scoliosis [10]. Reprinted with permission from SpringerNature publishers

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Fig. 9.9 Visual representation of a vertebral column affected by kyphosis [12]. Reprinted with permission from SpringerNature publishers

In the case of deformations caused by lordosis, the vertebral column presents a sagittal curve with anterior convexity, which can cause severe pain in the lumbar region, as shown in Fig. 9.10. There are different types of lordosis: • Normal: the patient does not suffer from any alteration of the vertebral column’s curves. • Hyperlordosis: the curves are more accentuated, causing a visible deformity. • Lumbar rectification: part of the healthy curvature is lost, causing severe pain in the lumbar region and forcing the patient to adopt an arched posture. • Lumbar strain: consequence of the lumbar rectification. The lumbar lordosis is not characterized by any kind of damage in the column. If healthy, the vertebral column presents this necessary curvature for the right functioning of the intervertebral discs, which in turn prevent hernia’s formation. Some of the causes that could possibly affect the curvature degrees of the column are set out below: • • • • • • • • •

Physical inactivity Lack of exercise Age Excessive stress Negative mental states (depression, sadness, discourage) Obesity Osteoporosis Kyphosis Excessive muscular tension

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Fig. 9.10 A: Visual representation of a healthy column. [13]. Reprinted with permission from SpringerNature publishers

• Discitis (infection in the intervertebral disc space that causes inflammation) • Spondylolisthesis (misalignment between the vertebrae). In some cases, the natural lordosis is partially lost. This particular condition is more common in inactive patients as a consequence of the constant load on the lumbar region, which therefore causes inflammation and lesions. The causes that affect the natural curvature of the column, causing an abnormal degree of the lordosis curvature, are diverse. Young patients could suffer from this illness due to an accelerated growth. Athletes and sportsmen are affected due to the adoption of incorrect postures or unequal muscle development [14].

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9.1.4 Alternative Measurement Procedures for Vertebral Column’s Deformations Nowadays, there is a wide range of methods and techniques to measure the deformity degree of a patient. Some of the most applied ones will be described as follows: • Optic techniques: making use of visual analysis, the posture of a person can be evaluated. • – Passive Triangulation: the dimension and shape of the object is deduced based on photographs. – Active Triangulation: the structural light is used to illuminate the shape of an object and the image is scanned to analyze the object’s structure. – Clinical photographs: as a comparison to evaluate and diagnose the severity of the deformation [15]. • Moire Topography: consists of a three-dimensional, morphometric procedure, through which the mapping of the object’s contour while superimposing one image over another is performed. The contour of the object is illuminated with different light beams to obtain the complete mapping [16]. • Computerized Tomography (CT): allows measuring the scoliosis from a threedimensional point of view. One of the main disadvantages is the high level of ionizing radiation to which the patient needs to be exposed; therefore, this method is not recommended for preoperative surgery evaluations [15]. • Clinical: the posture of the patient is analyzed to find any esthetic alterations that could possibly affect the trunk. Several points of reference are considered during the evaluation procedure: • – Body’s degree of inclination to one side of the body’s segments to determine if there is any rotation sign. – Discrepancy of the level of the shoulders. – Leveling of both iliac spines. – Discrepancy of the pelvic level. – Leveling of the gluteus. – Discrepancy of the knees’ level. – Size and symmetry of both knees. – Knees’ alignment [11]. • Radiology: different images are obtained and can be appreciated form different views through the use of X-ray radiation, with the objective of analyzing the patient’s deformity. In these images several variables can be calculated [17]: • – Ott’s Sign: method used for measuring the flexibility of the vertebral column. For this procedure, the patient’s parameters need to be measured while sitting down. – Schober’s Sign: just like Ott’s sign, the method is mainly used for measuring the column’s flexibility. The difference lies in the measuring technique. The column can be measured while the patient is sitting or standing [11]. • Risser-Ferguson Method: similar to the Cobb’s angle measurement technique. However different, thus, the column’s curvature is measured by marking the center

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Fig. 9.11 Graphic representation of the Risser-Ferguson method [18]. Reprinted with permission from SpringerNature publishers

of the superior vertebrae (apical and inferior), joining both points with a line, as shown in Fig. 9.11, [15]. • Scoliometry: the simplest of all methods, the column’s curvature is measured with a scoliometer. If the curvature’s degree increases, radiographies of the patient will have to be taken or more advanced methods shall be performed [11]. • Magnetic Resonance: the scoliosis can be measured based on a magnetic resonance tomography. This method is often used when the patient suffers from a specific pathology, e.g. tumors of the medulla or a medullary canal lesion [15]. • Lenke’s classification: this technique consists of three main steps to determine the scoliosis severity in teenagers. 1. First, the region of the curves needs to be identified (proximal, principal and lumbar). 2. Then, the regions are classified, and the structural quality of each curve is determined. 3. The third step consists of assigning a lumbar modifier (A, B, C), depending on the localization of the vertical line that crosses the center of the sacrum. This reference is vital for determining the type of modification the patient needs.

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4. Finally, the modifier is assigned according to the balance of the sagittal thorax (−, N, +), which is determined through the Cobb’s angle. • Hipo (−): the angle is minor to 10°. • Normal (N): angle is between 10° and 40°. • Hiper (+): the angle is mayor to 40° [15]. The Cobb’s angle is commonly used to evaluate the lateral curvature of the vertebral column in a frontal plane. This method is considered as the golden standard for the diagnosis of patients who present scoliosis and allows specialists to compare the development of the illness. It is also used for the following procedures: • Surgical procedures • Patient’s monitoring • Column deformities management. In order to accurately measure, the deformity’s degrees, specialists make often use of patient’s radiography to have a clear image that allows them to analyze the curvature’s structure and angles in patients that suffer from scoliosis. The Cobb’s angle method is performed as follows: • The first step consists of taking the superior intervertebral disc of the most inclined vertebra of the highest area of the curve. • A straight line is drawn as the continuation of the line that limits the intervertebral disc. • Then, the most inclined vertebra of the lowest area of the curve is taken as the second point of reference. • Again, a straight line is drawn to limit the intervertebral disc of the inferior area. • The intersection of both lines forms the angle that needs to be measured. If the lines do not enter the measurement area, two perpendicular lines are drawn to make the measurement process easier. Figure 9.12 shows two measurement methods to obtain the Cobb’s angle [19]. As mentioned before, the Cobb’s angle is of vital importance to analyze the evolution and progression of the patient’s scoliosis. Periodical revisions need to be performed in order to compare the obtained measurements during the medical consult. If the degree of the angle tends to be higher, the column will need to be treated. On the other hand, the Cobb’s angle method presents some problems that need to be analyzed. Firstly, in order to obtain an accurate measurement, an expert is needed. If the calculation of the angle is performed by several specialists, the process usually presents a range of error of 5° between measures, even if performed by one specialist several times. The physician in charge needs to make sure that the points of reference will always be the same bones so that the variation caused by the illness’s progression is not taken as a change of the column’s position.

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Fig. 9.12 Graphic representation of both measures for the Cobb’s angle determination [19]. Reprinted with permission from SpringerNature publishers

Another factor to be taken into account is the dimensions each time the measurement procedure is performed. This is because the measurement is made on a twodimensional plane, while the column has a three-dimensional structure. Furthermore, it is important to consider that the column’s curvature in scoliosis cases, is not only characterized by the deviation of the curve, but also a rotation of the vertebrae could be present. The Cobb’s angle has an angle’s range that oscillates between 10° and 120°. Patients that suffer from scoliosis enter the angle range of 20°–65°. The scoliosis classification depends on the value of the measured angles, as mentioned before in the Lenke’s classification parameters, which also makes use of the Cobb’s angle measurement method [15].

9.1.5 Lenke’s Classification Curve types: • Mayor curve: presents the highest Cobb’s angle and is always structural. • Minor curve: the curvature presents the minor Cobb’s angle and needs to present the following characteristics to be considered structural:

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• – The column presents a certain rigidity degree when the angle is superior or equal to 25°. Usually, the radiography shows the patient leading his or her own body to one side (to the curve’s side). – The column presents a hyperkyphosis mayor or equal to 20° in the following segments: T2, T5 r T10 and L2 [20]. The following six types of a curve can be defined according to these parameters: • Type I: (thoracic principal, only a mayor thoracic curve can be appreciated). The mayor curve is structural; the others are not. • Type II: (thoracic double, two thoracic curves can be appreciated). The mayor thoracic curve and the second, minor thoracic curve are structural, the rest is not structural. • Type III: (mayor double, two mayor thoracic curves). The thoracic, thoracolumbar or lumbar curve is structural; the thoracic curve is larger than the thoracolumbar or the lumbar curve. If a superior thoracic curve exists, is not structural. • Type IV: (triple mayor, three mayor thoracic curves). All three curves are structural; the thoracic curve is the mayor of all three. • Type V: (primary thoracolumbar/lumbar curve, or only the lumbar curve). The mayor curve is localized in the thoracolumbar transition or in the lumbar column and is structural. Neither the superior thoracic curve, nor the minor thoracic curve are structural. • Type VI: (primary thoracolumbar/lumbar, thoracic principal). The mayor curve, thoracolumbar or lumbar is structural, also the minor thoracic curve is structural, but the Cobb’s angle is of 5 or less degrees. Lenke established that a practical form for classifying the curve’s types included an arthrodesis (surgical intervention in which two osseous pieces are set, anchoring a joint to the structural curves) [21].

9.1.6 Definition of the Lumbar Column’s Modifier For these parameters, all the changes that could appear in the lumbar region due to scoliosis are taken into account and three different types of modifiers could be applied: • A (slight). • B (moderate). • C (severe). Taking the center of the sacrum as reference, a straight line is drawn up to the highest point of the column’s image (from an anterior–posterior point of view). • Type A lumbar column’s modifier (Fig. 9.13.) • Type B lumbar column’s modifier (Fig. 9.14.)

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Fig. 9.13 Graphic representation of the type A LCM [22]. Reprinted with permission from SpringerNature publishers

• Type C lumbar column’s modifier (Fig. 9.15.)

9.1.7 Definition of the Thoracic, Sagittal Column’s Modifier This parameter is defined by the hump’s extension. The values are expressed in “−, N, +” [21]: − kyphosis between T5 and T12 minor to 10°. N kyphosis between T5 and T12 between 10° and 40°. + kyphosis between T5 and T12 mayor to 40°.

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Fig. 9.14 Graphic representation of the type B LCM [23]. Reprinted with permission from SpringerNature publishers

9.2 Case of Study and Methodology With the support of the Germán Díaz Lombardo Hospital, the research team could have access to the clinical history of the patients and their archives, including radiographies, which were used to classify those patients who suffer from deformities of interest for the project. The archives were used as the basis for the classifications and measurements. The development of the present work considered the following methodology: • Stage 1 – Association to the biomechanical concepts of the column. – State of the art research. – Learning process of the measurement of the column’s deformities according to Lenke’s and Cobb’s methodology, making use of specialists’ expertise. • Stage 2 – Use of X-ray’s plates and patients’ tomography, case of study of healthy patients, patients with lordosis and scoliosis.

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Fig. 9.15 Graphic representation of the type C LCM, a intervertebral space of the apical region, pedicle of vertebral arch. b Apical vertebra [23]. Reprinted with permission from SpringerNature publishers

– Lenke’s and Cobb’s parameters measurement on the previously mentioned plates. – Tomographic data segmentation. – Three-dimensional printing of the vertebral column – Methodology application of QFD design (Quality Function’s Deployment): – Identification and classification of the client’s requirements (orthopedic physician). – Prioritization of the mandatory and desirable requirements. – Generation of the measurement system’s functions for lordosis and scoliosis. – Matrix generation for those concepts that need to satisfy every function.

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– Concept’s evaluation (manufacturing, feasibility, availability, technology) and definition of the winning concept. – Design of the winning concept (CAD drawings, quick prototyping, dimensioning according to the printed model of the column, mechanical evaluation, analytical calculus). • Stage 3 – – – –

Device elaboration and manufacturing for lordosis and scoliosis measurement. Adjustments. Measurements and testing. Results analysis (medical and engineering approved endorsement).

Figures 9.16, 9.17, 9.18, 9.19, 9.20, 9.21, 9.22 and 9.23 show the use and management of the X-ray plates for cases of scoliosis and lordosis, as well as their respective classifications according to Lenke and Cobb, which are shown simultaneously. In some cases, according to Lenke’s classification, thoracic modifiers should not be applied due to the lack of the lateral radiography of the patient (Figs. 9.23, 9.24 and 9.25). Curve Type: Type VI Type C lumbar column’s modifier Thoracic modifier. Fig. 9.16 Measurement of Cobb’s angle, case 1. Curve type: type V type C lumbar column’s modifier thoracic modifier

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Fig. 9.17 Measurement of Cobb’s angle, case 5. curve type: T type—lumbar column’s modifier thoracic modifier type: “+” (hyper)

Fig. 9.18 Measurement of curve type: type I type A lumbar column’s modifier thoracic modifier

9.3 Tomographic Data Segmentation In order to perform the tomographic segmentation, the computerized program Scan IP was used, with which all the slides of a tomography or a section of it can be uploaded and manipulated. For this case, a tomographic segmentation of the back-lumbar tomography was performed. For instance, when performing the reconstruction, the Fig. 9.26 was obtained. The complete reconstruction includes elements from the skull to the medial part of the femur, excluding all elements that are not osseous.

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Fig. 9.19 Measurement of Cobb’s angle, case 7. Curve type: type A type A lumbar column’s modifier thoracic modifier

Fig. 9.20 Measurement of Cobb’s angle, case 6

From the complete reconstruction of the tomography, the elements that are not part of the spine will be removed; therefore, the images which form Fig. 9.27 were obtained. Once the segmentation and reconstruction were obtained, the Cobb angle was obtained (Fig. 9.28).

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Fig. 9.21 Measurement of Cobb’s angle, case 8. Curve type: type I type A lumbar column’s modifier

Fig. 9.22 Measurement of Cobb’s angle, case 10. Curve type: lumbar column’s modifier thoracic modifier type: “N” (normal)

This segmentation gave a measurement of 5.6° that according to Cobb’s classification, being an angle less than 10°, is considered a scoliotic attitude. The patient does not need more than rehabilitation exercises to correct the posture.

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Fig. 9.23 Measurement of Cobb’s angle, case 12. Curve type: type II type A lumbar column’s modifier thoracic modifier

Fig. 9.24 Anterior view of an X-ray plate of a healthy patient’s case

9.3.1 3D Printing of the Vertebral Column To start the 3D printing of the column, acrylonitrile butadiene styrene (ABS) was used as the material. The height of the print was adjusted to 85% of the actual size

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Fig. 9.25 Lateral view of an X-ray plate of a healthy patient’s case

Fig. 9.26 Tomographic segmentation of a patient’s case. On the left-hand part, the posterior view can be appreciated and on the right-hand side the anterior view

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Fig. 9.27 Different views of the reconstruction of the patient’s spine: (1) anterior view of the spine, (2) right lateral view, (3) left lateral view, (4) posterior view, where the apophysis of the vertebrae can be seen

Fig. 9.28 Cobb’s angle of the reconstructed column

with a density of 10% to make good use of the printing material. Posteriorly, it was also split into two parts because the length of the column in a single piece is greater than the height of the printer, and therefore, it was not possible to print it in one single piece. The total printing time was 19 h and 20 min. As a result, the following models were obtained in less time (Figs. 9.29, 9.30, 9.31 and 9.32). Each layer of the printed material is 0.2 mm apart to improve the definition of the model and medium density supports. 120 m of 1.75 mm filament were used.

246 Fig. 9.29 CAD design of the column before printing

Fig. 9.30 Column divided into two parts for printing [22]

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Fig. 9.31 Printing time with an advance of 38% [22]

Fig. 9.32 Column printing view

9.3.2 Application of QFD Methodology Design In order to start making decisions regarding the design and functionality of the system, it was necessary to establish and follow a QFD methodology. For this, in conjunction with all those that are involved in the project, the matrix of which characteristics are necessary, was made and defined for the system and each of the team members proposed a way to get each of these characteristics. An evaluation was carried out with a scale of 0–5 (to allow an optimal margin) which helped to decide which one of the best proposals was the best. The features are described as follows: 1. 2. 3. 4. 5. 6.

Fixed. No radiation. Digital. Accurate and exact. Financially accessible. Comfortable.

Once the qualifications of the ideas given by the team members and the advisor in the QFD matrix were defined, the ideas that obtained the lowest average and at the

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same time did not offer a viable solution to the problem were discarded. Consequently, the ideas that obtained a high average were saved in order to solve the problems of the system; some examples of these averages are shown in Tables 9.1, 9.2, 9.3 and 9.4. In Annex 2, the matrices with the averages obtained for each category are presented, and based on these results, the next step will be to define which one of the proposals will obtain all or most of the initially characteristics proposed. Once these main points have been determined, based on the average result obtained from the matrix, the following solutions were proposed for the problems that the system could present in order to make it more efficient and begin its construction. The winning concepts according to the QFD matrix are: • To be able to solve this fixed system, it will be considered as stuck and parallel to the wall. • To avoid radiation, the system will be palpable and needs to use LVDT sensors. • A data acquisition (DAQ) system will be necessary as a digital system. • 6 LVDT sensors will be used in the system to allow the correct detection and analysis of the back. These sensors will be placed two by two on each part of the back, dividing it into three parts; high, medium and low. • To make it accessible, it was built with low-cost materials, without affecting the quality of the used materials. • This system should be comfortable for the patient’s use. Table 9.1 Average obtained from the characteristic being the structure attached to the wall Structure attached to the wall 5

5

5

5

5

0

0

0

0

0

0

0

0

0

0

0

0

2

0

3

0

0

1

0

4

0

0

0

0

0

0

3

0

3

3

0

1

1

1

0

Average

1

5

2

0

3

0

4

1

5

1

6

0

7

1.8

8

0.6

Total

1.75

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Table 9.2 Average obtained from the characteristic of the system with LVDT sensors LVDT sensors 0

0

3

0

0

5

5

5

5

5

0

3

4

4

5

0

1

3

2

4

3

3

3

3

3

0

3

3

3

4

0

0

2

0

2

2

2

3

3

4

Average

1

0.6

2

5

3

3.2

4

2

5

3

6

2.6

7

0.8

8

2.8

Total

2.5

Table 9.3 Average obtained from the feature of the system with an interface and a data acquisition card (DAQ) Interface with a data acquisition card 2

2

2

1

0

0

0

0

0

5

5

5

5

5

5

2

1

3

3

4

4

4

3

4

4

2

4

4

3

4

0

0

0

1

2

2

1

3

2

2

Average

1

1.4

2

1

3

5

4

2.6

5

3.8

6

3.4

7

0.6

8

2

Total

2.475

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Table 9.4 Average obtained from the characteristic that the system does not have guide points, which can be uncomfortable for the patient Guide points to avoid disturbing the patient 0

0

2

0

3

3

5

5

5

5

2

4

3

4

4

0

0

0

0

0

1

2

2

3

2

2

0

3

4

3

5

0

4

2

3

0

3

2

3

3

Average

1

1

2

4.6

3

3.4

4

0

5

2

6

2.4

7

2.8

8

2.2

Total

2.3

9.3.3 Manufacture of the Device To perform the design of the device, different physical factors of the possible user had to be considered. The factor that determined the type of sensor to be used in the device is the lumbar curve according to the sagittal arrow test. The evaluation of the lumbar curve using the sagittal arrow test was performed by determining the distance between the vertical plumb line with the back, as a final result a straight line is obtained, which is one of the most used tools to determine if the postural reference points of a person are aligned, as shown in Fig. 9.33. According to the values obtained from the measurement, lordosis can be classified as: • Hyperlordosis, if the value is greater than 35 mm. • Normal lordosis, if the value is between 20 and 35 mm. • Hypolordosis, if the value is less than 20 mm. According to these results, it was possible to determine the operation of the sensor and the necessary length for its placement. Based on the design of the folding mechanism shown in Fig. 9.34, the idea of designing an articulated system that can perform vertical movements to cover the entire back of the patient was developed [25–30].

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Fig. 9.33 Sagittal arrow test [24]. Reprinted with permission from SpringerNature publishers

Fig. 9.34 Folding mechanism

This mechanism was chosen due to its useful features such as portability, low cost, easy handling and its wide range of dimensions for different patients. Likewise, with a digital post-processing method, it is expected to achieve a spine deformation result considerably close to the obtained result through the use of medical images [31–33]. As mentioned above, based on the dynamics of the mechanism (Figs. 9.35 and 9.36), a device that could offer a vertical movement was assembled, with the aim of being able to cover the area of the back.

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Fig. 9.35 First advance of the system’s assembly

Fig. 9.36 System’s action area

The mechanism is an articulated system, which has six sensors that are distributed in pairs all along of its structure so that it can cover the upper, middle and lower back. A rail was designed for the base of the assembly in order to allow the system to be fixed, without affecting its vertical movement, as shown in Fig. 9.37. A second system was built with the same dynamic principle as the first one; the difference of this second system is the breadth. This with the objective of being able

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Fig. 9.37 Base of the assembly

to cover the entire area of the patient’s back in case the first system fails. Figure 9.38 shows this second system. In order to assemble the previous systems, the material was used as follows (Fig. 9.39): • Wood • 25 sticks with measures 2 × 40 × 1 cm. (each stick has perforations in the center with 3 cm of separation between each other.) • 75 screws with a width of 3/16, and an inch and a half long. • 75 nuts with a width of 3/16. • 150 washers with a width of 3/16. • 6 screws with a width of 3/16, and 3 inches long. Fig. 9.38 First advance of the alternative system

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Fig. 9.39 Material used for the system’s assembly

The measures of the sticks were defined according to the surface of the back of children, adolescents and adults [34–36]. To obtain the sticks with the measures 2 × 40 × 1 cm, seven wooden sticks with a length of 2.45 m, a width and length of 2 × 1 cm, respectively, were bought. Subsequently, the sticks were cut to 40 cm, with which the 25 sticks needed to assemble the system were obtained. Each stick was drilled through the center with a width of 3/16 cm, together with the sides using the same width measurement, with 3 cm of space between each perforation. To continue with the assembly of the system, two fixing methods for the shafts in the folding mechanism needed to be designed. The first method of fixation that was implemented in the system was a fixed support in the lower part of the system formed by a suitable wooden beam as follows (Fig. 9.40). Of the two extreme points of the folding mechanism, only one had to remain fixed to have a reference point. To achieve this, the lower beam was cut, creating two ditches that were 3 cm deep, making a transverse hole in the beam to limit the vertical movement of the system. For the moving part, a guide channel was made on both sides of the support. It was crossed transversely with a bolt-type screw to limit the movement range of the system.

Fig. 9.40 Fixed support (bottom of the system)

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The second method of attachment connects the support to a vertical beam using a square to have the two supports joined perpendicularly, the vertical beam joined to another beam that simulates the office wall that uses a hinge mechanism to give the system a range of motion in order to have a better positioning of the patient (Fig. 9.41). In both vertical beams, a safety system was installed using two overlapping curved wooden bars with multiple perforations, which also were strategically placed to achieve a range of mobility of 45° and defined the wanted position to fix the system (Fig. 9.42).

Fig. 9.41 Second method for fixing the system

Fig. 9.42 Safe system to lock the mechanism

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9.4 System Instrumentation According to the winning concept of the differential matrix, linear variable differential transformer (LVDT) sensors should be used. However, it was found that these sensors are very expensive and could not be used on this mechanism. Therefore, it was decided to switch to a linear potentiometer (Fig. 9.43), which has a similar operating principle to that of the LVDT sensors but with a very significant price difference. In order to transfer the obtained data with the linear potentiometer to the computer, a Phidget brand acquisition card was used. The Phidget Interface Kit 8/8/8 that has eight sensor inputs. In order to place the sensors over the three parts into which the back area was divided, thin wooden supports were used so that the movement of the mechanism was not obstructed, but with the necessary thickness to keep the sensors stable (Fig. 9.44). These brackets were screwed two at a time, covering each part of the three parts into which the system’s area of action was divided on the back (Fig. 9.45). The displacement sensors have a limit of 60 mm. In order to be able to carry out the measurements and the diagnosis, sensors should be placed in an initial position of 0 mm and when making contact with the back, move around the patient’s spine and return to their 0 mm position to cover the system’s entire area of action. To ensure that the sensors had the previously explained behavior, springs will be placed as shown in Fig. 9.46. These springs were bonded with special adhesive to 3D printed parts. Fig. 9.43 Linear potentiometer, slider 60 by Phidget

Fig. 9.44 Phidget interface kit 8/8/8

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Fig. 9.45 Supports for fixing the sensors

Fig. 9.46 Base pieces for the spring

Two different parts were printed in 3D for each sensor. One of these with the objective of creating a base to place the spring (Fig. 9.46) and the other piece as a cylindrical extension in order to assure contact with the patient’s back (Fig. 9.47). For Fig. 9.47 Cylindrical extension

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the base of the spring, the center was drilled through to be able to insert a screw into which together with a nut, the spring would fall; for greater security, it was adhered with special adhesive (Figs. 9.48 and 9.49). The spring on the other side was attached with special adhesive to the sensor stem. The second 3D-printed part, the cylindrical extension, was placed on the sensor stem. A ball was attached to prevent friction and to optimize the system at the time of moving around the back (Fig. 9.50). Finally, all the sensors were placed in their support and with their 3D printed parts in order, having a limited range between them strategically planned to cover the entire area of the back that is necessary for the diagnosis of spinal deformations. In Fig. 9.51, the final system and its completed instrumentation are shown after the assembly. Fig. 9.48 Supports for fixing the sensors

Fig. 9.49 Spring attached to the base piece

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Fig. 9.50 Cylindrical extension attached to a pellet

Fig. 9.51 Armed and instrumented system

9.5 Data Acquisition In this step, the necessary physical connections of each component to the plate are made (with support of the data sheets of each one of these components), always taking into account the pins to be used in it, because these will be used for the development

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of the algorithm. Figure 9.51 shows the connection of the components of the sensing system. These previously six sensors were distributed in three parts of the back (upper, middle and lower). To each part of the back, a pair of sensors was assigned to be able to sweep each area. In order to acquire this data, an acquisition program is needed to make a code in the Java language. For this case, the program NetBeans will be used, which allows to save the displayed data by the sensors in an interval of 15 s and then export the acquired information to the Microsoft Excel program to make a graph. The code includes the following information: • Import of libraries. import com.phidget22.*; import java.util.Scanner; import javax.swing.DefaultComboBoxModel; import javax.swing.table.DefaultTableModel; import java.io.BufferedReader; import java.io.File; import java.io.FileOutputStream; import java.io.FileReader; import java.io.FileWriter; import java.io.IOException; import javax.swing.JOptionPane; • Declaration of variables, which represent the matrixes with the obtained and stored data by the sensors. static Scanner s = new Scanner(System.in); static int n; //n, n1, m, m1, r, r1 //they are counters for the matrices static int n1; static int m; static int m1; static int r; static int r1; static double superior[][] = new double[2][15]; // Save sensor data from channels 0 and 1 static double medio[][] = new double[2][15]; // Save sensor data from channels 2 and 3 static double inferior[][] = new double[2][15]; // Save sensor data from channels 4 and 5 • This line of code was created for declaring the card’s channel. In addition to this one other five variables needed to be declared to represent the other five channels. VoltageRatioInput ch = new VoltageRatioInput();

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• The next part of the code represents a combination of methods which are applied to the declared variable of a Phidget card channel. The purpose of these methods is to obtain the value of the sensor that is connected to the channel. Since only the value of a single sensor is obtained, this part of the code was made five more times to obtain the data of the six sensors that are connected (the data of ch, ch1, ch2, ch3, ch4 and ch5). • The function “listener” shown below will control everything related to channel 0 (ch), because certain methods will be applied. ch.addAttachListener (new AttachListener() { • In the following lines of code, the working channel is declared as a class, and the measurements will be made in a time interval of 1 s. VoltageRatioInput ph = (VoltageRatioInput) ae.getSource(); int serialNumber = ph.getDeviceSerialNumber(); String channelClass = ph.getChannelClassName(); int channel = ph.getChannel(); ph.setDataInterval(1000); • Another function “listener” was added in order to control the functions for which the channel is being called, taking into consideration that it comes from a channel of a Phidget card, and from the port where the data comes from. ch.addDetachListener(new DetachListener() { public void onDetach(DetachEvent de) { try { System.out.print("\nAttach Event:"); Phidget ph = de.getSource(); int serialNumber = ph.getDeviceSerialNumber(); String channelClass = ph.getChannelClassName(); int channel = ph.getChannel(); DeviceClass deviceClass = ph.getDeviceClass if (deviceClass != DeviceClass.VINT) { int hubPort = ph.getHubPort(); • The last function “listener” that was added displays the value of the data marked by the sensor. ch.addVoltageRatioChangeListener(new System.out.println("[VoltageRatio Event 0] VoltageRatio 0: " + e.getVoltageRatio()); superior[0][n] =e.getVoltageRatio(); • Below is the code where the program specifies that the channels belong to the Phidget card. The card number needs to be specified, being 523,489. Subsequently, each variable is assigned to the channel to which it is connected and each channel

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has a specific serial number. Additionally, the channel number needs to be declared to its respective channel. This code represents only channel 0, the same must be done for each one. The complete code can be found in Annex 3. ch.setDeviceSerialNumber(523489); ch.setChannel(0); ch.open(5000); • The next line of code sends the order to stop the sensor measurement after 15 s. Thread.sleep(15000); • Subsequently, three cycles were used to save the data. Each cycle represents a matrix which stores the data of each back height: upper, middle and lower. In each cycle a method is declared so that the data obtained can be exported to Microsoft Excel. At last, only the code of the right matrix is shown, which covers the sensors of channels 0 and 1 (upper back). String salsup = ""; //Matrix printing System.out.println("\nMatriz Superior (canales 0 y 1)"); for(inti=0;i