The Computational Mechanics of Bone Tissue (eBook)

Preface 6
Acknowledgements 9
Contents 10
Contributors 12
Biological Characterization of Bone Tissue 14
Bone: Functions, Structure and Physiology 15
1 Introduction 15
2 The Complexity Behind Simplicity 16
2.1 Bone Functions 16
2.2 Bone Structure and Mechanical Behaviour 18
2.3 Regulation of Bone Metabolism (Modelling/Remodelling) 27
2.4 Bone Remodelling and Cell Interchange 31
2.5 Bone Mechanotransduction 32
2.6 Mechanotransduction Mechanisms 38
References 40
Bone Quality Assessment at the Atomic Scale 56
1 Introduction 57
2 Hydroxyapatite 57
3 Rietveld Refinement Method 59
3.1 Crystallite Size and Microdeformations: Scherrer Equation and Williamson-Hall Graph 61
4 Ultrasonometry of the Calcaneus 63
5 Materials and Methods 64
5.1 Ethical Aspects 64
5.2 Materials 64
5.3 Samples Pre-selection 65
5.4 Sample Preparation and Characterization 65
5.5 DRX and Rietveld Method Parameters 65
6 Results and Discussion 68
6.1 Ultrasonometry Analysis 68
6.2 Scanning Electron Microscopy (SEM) 69
6.3 Dispersive Energy Spectroscopy (DES) 70
6.4 Microhardness (HK) 71
6.5 X-Ray Diffractometry (XRD) and the Rietveld Method 73
7 Conclusion 76
References 76
Bone Remodelling Algorithms 80
Meshless, Bone Remodelling and Bone Regeneration Modelling 81
1 Introduction 82
1.1 Bone Regeneration 83
1.2 Bone Remodelling 84
1.3 Meshless Methods 87
2 Bone Remodelling and Regeneration Modelling 89
2.1 Mechanoregulatory Models 90
2.2 Bioregulatory Models 91
2.3 Mechanobioregulatory Models 93
3 Meshless Methods Applications 94
3.1 Meshless Methods and Mechanics 94
3.2 Meshless Methods and Biomechanics 95
3.3 Meshless Methods and Bone Remodelling 95
4 Conclusion 96
References 97
Dynamic Biochemical and Cellular Models of Bone Physiology: Integrating Remodeling Processes, Tumor Growth, and Therapy 104
1 Bone Remodeling Physiology 105
1.1 Healthy Bone Remodeling 105
1.2 Tumor in the Bone Remodeling Cycle 106
1.3 Bone Treatments 108
2 Mathematical Bone Remodeling Local Models 108
2.1 Healthy Remodeling Dynamics 109
2.2 Models Including Tumor Burden 112
2.3 Introducing Treatment 114
2.4 Models Based on Fractional and Variable Order Derivatives 123
3 Non-local Models 125
3.1 Healthy Bone Remodeling 126
3.2 Models Including the Tumor Burden 127
3.3 Non-local Treatment Approach 128
4 Conclusions and Future Work 132
References 135
Mathematical Modelling of Spatio-temporal Cell Dynamics Observed During Bone Remodelling 138
1 Introduction 139
2 Numerical Methods 141
2.1 Finite Element Method 142
2.2 Meshless Methods 143
3 New Spatio-temporal Model 149
3.1 Komarova’s Model 149
3.2 Ayati’s Model 151
3.3 Proposed Model 151
4 2D Bone Patch Analysis 157
4.1 Initial Conditions 157
4.2 Results and Discussion 159
5 Conclusion 163
References 164
A Mechanostatistical Approach to Multiscale Computational Bone Remodelling 168
1 Introduction 168
2 Part I: Macroscale FE Model 171
2.1 Model Construction 171
2.2 Mechanical Simulations 171
3 Part II: Microscale Haversian Model 173
3.1 Model Construction 173
3.2 Macro-microscale Link 174
3.3 Haversian Simulation 175
4 Part III: Statistical Modelling Using PLSR 181
4.1 Database Construction 181
4.2 Macroscale-PLSR Link 182
4.3 Example Prediction 182
5 Conclusions 183
References 184
Numerical Simulation of Bone Tissue and Adjacent Structures 186
Finite Element Analysis of Bone and Experimental Validation 187
1 Introduction 187
2 Element Types 188
3 Constitutive Models of Bone 189
3.1 Use of CT Scans and Density–Elasticity Relationship 192
3.2 Micro-Finite Element Modelling 197
3.3 Complex Constitutive Models 198
3.4 Observations Regarding Constitutive Models 200
4 Experimental Validation 200
4.1 Various Experimental Validation Techniques 201
4.2 Use of Modal Frequencies 203
4.3 Use of Synthetic Bone 203
4.4 Use of Strain Gauges 204
4.5 Use of Optical Recording Devices 205
4.6 Measurement of Micro-motions Between Implant and Bone 205
5 Discussion 206
References 207
Computational Modelling of Tissue-Engineered Cartilage Constructs 211
1 Introduction 211
2 Models for Solute Transport, Uptake and Release 214
3 Models for Cellular Dynamics 215
4 Models for ECM Growth 217
5 Models for Description of the Mechanical Behaviour and Remodelling of Mechanical Properties 219
6 Coupled Metabolic and Mechanical Remodelling Models 222
7 Concluding Remarks 225
References 226
On the Computational Biomechanics of the Intervertebral Disc 231
1 Introduction 232
1.1 Spine Anatomy 232
1.2 Intervertebral Disc Degeneration 234
1.3 Objectives 234
2 Materials and Methods 235
2.1 Finite Element Model 235
2.2 Numerical Simulations 236
3 Results 239
4 Discussion 241
4.1 Short Creep Tests 241
4.2 Long Creep Tests 243
5 Conclusions 244
References 245
Author Index 249