Multiscale Simulations and Mechanics of Biological Materials

Multiscale Simulations and Mechanics of Biological Materials

 A compilation of recent developments in multiscale simulation and computationalbiomaterials written by leading specialists in the field

Presenting the latest developments in multiscale mechanics and multiscale simulations, and offering a unique viewpoint on multiscale modelling of biological materials, this book outlines the latest developments in computational biological materials from atomistic and molecular scale simulation on DNA, proteins, and nano-particles, to meoscale soft matter modelling of cells, and to macroscale soft tissue and blood vessel, and bone simulations. Traditionally, computational biomaterials researchers come from biological chemistry and biomedical engineering, so this is probably the first edited book to present work from these talented computational mechanics researchers. 

The book has been written to honor Professor Wing Liu of Northwestern University, USA, who has made pioneering contributions in multiscale simulation and computational biomaterial in specific simulation of drag delivery at atomistic and molecular scale and computational cardiovascular fluid mechanics via immersed finite element method.

Key features:

• Offers a unique interdisciplinary approach to multiscale biomaterial modelling aimed at both accessible introductory and advanced levels
• Presents a breadth of computational approaches for modelling biological materials across multiple length scales (molecular to whole-tissue scale), including solid and fluid based approaches 
• A companion website for supplementary materials plus links to contributors? websites (www.wiley.com/go/li/multiscale)

About the Editors xv

List of Contributors xvii

Preface xxi

Part I MULTISCALE SIMULATION THEORY

1 Atomistic-to-Continuum Coupling Methods for Heat Transfer in Solids 3
Gregory J. Wagner

1.1 Introduction 3

1.2 The Coupled Temperature Field 5

1.2.1 Spatial Reduction 5

1.2.2 Time Averaging 6

1.3 Coupling the MD and Continuum Energy 7

1.3.1 The Coupled System 7

1.3.2 Continuum Heat Transfer 8

1.3.3 Augmented MD 8

1.4 Examples 9

1.4.1 One-Dimensional Heat Conduction 9

1.4.2 Thermal Response of a Composite System 10

1.5 Coupled Phonon-Electron Heat Transport 12

1.6 Examples: Phonon–Electron Coupling 14

1.6.1 Equilibration of Electron/Phonon Energies 14

1.6.2 Laser Heating of a Carbon Nanotube 15

1.7 Discussion 17

Acknowledgments 18

References 18

2 Accurate Boundary Treatments for Concurrent Multiscale Simulations 21
Shaoqiang Tang

2.1 Introduction 21

2.2 Time History Kernel Treatment 22

2.2.1 Harmonic Chain 22

2.2.2 Square Lattice 23

2.3 Velocity Interfacial Conditions: Matching the Differential Operator 27

2.4 MBCs: Matching the Dispersion Relation 30

2.4.1 Harmonic Chain 30

2.4.2 FCC Lattice 33

2.5 Accurate Boundary Conditions: Matching the Time History Kernel Function 36

2.6 Two-Way Boundary Conditions 39

2.7 Conclusions 41

Acknowledgments 41

References 41

3 A Multiscale Crystal Defect Dynamics and Its Applications 43
Lisheng Liu and Shaofan Li

3.1 Introduction 43

3.2 Multiscale Crystal Defect Dynamics 44

3.3 How and Why the MCDD Model Works 47

3.4 Multiscale Finite Element Discretization 47

3.5 Numerical Examples 52

3.6 Discussion 54

Acknowledgments 54

Appendix 55

References 57

4 Application of Many-Realization Molecular Dynamics Method to Understand the Physics of Nonequilibrium Processes in Solids 59
Yao Fu and Albert C. To

4.1 Chapter Overview and Background 59

4.2 Many-Realization Method 60

4.3 Application of the Many-Realization Method to Shock Analysis 62

4.4 Conclusions 72

Acknowledgments 74

References 74

5 Multiscale, Multiphysics Modeling of Electromechanical Coupling in Surface-Dominated Nanostructures 77
Harold S. Park and Michel Devel

5.1 Introduction 77

5.2 Atomistic Electromechanical Potential Energy 79

5.2.1 Atomistic Electrostatic Potential Energy: Gaussian Dipole Method 80

5.2.2 Finite Element Equilibrium Equations from Total Electromechanical Potential Energy 83

5.3 Bulk Electrostatic Piola–Kirchoff Stress 84

5.3.1 Cauchy–Born Kinematics 84

5.3.2 Comparison of Bulk Electrostatic Stress with Molecular Dynamics Electrostatic Force 86

5.4 Surface Electrostatic Stress 87

5.5 One-Dimensional Numerical Examples 89

5.5.1 Verification of Bulk Electrostatic Stress 89

5.5.2 Verification of Surface Electrostatic Stress 91

5.6 Conclusions and Future Research 94

Acknowledgments 95

References 95

6 Towards a General Purpose Design System for Composites 99
Jacob Fish

6.1 Motivation 99

6.2 General Purpose Multiscale Formulation 103

6.2.1 The Basic Reduced-Order Model 103

6.2.2 Enhanced Reduced-Order Model 104

6.3 Mechanistic Modeling of Fatigue via Multiple Temporal Scales 106

6.4 Coupling of Mechanical and Environmental Degradation Processes 107

6.4.1 Mathematical Model 107

6.4.2 Mathematical Upscaling 109

6.4.3 Computational Upscaling 110

6.5 Uncertainty Quantification of Nonlinear Model of Micro-Interfaces and Micro-Phases 111

References 113

Part II PATIENT-SPECIFIC FLUID-STRUCTURE INTERACTION MODELING, SIMULATION AND DIAGNOSIS

7 Patient-Specific Computational Fluid Mechanics of Cerebral Arteries with Aneurysm and Stent 119
Kenji Takizawa, Kathleen Schjodt, Anthony Puntel, Nikolay Kostov, and Tayfun E. Tezduyar

7.1 Introduction 119

7.2 Mesh Generation 120

7.3 Computational Results 124

7.3.1 Computational Models 124

7.3.2 Comparative Study 131

7.3.3 Evaluation of Zero-Thickness Representation 142

7.4 Concluding Remarks 145

Acknowledgments 146

References 146

8 Application of Isogeometric Analysis to Simulate Local Nanoparticulate Drug Delivery in Patient-Specific Coronary Arteries 149
Shaolie S. Hossain and Yongjie Zhang

8.1 Introduction 149

8.2 Materials and Methods 151

8.2.1 Mathematical Modeling 151

8.2.2 Parameter Selection 156

8.2.3 Mesh Generation from Medical Imaging Data 158

8.3 Results 159

8.3.1 Extraction of NP Wall Deposition Data 159

8.3.2 Drug Distribution in a Normal Artery Wall 160

8.3.3 Drug Distribution in a Diseased Artery Wall with a Vulnerable Plaque 160

8.4 Conclusions and Future Work 165

Acknowledgments 166

References 166

9 Modeling and Rapid Simulation of High-Frequency Scattering Responses of Cellular Groups 169
Tarek Ismail Zohdi

9.1 Introduction 169

9.2 Ray Theory: Scope of Use and General Remarks 171

9.3 Ray Theory 173

9.4 Plane Harmonic Electromagnetic Waves 177

9.4.1 General Plane Waves 177

9.4.2 Electromagnetic Waves 177

9.4.3 Optical Energy Propagation 178

9.4.4 Reflection and Absorption of Energy 179

9.4.5 Computational Algorithm 183

9.4.6 Thermal Conversion of Optical Losses 187

9.5 Summary 190

References 190

10 Electrohydrodynamic Assembly of Nanoparticles for Nanoengineered Biosensors 193
Jae-Hyun Chung, Hyun-Boo Lee, and Jong-Hoon Kim

10.1 Introduction for Nanoengineered Biosensors 193

10.2 Electric-Field-Induced Phenomena 193

10.2.1 Electrophoresis 194

10.2.2 Dielectrophoresis 195

10.2.3 Electroosmotic and Electrothermal Flow 198

10.2.4 Brownian Motion Forces and Drag Forces 199

10.3 Geometry Dependency of Dielectrophoresis 200

10.4 Electric-Field-Guided Assembly of Flexible Molecules in Combination with other Mechanisms 203

10.4.1 Dielectrophoresis in Combination with Fluid Flow 203

10.4.2 Dielectrophoresis in Combination with Binding Affinity 203

10.4.3 Dielectrophoresis in Combination with Capillary Action and Viscosity 203

10.5 Selective Assembly of Nanoparticles 204

10.5.1 Size-Selective Deposition of Nanoparticles 204

10.5.2 Electric-Property Sorting of Nanoparticles 205

10.6 Summary and Applications 205

References 205

11 Advancements in the Immersed Finite-Element Method and Bio-Medical Applications 207
Lucy Zhang, Xingshi Wang, and Chu Wang

11.1 Introduction 207

11.2 Formulation 208

11.2.1 The Immersed Finite Element Method 208

11.2.2 Semi-Implicit Immersed Finite Element Method 210

11.3 Bio-Medical Applications 211

11.3.1 Red Blood Cell in Bifurcated Vessels 211

11.3.2 Human Vocal Folds Vibration during Phonation 214

11.4 Conclusions 217

References 217

12 Immersed Methods for Compressible Fluid–Solid Interactions 219
Xiaodong Sheldon Wang

12.1 Background and Objectives 219

12.2 Results and Challenges 222

12.2.1 Formulations, Theories, and Results 222

12.2.2 Stability Analysis 227

12.2.3 Kernel Functions 228

12.2.4 A Simple Model Problem 231

12.2.5 Compressible Fluid Model for General Grids 231

12.2.6 Multigrid Preconditioner 232

12.3 Conclusion 234

References 234

Part III FROM CELLULAR STRUCTURE TO TISSUES AND ORGANS

13 The Role of the Cortical Membrane in Cell Mechanics: Model and Simulation 241
Louis Foucard, Xavier Espinet, Eduard Benet, and Franck J. Vernerey

13.1 Introduction 241

13.2 The Physics of the Membrane–Cortex Complex and Its Interactions 243

13.2.1 The Mechanics of the Membrane–Cortex Complex 243

13.2.2 Interaction of the Membrane with the Outer Environment 247

13.3 Formulation of the Membrane Mechanics and Fluid–Membrane Interaction 249

13.3.1 Kinematics of Immersed Membrane 249

13.3.2 Variational Formulation of the Immersed MCC Problem 251

13.3.3 Principle of Virtual Power and Conservation of Momentum 253

13.4 The Extended Finite Element and the Grid-Based Particle Methods 255

13.5 Examples 257

13.5.1 The Equilibrium Shapes of the Red Blood Cell 257

13.5.2 Cell Endocytosis 259

13.5.3 Cell Blebbing 260

13.6 Conclusion 262

Acknowledgments 263

References 263

14 Role of Elastin in Arterial Mechanics 267
Yanhang Zhang and Shahrokh Zeinali-Davarani

14.1 Introduction 267

14.2 The Role of Elastin in Vascular Diseases 268

14.3 Mechanical Behavior of Elastin 269

14.3.1 Orthotropic Hyperelasticity in Arterial Elastin 269

14.3.2 Viscoelastic Behavior 271

14.4 Constitutive Modeling of Elastin 272

14.5 Conclusions 276

Acknowledgments 276

References 277

15 Characterization of Mechanical Properties of Biological Tissue: Application to the FEM Analysis of the Urinary Bladder 283
Eugenio Oñate, Facundo J. Bellomo, Virginia Monteiro, Sergio Oller, and Liz G. Nallim

15.1 Introduction 283

15.2 Inverse Approach for the Material Characterization of Biological Soft Tissues via a Generalized Rule of Mixtures 284

15.2.1 Constitutive Model for Material Characterization 284

15.2.2 Definition of the Objective Function and Materials Characterization Procedure 286

15.2.3 Validation of the Inverse Model for Urinary Bladder Tissue Characterization 287

15.3 FEM Analysis of the Urinary Bladder 289

15.3.1 Constitutive Model for Tissue Analysis 290

15.3.2 Validation. Test Inflation of a Quasi-incompressible Rubber Sphere 292

15.3.3 Mechanical Simulation of Human Urinary Bladder 293

15.3.4 Study of Urine–Bladder Interaction 295

15.4 Conclusions 298

Acknowledgments 298

References 298

16 Structure Design of Vascular Stents 301
Yaling Liu, Jie Yang, Yihua Zhou, and Jia Hu

16.1 Introduction 301

16.2 Ideal Vascular Stents 303

16.3 Design Parameters that Affect the Properties of Stents 304

16.3.1 Expansion Method 305

16.3.2 Stent Materials 305

16.3.3 Structure of Stents 306

16.3.4 Effect of Design Parameters on Stent Properties 308

16.4 Main Methods for Vascular Stent Design 308

16.5 Vascular Stent Design Method Perspective 316

References 316

17 Applications of Meshfree Methods in Explicit Fracture and Medical Modeling 319
Daniel C. Simkins, Jr.

17.1 Introduction 319

17.2 Explicit Crack Representation 319

17.2.1 Two-Dimensional Cracks 320

17.2.2 Three-Dimensional Cracks in Thin Shells 323

17.2.3 Material Model Requirements 323

17.2.4 Crack Examples 323

17.3 Meshfree Modeling in Medicine 327

Acknowledgments 331

References 331

18 Design of Dynamic and Fatigue-Strength-Enhanced Orthopedic Implants 333
Sagar Bhamare, Seetha Ramaiah Mannava, Leonora Felon, David Kirschman, Vijay Vasudevan, and Dong Qian

18.1 Introduction 333

18.2 Fatigue Life Analysis of Orthopedic Implants 335

18.2.1 Fatigue Life Testing for Implants 335

18.2.2 Fatigue Life Prediction 337

18.3 LSP Process 338

18.4 LSP Modeling and Simulation 339

18.4.1 Pressure Pulse Model 339

18.4.2 Constitutive Model 340

18.4.3 Solution Procedure 341

18.5 Application Example 342

18.5.1 Implant Rod Design 342

18.5.2 Residual Stresses 342

18.5.3 Fatigue Tests and Life Predictions 344

18.6 Summary 348

Acknowledgments 348

References 349

Part IV BIO-MECHANICS AND MATERIALS OF BONES AND COLLAGENS

19 Archetype Blending Continuum Theory and Compact Bone Mechanics 353
Khalil I. Elkhodary, Michael Steven Greene, and Devin O’Connor

19.1 Introduction 353

19.1.1 A Short Look at the Hierarchical Structure of Bone 354

19.1.2 A Background of Generalized Continuum Mechanics 355

19.1.3 Notes on the Archetype Blending Continuum Theory 356

19.2 ABC Formulation 358

19.2.1 Physical Postulates and the Resulting Kinematics 358

19.2.2 ABC Variational Formulation 359

19.3 Constitutive Modeling in ABC 361

19.3.1 General Concept 361

19.3.2 Blending Laws for Cortical Bone Modeling 363

19.4 The ABC Computational Model 367

19.5 Results and Discussion 368

19.5.1 Propagating Strain Inhomogeneities across Osteons 368

19.5.2 Normal and Shear Stresses in Osteons 369

19.5.3 Rotation and Displacement Fields in Osteons 370

19.5.4 Damping in Cement Lines 372

19.5.5 Qualitative Look at Strain Gradients in Osteons 372

19.6 Conclusion 373

Acknowledgments 374

References 374

20 Image-Based Multiscale Modeling of Porous Bone Materials 377
Judy P. Yang, Sheng-Wei Chi, and Jiun-Shyan Chen

20.1 Overview 377

20.2 Homogenization of Porous Microstructures 379

20.2.1 Basic Equations of Two-Phase Media 379

20.2.2 Asymptotic Expansion of Two-Phase Medium 381

20.2.3 Homogenized Porous Media 386

20.3 Level Set Method for Image Segmentation 387

20.3.1 Variational Level Set Formulation 387

20.3.2 Strong Form Collocation Methods for Active Contour Model 389

20.4 Image-Based Microscopic Cell Modeling 391

20.4.1 Solution of Microscopic Cell Problems 391

20.4.2 Reproducing Kernel and Gradient-Reproducing Kernel Approximations 392

20.4.3 Gradient-Reproducing Kernel Collocation Method 393

20.5 Trabecular Bone Modeling 395

20.6 Conclusions 399

Acknowledgment 399

References 399

21 Modeling Nonlinear Plasticity of Bone Mineral from Nanoindentation Data 403
Amir Reza Zamiri and Suvranu De

21.1 Introduction 403

21.2 Methods 404

21.3 Results 407

21.4 Conclusions 408

Acknowledgments 408

References 408

22 Mechanics of Cellular Materials and its Applications 411
Ji Hoon Kim, Daeyong Kim, and Myoung-Gyu Lee

22.1 Biological Cellular Materials 411

22.1.1 Structure of Bone 411

22.1.2 Mechanical Properties of Bone 411

22.1.3 Failure of Bone 415

22.1.4 Simulation of Bone 417

22.2 Engineered Cellular Materials 421

22.2.1 Constitutive Models for Metal Foams 422

22.2.2 Structure Modeling of Cellular Materials 424

22.2.3 Simulation of Cellular Materials 428

References 431

23 Biomechanics of Mineralized Collagens 435
Ashfaq Adnan, Farzad Sarker, and Sheikh F. Ferdous

23.1 Introduction 435

23.1.1 Mineralized Collagen 435

23.1.2 Molecular Origin and Structure of Mineralized Collagen 436

23.1.3 Bone Remodeling, Bone Marrow Microenvironment, and Biomechanics of Mineralized Collagen 438

23.2 Computational Method 438

23.2.1 Molecular Structure of Mineralized Collagen 438

23.2.2 The Constant-pH Molecular Dynamics Simulation 441

23.3 Results 441

23.3.1 First-Order Estimation of pH-Dependent TC–HAP Interaction Possibility 441

23.3.2 pH-Dependent TC–HAP Interface Interactions 443

23.4 Summary and Conclusions 446

Acknowledgments 446

References 446

Index 449

Shaofan Li is Professor of Applied and Computational Mechanics in the Department of Civil and Environmental Engineering at University of California, Berkeley, USA. He gained his PhD in Mechanical Engineering from Northwestern University, Illinois, in 1997, having previously earned his MSc in Aerospace Engineering. His current research interests include Meshfree Simulations of Adiabatic Shear Band and Spall Fracture, Simulations of Stem Cell Differentiations, and Multiscale Non-equilibrium Equilibrium Molecular Dynamics. Dr Li is the author of numerous articles and conference proceedings.

Dong Qian is Associate Professor of Mechanical Engineering and Director of Graduate Study for the Mechanical Engineering Program at the University of Cincinnati, USA. He obtained his BS degree in Bridge Engineering in 1994 from Tongji University in China. He came to US in 1996 and obtained M.S. degree in civil engineering at the University of Missouri-Columbia in 1998. Dr. Qian is a member of the US association for computational mechanics and ASME. He has published over 40 journal papers and book chapters. His research interests include nano-scale modeling, simulation and applications, meshfree methods, and development of multi-scale methods in solid mechanics.