IUTAM Symposium on Cellular, Molecular and Tissue Mechanics (eBook)

IUTAM Symposium on C ellular, Molecular 
 
1 
Preface 
5 
Part I Tissue Mechanics 10
Experimental and Computational Investigation of Viscoelasticity of Native and Engineered Ligament and Tendon 11
1 Introduction 11
2 Experimental Methods 13
2.1 Native Tissue Isolation 13
2.2 Mechanical Evaluation of Native Ligament and Tendon 14
3 Mathematical Modeling of Mechanical Response 15
3.1 Micromechanical Modeling of Non-linear Viscoelasticity 15
3.2 Governing Equations of the Computational Model 17
4 Results 19
4.1 Engineered Ligament In Vitro, In Vivo and Young Animal MCL 19
4.2 Native Ligament and TA Tendon Mechanics 20
4.3 Computational Results 23
5 Conclusion 24
References 24
A Comparison of a Nonlinear and Quasilinear Viscoelastic Anisotropic Model for Fibrous Tissues 26
1 Introduction 26
2 Model Development 27
2.1 Anisotropic Nonlinear Viscoelastic Model 27
2.1.1 General Remarks 30
2.2 Anisotropic Quasilinear Viscoelastic Model 31
2.2.1 General Remarks 32
3 Numerical Examples 33
4 Conclusion 35
References 36
Hysteretic Behavior of Ligaments and Tendons: Microstructural Analysis of Damage, Softeningand Non-Recoverable Strain 37
1 Introduction 37
2 Viscoelastic Theory of Temporary Interfibrillar Bridges in the ECM Network 39
2.1 Definition of the Viscoelastic Strain Energy Function 39
2.2 Energy-Driven Evolution Equations for Structural Damage 40
2.3 Transition State Theory of the Softening Effect in the ECM 42
3 Numerical Results for Cyclic Uniaxial Traction 42
4 Discussion and Conclusion 46
References 48
On Measuring Stress Distributions in Epithelia 50
1 Introduction 50
2 Methods 51
2.1 Theoretical Framework 51
2.1.1 Equibiaxially Stretched Membrane with two Circular Holes 52
2.1.2 Circular Perforation of a Biaxially Pre-stretched Membrane 53
2.2 Embryo Preparation and Perforation Experiments 53
3 Results and Discussion 54
3.1 Effects of Hole Spacing 54
3.2 Effects of Anisotropic Stretch 55
3.3 Illustrative Example 58
4 Conclusions 58
References 59
A Viscoelastic Anisotropic Model for Soft Collageneous Tissues Based on Distributed Fiber–Matrix Units 60
1 Introduction 60
2 Constitutive Model 61
2.1 Nonlinear Fiber–Matrix Interaction Model 61
2.2 Small Strain Case 63
2.3 Three-Dimensional Anisotropic Generalization 64
3 Numerical Examples 65
3.1 Equilibrium Solution 66
3.2 Rate Dependent Behavior 67
3.3 Comparison to Experimental Data 67
4 Discussion and Concluding Remarks 68
References 69
Part II Cell-substrate Interactions 71
Chemical and Mechanical Micro-Diversity of the Extracellular Matrix 72
1 The Cell-Extracellular Matrix Interface and Environmental Signaling 73
2 The Varying Responses of Cells Adhering to Different Extracellular Matrices 73
3 Molecular Diversity of the Fibronectin ECM 76
4 Mechanical Forces Affect the Organization and Adhesive Properties of Fibronectin Fibrils 76
5 Involvement of Lamellar Retraction in Fibronectin Fibrillogenesis by Means of Cultured Fibroblasts 80
6 Conclusions 81
References 81
Tissue-to-Cellular Deformation Couplingin Cell-Microintegrated Elastomeric Scaffolds 83
1 Introduction 84
2 Methods 84
2.1 Specimen Fabrication 84
2.2 Image Acquisition and Construct Characterization 85
3 Results 85
3.1 Scaffold Micromechanics 85
3.2 Coupled Cell-Scaffold Deformation 87
4 Discussion 88
References 90
Orientational Polarizability and Stress Response of Biological Cells 92
1 Introduction 92
2 Theoretical Model 94
3 Orientational Polarizability 97
4 Discussion 100
References 101
Universal Temporal Response of Fibroblasts Adhering on Cyclically Stretched Substrates 103
1 Introduction 103
2 Materials and Methods 104
3 Results and Discussion 106
References 109
Part III Mechanics of DNA 110
Elastic and Electrostatic Model for DNA in Rotation–ExtensionExperiments 111
1 Introduction 111
2 Model 113
2.1 Geometry 113
2.2 Energy Formulation 114
2.3 Ubbink and Odijk Model of DNA–DNA Interactions 115
2.4 Equilibrium Equations 116
2.5 Vertical Extension of the Filament 117
3 Results 117
3.1 A Numerical Example 117
3.2 Extension–Rotation Curve 118
4 Discussion 119
References 120
Shape and Energetics of DNA Plectonemes 121
1 Introduction 121
2 Review of Kirchhoff's Theory of Rods 122
3 Localizing Solutions 123
4 Constructing the Plectonemic Solution 124
5 Variational Method 127
6 Configurational Entropy and Electrostatics in the Plectoneme 130
7 Conclusions 135
References 135
Part IV Mechanics of Biopolymer Networks 137
Constitutive Models for the Force-Extension Behavior of Biological Filaments 138
1 Introduction 139
2 Flexible and Semiflexible Filaments and Molecules 140
2.1 Freely Jointed Chain Model with Unfolding 140
2.2 Worm-Like Chain Models 143
3 Elastica Approximate Model 147
4 Discussion 153
References 154
Small Strain Topological Effects of Biopolymer Networks with Rigid Cross-Links 157
1 Introduction 157
2 Scaling Relations 158
3 Topology of Cytoskeletal Networks 159
4 Numerical Network Model 160
5 Results 160
5.1 Dependence on Concentration 162
5.2 Relation Between Connectivity and Filament Length 162
6 Conclusion 163
References 164
Part V Cell adhesion 166
An Observation on Bell's Model for Molecular Bond Separation Under Force 167
1 Introduction 167
2 Description of a Confining Potential 168
3 The Off-Rate 171
4 Comparison of Off-Rate Estimates 172
References 174
A Theoretical Study of the Thermodynamics and Kinetics of Focal Adhesion Dynamics 175
1 Introduction 175
2 Focal Adhesion Disassembly Is a Fracture Problem 177
3 Focal Adhesion Dynamics as a Chemo-Mechanically Controlled Rate Process 178
3.1 Thermodynamic Driving Forces 180
3.1.1 Mechanical Work as a Thermodynamic Driving Force 180
3.1.2 Chemical Driving Forces 181
3.1.3 Driving Force due to Elasticity 181
3.1.4 Work Done by Force Via Conformational Changes 182
3.2 Thermodynamically Driven Focal Adhesion Dynamics 182
3.3 State Diagram of Focal Adhesions 183
4 Discussion 184
References 185
Tension-Induced Growth of Focal Adhesions at Cell–SubstrateInterface 187
1 Introduction 187
2 Model 188
3 Monte Carlo Simulation 191
4 Results and Discussions 192
5 Conclusions 194
References 194
Pattern Formation and Force Generation by Cell Ensemblesin a Filamentous Matrix 196
1 Introduction 196
2 Model 198
3 Results 200
4 Discussion 203
References 204
Mechano-Chemical Coupling in Shell Adhesion 207
1 Introduction 207
2 Mechano-Chemical Model 208
2.1 Surface Thermodynamics and Chemical Equilibrium 208
2.2 Mechanical Equilibrium 210
2.3 Adhesion Parameters and Measures of Deformation 211
3 Solutions 212
4 Coupling Between Deformation and Chemical Activation 214
5 Conclusions 215
References 216
Catch-to-Slip Bond Transition in Biological Bonds by Entropic and Energetic Elasticity 218
1 Introduction 218
2 Theory 219
2.1 Off-Rates by Entropy Controlled Dissociation 220
2.2 Off-Rates by Energy Controlled Dissociation 221
2.3 Overall Bond Lifetime 221
3 Slip-to-Catch Bond Transition 221
4 Stiffness Dependence of Catch Bonds 222
5 Conclusion 223
References 224
Part VI Growth 225
Dilation and Hypertrophy: A Cell-Based Continuum Mechanics Approach Towards Ventricular Growthand Remodeling 226
1 Motivation 226
2 Governing Equations 228
3 Growth Laws 229
4 Example 230
5 Discussion 232
References 232
A Morpho-Elastic Model of Hyphal Tip Growthin Filamentous Organisms 234
1 Introduction 234
2 Nonlinear Elastic Models of Hyphal Growth 235
2.1 Hyphal Geometry 235
3 Modeling Cell Wall Properties and Growth 239
4 Results 241
5 Conclusion 242
References 243
Extracellular Control of Limb Regeneration 245
1 Introduction 245
2 Results and Discussion 248
2.1 Creation of Biologically Compatible Silicone Substrates 250
3 Conclusions 252
References 253
Part VII Poroelasticity of Bone 255
Bone Composite Mechanics Relatedto Collagen Hydration State 256
1 Introduction 256
2 Bone as a Composite 257
3 Poroelastic Indentation Theory 259
4 Identification of the Permeability 260
5 Discussion 261
References 262
Author Index 264