Note: Computational Modeling in Biomechanics -- Section I Biofluids and Mass Transport -- 1 Immersed Boundary/Continuum Methods -- 1 Introduction -- 1.1 Immersed Boundary -- Nodal Forces -- Incompressible Continuum -- 1.2 Mapping and Kernel -- 1.3 Fictitious Domain Method -- Immersed Continuum Method -- 1.4 Implicit/Compressible Solver -- 2 Discussions -- References -- 2 Computational Modeling of ATP/ADP Concentration at the Vascular Surface -- 1 Introduction -- 2 Mathematical Models -- 2.1 History of ATP/ADP Mathematical Models -- 2.2 Essential Physics -- 2.3 Governing Equations -- 2.4 Boundary Conditions -- 2.4.1 Modeling Flow-Induced ATP Release -- 2.4.2 Flow Conditions -- 2.5 Relevant Dimensionless Parameters -- 3 Model Results: Flow-Mediated Nucleotide Concentration at the EC Surface -- 3.1 Synopsis of Model Results and Implications -- 3.2 Understanding the Results of the Models: Contributions of Individual Flow Features -- 3.2.1 Steady Undisturbed Flow -- 3.2.2 Pulsatile Undisturbed Flow -- 3.2.3 Disturbed Flow: Flow Recirculation and Beyond -- 3.2.4 Impact of ATP-Free Perfusion on Nucleotide Concentration at the EC Surface -- 4 General Perspectives and Critical Future Directions -- References -- 3 Development of a Lattice-Boltzmann Method for Multiscale Transport and Absorption with Application to Intestinal Function -- 1 Introduction -- 2 Numerical Methods -- 2.1 Basic Lattice-Boltzmann Algorithm for Momentum and Pressure -- 2.2 Passive Scalar in the Lattice-Boltzmann Method -- 2.3 Moving Boundary Conditions for Momentum -- 2.4 Scalar Concentration Boundary Conditions -- 2.4.1 Fixed-Scalar Boundary Condition -- 2.4.2 Fixed-Flux Boundary Condition -- 2.5 Multi Grid Algorithm -- 2.6 Implementation of Multigrid Strategy in the Momentum Propagation Method -- 3 Validation of Algorithm with A Multiscale Model of Macro-to-Micro Scale Transport. , 3.1 Continuity Between Coarse and Fine Grids -- 3.2 Validation of the Multi Grid Strategy -- 3.3 Validation of Moving Boundary Conditions -- 4 Concluding Remarks -- References -- Section II Cardiovascular Biomechanics -- 4 Computational Models of Vascular Mechanics -- 1 Introduction -- 2 Healthy Vessels -- 2.1 Conducting Arteries -- 2.2 Distributing Arteries -- 3 Healthy Arterial Mechanical Response and Constitutive Relations -- 4 Mechanics Studies of Non-Atheromatous Arteries -- 4.1 Healthy Geometry, Healthy Material -- 4.2 High Pressure Response -- 5 Fluid-Structure Interaction -- 5.1 Stenotic Geometry, Healthy Material -- 6 Carotid Bifurcation -- 6.1 Healthy Carotid Bifurcation, Measurement-Based -- 7 Patient-Specific Studies -- 8 Imaging-Derived Geometry and Flow Boundary Conditions -- 8.1 Computed Tomography -- 8.2 Magnetic Resonance Imaging -- 8.3 Time-Of-Flight (TOF) Methods -- 8.4 2-D TOF Methods -- 8.5 3-D TOF Methods -- 8.6 Phase Contrast MRA/MRI -- 8.7 Contrast-Enhanced MRA (CE-MRA) -- 8.8 Black Blood MRI -- 8.9 Ultrasound -- 8.10 Image Segmentation -- 9 Image-Based Modeling of Healthy Vessels -- 10 The Atherosclerotic Artery Wall -- 11 Solid Mechanics of Idealized Plaque Lesions -- 11.1 Microcalcifications -- 12 2-D Patient-Specific Plaque Studies -- 13 3-D Patient-Specific Plaque Studies -- 13.1 Plaque Lesion Fracture, Dissection, Stenting, and Angioplasty -- 13.2 Stenting -- 14 Current Developments -- References -- 5 Computational Modeling of Vascular Hemodynamics -- 1 Hemodynamics and Vascular Disease -- 1.1 A Brief Description of Atherosclerotic and Aneurismal Diseases -- 1.2 Hemodynamics in the Initiation and Progression of Atherosclerotic Lesions -- 1.3 Hemodynamics in Aneurismal Blood Vessels -- 2 Computational Fluid Dynamics -- 2.1 Numerical Methods -- 2.1.1 Governing Equations and Modeling Assumptions. , 2.1.2 Numerical Solution of the Flow Equations -- 2.2 Flow Boundary Conditions -- 2.2.1 Typical Assumptions for the Inlet and Outlet Boundary Conditions -- 2.2.2 Accounting for the Proximal and Distal Circulation -- 2.3 Post-processing and Visualization of Numerical and Experimental Results -- 2.3.1 Various Flow Descriptors -- 2.3.2 Flow Characterization and Lagrangian Particle Tracking -- 2.4 Non-Newtonian Blood Behavior -- 2.4.1 Shear Thinning and Yield Stress Properties -- 2.4.2 Commonly Used Non-Newtonian Viscosity Models -- 2.5 Transitional and Turbulent Flow -- 2.6 Compliant Arterial Wall -- 2.6.1 CFD Simulations with Moving Boundaries -- 3 Patient-Specific Computational Modeling -- 3.1 Medical Imaging Modalities -- 3.2 Patient-Specific Lumenal Geometries -- 3.2.1 Geometry Reconstruction -- 3.2.2 Longitudinal Studies -- 3.3 Patient-Specific Flow Measurements -- 3.3.1 MR Velocimetry -- 4 Modeling of the Flow in Diseased Blood Vessels -- 4.1 Flow in Atherosclerotic Carotid Bifurcations -- 4.2 Flow in Aneurysmal Arteries -- 4.3 Accuracy and Reliability of CFD Results -- 4.3.1 Validation with Clinical Data -- 4.3.2 Validation with Experimental Results -- 5 Current Developments -- 5.1 Prediction of Disease Progression for a Given Patient and Guidance for Interventions -- References -- 6 Computational Modeling of Coronary Stents -- 1 Introduction -- 1.1 Computational Simulations -- 1.1.1 Governing Equations -- 1.1.2 Material Models -- 1.1.3 Geometries -- 1.2 Spatial and Temporal Gradients of Shear Stress -- 1.3 Arbitrary Lagrange Eulerian (ALE) Method -- 1.4 Fluid-Structure Coupling -- 1.5 Stent Simulation Results -- 1.6 Solid Mechanics Simulations -- 1.6.1 Under-sizing of Stent -- 1.6.2 Over-sizing of Stent -- 1.7 Mechanical Stresses and Vessel Function -- 2 Summary and Conclusions -- References -- 7 Computational Modeling of Aortic Heart Valves. , 1 Introduction -- 2 The Aortic Valve -- 3 Anatomical and Material Properties -- 4 Simulation of the Cardiac Cycle -- 5 Fluid-Structure Interaction -- 6 Multiscale Approach -- 7 Applications -- 7.1 Natural Aortic Valve -- 7.2 Diseased Aortic Valve -- 7.3 Modeling Surgical Repair -- 7.4 Optimizing Artificial Heart Valve Design -- 8 Future Directions -- 9 Conclusion -- References -- 8 Computational Modeling of Growth and Remodeling in Biological Soft Tissues: Application to Arterial Mechanics -- 1 Introduction -- 2 Towards a Theory of Growth and Remodeling (G& -- R) -- 3 Theoretical Framework for Growth and Remodeling (G& -- R) -- 4 Computational Considerations -- 5 Illustrative Results -- 6 Conclusion -- References -- Section III Musculoskeletal Biomechanics -- 9 Computational Modeling of Trabecular Bone Mechanics -- 1 Introduction -- 2 The Finite Element Method -- 3 Idealized Geometric Trabecular Models -- 3.1 Historical Context -- 3.2 Beam Models -- 3.3 Image-Based Beam and Plate Models -- 4 Micro-FEA Modeling -- 4.1 Mesh Generation -- 4.2 Convergence and Accuracy of Micro-FEA Models -- 4.3 Material Property Assignment -- 4.4 Calculation of Trabecular Tissue Modulus -- 4.5 Homogenization -- 4.6 Nonlinear Behavior -- 4.6.1 Geometric Nonlinearity -- 4.6.2 Softening Materials -- 4.6.3 Fracture Simulations -- 4.7 Evaluation of Measurement Techniques -- 4.8 In vivo Applications -- 4.9 Result Post-processing -- 4.10 Whole Bone Simulations -- 5 Future Challenges -- 6 Summary -- References -- 10 Computational Modeling of Extravascular Flow in Bone -- 1 Introduction -- 1.1 Defining ``The System'' Bone -- 1.2 Endogeneous Structural and Fluid Components of Bone -- 1.3 Role of Fluid Flow and Mass Transport in Bone Physiology -- 1.4 Role of Computational Models in Understanding Extravascular Flow in Bone Health and Disease. , 2 Multiscale Models of Extravascular Fluid Flow in Bone -- 3 Parametric Study: Importance of Spatially Defined Material Parameters on Flow Predictions -- 4 Spatially Resolved Permeabilities and Porosities -- 5 Idealization of Geometries at the Cell Scale and Below Results in a Profound Underprediction of Flow Velocities -- 6 Current Hurdles and Future Vision -- References -- 11 Computational Modeling of Cell Mechanics in Articular Cartilage -- 1 Introduction -- 2 Continuum Models of Cell Mechanics -- 2.1 Single Phase Models -- 2.2 Biphasic (Solid-Fluid) Model -- 2.3 Biot Poroelastic Model -- 3 Computational Methods -- 3.1 Boundary Element Methods -- 3.1.1 Axisymmetric Elastic BEM -- 3.1.2 Axisymmetric Incompressible Viscoelastic BEM -- 3.1.3 Biphasic (Poroelastic) BEM -- 3.2 Finite Element Methods -- 4 Applications -- 4.1 Micropipette Aspiration -- 4.1.1 Boundary Element Models of Micropipette Aspiration -- 4.1.2 Multiphasic Finite Element Models of Micropipette Aspiration -- 4.2 Multiphasic Models of Mechanical Cell-Matrix Interactions -- 5 Summary -- References -- 12 Computational Models of Tissue Differentiation -- 1 Introduction -- 2 Approaches to Modelling -- 3 Simulation Architecture -- 3.1 Overview -- 3.2 Algorithms as Building Blocks of the Simulation -- 3.2.1 Cell Movement -- 3.2.2 Cell Proliferation and Cell Apoptosis -- 3.2.3 Determination of Stem Cell Fate and Stem Cell Differentiation -- 3.2.4 Angiogenesis -- 3.2.5 Synthesis of Matrix -- 3.3 Implementation Using Finite Element Analysis -- 3.4 Applications in Tissue Engineering -- 4 Possibilities for Scaffold/Bioreactor Modelling -- 5 Discussion and Conclusion -- References -- Section IV Soft Tissue Biomechanics -- 13 A Review of the Mathematical and Computational Foundations of Biomechanical Imaging -- 1 Introduction -- 2 Background -- 2.1 Motivation -- 2.2 Imaging Tissue Deformation. , 2.2.1 Ultrasound Imaging of Quasi-Static Compression.