Computer Modeling in Bioengineering -- Contents -- Contributors -- Preface -- Part I Theoretical Background of Computational Methods -- 1 Notation - Matrices and Tensors -- 1.1 Matrix representation of mathematical objects -- 1.2 Basic relations in matrix algebra -- 1.3 Definition of tensors and some basic tensorial relations -- 1.4 Vector and tensor differential operations and integral theorems -- 1.5 Examples -- 2 Fundamentals of Continuum Mechanics -- 2.1 Definitions of stress and strain -- 2.1.1 Stress -- 2.1.2 Strain and strain rate -- 2.1.3 Examples -- 2.2 Linear elastic and viscoelastic constitutive relations -- 2.2.1 Linear elastic constitutive law -- 2.2.2 Viscoelasticity -- 2.2.3 Transformation of constitutive relations -- 2.2.4 Examples -- 2.3 Principle of virtual work -- 2.3.1 Formulation of the principle of virtual work -- 2.3.2 Examples -- 2.4 Nonlinear continuum mechanics -- 2.4.1 Deformation gradient and the measures of strain and stress -- 2.4.2 Nonlinear elastic constitutive relations -- 2.4.3 Examples -- 3 Heat Transfer, Diffusion, Fluid Mechanics, and Fluid Flow through Porous Deformable Media -- 3.1 Heat conduction -- 3.1.1 Governing relations -- 3.1.2 Examples -- 3.2 Diffusion -- 3.2.1 Differential equations of diffusion -- 3.2.2 Examples -- 3.3 Fluid flow of incompressible viscous fluid with heat and mass transfer -- 3.3.1 Governing equations of fluid flow and of heat and mass transfer -- 3.3.2 Examples -- 3.4 Fluid flow through porous deformable media -- 3.4.1 The governing equations -- 3.4.2 Examples -- Part II Fundamentals of Computational Methods -- 4 Isoparametric Formulation of Finite Elements -- 4.1 Introduction to the finite element method -- 4.2 Formulation of 1D finite elements and equilibrium equations -- 4.2.1 Truss finite element -- 4.2.2 Equilibrium equations of the FE assemblage and boundary conditions.

4.2.3 Examples -- 4.3 Three-dimensional (3D) isoparametric finite element -- 4.3.1 Element formulation -- 4.3.2 Examples -- 4.4 Two-dimensional (2D) isoparametric finite elements -- 4.4.1 Formulation of the elements -- 4.4.2 Examples -- 4.5 Isoparametric shell finite element for general 3D analysis -- 4.5.1 Basic assumptions about shell deformation -- 4.5.2 Formulation of a four-node shell element -- 4.5.3 Examples -- 5 Dynamic Finite Element Analysis -- 5.1 Introduction to dynamics of structures -- 5.2 Differential equations of motion -- 5.3 Integration of differential equations of motion -- 5.4 System frequencies and modal shapes -- 5.5 Examples -- 6 Introduction to Nonlinear Finite Element Analysis -- 6.1 Introduction -- 6.2 Principle of virtual work and equilibrium equations in nonlinear incremental analysis -- 6.2.1 Discrete system -- 6.2.2 Principle of virtual work for a continuum -- 6.2.3 Finite element model -- 6.2.4 Finite element model with logarithmic strains -- 6.3 Examples -- 7 Finite Element Modeling of Field Problems -- 7.1 Introduction -- 7.1.1 General considerations -- 7.1.2 The Galerkin method -- 7.2 Heat conduction -- 7.2.1 The finite element equations -- 7.2.2 Examples -- 7.3 Diffusion -- 7.3.1 The finite element equations -- 7.3.2 Examples -- 7.4 Fluid flow with heat and mass transfer -- 7.4.1 The finite element equations -- 7.4.2 Examples -- 7.5 FE equations for modeling large change of fluid domain - Arbitrary Lagrangian-Eulerian (ALE) formulation -- 7.5.1 The ALE formulation -- 7.5.2 Examples -- 7.6 Solid-fluid interaction -- 7.6.1 Loose coupling method -- 7.6.2 Examples -- 7.7 Fluid flow through porous deformable media -- 7.7.1 Finite element balance equations -- 7.7.2 Examples -- 8 Discrete Particle Methods for Modeling of Solids and Fluids -- 8.1 Molecular dynamics -- 8.1.1 Introduction.

8.1.2 Differential equations of motion and boundary conditions -- 8.1.3 Examples -- 8.2 Dissipative Particle Dynamics (DPD) method -- 8.2.1 Introduction to mesoscale DPD modeling -- 8.2.2 Basic DPD equations -- 8.2.3 Examples -- 8.3 Multiscale modeling, coupling DPD-FE for fluid flow -- 8.3.1 Introduction to multiscale modeling -- 8.3.2 Basic equations and boundary conditions -- 8.3.3 Examples -- 8.4 Smoothed Particle Hydrodynamics (SPH) -- 8.4.1 Introduction -- 8.4.2 The basic equations of the SPH method -- 8.4.3 Examples -- 8.5 Element-Free Galerkin (EFG) method -- 8.5.1 Introduction -- 8.5.2 Formulation of the EFG method -- 8.5.3 Examples -- Part III Computational Methods in Bioengineering -- 9 Introduction to Bioengineering -- 9.1 The subject and scope of bioengineering -- 9.2 The role of computer modeling in bioengineering -- 9.2.1 Computational models -- 9.2.2 Future advances in computer modeling -- 10 Bone Modeling -- 10.1 The structure and forms of bones -- 10.1.1 The structure of bone tissue -- 10.1.2 The form of bones -- 10.1.3 Osteoporosis and bone density -- 10.2 The mechanical properties of bone and FE modeling -- 10.3 Bone fracture - medical treatment and computer modeling -- 10.3.1 General considerations -- 10.3.2 Fracture treatment -- 10.3.3 FE modeling of femur comminuted fracture -- 10.4 Internal fixation of hip fracture - two solutions and computer models -- 10.4.1 Solutions by parallel screws and by dynamic hip implant -- 10.4.2 Finite element models of intracapsular fractures of the femoral neck -- 11 Biological Soft Tissue -- 11.1 Introduction to mechanics of biological tissue -- 11.1.1 Structure and function of biological tissue -- 11.1.2 Basic experiments and mechanical models -- 11.2 Modeling methods for isotropic tissue -- 11.2.1 General concept of computational procedures.

11.2.2 Biaxial models of membranes, hardening and hysteretic behavior, action of surfactant -- 11.2.3 Use of strain energy functions -- 11.3 Examples -- 12 Skeletal Muscles -- 12.1 Introduction -- 12.1.1 Basic physiology of muscle mechanics -- 12.1.2 Basics of muscle finite element modeling -- 12.2 Muscle modeling -- 12.2.1 Hill's phenomenological model -- 12.2.2 Determination of stresses within muscle fiber -- 12.2.3 Hill's model which includes fatigue -- 12.2.4 An extension of Hill's model to include different fiber types -- 12.3 Examples -- 13 Blood Flow and Blood Vessels -- 13.1 Introduction to the cardiovascular system -- 13.1.1 The circulatory system -- 13.1.2 Blood -- 13.1.3 Blood vessels -- 13.2 Methods of modeling blood flow and blood vessels -- 13.2.1 Introduction -- 13.2.2 Methods of blood flow modeling in large blood vessels -- 13.2.3 Modeling the deformation of blood vessels -- 13.2.4 Blood-blood vessel interaction -- 13.3 Human aorta -- 13.3.1 Introduction -- 13.3.2 Finite element model of the aorta -- 13.3.3 Results and discussion -- 13.4 Abdominal Aortic Aneurysm (AAA) -- 13.4.1 Introduction -- 13.4.2 Modeling of blood flow within the AAA -- 13.4.3 Results -- 13.5 Blood flow through the carotid artery bifurcation -- 13.5.1 Introduction -- 13.5.2 Finite element model of the carotid artery bifurcation -- 13.5.3 Example solutions -- 13.6 Femoral artery with stent -- 13.6.1 Femoral artery anatomical and physiological considerations and endovascular solutions -- 13.6.2 Analysis of the combined effects of the surrounding muscle tissue and inner blood pressure to the arterial wall with implanted stent -- 13.7 Blood flow in venous system -- 13.7.1 Introduction -- 13.7.2 Modeling blood flow through the veins -- 13.8 Heart model -- 13.8.1 Description of heart functioning -- 13.8.2 Computational model.

14 Modeling Mass Transport and Thrombosis in Arteries -- 14.1 Introduction -- 14.2 Modeling mass transport in arteries by continuum-based methods -- 14.2.1 The basic relations for mass transport in arteries -- 14.2.2 Finite element modeling of diffusion-transport equations -- 14.2.3 Examples -- 14.3 Modeling thrombosis by continuum-based methods -- 14.3.1 Model description -- 14.3.2 Examples -- 14.4 Modeling of thrombosis by DPD -- 14.4.1 General considerations -- 14.4.2 Examples -- 15 Cartilage Mechanics -- 15.1 Introduction -- 15.2 Differential equations of balance in cartilage mechanics -- 15.2.1 Basic physical quantities, swelling pressure and electrokinetic coupling -- 15.2.2 Equations of balance -- 15.3 Finite element modeling of cartilage deformation -- 15.3.1 Finite element balance equations -- 15.4 Examples -- 16 Cell Mechanics -- 16.1 Introduction to mechanics of cells -- 16.2 Cell mechanical models -- 16.2.1 Stabilizing influence of CSK prestress - cellular tensegrity model -- 16.2.2 Mathematical model of a six-strut tensegrity structure -- 16.2.3 Biphasic models -- 16.3 Examples: modeling of cell in various mechanical conditions -- 17 Extracellular Mechanotransduction: Modeling Ligand Concentration Dynamics in the Lateral Intercellular Space of Compressed Airway Epithelial Cells -- 17.1 Autocrine signaling in airway epithelial cells -- 17.1.1 Introduction -- 17.1.2 The EGF-receptor autocrine loop in the LIS -- 17.1.3 Modeling the effects of compressive stress on epithelial cells in vitro -- 17.2 The dynamic diffusion model -- 17.2.1 Introduction -- 17.2.2 Finite element model of dynamic diffusion -- 17.2.3 Exploring the parameter space of the diffusion equation -- 17.3 The dynamic diffusion and convection model -- 17.3.1 Introduction -- 17.3.2 Finite element model of coupled diffusion and convection.

17.3.3 Exploring the parameter space of the governing equations.