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Computational Biomechanics
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Rapid developments have taken place in biological/biomedical measurement and imaging technologies as well as in computer analysis and information technologies. The increase in data obtained with such technologies invites the reader into a virtual world that represents realistic biological tissue or organ structures in digital form and allows for simulation and what is called "in silico medicine." This volume is the third in a textbook series and covers both the basics of continuum mechanics of biosolids and biofluids and the theoretical core of computational methods for continuum mechanics analyses. Several biomechanics problems in orthopedic and cardiovascular biomechanics, among others, are provided for better understanding of computational analysis and modeling. Topics include the mechanics of solid and fluid bodies, fundamental characteristics of biosolids and biofluids, computational methods in biomechanics analysis/simulation, practical problems in orthopedic biomechanics, dental biomechanics, ophthalmic biomechanics, hemodynamics, cell mechanics, and model-, rule-, and image-based methods in computational biomechanics analysis and simulation. The book is an excellent resource for graduate school-level engineering students and young researchers in bioengineering and biomedicine.
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Table of Contents

Chapter 1: Introduction 1.1 Biomechanics: Mechanics in/for biology and medicine 1.2 One-dimensional mechanics of biosolids and biofluids 1.2.1 A dip into biosolid mechanics 1.2.2 A dip into biofluid mechanics 1.3 Addendum to one-dimensional mechanics 1.3.1 Law of mixture 1.3.2 Discrete model of continuum 1.4 Biomechanics in biology and medicine: a tiny showcase References Chapter 2: Mechanics of biosolids and computational analysis 2.1 Fundamentals of solid mechanics 2.1.1 Stress and force: Equilibrium equations 2.1.2.Strain and displacement: Kinematic equations 2.1.3 Constitutive equiations: Linear elasticity 2.1.4 Constitutive equations: Nonlinear elasticity 2.2 Mechanical properties of bone 2.1.2 Cortical bone 2.2.2 Cancellous bone 2.3 Mechanical properties of soft tissue 2.3.1 Arteial wall 2.3.2 Skin 2.3.3 Cornea 2.4 Principles of stationary potential energy and virtual work 2.4.1 Boundary value problems for equilibrium 2.4.2 Principle of virtual work 2.4.3 Principle of stationary potential energy 2.5 Finite element method 2.5.1 Finite element discretization and approximation 2.5.2 Finite element equations for small strain linear elasticity 2.5.3 Finite element equations for finite strain hyperelasticity 2.5.4 Shape functions: Simplex, complex and multiplex elements 2.5.5 Shape functions: Isoparametric elements 2.6 Computational biomechanics problems 2.6.1 Lattice continuum modeling for cancellous bone structure 2.6.2 Scoliotic deformation analysis of spinal column 2.6.3 Stress analysis of temporomandibular joint disc 2.6.4 Deformation analysis of cornea: inverse problems 2.6.5 Stress analysis of proximal femur: Image-based analysis and simulation 2.7 Summary References Chapter 3 Mechanics of biofluid and computational analysis 3.1 Fundamentals of fluid mechanics 3.1.1 Viscous and inviscid fluid 3.1.2 Newtonian and non-Newtonian fluid 3.1.3 Compressible and incompressible fluids 3.2 Dimensionless numbers 3.2.1 Reynolds number 3.2.2 Womersley number 3.3 Eulerian and Lagrangian representations of fluid flow 3.4 Governing equation of fluid flow 3.4.1 Equation of continuity 3.4.2 Navier-Stokes equation 3.5 Euler-based Computational Fluid Dynamics 3.5.1 Discretization 3.5.2 Finite Volume Method 3.6 Lagrange-based Computational Fluid Dynamics 3.6.1 Governing equations 3.6.2 Modeling of the interaction between particles 3.6.3 Algorithm of the MPS method 3.7 Applications of Flow simulations to Biomechanical Problems 3.7.1 Analysis of Blood Flow in the Aorta 3.7.2 Analysis of Blood Flow in the Left Ventricle for the Interpretation of Color M-mode Doppler Echocardiogram 3.7.3 Fluid-Structure Interaction Analysis of Blood Flow for Differentiation of Vascular Diseases by Pulse Wave Propagation WAVE PROPAGATION 3.7.4 PrimaryThrombus Formation by Platelet Aggregation by the Particle Method 3.7.5 Fluid-Structure Interaction Analysis on the Behavior of Spherical Embolic Agents in a Vascular Bifurcation toward Pre-operation Planning of Transcatheter Embolization 3.8 Summary References Chapter 4: Spring Network Modeling based on the Energy Concept 4.1 Fundamentals of spring network model 4.1.1 Single spring model 4.1.2 Network spring model 4.1.3 Bending spring model 4.1.4 Extended spring model 4.1.5 Extension to continuum model 4.2 Formulation and solving method 4.2.1 Minimum energy problem 4.2.2 Solving method 4.3 Parameter identification of the spring network model 4.3.1 Stretching spring constant 4.3.2 Bending spring constant 4.4 Mechanical behavior of a single red blood cell 4.4.1 Minimum energy problem to determine the shape of RBC 4.4.2 RBC behavior in a shear flow 4.5 Mechanical properties of a eukaryotic cell 4.5.1 Mechanocell model 4.5.2 Application of mechanocell model to micro biomechanics 4.6 Aneurysm development 4.6.1 Modeling of aneurysm 4.6.2 Rule-based simulation of aneurysm development 4.7 Multiscale blood flow 4.7.1 Modeling of multiple red blood cell flow 4.7.2 Multiscale simulation of blood flow 4.8 Summary References Chapter 5 Toward in silico medicine 5.1 Computational biomechanics in medical engineering 5.2 Model-based diagnosis 5.3 Multiscale modeling and analysis 5.4 Subject-/patient-specific modeling and simulation 5.5 Towards predictive medicine Chapter 2: Mechanics of biosolids and computational analysis 2.1 Fundamentals of solid mechanics 2.1.1 Stress and force: Equilibrium equations 2.1.2.Strain and displacement: Kinematic equations 2.1.3 Constitutive equiations: Linear elasticity 2.1.4 Constitutive equations: Nonlinear elasticity 2.2 Mechanical properties of bone 2.1.2 Cortical bone 2.2.2 Cancellous bone 2.3 Mechanical properties of soft tissue 2.3.1 Arteial wall 2.3.2 Skin 2.3.3 Cornea 2.4 Principles of stationary potential energy and virtual work 2.4.1 Boundary value problems for equilibrium 2.4.2 Principle of virtual work 2.4.3 Principle of stationary potential energy 2.5 Finite element method 2.5.1 Finite element discretization and approximation 2.5.2 Finite element equations for small strain linear elasticity 2.5.3 Finite element equations for finite strain hyperelasticity 2.5.4 Shape functions: Simplex, complex and multiplex elements 2.5.5 Shape functions: Isoparametric elements 2.6 Computational biomechanics problems 2.6.1 Lattice continuum modeling for cancellous bone structure 2.6.2 Scoliotic deformation analysis of spinal column 2.6.3 Stress analysis of temporomandibular joint disc 2.6.4 Deformation analysis of cornea: inverse problems 2.6.5 Stress analysis of proximal femur: Image-based analysis and simulation 2.7 Summary References Chapter 3 Mechanics of biofluid and computational analysis 3.1 Fundamentals of fluid mechanics 3.1.1 Viscous and inviscid fluid 3.1.2 Newtonian and non-Newtonian fluid 3.1.3 Compressible and incompressible fluids 3.2 Dimensionless numbers 3.2.1 Reynolds number 3.2.2 Womersley number 3.3 Eulerian and Lagrangian representations of fluid flow 3.4 Governing equation of fluid flow 3.4.1 Equation of continuity 3.4.2 Navier-Stokes equation 3.5 Euler-based Computational Fluid Dynamics 3.5.1 Discretization 3.5.2 Finite Volume Method 3.6 Lagrange-based Computational Fluid Dynamics 3.6.1 Governing equations 3.6.2 Modeling of the interaction between particles 3.6.3 Algorithm of the MPS method 3.7 Applications of Flow simulations to Biomechanical Problems 3.7.1 Analysis of Blood Flow in the Aorta 3.7.2 Analysis of Blood Flow in the Left Ventricle for the Interpretation of Color M-mode Doppler Echocardiogram 3.7.3 Fluid-Structure Interaction Analysis of Blood Flow for Differentiation of Vascular Diseases by Pulse Wave Propagation WAVE PROPAGATION 3.7.4 PrimaryThrombus Formation by Platelet Aggregation by the Particle Method 3.7.5 Fluid-Structure Interaction Analysis on the Behavior of Spherical Embolic Agents in a Vascular Bifurcation toward Pre-operation Planning of Transcatheter Embolization 3.8 Summary References Chapter 4: Spring Network Modeling based on the Energy Concept 4.1 Fundamentals of spring network model 4.1.1 Single spring model 4.1.2 Network spring model 4.1.3 Bending spring model 4.1.4 Extended spring model 4.1.5 Extension to continuum model 4.2 Formulation and solving method 4.2.1 Minimum energy problem 4.2.2 Solving method 4.3 Parameter identification of the spring network model 4.3.1 Stretching spring constant 4.3.2 Bending spring constant 4.4 Mechanical behavior of a single red blood cell 4.4.1 Minimum energy problem to determine the shape of RBC 4.4.2 RBC behavior in a shear flow 4.5 Mechanical properties of a eukaryotic cell 4.5.1 Mechanocell model 4.5.2 Application of mechanocell model to micro biomechanics 4.6 Aneurysm development 4.6.1 Modeling of aneurysm 4.6.2 Rule-based simulation of aneurysm development 4.7 Multiscale blood flow 4.7.1 Modeling of multiple red blood cell flow 4.7.2 Multiscale simulation of blood flow 4.8 Summary References Chapter 5 Toward in silico medicine 5.1 Computational biomechanics in medical engineering 5.2 Model-based diagnosis 5.3 Multiscale modeling and analysis 5.4 Subject-/patient-specific modeling and simulation 5.5 Towards predictive medicine Chapter 3 Mechanics of biofluid and computational analysis 3.1 Fundamentals of fluid mechanics 3.1.1 Viscous and inviscid fluid 3.1.2 Newtonian and non-Newtonian fluid 3.1.3 Compressible and incompressible fluids 3.2 Dimensionless numbers 3.2.1 Reynolds number 3.2.2 Womersley number 3.3 Eulerian and Lagrangian representations of fluid flow 3.4 Governing equation of fluid flow 3.4.1 Equation of continuity 3.4.2 Navier-Stokes equation 3.5 Euler-based Computational Fluid Dynamics 3.5.1 Discretization 3.5.2 Finite Volume Method 3.6 Lagrange-based Computational Fluid Dynamics 3.6.1 Governing equations 3.6.2 Modeling of the interaction between particles 3.6.3 Algorithm of the MPS method 3.7 Applications of Flow simulations to Biomechanical Problems 3.7.1 Analysis of Blood Flow in the Aorta 3.7.2 Analysis of Blood Flow in the Left Ventricle for the Interpretation of Color M-mode Doppler Echocardiogram 3.7.3 Fluid-Structure Interaction Analysis of Blood Flow for Differentiation of Vascular Diseases by Pulse Wave Propagation WAVE PROPAGATION 3.7.4 PrimaryThrombus Formation by Platelet Aggregation by the Particle Method 3.7.5 Fluid-Structure Interaction Analysis on the Behavior of Spherical Embolic Agents in a Vascular Bifurcation toward Pre-operation Planning of Transcatheter Embolization 3.8 Summary References Chapter 4: Spring Network Modeling based on the Energy Concept 4.1 Fundamentals of spring network model 4.1.1 Single spring model 4.1.2 Network spring model 4.1.3 Bending spring model 4.1.4 Extended spring model 4.1.5 Extension to continuum model 4.2 Formulation and solving method 4.2.1 Minimum energy problem 4.2.2 Solving method 4.3 Parameter identification of the spring network model 4.3.1 Stretching spring constant 4.3.2 Bending spring constant 4.4 Mechanical behavior of a single red blood cell 4.4.1 Minimum energy problem to determine the shape of RBC 4.4.2 RBC behavior in a shear flow 4.5 Mechanical properties of a eukaryotic cell 4.5.1 Mechanocell model 4.5.2 Application of mechanocell model to micro biomechanics 4.6 Aneurysm development 4.6.1 Modeling of aneurysm 4.6.2 Rule-based simulation of aneurysm development 4.7 Multiscale blood flow 4.7.1 Modeling of multiple red blood cell flow 4.7.2 Multiscale simulation of blood flow 4.8 Summary References Chapter 5 Toward in silico medicine 5.1 Computational biomechanics in medical engineering 5.2 Model-based diagnosis 5.3 Multiscale modeling and analysis 5.4 Subject-/patient-specific modeling and simulation 5.5 Towards predictive medicine Chapter 4: Spring Network Modeling based on the Energy Concept 4.1 Fundamentals of spring network model 4.1.1 Single spring model 4.1.2 Network spring model 4.1.3 Bending spring model 4.1.4 Extended spring model 4.1.5 Extension to continuum model 4.2 Formulation and solving method 4.2.1 Minimum energy problem 4.2.2 Solving method 4.3 Parameter identification of the spring network model 4.3.1 Stretching spring constant 4.3.2 Bending spring constant 4.4 Mechanical behavior of a single red blood cell 4.4.1 Minimum energy problem to determine the shape of RBC 4.4.2 RBC behavior in a shear flow 4.5 Mechanical properties of a eukaryotic cell 4.5.1 Mechanocell model 4.5.2 Application of mechanocell model to micro biomechanics 4.6 Aneurysm development 4.6.1 Modeling of aneurysm 4.6.2 Rule-based simulation of aneurysm development 4.7 Multiscale blood flow 4.7.1 Modeling of multiple red blood cell flow 4.7.2 Multiscale simulation of blood flow 4.8 Summary References Chapter 5 Toward in silico medicine 5.1 Computational biomechanics in medical engineering 5.2 Model-based diagnosis 5.3 Multiscale modeling and analysis 5.4 Subject-/patient-specific modeling and simulation 5.5 Towards predictive medicine Chapter 5 Toward in silico medicine 5.1 Computational biomechanics in medical engineering 5.2 Model-based diagnosis 5.3 Multiscale modeling and analysis 5.4 Subject-/patient-specific modeling and simulation 5.5 Towards predictive medicine

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