Computer Modeling in Bioengineering

Transcription

1 Computer Modeling in Bioengineering Theoretical Background, Examples and Software Milos Kojic Harvard School of Public Health, USA University of Kragujevac, Serbia University of Texas Health Science Center at Houston, USA Nenad Filipovic Faculty of Mechanical Engineering, University of Kragujevac, Serbia Boban Stojanovic Center for Scientific Research of Serbian Academy of Sciences and Arts and University of Kragujevac, Serbia Nikola Kojic Harvard-MIT Division of Health Sciences and Technology, USA Harvard Medical School, USA John Wiley & Sons, Ltd

2 Contents Contributors Preface xv xvii Part I Theoretical Background of Computational Methods 1 1 Notation - Matrices and Tensors Matrix representation of mathematical objects Basic relations in matrix algebra Definition of tensors and some basic tensorial relations Vector and tensor differential Operations and integral theorems Examples 11 2 Fundamentals of Continuum Mechanics Definitions of stress and strain Stress Strain and strain rate Examples Linear elastic and viscoelastic constitutive relations Linear elastic constitutive law Viscoelasticity Transformation of constitutive relations Examples Principle of Virtual work Formulation of the principle of Virtual work Examples Nonlinear continuum mechanics Deformation gradient and the measures of strain and stress Nonlinear elastic constitutive relations Examples 47 3 Heat Transfer, Diffusion, Fluid Mechanics, and Fluid Flow through Porous Deformable Media Heat conduction Governing relations Examples 53

3 vin CONTENTS 3.2 Diffusion Differential equations of diffusion Examples Fluid flow of incompressible viscous fluid with heat and mass transfer Governing equations of fluid flow and of heat and mass transfer Examples Fluid flow through porous deformable media The governing equations Examples 66 Part II Fundamentals of Computational Methods 69 4 Isoparametric Formulation of Finite Elements Introduction to the finite dement method Formulation of 1D finite elements and equilibrium equations Truss finite element Equilibrium equations of the FE assemblage and boundary conditions Examples Three-dimensional (3D) isoparametric finite element Element formulation Examples Two-dimensional (2D) isoparametric finite elements Formulation of the elements Examples Isoparametric shell finite element for general 3D analysis Basic assumptions about shell deformation Formulation of a four-node shell element Examples 95 5 Dynamic Finite Element Analysis Introduction to dynamics of structures Differential equations of motion Integration of differential equations of motion System frequencies and modal shapes Examples Introduction to Nonlinear Finite Element Analysis Introduction Principle of Virtual work and equilibrium equations in nonlinear incremental analysis Discrete System Principle of Virtual work for a continuum Finite element model Finite element model with logarithmic strains Examples 118

4 CONTENTS Finite Element Modeling of Field Problems Introduction General considerations The Galerkin method Heat conduction The finite element equations Examples Diffusion The finite element equations Examples Fluid flow with heat and mass transfer The finite element equations Examples FE equations for modeling large change of fluid domain - Arbitrary Lagrangian-Eulerian (ALE) formulation The ALE formulation Examples Solid-fluid interaction Loose coupling method Examples Fluid flow through porous deformable media Finite element balance equations Examples 145 Discrete Particle Methods for Modeling of Solids and Fluids Molecular dynamics Introduction Differential equations of motion and boundary conditions Examples Dissipative Particle Dynamics (DPD) method Introduction to mesoscale DPD modeling Basic DPD equations Examples Multiscale modeling, coupling DPD-FE for fluid flow Introduction to multiscale modeling Basic equations and boundary conditions Examples Smoofhed Particle Hydrodynamics (SPH) Introduction The basic equations of the SPH method Examples Element-Free Galerkin (EFG) method Introduction Formulation of the EFG method Examples 168

5 X CONTENTS Part III Computational Methods in Bioengineering Introduction to Bioengineering The subject and scope of bioengineering The role of Computer modeling in bioengineering Computational modeis Future advances in Computer modeling Bone Modeling The structure and forms of bones The structure of bone tissue The form of bones Osteoporosis and bone density The mechanical properties of bone and FE modeling Bone fracture - medical treatment and Computer modeling General considerations Fracture treatment FE modeling of femur comminuted fracture Internal fixation of hip fracture - two Solutions and Computer modeis Solutions by parallel screws and by dynamic hip implant Finite element modeis of intracapsular fractures of the femoral neck Biological Soft Tissue Introduction to mechanics of biological tissue Structure and function of biological tissue Basic experiments and mechanical modeis Modeling methods for isotropic tissue General concept of computational procedures Biaxial modeis of membranes, hardening and hysteretic behavior, action of Surfactant Use of strain energy functions Examples Skeletal Muscles Introduction Basic physiology of muscle mechanics Basics of muscle finite element modeling Muscle modeling Hill's phenomenological model Determination of Stresses within muscle fiber Hill's model which includes fatigue An extension of Hill's model to include different fiber types Examples Blood Flow and Blood Vessels Introduction to the cardiovascular System The circulatory system 249

6 Blood Blood vessels Methods of modeling blood flow and blood vessels Introduction Methods of blood flow modeling in large blood vessels Modeling the deformation of blood vessels Blood-blood vessel interaction Human aorta Introduction Finite dement model of the aorta Results and discussion Abdominal Aortic Aneurysm (AAA) Introduction Modeling of blood flow within the AAA Results Blood flow through the carotid artery bifurcation Introduction Finite element model of the carotid artery bifurcation Example Solutions Femoral artery with Stent Femoral artery anatomical and physiological considerations and endovascular Solutions Analysis of the combined effects of the surrounding muscle tissue and inner blood pressure to the arterial wall with implanted Stent Blood flow in venous System Introduction Modeling blood flow through the veins Heart model Description of heart functioning Computational model Modeling Mass Transport and Thrombosis in Arteries Introduction Modeling mass transport in arteries by continuum-based methods The basic relations for mass transport in arteries Finite element modeling of diffusion-transport equations Examples Modeling thrombosis by continuum-based methods Modeidescription Examples Modeling of thrombosis by DPD General considerations Examples Cartilage Mechanics Introduction Differential equations of balance in cartilage mechanics 316 XI

7 Xll CONTENTS Basic physical quantities, swelling pressure and electrokinetic coupling Equations ofbalance Finite element modeling of cartilage deformation Finite element balance equations Examples Cell Mechanics Introduction to mechanics of cells Cell mechanical modeis Stabilizing influence of CSK prestress - cellular tensegrity model Mathematical model of a six-strut tensegrity structure Biphasic modeis Examples: modeling of cell in various mechanical conditions Extracellular Mechanotransduction: Modeling Ligand Concentration Dynamics in the Lateral Intercellular Space of Compressed Airway Epithelial Cells Autocrine signaling in airway epithelial cells Introduction The EGF-receptor autocrine loop in the LIS Modeling the effects of compressive stress on epithelial cells in vitro The dynamic diffusion model Introduction Finite element model of dynamic diffusion Exploring the parameter space of the diffusion equation The dynamic diffusion and convection model Introduction Finite element model of coupled diffusion and convection Exploring the parameter space of the governing equations Rate sensitivity of extracellular mechanotransduction HB-EGF vs. TGF-alpha concentration dynamics Discussion Spider SUk: Modeling Solvent Removal during Synthetic and Nephila clavipes Fiber Spinning Determination of the solvent diffusion coefficient in a concentrated polymer Solution Introduction Numerical procedure Example Modeling solvent removal during synthetic fiber spinning Introduction Governing process during synthetic solvent removal Numerical modeling of synthetic internal solvent diffusion Example: Synthetic fiber spinning 394

8 CONTENTS Xlll 18.3 Modeling solvent removal during Nephila clavipes fiber spinning Introduction Nephila water diffusion coefficient Modeling of internal water diffusion Example: The Nephila spinning canal Modeling in Cancer Nanotechnology Introduction The transport of particulates in capillaries The mathematical model The governing equations The initial and boundary conditions Solution for K 0 and / Solution for K x and f x Solution for K The velocity distribution (effect of boundary depletion of the solvent) The concentration profile The mean dimensionless concentration y J f m The local dimensionless concentration *P A1A 19.5 Comments and discussions of the analytical modeis and Solutions Numerical modeling of particle motion within capillary Computational procedure Example - trajectories of spherical and elliptical particles 429 Index 433