图书简介
This textbook serves as a modern introduction to vascular biomechanics and provides the comprehensive overview of the entire vascular system that is needed to run successful vascular biomechanics simulations. It aims to provide the reader with a holistic analysis of the vascular system towards its biomechanical description and includes numerous fully through-calculated examples. Various topics covered include vascular system descriptions, vascular exchange, blood vessel mechanics, vessel tissue characterization, blood flow mechanics, and vascular tissue growth and remodeling.This textbook is ideally suited for students and researchers studying and working in classical and computational vascular biomechanics. The book could also be of interest to developers of vascular devices and experts working with the regulatory approval of biomedical simulations.Follows the principle of “learning by doing” and provides numerous fully through-calculated examples for active learning, immediate recall, and self-examination;Provides a holistic understanding of vascular functioning and the integration of information from different disciplines to enable students to use sophisticated numerical methods to simulate the response of the vascular system;Includes several case studies that integrate the presented material. Case studies address problems, such as the biomechanical rupture risk assessment of Abdominal Aortic Aneurysms, Finite Element analysis of structural and blood flow problems, the computation of wall stress and wall shear stress in the aorta.
1 Modeling in Biomechanics 1.- 1.1 The different perspectives 2.- 1.1.1 The engineering approach 2.- 1.1.2 The clinical approach 2.- 1.1.3 The pre- clinical approaches 2.- 1.2 Opportunities and challenges 2.- 1.3 Statistical analysis 3.- 1.3.1 Probability distributions 4.- 1.3.2 Hypothesis testing 7.- 1.3.3 Correlation amongst variables 9.- 1.3.4 Regression modeling 10.- 1.3.5 Mean difference test 13.- 1.3.6 Study design 14.- 1.4 Model definition 16.- 1.5 Model development and testing 17.- 1.5.1 Sensitivity analysis 17.- 1.5.3 Validation 21.- 1.6 Case study: Biomechanical Rupture Risk Assessment (BRRA) 21.- 1.6.1 Short comings of the current AAA risk assessment 21.- 1.6.2 Intended Model Application (IMA) 21.- 1.6.3 Failure hypothesis 22.- 1.6.4 Work flow and diagnostic information 22.- 1.6.5 Key modeling assumptions 23.- 1.6.6 Clinical validation 24.- 1.7 Summary and conclusion 25.- Appendix: Biomechanics Modeling 27.- A.1 Definitions and terminology in statistics 27.- 2 The circulatory system 29.- 2.1 Physiology 29.- 2.1.1 Vascular system 29.- 2.1.2 Key concepts 31.- 2.1.3 Cells in the vascular system 32.- 2.1.4 Macrocirculation 33.- 2.1.5 Lymphatic system 37.- 2.1.6 Microcirculation 38.- 2.1.7 Hemodynamic regulation 41.- 2.2 Mechanical system properties 42.- 2.2.1 Vascular pressure 43.- 2.2.2 Vascular flow 44.- 2.2.3 Vascular resistance 45.- 2.2.4 Transcapillary transport 45.- 2.3 Modeling the macrocirculation 45.- 2.3.1 Windkessel (WK) models 46.- 2.3.2 Vessel network modeling 57.- 2.4 Modeling the Microcirculation 63.- 2.4.1 Transcapillary concentration difference 63.- 2.4.2 Filtration 65.- 2.5 Summary and conclusion 70.- Appendix: Mathematical preliminaries 72.- A.1 Complex numbers 72.- A.2 Fourier series approximation 72.- Appendix: Basic circuit elements 73.- B.1 Resistor element 73.- B.2 Capacitor element 73.- B.3 Inductor element 74.- Appendix: Transport mechanisms 74.- C.1 Diffusion 74.- C.2 Advection 75.- Appendix: Osmosis 75.- D.1 Osmotic pressure 75.- D.2 Transport across semipermeable membranes 76.- 3 Continuum Mechanics 77.- 3.1 Kinematics 78.- 3.1.1 Deformation gradient 78.- 3.1.2 Multiplicative decomposition 79.- 3.1.3 Polar decomposition 79.- 3.1.4 Deformation of the line element 79.- 3.1.5 Deformation of the volume element 80.- 3.1.6 Deformation of the area element 80.- 3.1.7 Concept of strain 81.- 3.2 Concept of stress 85.- 3.2.1 Cauchy stress theorem 86.- 3.2.2 Principal stresses 87.- 3.2.3 Isochoric and volumetric stress 89.- 3.2.4 Octahedral stress and von Mises stress 89.- 3.2.5 Cauchy stress in rotated coordinates 91.- 3.2.6 First Piola-Kirchhoff stress 91.- 3.2.7 Second Piola-Kirchhoff stress 92.- 3.2.8 Implication of material incompressibility on the stress state 93.- 3.3 Material time derivatives 94.- 3.3.1 Kinematic variables 94.- 3.3.2 Stress rates 95.- 3.3.3 Power-conjugate stress and strain rates 96.- 3.4 Constitutive modeling 97.- 3.4.1 Some mechanical properties of materials 97.- 3.4.2 Linear elastic material 100.- 3.4.3 Hyperelasticity 102.- 3.4.4 Viscoelasticity 105.- 3.5 Governing laws 113.- 3.5.1 Mass balance 114.- 3.5.2 Balance of linear momentum 116.- 3.5.3 Maxwell transport and localization 118.- 3.5.4 Thermodynamic principles 119.- 3.6 General principles 125.- 3.6.1 Free body diagram 125.- 3.6.2 Initial Boundary Value Problem 126.- 3.6.3 Principle of Virtual.- 3.7 Damage and failure 129.- 3.7.1 Physical consequences 129.- 3.7.2 Strain localization 130.- 3.7.3 Linear Fracture Mechanics 132.- 3.7.4 J.- Integral 133.- 3.7.5 Cohesive zone modeling 133.- 3.8 Multiphasic continuum theories 134.- 3.8.1 Mixture theory 134.- 3.8.2 Poroelasticity theory 134.- 3.9 Summary and conclusion 135.- Appendix: Mathematical preliminaries 136.- A.1 Laplace and Fourier transforms 136.- A.2 Matrix algebra 136.- A.2.1 Trace of a matrix 137.- A.2.2 Identity matrix 137.- A.2.3 Determinant of a matrix 137.- A.2
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