Page 5 - Computational Modeling in Biomedical Engineering and Medical Physics

Contents

Preface xi
Acknowledgments xv

1. Physical, mathematical, and numerical modeling 1
1.1 Experiments and numerical simulation 1
1.2 The system and its boundary 2
1.3 First law analysis: energy, heat, and work interactions 3
Electromagnetic power transferred through the boundary
(at the electrical terminals) 5
1.4 Multidisciplinary (multiphysics) problems 7
1.5 Mathematical models 8
Complete and independent, coherent, and noncontradictory system of laws 8
Boundary conditions (external interactions) and initial conditions (initial state) 9
Initial values problems 10
Boundary and initial values problems 11
1.6 Numerical solutions to the mathematical models 14
1.7 Coupled (multiphysics) problems 15
1.8 Time and space scales 16
1.9 Properties of anatomic media 20
Electrical properties 20
Rheological properties of blood 23
Bioheat models, homogenization methods 24
1.10 The computational domain 27
Allometric laws, fractal geometry, and constructal law 28
Medical image-based construction, CAD and fused computational domains 30
1.11 Diffusion convection problems: heatfunction and massfunction 30
1.12 A roadmap to a well-posed, direct problem and its solution 33
References 35
A.1 Scalar and Vector Fields 38
Scalar fields 39
Vector fields 39

2. Shape and structure morphing of systems with internal flows 43
2.1 Natural form and organization—quandary, observation, and rationale 43
2.2 Biomimetics, bionics, fractal geometry, constructal theory 45
2.3 Shape and structure 47
The fundamental problem of volume to point flow and the constructal growth 47

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