Partial Differential Equation Analysis in Biomedical Engineering Case Studies with Matlab 1st Edition by William Schiesser ISBN 1107022800 978-1107022805
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Product details:
ISBN 10: 1107022800
ISBN 13: 978-1107022805
Author: William E. Schiesser
Aimed at graduates and researchers, and requiring only a basic knowledge of multi-variable calculus, this introduction to computer-based partial differential equation (PDE) modeling provides readers with the practical methods necessary to develop and use PDE mathematical models in biomedical engineering. Taking an applied approach, rather than using abstract mathematics, the reader is instructed through six biomedical example applications, each example characterized by step-by-step discussions of established numerical methods and implemented in reliable computer routines. Adopting this technique, the reader will understand how PDE models are formulated, implemented and tested. Supported by a set of rigorously tested general purpose PDE routines online, and with enhanced understanding through animations, this book will be ideal for anyone faced with interpreting large experimental data sets that need to be analyzed with PDE models in biomedical engineering.
Table of contents:
1. Introduction to partial differential equation integration in space and time
1.1 Introduction
1.2 Hyperbolic PDEs
1.3 Parabolic PDEs
1.4 Hyperbolic-parabolic PDEs
2. Antibody binding kinetics
2.1 ODE/PDE model equations
2.2 Units check
2.3 MOL routines
2.4 Model output
2.5 ODE stiffness
2.6 Parameter sensitivity analysis
2.7 Spatial derivatives by stagewise differentiation
2.8 Spatial derivatives by direct calculation
3. Acid-mediated tumor growth
3.1 Tumor growth PDE model
3.2 MOL routines
3.3 Model output
3.4 Supplemental output
3.5 Extension of the model
3.6 Additional references
4. Retinal O₂ transport
4.1 Four-section PDE model
4.2 MOL routines
4.3 Base case output
4.4 Model including photoreceptor cell density
4.5 Model including VEGF production
5. Hemodialyzer dynamics
5.1 1D PDE model
5.2 MOL routines
5.3 Model output
6. Epidermal wound healing
6.1 One-PDE model
6.2 Two-PDE model
6.3 Conclusions concerning space and time discretizations
7. Drug distribution from a polymer matrix
7.1 Linear model
7.2 Variable coefficient model
7.3 Nonlinear model
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Tags:
William Schiesser,Partial Differential,Equation Analysis,Biomedical Engineering