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E-grāmata: Partial Differential Equation Analysis in Biomedical Engineering: Case Studies with Matlab

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(Lehigh University, Pennsylvania)
  • Formāts: PDF+DRM
  • Izdošanas datums: 15-Nov-2012
  • Izdevniecība: Cambridge University Press
  • Valoda: eng
  • ISBN-13: 9781139512602
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Partial Differential Equation Analysis in Biomedical Engineering: Case Studies with MatlabPalielināt
  • Formāts: PDF+DRM
  • Izdošanas datums: 15-Nov-2012
  • Izdevniecība: Cambridge University Press
  • Valoda: eng
  • ISBN-13: 9781139512602
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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.

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Gives graduate students and researchers an introductory overview of partial differential equation analysis of biomedical engineering systems through detailed examples.
Preface ix
1 Introduction to partial differential equation integration in space and time
1(147)
1.1 Introduction
1(1)
1.2 Hyperbolic PDEs
2(86)
1.3 Parabolic PDEs
88(42)
1.4 Hyperbolic-parabolic PDEs
130(18)
2 Antibody binding kinetics
148(36)
2.1 ODE/PDE model equations
148(2)
2.2 Units check
150(3)
2.3 MOL routines
153(14)
2.4 Model output
167(4)
2.5 ODE stiffness
171(1)
2.6 Parameter sensitivity analysis
172(6)
2.7 Spatial derivatives by stagewise differentiation
178(3)
2.8 Spatial derivatives by direct calculation
181(3)
3 Acid-mediated tumor growth
184(37)
3.1 Tumor growth PDE model
184(5)
3.2 MOL routines
189(16)
3.3 Model output
205(9)
3.4 Supplemental output
214(5)
3.5 Extension of the model
219(1)
3.6 Additional references
220(1)
4 Retinal O2 transport
221(63)
4.1 Four-section PDE model
221(3)
4.2 MOL routines
224(17)
4.3 Base case output
241(6)
4.4 Model including photoreceptor cell density
247(15)
4.5 Model including VEGF production
262(22)
5 Hemodialyzer dynamics
284(24)
5.1 ID PDE model
284(4)
5.2 MOL routines
288(11)
5.3 Model output
299(9)
6 Epidermal wound healing
308(31)
6.1 One-PDE model
308(14)
6.2 Two-PDE model
322(14)
6.3 Conclusions concerning space and time discretizations
336(3)
7 Drug distribution from a polymer matrix
339(49)
7.1 Linear model
339(28)
7.2 Variable coefficient model
367(1)
7.3 Nonlinear model
368(20)
Appendix 1 Origin of convection-diffusion-reaction PDEs
388(18)
A1.1 Derivation of a PDE from a conservation principle
388(4)
A1.2 Approximations of derivatives
392(2)
A1.3 Approximation of boundary conditions
394(3)
A1.4 Derivation of a convection-diffusion-reaction PDE
397(9)
Appendix 2 Stiffness and eigenvalue analysis of ODE systems
406(10)
A2.1 Linear algebraic eigenvalue problem
406(3)
A2.2 Exponential solutions
409(3)
A2.3 Laplace transform solutions
412(2)
A2.4 Numerical eigenvalue analysis
414(2)
Index 416
William E. Schiesser is Emeritus R. L. McCann Professor of Chemical Engineering and Professor of Mathematics at Lehigh University.
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