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Method of Lines PDE Analysis in Biomedical Science and Engineering [Kõva köide]

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(Lehigh University)
  • Formaat: Hardback, 370 pages, kõrgus x laius x paksus: 241x158x28 mm, kaal: 658 g
  • Ilmumisaeg: 17-Jun-2016
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 1119130484
  • ISBN-13: 9781119130482
Teised raamatud teemal:
Method of Lines PDE Analysis in Biomedical Science and EngineeringSuurem pilt
  • Formaat: Hardback, 370 pages, kõrgus x laius x paksus: 241x158x28 mm, kaal: 658 g
  • Ilmumisaeg: 17-Jun-2016
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 1119130484
  • ISBN-13: 9781119130482
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781119130482.html
Märksõnad:

Presents the methodology and applications of ODE and PDE models within biomedical science and engineering

With an emphasis on the method of lines (MOL) for partial differential equation (PDE) numerical integration, Method of Lines PDE Analysis in Biomedical Science and Engineeringdemonstrates the use of numerical methods for the computer solution of PDEs as applied to biomedical science and engineering (BMSE). Written by a well-known researcher in the field, the book provides an introduction to basic numerical methods for initial/boundary value PDEs before moving on to specific BMSE applications of PDEs.

Featuring a straightforward approach, the book’s chapters follow a consistent and comprehensive format. First, each chapter begins by presenting the model as an ordinary differential equation (ODE)/PDE system, including the initial and boundary conditions.  Next, the programming of the model equations is introduced through a series of R routines that primarily implement MOL for PDEs. Subsequently, the resulting numerical and graphical solution is discussed and interpreted with respect to the model equations. Finally, each chapter concludes with a review of the numerical algorithm performance, general observations and results, and all possible extensions of the model.Method of Lines PDE Analysis in Biomedical Science and Engineering also includes:

  • Examples of MOL analysis of PDEs, including BMSE applications in wave front resolution in chromatography, VEGF angiogenesis, thermographic tumor location, blood-tissue transport, two fluid and membrane mass transfer, artificial liver support system, cross diffusion epidemiology, oncolytic virotherapy, tumor cell density in glioblastomas, and variable grids
  • Discussions on the use of R software, which facilitates immediate solutions to differential equation problems without having to first learn the basic concepts of numerical analysis for PDEs and the programming of PDE algorithms
  • A companion website that provides source code for the R routines
Method of Lines PDE Analysis in Biomedical Science and Engineering is an introductory reference for researchers, scientists, clinicians, medical researchers, mathematicians, statisticians, chemical engineers, epidemiologists, and pharmacokineticists as well as anyone interested in clinical applications and the interpretation of experimental data with differential equation models. The book is also an ideal textbook for graduate-level courses in applied mathematics, BMSE, biology, biophysics, biochemistry, medicine, and engineering.

Arvustused

"This book demonstrates the use of numerical methods for the computer solution of partial differential equations (PDEs) as applied to biomedical science and engineering...The book is worth reading not only for mathematicians but also for, e.g., chemical engineers, medical researchers, clinicians, epidemiologists and statisticians." (Mathematical Reviews/MathSciNet June 2017)

Preface xi
About the Companion Website xiii
1 An Introduction to MOL Analysis of PDEs: Wave Front Resolution in Chromatography 1(68)
1.1 1D 2-PDE model
2(5)
1.2 MOL routines
7(14)
1.2.1 Main program
7(9)
1.2.2 MOL/ODE routine
16(4)
1.2.3 Subordinate routines
20(1)
1.3 Model output, single component chromatography
21(32)
1.3.1 FDs, step BC
21(18)
1.3.2 Flux limiters, step BC
39(9)
1.3.3 FDs, pulse BC
48(2)
1.3.4 Flux limiters, pulse BC
50(3)
1.4 Multi component model
53(1)
1.5 MOL routines
54(13)
1.5.1 Main program
54(8)
1.5.2 MOL/ODE routine
62(5)
1.6 Model output, multi component chromatography
67(1)
References
68(1)
2 Wave Front Resolution in VEGF Angiogenesis 69(22)
2.1 1D 2-PDE model
70(2)
2.2 MOL routines
72(14)
2.2.1 Main program
72(9)
2.2.2 MOL/ODE routine
81(4)
2.2.3 Subordinate routines
85(1)
2.3 Model output
86(2)
2.3.1 Comparison of numerical and analytical solutions
86(2)
2.3.2 Effect of diffusion on the traveling-wave solution
88(1)
2.4 Conclusions
88(1)
References
89(2)
3 Thermographic Tumor Location 91(22)
3.1 2D 1-PDE model
92(2)
3.2 MOL analysis
94(11)
3.2.1 ODE routine
94(6)
3.2.2 Main program
100(5)
3.3 Model output
105(5)
3.4 Summary and conclusions
110(1)
References
111(2)
4 Blood-Tissue Transport 113(32)
4.1 1D 2-PDE model
114(1)
4.2 MOL routines
115(14)
4.2.1 MOL/ODE routine
115(4)
4.2.2 Main program
119(9)
4.2.3 Bessel function routine
128(1)
4.3 Model output
129(4)
4.4 Model extensions
133(9)
4.5 Conclusions and summary
142(1)
References
143(2)
5 Two-Fluid/Membrane Model 145(20)
5.1 2D 3-PDE model
146(1)
5.2 MOL analysis
147(13)
5.2.1 MOL/ODE routine
148(5)
5.2.2 Main program
153(7)
5.3 Model output
160(2)
5.4 Summary and conclusions
162(3)
6 Liver Support Systems 165(40)
6.1 2-ODE patient model
166(1)
6.2 Patient ODE model routines
167(7)
6.2.1 Main program
167(5)
6.2.2 ODE routine
172(2)
6.3 Model output
174(2)
6.4 8-PDE ALSS model
176(4)
6.4.1 Membrane unit MU1
177(1)
6.4.2 Adsorption unit AU1
177(1)
6.4.3 Adsorption unit AU2
178(1)
6.4.4 Membrane unit MU2
179(1)
6.5 Patient-ALSS ODE/PDE model routines
180(15)
6.5.1 Main program
180(8)
6.5.2 ODE routine
188(7)
6.6 Model output
195(1)
6.7 Summary and conclusions
196(4)
Appendix - Derivation of PDEs for Membrane and Adsorption Units
200(3)
A.1 PDEs for Membrane Units
200(2)
A.2 PDEs for Adsorption Units
202(1)
References
203(2)
7 Cross Diffusion Epidemiology Model 205(22)
7.1 2-PDE model
205(2)
7.2 Model routines
207(11)
7.2.1 Main program
207(8)
7.2.2 ODE routine
215(3)
7.3 Model output
218(6)
7.3.1 ncase = 1, time-invariant solution
218(2)
7.3.2 ncase = 2, transient solution, no cross diffusion
220(2)
7.3.3 ncase = 3, transient solution with cross diffusion
222(2)
7.4 Summary and conclusions
224(1)
Reference
225(2)
8 Oncolytic Virotherapy 227(48)
8.1 1D 4-PDE model
228(1)
8.2 MOL routines
229(17)
8.2.1 Main program
230(10)
8.2.2 MOL/ODE routine
240(5)
8.2.3 Subordinate routine
245(1)
8.3 Model output
246(27)
8.4 Summary and conclusions
273(1)
Reference
274(1)
9 Tumor Cell Density in Glioblastomas 275(28)
9.1 1D PDE model
276(1)
9.2 MOL routines
277(12)
9.2.1 Main program
277(9)
9.2.2 MOL/ODE routine
286(3)
9.3 Model output
289(10)
9.3.1 Output for ncase = 1, linear
290(5)
9.3.2 Output for ncase = 2, logistic
295(1)
9.3.3 Output for ncase = 3, Gompertz
296(3)
9.4 p-refinement error analysis
299(2)
9.5 Summary and conclusions
301(1)
References
301(2)
10 MOL Analysis with a Variable Grid: Antigen-Antibody Binding Kinetics 303(38)
10.1 ODE/PDE model
303(3)
10.2 MOL routines
306(12)
10.2.1 Main program
306(8)
10.2.2 MOL/ODE routine
314(4)
10.3 Model output
318(7)
10.3.1 Uniform grid
318(3)
10.3.2 Variable grid
321(4)
10.4 Summary and conclusions
325(2)
Appendix: Variable Grid Analysis
327(13)
A.1 Derivation of numerical differentiators
327(4)
A.2 Testing of numerical differentiators
331(9)
A.2.1 Differentiation matrix
331(1)
A.2.2 Test functions
332(8)
References
340(1)
Appendices
Appendix A Derivation of Convection-Diffusion-Reaction Partial Differential Equations
341(4)
Appendix B Functions dss012, dss004, dss020, vanl
345(6)
Index 351
William E. Schiesser, PhD, ScD (hon.), is Emeritus McCann Professor of Biomolecular and Chemical Engineering and Professor of Mathematics at Lehigh University. His research interests include numerical software; ordinary, differential algebraic, and partial differential equations; and computational mathematics. Dr. Schiesser is the author or coauthor of fifteen books, including Differential Equation Analysis in Biomedical Science and Engineering: Ordinary Differential Equation Applications with R and Differential Equation Analysis in Biomedical Science and Engineering: Partial Differential Equation Applications with R, both published by Wiley.