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E-raamat: Chemotaxis Modeling of Autoimmune Inflammation: PDE Computer Analysis in R [Taylor & Francis e-raamat]

(Lehigh University, Bethlehem, Pennsylvania, USA Lehigh University)
  • Formaat: 144 pages, 13 Tables, black and white; 47 Line drawings, black and white; 47 Illustrations, black and white
  • Ilmumisaeg: 21-Sep-2022
  • Kirjastus: CRC Press
  • ISBN-13: 9781003311201
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  • Taylor & Francis e-raamat
  • Hind: 133,87 €*
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Chemotaxis Modeling of Autoimmune Inflammation: PDE Computer Analysis in RSuurem pilt
  • Formaat: 144 pages, 13 Tables, black and white; 47 Line drawings, black and white; 47 Illustrations, black and white
  • Ilmumisaeg: 21-Sep-2022
  • Kirjastus: CRC Press
  • ISBN-13: 9781003311201
Teised raamatud teemal:
Taylor & Francis e-raamatudRohkem infot Taylor & Francis e-raamatute kohta
Raamatu kodulehekülg: https://www.taylorfrancis.com/books/9781003311201
In response to an infection (e.g., from pathogens such as bacteria and viruses), the immune system can deplete macrophages (specialized white blood cells) and produce cytokines that are pro-inflammatory or anti-inflammatory. This counterproductive autoimmune response is represented mathematically as nonlinear chemotaxis diffusion.

This book is directed to the computer-based modeling of chemotaxis inflammation. The spatiotemporal analysis is based on a model of three partial differential equations (PDEs).

The three PDE model is coded (programmed) as a set of routines in R, a quality, open-source, scientific programming system. The numerical integration (solution) of the PDEs is by the method of lines (MOL).

The three PDE model can be used for computer-based experimentation, for example, parameter variation and changes in the model equations or alternate models, to enhance a quantitative understanding of a postulated inflammation.

This experimentation is illustrated by chapters pertaining to: (1) the computation and display of the PDE time derivatives, (2) the RHS terms of the PDEs with emphasis on the chemotaxis terms, (3) parameter variations to demonstrate parameter effects and sensitivities and (4) additonal terms in the PDEs to include PDE coupling and extensions of the basic PDE model.
Preface vii
Chapter 1 PDE Chemotaxis Model Formulation
1(6)
1.1 Introduction
1(1)
1.2 Three PDE model coordinate-free formulation
1(2)
1.3 Three PDE model formulation in spherical coordinates
3(4)
Summary and conclusion
5(1)
References
5(2)
Chapter 2 PDE Chemotaxis Model Implementation
7(24)
2.1 Introduction
7(1)
2.2 Coding of the chemotaxis model
7(24)
2.2.1 Main program
7(6)
2.2.2 ODE/MOL routine
13(6)
2.2.3 Numerical, graphical output
19(10)
Summary and conclusion
29(1)
References
29(2)
Chapter 3 Analysis of the Chemotaxis Model Time Derivatives
31(14)
3.1 Introduction
31(1)
3.2 Analysis of the chemotaxis model time derivatives
31(14)
3.2.1 Main program
31(8)
3.2.2 ODE/MOL routine
39(1)
3.2.3 Numerical, graphical output
39(5)
Summary and conclusion
44(1)
References
44(1)
Chapter 4 Analysis of the Chemotaxis PDE Model Terms
45(18)
4.1 Introduction
45(1)
4.2 R routines for PDE RHS, LHS terms
45(18)
4.2.1 Main program
45(12)
4.2.2 ODE/MOL routine
57(1)
4.2.3 Numerical, graphical output
58(3)
Summary and conclusion
61(1)
References
62(1)
Chapter 5 Sensitivity Analysis of the Chemotaxis PDE Model Parameters
63(20)
5.1 Introduction
63(1)
5.2 R routines for Case 1
63(7)
5.3 R routines for Case 2
70(6)
5.4 R routines for Case 3
76(7)
Summary and conclusion
82(1)
References
82(1)
Chapter 6 Extensions of the Three PDE Chemotaxis Model
83(46)
6.1 Introduction
83(1)
6.2 PDE chemotaxis model with anti-inflammatory drug
83(10)
6.2.1 Main program
84(1)
6.2.2 MOL/ODE routine
85(1)
6.2.3 Numerical, graphical output
86(7)
6.3 Multicomponent extension of PDE chemotaxis model
93(36)
6.3.1 Main program
94(9)
6.3.2 ODE/MOL routine
103(8)
6.3.3 Numerical, graphical output
111(16)
Summary and conclusion
127(1)
References
127(2)
Appendix A1 Functions dss004, dss044
129(6)
A1.1 dss004 listing
129(1)
A1.2 dss044 listing
130(5)
Appendix A2 Accuracy of Numerical PDE Solutions
135(6)
A2.1 H Refinement
135(1)
A2.2 P Refinement
136(5)
Index 141
William E. Schiesser is Emeritus McCann Professor of Computational Biomedical Engineering, Chemical and Biomolecular Engineering and Professor of Mathematics at Lehigh University. His research is directed toward numerical methods and associated software for ordinary, differential-algebraic and partial differential equations (ODE/DAE/PDEs), and the development of mathematical models based on ODE/DAE/PDEs. He is the author, coauthor or coeditor of 30+ books, and his ODE/DAE/PDE computer routines have been accessed by thousands of colleges and universities, corporations and government agencies.
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