Modeling of Post-Myocardial Infarction: ODE/PDE Analysis with R presents mathematical models for the dynamics of a post-myocardial (post-MI), aka, a heart attack. The mathematical models discussed consist of six ordinary differential equations (ODEs) with dependent variables Mun; M1; M2; IL10; T?; IL1. The system variables are explained as follows: dependent variable Mun = cell density of unactivated macrophage; dependent variable M1 = cell density of M1 macrophage; dependent variable M2 = cell density of M2 macrophage; dependent variable IL10 = concentration of IL10, (interleuken-10); dependent variable T? = concentration of TNF-? (tumor necrosis factor-?); dependent variable IL1 = concentration of IL1 (interleuken-1).
The system of six ODEs does not include a spatial aspect of an MI in the cardiac tissue. Therefore, the ODE model is extended to include a spatial effect by the addition of diffusion terms. The resulting system of six diffusion PDEs, with x (space) and t (time) as independent variables, is integrated (solved) by the numerical method of lines (MOL), a general numerical algorithm for PDEs.
Sprache
Verlagsort
Verlagsgruppe
Elsevier Science Publishing Co Inc
Zielgruppe
Produkt-Hinweis
Broschur/Paperback
Klebebindung
Maße
Höhe: 235 mm
Breite: 191 mm
Gewicht
ISBN-13
978-0-443-13611-5 (9780443136115)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Dr. William E. Schiesser is Emeritus McCann Professor of Chemical and Biomolecular Engineering, and Professor of Mathematics at Lehigh University. He holds a PhD from Princeton University and a ScD (hon) from the University of Mons, Belgium. 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 or coauthor of more than 16 books, and his ODE/DAE/PDE computer routines have been accessed by some 5,000 colleges and universities, corporations, and government agencies.
Autor*in
Emeritus McCann Professor of Chemical and Biomolecular Engineering, and Professor of Mathematics, Lehigh University, USA
1. ODE Model Development
2. ODE Model Implementation
3. PDE Model Formulation and Implementation
4. PDE Model Temporal Derivative Analysis
5. Analysis of the PDE Model Terms
Appendix A: Functions dss004, dss044
