Modeling of Post-Myocardial Infarction (eBook)

ODE/PDE Analysis with R

William E. Schiesser (Autor)

eBook Download: PDF | EPUB

2023 | 1. Auflage
200 Seiten
Elsevier Science (Verlag)
978-0-443-13612-2 (ISBN)

Infos

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; Ta; 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 Ta = concentration of TNF-a (tumor necrosis factor-a); 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. - Includes PDE routines based on the method of lines (MOL) for computer-based implementation of PDE models - Offers transportable computer source codes for readers in R, with line-by-line code descriptions as it relates to the mathematical model and algorithms - Authored by a leading researcher and educator in PDE models

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.

Produkt-Details

• Erscheint lt. Verlag: 23.8.2023
• Sprache: englisch
• Themenwelt: Informatik ► Weitere Themen ► Bioinformatik
• Themenwelt: Medizin / Pharmazie
• Themenwelt: Naturwissenschaften ► Biologie ► Genetik / Molekularbiologie
• ISBN-10: 0-443-13612-2 / 0443136122
• ISBN-13: 978-0-443-13612-2 / 9780443136122