Modeling of Post-Myocardial Infarction

Ode/Pde Analysis with R

von William E Schiesser

144 Seiten, Taschenbuch

Kurzbeschreibung des Verlags

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.

• Themen: Mathematik und Naturwissenschaften Biologie, Biowissenschaften Biowissenschaften, allgemein DV-gestützte Biologie/Bioinformatik
• ISBN: 9780443136115
• Sprache: Englisch
• Erscheinungsdatum: 25.08.2023
• Größe: 236 x 186 mm
• Verlag: Elsevier Science