PDE Models for Atherosclerosis Computer Implementation in R
Aus der Reihe
Synthesis Lectures on Mathematics & Statistics
-
- Englisch ausgewählt
Fr. 72.90
inkl. gesetzl. MwSt.,
Beschreibung
Produktdetails
Einband
Taschenbuch
Erscheinungsdatum
07.11.2018
Verlag
SpringerSeitenzahl
129
Maße (L/B/H)
23.5/19.1/0.9 cm
Gewicht
284 g
Sprache
Englisch
ISBN
978-3-031-01286-0
Atherosclerosis is a pathological condition of the arteries in which plaque buildup and stiffening (hardening) can lead to stroke, myocardial infarction (heart attacks), and even death. Cholesterol in the blood is a key marker for atherosclerosis, with two forms: (1) LDL - low density lipoproteins and (2) HDL - high density lipoproteins. Low LDL and high HDL concentrations are generally considered essential for limited atherosclerosis and good health.
This book pertains to a mathematical model for the spatiotemporal distribution of LDL and HDL in the arterial endothelial inner layer (EIL, intima). The model consists of a system of six partial differential equations (PDEs) with the dependent variables 1. ¿¿¿¿(¿¿¿¿,¿¿¿¿): concentration of modified LDL 2. ¿(¿¿¿¿,¿¿¿¿): concentration of HDL 3. ¿¿¿¿(¿¿¿¿,¿¿¿¿): concentration of chemoattractants 4. ¿¿¿¿(¿¿¿¿,¿¿¿¿): concentration of ES cytokines 5. ¿¿¿¿(¿¿¿¿,¿¿¿¿): density of monocytes/macrophages 6. ¿¿¿¿(¿¿¿¿,¿¿¿¿): density of foam cells and independent variables 1. ¿¿¿¿: distance from the inner arterial wall 2. ¿¿¿¿: time The focus of this book is a discussion of the methodology for placing the model on modest computers for study of the numerical solutions. The foam cell density ¿¿¿¿(¿¿¿¿,¿¿¿¿) as a function of the bloodstream LDL and HDL concentrations is of particular interest as a precursor for arterial plaque formation and stiffening. The numerical algorithm for the solution of the model PDEs is the method of lines (MOL), a general procedure for the computer-based numerical solution of PDEs. The MOL coding (programming) is in R, a quality, open-source scientific computing system that is readily available from the Internet. The R routines for the PDE model are discussed in detail, and are available from a download link so that the reader/analyst/researcher can execute the model to duplicate the solutions reported in the book, then experiment with the model, for example, by changing the parameters (constants) and extending the model with additional equations.
Noch keine Bewertungen vorhanden
Verfassen Sie die erste Bewertung zu diesem Artikel
Helfen Sie anderen Kundinnen und Kunden durch Ihre Meinung.