Moving Boundary PDE Analysis: Biomedical Applications in R, 1st Edition (Hardback) book cover

Moving Boundary PDE Analysis

Biomedical Applications in R, 1st Edition

By William Schiesser

CRC Press

128 pages | 86 B/W Illus.

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Hardback: 9780367224837
pub: 2019-06-13
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Description

Mathematical models stated as systems of partial di

erential equations (PDEs) are

broadly used in biology, chemistry, physics and medicine (physiology). These models

describe the spatial and temporial variations of the problem system dependent variables,

such as temperature, chemical and biochemical concentrations and cell densities, as a

function of space and time (spatiotemporal distributions).

For a complete PDE model, initial conditions (ICs) specifying how the problem system

starts and boundary conditions (BCs) specifying how the system is de ned at its spatial

boundaries, must also be included for a well-posed PDE model.

In this book, PDE models are considered for which the physical boundaries move with

time. For example, as a tumor grows, its boundary moves outward. In atherosclerosis,

the plaque formation on the arterial wall moves inward, thereby restricting blood ow

with serious consequences such as stroke and myocardial infarction (heart attack).

These two examples are considered as applications of the reported moving boundary

PDE (MBPDE) numerical method (algorithm). The method is programmed in a set of

documented routines coded in R, a quality, open-source scienti c programming system.

The routines are provided as a download so that the teacher/analyst/researcher can

use MFPDE models without having to rst study numerical methods and computer

programming

Table of Contents

1. PDE Model Formulation. 2. PDE Model Implementation. 3. PDE Model Output. 4. Tumor growth. 5. Plaque Formation in Atherosclerosis. Appendix A1. Test of Spline Regridding. Appendix A2. Test of Moving Boundary Algorithm Spline Formulation. Appendix A3. Test of Moving Boundary Algorithm Finite Difference Formulation.

About the Author

William E. Schiesser, emeritus professor at Lehigh University. Schiesser is the Emeritus McCann Professor in the chemical and biomolecular engineering department as well as a former professor in the mathematics department. recently authored several books on computer-based solutions to model real-life phenomena, such as the development of Parkinson’s disease.Schiesser holds a Ph.D. from Princeton University and an honorary Sc.D. from the University of Mons, Belgium. He is the author or co-author of numerous books in his field of research on 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.

Subject Categories

BISAC Subject Codes/Headings:
MAT003000
MATHEMATICS / Applied
MED009000
MEDICAL / Biotechnology