Differential Equation Analysis in Biomedical Science and Engineering : Partial Differential Equation Applications with R

344 Pages·2014·2.217 MB·English

by  William E. Schiesser

DIFFERENTIAL
EQUATION ANALYSIS IN
BIOMEDICAL SCIENCE
AND ENGINEERING

DIFFERENTIAL
EQUATION ANALYSIS IN
BIOMEDICAL SCIENCE
AND ENGINEERING
PARTIAL DIFFERENTIAL
EQUATION APPLICATIONS WITH R
William E. Schiesser
Department of Chemical Engineering
Lehigh University
Bethlehem, PA
CoverDesign:Wiley
CoverIllustration:Courtesyoftheauthor
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LibraryofCongressCataloging-in-PublicationData:
Schiesser,W.E.
Differentialequationanalysisinbiomedical scienceandengineering : partial
differentialequationapplications withR/WilliamE.Schiesser,DepartmentofChemical
Engineering,LehighUniversity,Bethlehem,PA.
pagescm
Includes bibliographicalreferences andindex.
ISBN978-1-118-70518-6(cloth)
1. Biomedicalengineering–Computersimulation. 2. Developmental biology–Simulation
methods. 3. Chemotaxis–Dataprocessing. 4. Differentialequations. I.Title.
R857.M34.S3452013
610.280285–dc23
2013020441
PrintedintheUnitedStatesofAmerica.
10987654321
To John von Neumann and Alan Turing

CONTENTS
Preface ix
1. Introduction to Partial Differentiation Equation
Analysis: Chemotaxis 1
2. Pattern Formation 43
3. Belousov–Zhabotinskii Reaction System 103
4. Hodgkin–Huxley and Fitzhugh–Nagumo Models 127
5. Anesthesia Spatiotemporal Distribution 163
6. Influenza with Vaccination and Diffusion 207
7. Drug Release Tracking 243
8. Temperature Distributions in Cryosurgery 287
Index 323
vii