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

Content: Cover
 Title Page
 Contents
 Preface
 Chapter 1 Introduction to Partial Differentiation Equation Analysis: Chemotaxis
 1.1 Introduction
 1.2 Linear Diffusion Model
 1.3 Nonlinear Chemotaxis Model
 1.4 Method of Lines Solution of 2-PDE Chemotaxis Model
 1.4.1 Main Program
 1.4.2 ODE Routine
 1.5 Model Output
 1.6 Computation of PDE Terms
 1.7 Conclusions
 References
 Chapter 2 Pattern Formation
 2.1 Introduction
 2.2 Two PDE Model
 2.2.1 ODE Routine
 2.2.2 Main Program
 2.2.3 Numerical Solution
 2.3 Three PDE Model
 2.3.1 ODE Routine
 2.3.2 Main Program
 2.3.3 Supplemental Routine. 2.3.4 Numerical Solution2.4 Conclusions
 References
 Chapter 3 Belousov-Zhabotinskii Reaction System
 3.1 Introduction
 3.2 The Belousov-Zhabotinskii Reaction System
 3.2.1 ODE Routine
 3.2.2 Main Program
 3.2.3 Model Output
 3.3 Conclusions
 Reference
 Chapter 4 Hodgkin-Huxley and Fitzhugh-Nagumo Models
 4.1 Introduction
 4.2 PDE Model
 4.3 MOL Routines
 4.3.1 ODE Routine
 4.3.2 Main Program
 4.4 Model Output
 4.5 Discontinuous Initial Condition
 4.6 Conclusions
 References
 Chapter 5 Anesthesia Spatiotemporal Distribution
 5.1 Introduction
 5.2 Two PDE Model
 5.2.1 Main Program. 5.2.2 ODE Routine5.2.3 Other PDE Routines
 5.2.4 Model Output
 5.3 Conclusions
 5.4 Model Extension
 5.4.1 ODE Routine for the Extended Model
 5.4.2 Main Program for the Extended Model
 5.4.3 Output for the Extended Model
 Acknowledgment
 References
 Chapter 6 Influenza with Vaccination and Diffusion
 6.1 Introduction
 6.2 Five PDE Model
 6.2.1 ODE Routine
 6.2.2 Main Program
 6.2.3 Model Output
 6.3 Summary
 References
 Chapter 7 Drug Release Tracking
 7.1 Introduction
 7.2 Three PDE Model
 7.2.1 ODE Routine
 7.2.2 Rate Functions
 7.2.3 Main Program
 7.3 Model Output
 7.3.1 Base Case. 7.3.2 Variation of Spatial Differentiation7.3.3 Variation of Polymer Stress
 7.4 Alternate Coordinate Systems
 7.5 Summary
 References
 Chapter 8 Temperature Distributions in Cryosurgery
 8.1 Introduction
 8.2 PDE Model
 8.3 Method of Lines Analysis
 8.3.1 ODE Routine
 8.3.2 Physical Property Routines
 8.3.3 Main Program
 8.4 Numerical Output
 8.5 Variations in the Model
 8.6 Summary
 References
 Index.