Differential equation analysis in biomedical science and engineering : ordinary differential equation applications with R

Content: Cover
 Title Page
 Contents
 Preface
 Chapter 1 Introduction to Ordinary Differential Equation Analysis: Bioreactor Dynamics
 1.1 Introduction
 1.2 A 7 x 7 ODE System for a Bioreactor
 1.3 In-Line ODE Routine
 1.4 Numerical and Graphical Outputs
 1.5 Separate ODE Routine
 1.6 Alternative Forms of ODE Coding
 1.7 ODE Integrator Selection
 1.8 Euler Method
 1.9 Accuracy and Stability Constraints
 1.10 Modified Euler Method as a Runge-Kutta Method
 1.11 Modified Euler Method as an Embedded Method
 1.12 Classic Fourth-Order Runge-Kutta Method as an Embedded Method
 1.13 RKF45 Method
 References. Chapter 2 Diabetes Glucose Tolerance Test2.1 Introduction
 2.2 Mathematical Model
 2.2.1 Glucose Balance
 2.2.2 Insulin Balance
 2.3 Computer Analysis of the Mathematical Model
 2.3.1 ODE Integration by lsoda
 2.3.2 ODE Integration by RKF45
 2.3.3 ODE Integration with RKF45 in a Separate Routine
 2.3.4 h Refinement
 2.3.5 p Refinement
 2.4 Conclusions
 References
 Chapter 3 Apoptosis
 3.1 Introduction
 3.2 Mathematical Model
 3.3 Main Program
 3.4 ODE Routine
 3.5 Base Case Output
 3.6 Base Case with Variation in ICs
 3.7 Variation in ODEs
 3.8 Selection of Units. 3.9 Model Solution with RKF453.10 Conclusion
 Reference
 Chapter 4 Dynamic Neuron Model
 4.1 Introduction
 4.2 The Dynamic Neuron Model
 4.3 ODE Numerical Integration
 4.3.1 Explicit Euler Integration
 4.3.2 Numerical and Graphical Solutions
 4.3.3 Evaluation and Plotting of the ODE Derivative Vector
 4.3.4 p Refinement
 4.4 Conclusions
 References
 Chapter 5 Stem Cell Differentiation
 5.1 Introduction
 5.2 Model Equations
 5.3 R Routines
 5.3.1 Main Program
 5.3.2 ODE Routine
 5.3.3 Numerical and Graphical Output
 5.3.4 Analysis of the Terms in the ODEs
 5.3.5 Stable States
 5.4 Summary. ReferenceChapter 6 Acetylcholine Neurocycle
 6.1 Introduction
 6.2 ODE Model
 6.3 Numerical Solution of the Model
 6.3.1 ODE Routine
 6.3.2 Main Program
 6.4 Model Output
 6.4.1 Equilibrium Solution
 6.4.2 Nonequilibrium Solutions
 6.4.3 Analysis of the Terms in the ODEs
 6.5 ODE/PDE Model
 Appendix A1: IC Vector by a Differential Levenberg Marquardt Method
 A1.1 ODE Jacobian Matrix
 A1.2 Newton's Method
 A1.3 Steepest Descent Method
 A1.4 The Levenberg Marquardt Method
 A1.5 Differential Newton's Method
 A1.6 Differential Steepest Descent Method
 A1.7 Differential Levenberg Marquardt Method. A1.8 Solution for the IC Vector of the 8 x 8 ODE SystemReferences
 Chapter 7 Tuberculosis with Differential Infectivity
 7.1 Introduction
 7.2 Mathematical Model
 7.3 R Routines for the ODE Model
 7.3.1 ODE Routine
 7.3.2 Main Program
 7.4 Model Output
 7.5 Conclusions
 References
 Chapter 8 Corneal Curvature
 8.1 Introduction
 8.2 Model Equations
 8.3 Method of Lines Solution
 8.4 R Routines
 8.4.1 Main Program
 8.4.2 ODE Routine
 8.5 Numerical Solution
 8.6 Error Analysis of the Numerical Solution
 8.7 Library Routines for Differentiation in Space
 8.8 Summary
 References.