Mathematical Modelling in Biomedicine Optimal Control of Biomedical Systems
Approach your problems from the right It isn't that they can't see the solution. It end and begin with the answers. Then is that they can't see the problem. one day, perhaps you will find the final question. G.K. Chesterton. The Scandal of Father Brown 'The point of a Pin'....
Main Author:  

Format:  eBook 
Language:  English 
Published: 
Dordrecht
Springer Netherlands
1986, 1986

Edition:  1st ed. 1986 
Series:  Mathematics and Its Applications

Subjects:  
Online Access:  
Collection:  Springer Book Archives 2004  Collection details see MPG.ReNa 
Table of Contents:
 0 Introduction
 1 General Remarks on Modelling
 1.1 Definitions
 1. 2 The main techniques for modeling
 1.3 Difficulties in modeling
 2 Identification and Control in Linear Compartmental Analysis
 2.1 The identification problem
 2.2 The uniqueness problem
 2.3 Numerical methods for identification
 2.4 About the nonlinear case
 2.5 Optimization techniques
 3 Optimal Control in Compartmental Analysis
 3.1 General considerations
 3.2 A first explicit approach
 3.3 The general solution
 3.4 Numerical method
 3.5 Optimal control in nonlinear cases
 4 Relations Between dose and Effect
 4.1 General considerations
 4.2 The nonlinear approach
 4.3 Simple functional model
 4.4 Optimal therapeutics
 4.5 Numerical results
 4.6 Nonlinear compartment approach
 4.7 Optimal therapeutics using a linear approach
 4.8 Optimal control in a compartmental model with time lag
 5 General Modelling in Medicine
 5.1 The problem and the corresponding model
 5.2 The identification problem
 5.3 A simple method for defining optimal therapeutics
 5.4 The Pontryagin method
 5.5 A simplified technique giving a suboptimum
 5.6 A naive but useful method
 6 Blood Glucose Regulation
 6.1 Identification of parameters in dogs
 6.2 The human case
 6.3 Optimal control for optimal therapeutics
 6.4 Optimal control problem involving several criteria
 7 Integral Equations in Biomedicine
 7.1 Compartmental analysis
 7.2 Integral equations from biomechanics
 7.3 Other applications of integral equations
 8 Numerical Solution of Integral Equations
 8.1 Linear integral equations
 8.2 Numerical techniques for nonlinear integral equations
 8.3 Identification and optimal control using integral equations
 8.4 Optimal control and nonlinear integral equations
 9 ProblemsRelated to Partial Differential Equations
 9.1 General remarks
 9.2 Numerical resolution of partial differential equations
 9.3 Identification in partial differential equations
 9.4 Optimal control with partial differential equations
 9.5 Other approaches for optimal control
 9.6 Other partial differential equations
 10 Optimality in Human Physiology
 10.1 General remarks
 10.2 A mathematical model for thermoregulation
 10.3 Optimization of pulmonary mechanics
 10.4 Conclusions
 11 Errors in Modelling
 11.1 Compartmental modeling
 11.2 Sensitivity analysis
 12 Open Problems in Biomathematics
 12.1 Biological systems with internal delay
 12.2 Biological systems involving retroaction
 12.3 Action of two (or more) drugs in the human organism
 12.4 Numerical techniques for global optimization
 12.5 Biofeedback and systems theory
 12.6 Optimization of industrial processes
 12.7 Optimality in physiology
 13 CONCLUSIONS
 Appendix — The Alienor program
 References