### 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'....

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Main Author: eBook English Dordrecht Springer Netherlands 1986, 1986 1st ed. 1986 Mathematics and Its Applications Springer Book Archives -2004 - Collection details see MPG.ReNa
• 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 non-linear 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 non-linear cases
• 4 Relations Between dose and Effect
• 4.1 General considerations
• 4.2 The non-linear approach
• 4.3 Simple functional model
• 4.4 Optimal therapeutics
• 4.5 Numerical results
• 4.6 Non-linear 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 sub-optimum
• 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 non-linear integral equations
• 8.3 Identification and optimal control using integral equations
• 8.4 Optimal control and non-linear 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 thermo-regulation
• 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