Author | Cherruault, Y. author |
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Title | Mathematical Modelling in Biomedicine [electronic resource] : Optimal Control of Biomedical Systems / by Y. Cherruault |
Imprint | Dordrecht : Springer Netherlands, 1986 |
Connect to | http://dx.doi.org/10.1007/978-94-009-5492-2 |
Descript | XVIII, 258 p. online resource |
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 Problems Related 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 โ The Alienor program -- References