Mathematical modelling in biomedicine : optimal control of biomedical systems

Y. Cherruault

[目次]

  • 0 Introduction.- 1 General Remarks on Modelling.- 1.1 Definitions.- 1. 2 The main techniques for modeling.- 1.2.1 Compartmental analysis.- 1.2.2 Systems with diffusion-convection reactions.- 1.2.3 Simulation models.- 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.- 2.5.1 General considerations.- 2.5.2 Numerical methods.- 2.5.3 Descent methods.- 2.5.4 A global optimization technique.- 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.- 3.5.1 A general technique.- 3.5.2 A method for non-linear compartmental systems.- 3.5.3 Another practical approach.- 3.5.3 A variant of dynamic programming technique.- 3.5.4 A simple idea applied to optimal control problems.- 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.- 8.2.1 Numerical solution using a sequence of linear integral equations.- 8.2.2 A discretised technique.- 8.2.3 An iterative diagram with regularity constraints.- 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.- 9.2.1 Semi-discretization technique.- 9.2.2 Optimization method for solving partial differential equations.- 9.2.3 Solution of partial differential equations using a complete discretization.- 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.

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この本の情報

書名 Mathematical modelling in biomedicine : optimal control of biomedical systems
著作者等 Cherruault, Y.
シリーズ名 Mathematics and its applications
出版元 D.Reidel
Sold and Kluwer Academic
刊行年月 c1986
ページ数 xviii, 258 p.
大きさ 23 cm
ISBN 9027721491
NCID BA00198105
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言語 英語
出版国 オランダ
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