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Author:   Y. Cherruault
Publisher:   Springer
Imprint:   Kluwer Academic Publishers
Edition:   1986 ed.
Volume:   23
Dimensions:   Width: 15.50cm , Height: 1.70cm , Length: 23.50cm
Weight:   1.260kg
ISBN:  

9789027721495

ISBN 10:   9027721491
Pages:   258
Publication Date:   28 February 1986
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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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 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.

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