Titlebook: Mathematical Modelling in Biomedicine; Optimal Control of B Y. Cherruault Book 1986 Springer Science+Business Media Dordrecht 1986 calculus

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Optimal Control in Compartmental Analysis, t = 0 plays the role of an action variable. For simplicity the mathematical and numerical methods will be developed on a two-compartment system, but the extension to n compartments may be done without difficulty.

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Relations Between Dose and Effect,ction, especially when there is a direct and linear relation to the concentration in the blood compartment [72]. In many cases the action of the drug cannot be related to the concentration in the blood by a simple model. This happens when sophisticated biochemical transformations arise [35]. In this

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Blood Glucose Regulation,ed treatment exists. We do not have the possibility of measuring blood glucose level continuously. Optimal control in real time is therefore impossible. A great deal of experimental data on patients is available and it is easy to improve the medical treatment, based on the experience gained by physi

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Numerical Solution of Integral Equations, equations in this book. There are many good works on these subjects [1], [69]. Let us consider the following general linear integral equation: . where f and K are given. The problem is to determine u(t) numerically such that (8.1) is satisfied. For that we shall use the approximation: . where the f

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Problems Related to Partial Differential Equations,uman organism. Similar models are obtained when considering phenomena based on space and time. For instance, another example leading to partial differential equations comes from enzyme biochemistry, where an enzyme E added to a substrate S [48] gives a product in accordance with: . Then the complex

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Optimality in Human Physiology, and chemical study are often insufficient [7] to obtain a mathematically well-defined problem. In general, the uniqueness of solutions is not assured, and so it is necessary to find some other relations or criteria. In practice, an optimality criterion is often chosen. The most intuitive one is to

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Errors in Modelling,perimental error Δx(t.) on each measure x(t.) is known. More precisely, it is sufficient to have a bound for this error. It would be interesting to calculate the error on a. and λ. as a function of the error Δx(t.) of the experimental data. To obtain this relation, let us differentiate (11.1) with r

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