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Optimisation of time-scheduled regimen for anti-cancer drug infusion

Claude Basdevant, Jean Clairambault, Francis Lévi (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The chronotherapy concept takes advantage of the circadian rhythm of cells physiology in maximising a treatment efficacy on its target while minimising its toxicity on healthy organs. The object of the present paper is to investigate mathematically and numerically optimal strategies in cancer chronotherapy. To this end a mathematical model describing the time evolution of efficiency and toxicity of an oxaliplatin anti-tumour treatment has been derived. We then applied an optimal control technique...

Optimisation of time-scheduled regimen for anti-cancer drug infusion

Claude Basdevant, Jean Clairambault, Francis Lévi (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The chronotherapy concept takes advantage of the circadian rhythm of cells physiology in maximising a treatment efficacy on its target while minimising its toxicity on healthy organs. The object of the present paper is to investigate mathematically and numerically optimal strategies in cancer chronotherapy. To this end a mathematical model describing the time evolution of efficiency and toxicity of an oxaliplatin anti-tumour treatment has been derived. We then applied an optimal control...

Optimizing the linear quadratic minimum-time problem for discrete distributed systems

Mostafa Rachik, Ahmed Abdelhak (2002)

International Journal of Applied Mathematics and Computer Science

With reference to the work of Verriest and Lewis (1991) on continuous finite-dimensional systems, the linear quadratic minimum-time problem is considered for discrete distributed systems and discrete distributed time delay systems. We treat the problem in two variants, with fixed and free end points. We consider a cost functional J which includes time, energy and precision terms, and then we investigate the optimal pair (N, u) which minimizes J.

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