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Optimal Control of Leukemic Cell PopulationDynamics

Published online by Cambridge University Press:  07 February 2014

X. Dupuis
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Abstract

We are interested in optimizing the co-administration of two drugs for some acute myeloidleukemias (AML), and we are looking for in vitro protocols as a first step. This issue canbe formulated as an optimal control problem. The dynamics of leukemic cell populations inculture is given by age-structured partial differential equations, which can be reduced toa system of delay differential equations, and where the controls represent the action ofthe drugs. The objective function relies on eigenelements of the uncontrolled model and ongeneral relative entropy, with the idea to maximize the efficiency of the protocols. Theconstraints take into account the toxicity of the drugs. We present in this paper themodeling aspects, as well as theoretical and numerical results on the optimal controlproblem that we get.

Keywords

acute myeloid leukemiaoptimal controldelay differential equationspopulation dynamicsgeneral relative entropyin vitro therapeutic optimization
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 9 , Issue 1: Issue dedicated to Michael Mackey , 2014 , pp. 4 - 26
Copyright
© EDP Sciences, 2014

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