Optimal control of leukemic cell population dynamics

Xavier Dupuis 1, 2
2 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées
Abstract : We are interested in optimizing the co-administration of two drugs for some acute myeloid leukemias (AML), and we are looking for in vitro protocols as a first step. This issue can be formulated as an optimal control problem. The dynamics of leukemic cell populations in culture is given by age-structured partial differential equations, which can be reduced to a system of delay differential equations, and where the controls represent the action of the drugs. The objective function relies on eigenelements of the uncontrolled model and on general relative entropy, with the idea to maximize the efficiency of the protocols. The constraints take into account the toxicity of the drugs. We present in this paper the modeling aspects, as well as theoretical and numerical results on the optimal control problem that we get.
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Submitted on : Wednesday, September 4, 2013 - 8:30:27 PM
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Xavier Dupuis. Optimal control of leukemic cell population dynamics. Mathematical Modelling of Natural Phenomena, EDP Sciences, 2014, Issue dedicated to Michael Mackey, 9 (1), pp.4-26. ⟨10.1051/mmnp/20149102⟩. ⟨hal-00858208⟩

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