Math. Model. Nat. Phenom.
Volume 9, Number 1, 2014Issue dedicated to Michael Mackey
|Page(s)||4 - 26|
|Published online||07 February 2014|
Optimal Control of Leukemic Cell Population Dynamics
CMAP, Ecole Polytechnique & Inria Saclay,
⋆ Corresponding author. E-mail:
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.
Mathematics Subject Classification: 49N90 / 49K21 / 92C50
Key words: acute myeloid leukemia / optimal control / delay differential equations / population dynamics / general relative entropy / in vitro therapeutic optimization
© EDP Sciences, 2014
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