Geodesic
Optimal Control in a Model of Chemotherapy-induced Radiosensilisation
Mathematica Applicanda, Tome 47 (2019) no. 1, pp. 81-91.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

In this work, we consider a simple mathematical model of radiochemotherapy which includes a term responsible for radiosensitization. We focus on finding theoretically optimal controls which maximise tumour cure probability for a finite, fixed therapeutic horizon. We prove that the optimal controls for both therapies are of 0-bang type, a result which is not altered by the inclusion of the radiosensilization term. By means of numerical simulations, we show that optimal control offers a moderate increase in survival time over a sequential treatment. We then revisit in more detail a question of measuring the synergy between the therapies by means of isobolograms, a common experimental technique for measuring the additivity of two treatments.
DOI : 10.14708/ma.v47i1.6480
Classification : Primary: 92C50, Secondary: 49K15
Mots-clés : radiochemotherapy, optimal control, survival curves, radiosensilisation 
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Piotr Bajger; Krzysztof Fujarewicz; Andrzej Świerniak. Optimal Control in a Model of Chemotherapy-induced Radiosensilisation. Mathematica Applicanda, Tome 47 (2019) no. 1, pp.  81-91. doi : 10.14708/ma.v47i1.6480. http://geodesic.mathdoc.fr/articles/10.14708/ma.v47i1.6480/

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