Propagation de fronts et croissance tumorale (HDR Guillemette Chapuisat)

Guillemette Chapuisat
I2M, Aix-Marseille Université

Date(s) : 10/07/2019   iCal
14 h 00 min - 15 h 30 min

Soutenance HDR (Habilitation à Diriger des Recherches)

Progressive fronts and cancer growth

This work deals with the analysis of reaction-diffusion equations and modeling in health science. In a first part, we are interested in understanding the propagation or not of depolarization wave in the brain. This problem arises from the modeling of cortical spreading depressions and amounts to studying the influence of the geometry of the domain on the propagation of a generalized transition front for a bistable reaction-diffusion equation. Sliding methods are used to prove the propagation of a front and energy methods to construct stationary solutions blocking the front. Finally, a numerical study of an open case is presented. The second part of this work concerns the modeling in cancerology and more precisely the study and the optimization of the chemotherapy protocols to fight cancer. In particular, the “Maximum Tolerated Dose” protocols in which a high dose of chemotherapy followed by a long pause is periodically given, is compared with the metronomic protocols in which lower but more frequent doses are given, using different models. Finally, optimal control tools are used to obtain new protocols.

Membres du jury :
– Emmanuel GRENIER (ENS Lyon)
– François HAMEL (Aix-Marseille Université)
– Raphaèle HERBIN (Aix-Marseille Université)
– Florence HUBERT (Aix-Marseille Université)
– Élisabeth LOGAK (Université de Cergy-Pontoise)
– Hasnaa ZIDANI (ENSTA Paris)

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