This PhD subject at the intersection of biophysics and mathematical physics is an extension of ongoing work at LPCT. It has two main components. A first work will consist in incorporating the fractal structure of the tissue and the Cattaneo correction into existing models. The resolution of the bioheat equation can be done theoretically and numerically, starting with the two-dimensional case. The sensitivity of thermal responses to different types of boundary conditions will be studied and the search for effective parameters of the problem such as average thermophysical properties, fractal dimension or relaxation time will be the subject of particular attention. Several aspects of fractality and possible long-term memory effects have already been investigated by our team before (Fumeron, Henkel, López 2023, Manapany, Fumeron, Henkel 2024) and they continue to be the subject of active studies.
The second step deals with including in the Pennes model a detailed description of perfusion, by taking into account the couplings of the blood system with temperature (vasodilation) and the changes in morphology following angiogenesis. Angiogenesis is in fact one of the 6 cellular markers of malignancy and an increase in the fractal dimension of the vascular network has been observed when a tumor becomes malignant : this larger fractal dimension is explained by a larger exchange surface, which favors the metabolic supply (Risser et al. 2007). It will therefore be a question of developing and then numerically solving a 2D then 3D bioheat equation with a memory effect and a perfusion term including the fractal structure of the blood network at the tumor level, then discussing its consequences on the effectiveness of hyperthermia protocols.
See also this document
Contacts :
Malte Henkel <malte.henkel@univ-lorraine.fr>,
Sébastien Fumeron <sebastien.fumeron@univ-lorraine.fr>
Modifié 2 fois. Dernière modification le 20/12/24 03:28 par Frédéric Chevy.