Electroporation-based therapies (EPTs) consist in applying high voltage short pulses to cells in order to create defects in the plasma membrane. They provide interesting alternatives to standard ablative techniques, for instance for deep seated badly located tumors. However their use is still limited due to a lack of knowledge of tissue electroporation. The goal of the associate team is to focus on the multiscale numerical modeling of spheroid electroporation, in order to provide new insights in electroporation at the mesoscopic scales (spheroids provide interesting tumor-like biological models). Benefiting from the expertise of F. Gibou’s team in HPC for multiphysics, and the expertise of the team MONC in tumor growth and cell electroporation modeling, the goal of the associate team Num4SEP is to obtain accurate and efficient numerical tools for the quantitative evaluation of the EPTs at the mesoscopic scale.
Num4SEP is lead by C. Poignard, research scientist at Inria and F. Gibou, Prof. at UCSB.
The associate team proposes to develop multiscale numerical tools for quantitative in vitro evaluation of EPTs on spheroids using biological data. Gathering the HPC skills of the American partner coupled to the expertise in electroporation modeling of the Inria team MONC, we aim at developing specific and efficient schemes for spheroid electroporation and molecule uptake, in quantitative agreement with the experiments performed with the consortium NUMEP. 1. Numerical schemes based on Quad-/Oc-trees. (First year) We first propose to derive numerical schemes based on Quad-/Oc-trees techniques to solve appropriately the non-linear equation on a large number of cells in the same vein as the preliminary work of Guittet, Gibou and Poignard thanks to the single cell model of Leguèbe et al. Quad-/Oc-trees mesh is an interesting tools for mesh refinements in the region affected by the electric field, close to cell membranes, in order to focus on the interesting regions (the cell membranes) and to reduce the computational cost far from the interfaces. 2. Numerical homogenization from cell scale models. (First and second year) In a second step, well-adapted numerical homogenization5 for Finite Volume Methods (FVM) will be developed for the electric field distribution. Note that homogenization is not trivial since different regimes may appear depending on the scaling, and we will have to discriminate between the asymptotic regimes. The skill of A. Collin and C. Poignard in asymptotic analysis and homogenization will be helpful for this purpose. Numerical comparisons between the full description of the first task and the homogenized models will make it possible to understand quantitatively the pros and cons of each approach, in order to build a relevant tissue model of electroporation. 3. Calibration and comparison of the models with the experiments. (Second and third year) Then, the modeling of the growth of Multi-Cellular Tumor Spheroid (MCTS) submitted to IRE and ECT will be investigated, in tight links with the experiments6. Thanks to efficient numerical tools, the sensitivity analysis and the calibration of the models thanks to the biological data will be finally investigated. The team will benefit from the skills of O. Saut in tumor growth modeling and S. Benz ́ekry in the estimation of uncertainties associated to the model calibration. The long term-goal of the team is to highlight the differences of treatment efficacies on healthy, quiescent and proliferative cells, as well as the regrowth of MCTS after EPTs.