PhD Thesis

Manuscript
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Abstract

Cell permeabilization by intense electric pulses, called electropermeabilization, is a biological phenomenon involved in recent anticancer therapies. It allows, for example, to increase the efficacy of chemotherapies still reducing their side effects, to improve gene transfer, or to proceed tumor ablation. However, mechanisms of electropermeabilization are not clearly explained yet, and the mostly adopted hypothesis of the formation of pores at the membrane surface is in contradiction with several experimental results.

This thesis modeling work is based on a different approach than existing electroporation models. Instead of deriving equations on membranes properties from hypothesis at the molecular scale, we prefer to write ad hoc laws to describe them, based on available experimental data only. Moreover, to be as close as possible to these data, and to ease the forthcoming work of parameter calibration, we added to our model equations of transport and diffusion of molecules in the cell. Another important feature of our model is that we differentiate the conductive state of membranes from their permeable state.

Numerical methods, as well as a 3D parallel C++ code were written and validated in order to solve the partial differential equations of our models. The modeling work was validated by showing qualitative match between our simulations and the behaviours that are observed in vitro.

Keywords : electropermeabilization, cells, partial differential equations, numerical methods on cartesian grid, discrete surface diffusion.