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We propose a non-linear steady-state model of irreversible electropermeabilization in a biological tissue. The non-linear problem is solved using a modified fixed point iteration. The unknown parameters are experimentally estimated from the observation of the necrosis on a potato tissue for different applied voltages. A variability study of the parameters involved in the model is performed.Index Terms-Electropermeabilization (EP), non-linear conductivity.

In this paper, we propose a new dynamical model of tissue electroporation. The model is based on equivalent circuit approach at the tissue. Considering two current densities from cells and extracellular matrix, we identify the macroscopic homogenised contribution of the cell membranes. Our approach makes it possible to define a macroscopic homogenised electric field and a macroscopic homogenised transmembrane potential. This provides a direct link between the cell scale electroporation models and the tissue models. Finite element method adapted to the new non-linear model of tissue electroporation is used to compare experiments with simulations. Adapting the phenomenological electroporation model of Leguèbe et al. to the tissue scale, we calibrate the tissue model with experimental data. This makes two steps appear in the tissue electroporation process, as for cells. The new insight of the model lies in the well-established equivalent circuit approach to provide a homogenised version of cell scale models. Our approach is tightly linked to numerical homogenisation strategies adapted to bioelectrical tissue modeling.

Eddy current problems are addressed in a bidimensional setting where the conducting medium is non-magnetic and has a corner singularity. For any fixed parameter δ linked to the skin depth for a plane interface, we show that the flux density |∇A δ | is bounded near the corner unlike the perfect conducting case. Then as δ goes to zero, the first two terms of a multiscale expansion of the magnetic potential are introduced to tackle the magneto-harmonic problem. The heuristics of the method are given and numerical computations illustrate the obtained accuracy.

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