Speaker
Description
In this work, we study the homogenization of the phenomenological electropermeabilization model introduced by Kavian et al (2014) in a periodic tissue subject to an applied electric field. We introduce a small parameter epsilon and derive the most relevant scaling of the equations in epsilon through dimension analysis. Asymptotic expansions yield a macroscopic model, where we are able to define an effective conductivity of the medium in terms of solutions to cell problems on the microscopic scale. The effective conductivity agrees qualitatively with experimental data from real tissue and depends non-linearly both on time and the applied electric field. Due to the non-linearities in the equations, the macroscopic and microscopic problems do not fully decouple, and the effective conductivity exhibits memory effects. Still, we are able to prove two-scale convergence of the solutions as epsilon tends to zero using monotonicity arguments. Our results therefore provide a rigorous mathematical coupling between cell-scale properties in the tissue and the observed macroscopic conductivity dynamics.
The talk will provide an overview of the above results. Some numerical results will also be shown, varying parameters including size and shape of the biological cells.
