On the reconstruction of cavities in a nonlinear model arising from cardiac electrophysiology

TL;DR

This paper introduces a new method for reconstructing insulating cavities in nonlinear models from boundary data, using $ extGamma$-convergence, with demonstrated effectiveness through numerical experiments.

Contribution

It proposes a novel reconstruction algorithm based on $ extGamma$-convergence for identifying cavities in nonlinear elliptic equations from boundary measurements.

Findings

Successful reconstruction of cavities demonstrated in numerical experiments

The $ extGamma$-convergence based approach is effective and applicable

Improves upon previous methods in nonlinear cardiac electrophysiology models

Abstract

In this paper, we deal with the problem of determining perfectly insulating regions (cavities) from one boundary measurement in a nonlinear elliptic equation arising from cardiac electrophysiology. Based on the results obtained in [9] we propose a new reconstruction algorithm based on $\Gamma$-convergence. The relevance and applicability of this approach are then shown through several numerical experiments.