# On the determination of ischemic regions in the monodomain model of cardiac electrophysiology from boundary measurements

## TL;DR

This paper develops a mathematical method to detect small ischemic regions in the heart tissue by analyzing boundary measurements within the monodomain model of cardiac electrophysiology, using asymptotic expansions and topological gradients.

## Contribution

It introduces a novel approach combining asymptotic analysis and topological derivatives to identify ischemic regions from boundary data in cardiac models.

## Key findings

- The method accurately detects small ischemic regions.
- Numerical experiments confirm the robustness of the detection algorithm.
- The approach is theoretically grounded and computationally validated.

## Abstract

In this paper we consider the monodomain model of cardiac electrophysiology. After an analysis of the well-posedness of the model, we determine an asymptotic expansion of the perturbed potential due to the presence of small conductivity inhomogeneities (modeling small ischemic regions in the cardiac tissue) and use it to detect the anomalies from partial boundary measurements. This is done by determining the topological gradient of a suitable boundary misfit functional. The robustness of the algorithm is confirmed by several numerical experiments.