Immersed Boundary Method for the Complete Electrode Model in Electrical Impedance Tomography

TL;DR

This paper introduces an immersed boundary numerical scheme for Electrical Impedance Tomography that simplifies boundary discretization, proves its convergence, and demonstrates its effectiveness in medical imaging inverse problems.

Contribution

It presents a novel immersed boundary method for the Complete Electrode Model, enabling easier handling of complex and dynamic boundaries in EIT.

Findings

Method converges reliably.

Effective in 2D direct and inverse problems.

Simplifies boundary discretization in complex geometries.

Abstract

We propose an immersed boundary scheme for the numerical resolution of the Complete Electrode Model in Electrical Impedance Tomography, that we use as a main ingredient in the resolution of inverse problems in medical imaging. Such method allows to use a Cartesian mesh without accurate discretization of the boundary, which is useful in situations where the boundary is complicated and/or changing. We prove the convergence of our method, and illustrate its efficiency with two dimensional direct and inverse problems.