A Path Integral Monte Carlo Method based on Feynman-Kac Formula for Electrical Impedance Tomography

TL;DR

This paper introduces a novel path integral Monte Carlo method based on the Feynman-Kac formula to accurately solve the forward problem in electrical impedance tomography, facilitating improved medical imaging and material testing.

Contribution

It presents a new PIMC approach utilizing reflecting Brownian motion and local time calculations for mixed boundary conditions in 3D EIT problems, enabling parallel computation.

Findings

Accurate voltage-to-current maps for 3D spherical objects with electrodes.

Method efficiently handles mixed boundary conditions.

Parallelizable solution process for local boundary problems.

Abstract

A path integral Monte Carlo method (PIMC) based on Feynman-Kac formula for mixed boundary conditions of elliptic equations is proposed to solve the forward problem of electrical impedance tomography (EIT) on the boundary to obtain electrical potentials. The forward problem is an important part for iterative algorithms of the inverse problem of EIT, which has attracted continual interest due to its applications in medical imaging and material testing of materials. By simulating reflecting Brownian motion with walk-on-sphere techniques and calculating its corresponding local time, we are able to obtain accurate voltage-to-current map for the conductivity equation with mixed boundary conditions for a 3-D spherical object with eight electrodes. Due to the local property of the PIMC method, the solution of the map can be done locally for each electrode in a parallel manner.