A path integral Monte Carlo (PIMC) method based on Feynman-Kac formula for electrical impedance tomography.

A path integral Monte Carlo method (PIMC) based on a Feynman-Kac formula for the Laplace equation with mixed boundary conditions is proposed to solve the forward problem of the electrical impedance tomography (EIT). The forward problem is an important part of iterative algorithms of the inverse EIT problem, and the proposed PIMC provides a local solution to find the potentials and currents on individual electrodes. Improved techniques are proposed to compute with better accuracy both the local time of reflecting Brownian motions (RBMs) and the Feynman-Kac formula for mixed boundary problems of the Laplace equation. Accurate voltage-to-current maps on the electrodes of a model 3-D EIT problem with eight electrodes are obtained by solving a mixed boundary problem with the proposed PIMC method. • An accurate stochastic algorithm is first proposed for the Laplace equation with mixed/Robin boundary conditions. • An more accurate allocation scheme for calculating local time of Neumann and Robin boundaries improves errors from 4% to 1%. • The proposed method can be applied to the voltage-to-current mapping for the forward EIT problem. [ABSTRACT FROM AUTHOR]