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.

提出了一种基于Feynman-Kac 公式的混合边界条件拉普拉斯方程的路径积分蒙特卡洛方法(PIMC) 来求解电阻抗层析成像(EIT) 的正演问题。正向问题是逆向 EIT 问题迭代算法的重要组成部分，所提出的 PIMC 提供了一种局部解决方案来查找单个电极上的电势和电流。提出了改进的技术，以更准确地计算反射布朗运动 (RBM) 的局部时间和拉普拉斯方程混合边界问题的费曼-卡茨公式。具有八个电极的模型 3-D EIT 问题的电极上的精确电压到电流映射是通过使用所提出的 PIMC 方法求解混合边界问题获得的。