Estimating electrical conductivity tensors of biological tissues using microelectrode arrays

Finding the electrical conductivity of tissue is important for understanding the tissue's structure and functioning. However, the inverse problem of inferring spatial conductivity from data is highly ill-posed and computationally intensive. In this paper, we propose a novel method to solve the inverse problem of inferring tissue conductivity from a set of transmembrane potential and stimuli measurements made by microelectrode arrays (MEA). We propose a parallel optimization algorithm based on a single-step approximation with a parallel alternating optimization routine. This algorithm simplifies the joint tensor field estimation problem into a set of computationally tractable subproblems, allowing the use of efficient standard optimization tools.