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.