Localization of three-dimensional sources in cardiac tissue using optical mapping

Optical mapping allows the visualization of cardiac action potentials on cardiac tissue surfaces by fluorescence using voltage-sensitive dyes. So far, the surface measurements are directly related to surface action potentials. We aim at exploiting these measurements in order to reconstruct three-dimensional action potentials. In this preliminary work, we tried to localize fixed electrical sources in a three-dimensional slab of tissue. Therefore, we minimized the difference between the measure and a model, in a least squares sense. The model is based on the diffusion equation for the propagation of light, and simplified spherical or ellipsoidal electrical wavefronts. The inverse problem is solved by combining the gradient method and the BFGS algorithm. The method was challenged on data in silico, and then on experimental data. The results show improvements over previous localization methods on data in silico, although its use on experimental data still requires some work.