Abstract
One of the main objectives in electrocardiology is to extract physical properties of cardiac tissues from measured information on electrical activity of the heart. Mathematically, this is an inverse problem for reconstructing coefficients in electrocardiology models from partial knowledge of the solutions of the models. In this work, we consider such parameter extraction problems for two well-studied electrocardiology models: the bidomain model and the FitzHugh-Nagumo model. We propose a systematic reconstruction method based on the Born approximation of the original nonlinear inverse problem. We describe a two-step procedure that allows us to reconstruct not only perturbations of the unknowns, but also the backgrounds around which the linearization is performed. We show some numerical simulations under various conditions to demonstrate the performance of our method. We also introduce a parameterization strategy using eigenfunctions of the Laplacian operator to reduce the number of unknowns in the parameter extraction problem.