Variational Estimation of Cardiac Conductivities by a Data Assimilation Procedure

Numerical simulations of cardiac potential are in general significantly sensitive to the parameters of the Bidomain model, the current standard model in electrocardiology. Unfortunately, these parameters and in particular the cardiac conductivities are quite problematic to measure in vivo and even more in clinical practice. On the other hand, no common agreement has been reached in the literature about cardiac conductivities. In this paper, we consider a data assimilation approach for estimating those parameters. More specifically, we consider the parameters as control variables to minimize the mismatch between the computed and the measured potentials, under the constraint of the Bidomain equations. The functional to be minimized is suitably regularized a lá Tikhonov. We prove the existence of a minimizer and we solve the problem with the BFGS method based on dual equations, showing that this method compares favorably with other methods present in the literature. We provide preliminary numerical results in 2D, showing the reliability of the approach with different numbers of measurement sites and in presence of noise.