A critical step when using computational tools in clinical routines is the customization of mathematical models by an appropriate patient-specific parameter estimation. In cardiac electrophysiology, crucial parameters are the conductivity tensors. The quantification of cardiac conductivities is quite troublesome in living organisms, as witnessed by different discordant data in the literature. The approach considered in this talk stems from a Data Assimilation procedure, where the tensors are used as a control variable to minimize the mismatch between the computed and the measured potentials. This procedure has been analyzed for what concerns the existence of at least a solution and implemented in 2D and 3D models.

An important drawback of this procedure is the computational cost, that is quite significant as for any minimization procedure constrained by a set of partial differential equations. We will illustrate some possible model reduction techniques that help in containing the computational costs. Several numerical results will be discussed for an insightful assessment of the procedure, in particular for the interplay between the estimation of Monodomain and Bidomain conductivities. Conductivities will be considered to be space-dependent. Preliminary results of an experimental validation with ex-vivo animal tissues will be presented, as well.

This is a joint work with F. Fenton (GA Tech), A. Gizzi (Campus Biomedico, Rome, IT) and A. Barone (Emory). This work is supported by the NSF DMS 1412973/1413037.