The accurate quantification of cardiac conductivities is crucial for extending computational electrocardiology from medical research to clinical practice. However, experimental results in the literature significantly disagree on the values and ratios between longitudinal and tangential coefficients. Moreover, many popular models in computational electrocardiology, such as the monodomain and bidomain models, have been shown to be strongly sensitive to the cardiac conductivity parameters.

With this motivation, we investigate a novel variational data assimilation approach for the estimation of the cardiac conductivity parameters able to combine available patient-specific measures with mathematical models. In particular, it relies on the least-square minimization of the misfit between experiments and simulations, constrained by the underlying mathematical model. Operating on the conductivity tensors as control variables of the minimization, we obtain a parameter estimation procedure. As the theory of this approach currently provides only an existence proof and it is not informative for practical experiments, we present here an extensive numerical simulation campaign to assess practical critical issues such as the size and the location of the measurement sites for in silico test cases reproducing experimental and realistic settings. This will be finalized with a real validation of the variational data assimilation procedure. Results indicate the presence of lower and upper bounds for the number of sites which guarantee an accurate and minimally redundant parameter estimation; the location of sites being generally non critical for properly designed experiments.

This is a joint work with Alessandro Veneziani (Emory University) and Flavio Fenton (Georgia Institute of Technology).

This work has been supported by the NSF Project DMS 1412973/1413037 "Collaborative Research: Novel data assimilation techniques in mathematical cardiology - development, analysis and validation".