No abstract

While the potential groundbreaking role of mathematical modeling in electrophysiology has been demonstrated for therapies like cardiac resynchronization or catheter ablation, its extensive use in clinics is prevented by the need of an accurate customized conductivity identification. Data assimilation techniques are, in general, used to identify parameters that cannot be measured directly, especially in patient-specific settings. Yet, they may be computationally demanding. This conflicts with the clinical timelines and volumes of patients to analyze. In this paper, we adopt a model reduction technique, developed by F. Chinesta and his collaborators in the last 15 years, called Proper Generalized Decomposition (PGD), to accelerate the estimation of the cardiac conductivities required in the modeling of the cardiac electrical dynamics. Specifically, we resort to the Monodomain Inverse Conductivity Problem (MICP) deeply investigated in the literature in the last five years. We provide a significant proof of concept that PGD is a breakthrough in solving the MICP within reasonable timelines. As PGD relies on the offline/online paradigm and does not need any preliminary knowledge of the high-fidelity solution, we show that the PGD online phase estimates the conductivities in real-time for both two-dimensional and three-dimensional cases, including a patient-specific ventricle.

An accurate estimation of cardiac conductivities is critical in computational electro-cardiology, yet experimental results in the literature significantly disagree on the values and ratios between longitudinal and tangential coefficients. These are known to have a strong impact on the propagation of potential particularly during defibrillation shocks. Data assimilation is a procedure for merging experimental data and numerical simulations in a rigorous way. In particular, variational data assimilation relies on the least-square minimization of the misfit between simulations and experiments, constrained by the underlying mathematical model, which in this study is represented by the classical Bidomain system, or its common simplification given by the Monodomain problem. 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 needed for in silico test cases of potential 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. An effective combination of parameter estimation based on the Monodomain and Bidomain models is tested for the sake of computational efficiency. Parameter estimation based on the Monodomain equation potentially leads to the accurate computation of the transmembrane potential in real settings.