Numerical sensitivity analysis of a variational data assimilation procedure for cardiac conductivities

Abstract

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.

Key aspects for effective mathematical modelling of fractional-diffusion in cardiac electrophysiology: A quantitative study

“…Therefore, optimal parameters do not necessarily produce an ideal profile of APD along the entire cable. This could be improved, for example, by introducing a more comprehensive fitness function (or through the implementation of a multi-objective GA) considering additional aspects of excitation wave dynamics that go beyond the restitution data considered in this work, or perhaps by tuning a larger subset of model parameters instead of the three time constants selected here (e.g., see recent approaches on data assimilation in cardiac electrophysiology [48,49,50,51]).…”

Efficient estimation of cardiac conductivities: A proper generalized decomposition approach

“…An existence analysis for this problem is reported in [23], whereas numerical and experimental validations are extensively discussed in [24,25]. As it is promptly realized, the iterative minimization procedure based on the introduction of Lagrange multipliers and the solution of the Monodomain adjoint problem is computationally demanding.…”

“…. , 9 refer to the second order term in (24), while the last line (α = 10), refers to the reactive contribution. Table 3: Factorization of the PGD extended linear form in (26).…”

“…We evaluate the performance of the PGD method to solve the MICP varying the tolerance tol e and the anisotropic ratio, R a = 2, 4, 6 corresponding to σ = (0.07, 0.035) cm 2 /ms, σ =(0.08, 0.02) cm 2 /ms and σ =(0.084, 0.014) cm 2 /ms, respectively. The computational cost for solving the MICP with PGD is negligible and cannot be directly compared with the variational technique used in [24,25], as PGD takes advantage of the offline phase. However, we will demonstrate that the PGD-based solution of the MICP is advantageous even when including offline costs.…”

“…In particular, variational techniques for the estimation of the tensor of the cardiac conductivities of the classical Bidomain and Monodomain models have been addressed and analyzed in [23]. The reliability of this approach for solving the Bidomain/Monodomain Inverse Conductivity Problem has been demonstrated on several benchmarks, covering synthetic as well as in vitro cases [24,25].…”