Conference abstracts

Session A6 - Mathematical Foundations of Data Assimilation and Inverse Problems

July 11, 15:30 ~ 16:00 - Room T1

Inverse problem of electrocardiography: a multiphysics data assimilation approach

Jean-Frédéric Gerbeau

Inria, France   -   jean-frederic.gerbeau@inria.fr

We address the inverse problem of electrocardiography by combining electrical and mechanical measurements. Our strategy, proposed in [1], relies on a model of the electromechanical contraction which is registered on ECG data [2,3] but also on measured mechanical displacements of the heart tissue typically extracted from medical images. In this respect, we establish the convergence of a sequential estimator which combines for such coupled problems various state of the art sequential data assimilation methods in an efficient framework [4]. We aggregate a Luenberger observer for the mechanical state and a Reduced Order Unscented Kalman Filter applied on the parameters to be identified, and a POD projection of the electrical state. Then using synthetic data we show the benefits of our approach for the estimation of the electrical state of the ventricles along the heart beat compared with more classical strategies which only consider an electrophysiological model with ECG measurements. Our numerical results actually show that the mechanical measurements improve the identifiability of the electrical problem allowing to reconstruct the electrical state of the coupled system more precisely. Therefore, this work is intended to be a first proof of concept, with theoretical justifications and numerical investigations, of the advantage of using available multi-modal observations for the estimation and identification of an electromechanical model of the heart.

References:

[1] C. Corrado, J-F. Gerbeau, P. Moireau. Identification of weakly coupled multiphysics problems. Application to the inverse problem of electrocardiography. Journal of Computational Physics, 283, pp. 271-298, 2015.

[2] M. Boulakia, S. Cazeau, M. Fern\'andez, J-F. Gerbeau, N. Zemzemi. Mathematical modeling of electrocardiograms: a numerical study, Annals of biomedical engineering, 38 (3), 1071-1097, 2010.

[3] E. Schenone, A. Collin, J-F. Gerbeau. Numerical simulation of electrocardiograms for full cardiac cycles in healthy and pathological conditions. International journal for numerical methods in biomedical engineering, 32(5), 2016

[4] P. Moireau, D. Chapelle, P. Le Tallec. Joint state and parameter estimation for distributed mechanical systems. Computer methods in applied mechanics and engineering, 197 (6), 659-677, 2008.

Joint work with Philippe Moireau (Inria, France) and Cesare Corrado (King's College London, UK)..

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