This work addresses the inverse problem of electrocardiography from a new perspective, by combining electrical and mechanical measurements. Our strategy relies on the definition of a model of the electromechanical contraction which is registered on ECG data but also on measured mechanical displacements of the heart tissue typically extracted from medical images. In this respect, we establish in this work the convergence of a sequential estimator which combines for such coupled problems various state of the art sequential data assimilation methods in a unified consistent and efficient framework. Indeed, 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.
In @cite_9 , the authors note that the usual regularization techniques have no physical ground. Instead, they propose to regularize the inverse solution with the monodomain equations coupled to the Fenton-Karma ionic model. The strategy proposed in the present paper has some similarities with this approach. We rely on a full electrophysiological model of the action potential coupled to the Poisson problem to estimate the solution of the heart electrical activation. This physical model is personalized on the fly with respect to its parameters in order to adapt it to a specific patient. Furthermore, we propose an additional step of modeling by considering the mechanical response to the electrophysiological activation, so we are able to also integrate mechanical measurements. Indeed, we believe that multimodal observations improve the identifiability of the complete model and therefore improve the quality of the electrical and mechanical state reconstruction. Another originality of our work is the use of a sequential data assimilation strategy that is adapted to a coupled electromechanical evolution model. Here we demonstrate how state-of-the-art gain filter on the electrophysiological model and on the mechanical model can be aggregated to propose a joint gain filter for the coupled problem.
@cite_9
2081699235
The inverse problem in electrocardiography is to reconstruct the voltage in the surface of the heart, using a high density electrocardiogram. This problem is usually solved using regularization techniques, which tend to give the minimum energy response in a static scheme. In our work, we propose to calculate a dynamic inverse solution using the Monodomain as a model of electrical heart activity, thus constraining the family of solutions to one that satisfies the model.