Stochastic forward and inverse Problems In Cardiac electrophysiologY
- Mourad Bellasoued, University of Tunis El Manar, Tunisia
- Mostafa Bendahmane, CARMEN research team, Inria Bordeaux – Sud-Ouest
The electrocardiography imaging inverse problem is frequently solved using the deterministic quasi-static models. These models don’t take into account the heart dynamic in time, channel noise and external random perturbations acting in the torso. Recent numerical studies in the direct problem have shown that such randomness cannot be suppressed. Occasionally deterministic equations give qualitatively incorrect results. Therefore, it is important to quantify the nature of the noise and choose an appropriate model incorporating randomness. In our project, we study the inverse problem constrained by the stochastic monodomain or bidomain equations in electrocardiology. The state equations consist in a coupled stochastic reaction-diffusion system modelling the propagation of the intracelullar and extracellular electrical potentials, and stochastic ionic currents in the heart. These equations are coupled to the stochastic quasi-static elliptic equation in the torso. Thus, we will demonstrate that the novel concept of applying the stochastic model will be useful to improve noninvasive reconstruction of electrical heart activity. We will perform numerical experiments representing the effect of the stochastic heart dynamic on the inverse solutions. Moreover, we will study the stability result for the conductivities and numerically solve the parameters estimations problem in the stochastic model.
Key words: electrocardiography, inverse problem, stochastic bidomain model, parameter estimations, cardiac modeling
Website: in progress