Solving the ECGI problem with known locations of scar regions

Mohamadou Malal Diallo (1, 2, 3) , Mark Potse (1, 2, 3) , Rémi Dubois (3, 4, 5) , Yves Coudière (1, 2, 3)

1 CARMEN - Modélisation et calculs pour l'électrophysiologie cardiaque
2 IMB - Institut de Mathématiques de Bordeaux
3 IHU Liryc - Institut de rythmologie et modélisation cardiaque [Pessac]
4 INSERM - Institut National de la Santé et de la Recherche Médicale
5 CRCTB - Centre de recherche Cardio-Thoracique de Bordeaux [Bordeaux]

We propose a methodology to take into account the location of scars in ECGI problem. The method is to consider the whole body, including blood, heart and remaining volume as a conductor with an electric current source field localized in the heart. We identify the source best matching a given body surface potential map, by solving the classical quadratic optimization problem with a Tikhonov regu-larization term. The method behaves better than the MFS method in presence of a scar. The correlation coefficients of the activation times around the scar are improved up to 10 % on the epicardium, and 7 % on the endocardium, by adapting the Tikhonov regularization parameter and conductivity coefficient in the scar. 1. Introduction Electrocardiographic imaging (ECGI) is a non-invasive technique that is used to reconstruct the electrical activity of the heart from body surface electrical potential maps (BSPM), and the geometry of the heart and torso. The most common approach to compute this reconstruction is based on the model of the torso as a passive volume conductor , outside the heart. Hence the Laplace equation is set on the volume between the epicardium and the body surface. The method of fundamental solutions (MFS) with Tikhonov regularization is commonly used to solve the corresponding ECGI problem [1]. In clinical care, structural images of the patient are often available. A major question is therefore how to integrate this information in order to drive the inverse problem. It is limited because it cannot easily take into account scars inside the heart volume , and also because it assumes that cardiac sources are only distributed on the epicardium. In this paper, we consider the torso as a volume conductor including the intracavitary blood, the heart and the remaining torso volume, in which only the heart volume behaves as an electric current source field. Hence we try to reconstruct the cardiac electrical volume source, and we can take into account a different electrical conductivity in each of the regions, and in particular in the scar. We dis-cretize the equation with a standard finite element method, and apply the same Tikhonov regularization technique as with the MFS. We will refer to this method as the volume method (VM). In order to account for scars, we propose to increase the regularization parameter in the scar, which is possible with both the usual MFS and the proposed VM, but also to decrease the conductivity in the scar, which is possible only with the VM method. Datasets computed on a realistic human-based anatomical model [2] were used to evaluate the method. The activation times (ATs) recovered by the standard MFS and VM method were compared to the reference ATs obtained from the model. We found that weighting the regulariza-tion parameter and decreasing the electrical conductivity by a factor 10 in the scar improved the correlation between the estimated and the true ATs, especially near the scar.

Domaines: Equations aux dérivées partielles [math.AP]; Mathématiques [math]

Mohamadou Malal Diallo, Mark Potse, Rémi Dubois, Yves Coudière. Solving the ECGI problem with known locations of scar regions. CinC 2020 - Computing in Cardiology, Sep 2020, Rimini / Virtual, Italy. ⟨hal-02945886⟩