Sensitivity of the Electrocardiography Inverse Solution to the Torso Conductivity Uncertainties

Nejib Zemzemi (1, 2) , Rajae Aboulaich (3) , Najib Fikal (3) , Emahdi El Guarmah (3)

1 IHU-LIRYC
2 CARMEN - Modélisation et calculs pour l'électrophysiologie cardiaque
3 LERMA - Laboratoire d'Etudes et Recherche en Mathématiques Appliquées

Electrocardiography imaging (ECGI) is a new non invasive technology used for heart diagnosis. It allows to construct the electrical potential on the heart surface only from measurement on the body surface and some geometrical informations of the torso. The purpose of this work is twofold: First, we propose a new formulation to calculate the distribution of the electric potential on the heart, from measurements on the torso surface. Second, we study the influence of the errors and uncertainties on the conductivity parameters, on the ECGI solution. We use an optimal control formulation for the mathematical formulation of the problem with a stochastic diffusion equation as a constraint. The descretization is done using stochastic Galerkin method allowing to separate random and de-terministic variables. The optimal control problem is solved using a conjugate gradient method where the gradient of the cost function is computed with an ad-joint technique. The efficiency of this approach to solve the inverse problem and the usability to quantify the effect of conductivity uncertainties in the torso are demonstrated through a number of numerical simulations on a 2D geometrical model. Our results show that adding ±50% uncertainties in the fat conductivity does not alter the inverse solution, whereas adding ±50% uncertainties in the lung conductivity affects the reconstructed heart potential by almost 50%.

Mots clés: Inverse problem; Electrocardiography Imaging; Stochastic Differential Equation

Domaines: Modélisation et simulation; Optimisation et contrôle [math.OC]; Equations aux dérivées partielles [math.AP]

Nejib Zemzemi, Rajae Aboulaich, Najib Fikal, Emahdi El Guarmah. Sensitivity of the Electrocardiography Inverse Solution to the Torso Conductivity Uncertainties. Hans van Assen; Peter Bovendeerd ; Tammo Delhaas. Functional Imaging and Modeling of the Heart, Lecture Notes in Computer Science (9126), Springer, pp.475-483, 2015, 8th International Conference, FIMH 2015, Maastricht, The Netherlands, June 25-27, 2015. Proceedings, 978-3-319-20308-9. ⟨10.1007/978-3-319-20309-6_54⟩. ⟨hal-01222381⟩