Stochastic Finite Element Method for Torso Conductivity Uncertainties Quantification in Electrocardiography Inverse Problem

¹ Mohammed V University of Rabat, Mohammadia school of Engineering LERMA and LIRIMA Laboratories. Av. Ibn Sina Agdal, Rabat Morocco
² Royal Air School, Informatics and Mathematics Department DFST, BEFRA, POB40002, Marrakech, Morocco
³ INRIA Bordeaux Sud-Ouest, Carmen project 200 rue de la vieille tour 33405 Talence Cedex, France
⁴ IHU Liryc, Electrophysiology and heart modeling institute. Avenue du Haut-Lévêque, 33604 Pessac, France

^⋆ Corresponding author. E-mail: aboulaich@gmail.com

Abstract

The purpose of this paper is to study the influence of errors and uncertainties of the input data, like the conductivity, on the electrocardiography imaging (ECGI) solution. In order to do that, we propose a new stochastic optimal control formulation, permitting to calculate the distribution of the electric potentiel on the heart from the measurement on the body surface. The discretization is done using stochastic Galerkin method allowing to separate random and deterministic variables. Then, the problem is discretized, in spatial part, using the finite element method and the polynomial chaos expansion in the stochastic part of the problem. The considered problem is solved using a conjugate gradient method where the gradient of the cost function is computed with an adjoint 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 analytical geometry and on a 2D cross section of a real torso.