Propagation of two independent sources of uncertainty in the electrocardiography imaging inverse solution

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, POB 40002, 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: nejib.zemzemi@inria.fr

Accepted: 9 October 2018

Abstract

This study investigates the effects of the input parameter uncertainties (organ conductivities, boundary data, etc.) on the electrocardiography (ECG) imaging problem. These inputs are very important for the construction of the torso potential for the forward problem and for the non-invasive electrical potential on the heart surface in the case of the inverse problem.

We propose a new stochastic formulation that allows us to combine both sources of errors. We formulate the forward and inverse stochastic problems by considering the input parameters as random fields and a stochastic optimal control formulation. In order to quantify multiple independent sources of uncertainties on the forward and inverse solutions, we attribute suitable probability density functions for each randomness source and apply stochastic finite elements based on generalized polynomial chaos method. The efficiency of this approach to solve the forward and inverse ECG problems and the usability to quantify the effect of organ conductivity and epicardial boundary data uncertainties in the torso are demonstrated by a number of numerical simulations on a two-dimensional computational mesh of a realistic torso geometry.