Math. Model. Nat. Phenom.
Volume 14, Number 2, 2019
Mathematical modelling in cardiology
|Number of page(s)||16|
|Published online||15 February 2019|
Propagation of two independent sources of uncertainty in the electrocardiography imaging inverse solution
Mohammed V University of Rabat, Mohammadia School of Engineering LERMA and LIRIMA Laboratories,
Av. Ibn Sina Agdal,
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: firstname.lastname@example.org
Accepted: 9 October 2018
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.
Mathematics Subject Classification: 65N20 / 65N21 / 65N22 / 65N25 / 65N30 / 60H35
Key words: Electrocardiography imaging forward and inverse problems / Stochastic finite elements / Uncertainty quantification / ill-posed problem / boundary value problem
© EDP Sciences, 2019
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