Issue |
Math. Model. Nat. Phenom.
Volume 11, Number 2, 2016
Spectral problems
|
|
---|---|---|
Page(s) | 1 - 19 | |
DOI | https://doi.org/10.1051/mmnp/201611201 | |
Published online | 21 March 2016 |
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
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.
Mathematics Subject Classification: 35Q53 / 34B20 / 35G31
Key words: electrocardiography forward problem / electrocardiography inverse problem / stochastic finite elements / chaos polynomial / uncertainty quantification / stochastic processes / stochastic Galerkin method
© EDP Sciences, 2016
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