Misfit functional for recovering data in 2D ElectroCardioGraphy problems

Hariga-Tlatli, Nejla; Baranger, Thouraya; Erhel, Jocelyne

doi:10.1016/j.enganabound.2009.12.006

Cited by 5 publications

(2 citation statements)

References 17 publications

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“…For certain pathologies, one should solve the Cauchy problem hundreds or thousands of times in order to obtain the dynamics of the electrical information on the heart surface. In terms of computational cost, this reduces the competitiveness of the iterative methods like in [5], [15], [2], [20] and [26]) and gives more advantage for mesh-free methods like MFS ( [25]), where a transfer matrix is computed once for all. In this work we use the same energy function as defined in [5], but we formulate it at the continuous level using Dirichlet-Neumann and Neumann-Dirichlet mappings.…”

Section: Statement Of the Problemmentioning

confidence: 99%

“…The transfer matrix was later computed using different approaches like boundary elements, finite elements or MFS. Recent works (Bouyssier et al [10]; Hariga et al [15]; Zemzemi, [26]; Zemzemi et al [27] ) presented novel approaches based on recent advances in boundary-value inverse problem techniques. These works use an energy-based cost function.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of the ECGI inverse problem solution with respect to the measurement boundary size and the distribution of noise

Addouche

Bouarroudj

Jday

et al. 2019

Math. Model. Nat. Phenom.

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In this work, we analyze the influence of adding a body surface missing data on the solution of the electrocardiographic imaging inverse problem. The difficulty comes from the fact that the measured Cauchy data is provided only on a part of the body surface and thus a missing data boundary is adjacent to a measured boundary. In order to construct the electrical potential on the heart surface, we use an optimal control approach where the unknown potential at the external boundary is also part of the control variables. We theoretically compare this case to the case where the Dirichlet boundary condition is given on the full accessible surface. We then compare both cases and based on the distribution of noise in the measurements, we conclude whether or not it is worth to use all the data. We use the method of factorization of elliptic boundary value problems combined with the finite element method. We illustrate the theoretical results by some numerical simulations in a cylindrical domain. We numerically study the effect of the size of the missing data zone on the accuracy of the inverse solution.

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Section: Statement Of the Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analysis of the ECGI inverse problem solution with respect to the measurement boundary size and the distribution of noise

Addouche

Bouarroudj

Jday

et al. 2019

Math. Model. Nat. Phenom.

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On numerical resolution of an inverse Cauchy problem modeling the airflow in the bronchial tree

Chakib

Ouaissa

2021

Comp. Appl. Math.

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This paper is devoted to the numerical resolution of an inverse Cauchy problem governed by Stokes equation modeling the airflow in the lungs. It consists in determining the air velocity and pressure on the artificial boundaries of the bronchial tree. This data completion problem is one of the highly ill-posed problems in the Hadamard sense (Hadamard in Lectures on Cauchy's problem in linear partial differential equations. Dover, New York, 1953). This gives great importance to its numerical resolution and in particular to carry out stable numerical approaches, mostly in the case of noisy data. The main idea of this work is to extend some regularizing, stable and fast iterative algorithms for solving this problem based on the domain decomposition approach (Chakib et al. in Inverse Prob 35(1):015008, 2018). We discuss the efficiency and the feasibility of the proposed approach through some numerical tests performed using different domain decomposition algorithms. Finally, we opt for the Robin-Robin algorithm, which showed its performance, for the numerical simulation of the airflow in the bronchial tree configuration.

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Constitutive law gap functionals for solving the Cauchy problem for linear elliptic PDE

Baranger

Andrieux²

2011

Applied Mathematics and Computation

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Misfit functional for recovering data in 2D ElectroCardioGraphy problems

Cited by 5 publications

References 17 publications

Analysis of the ECGI inverse problem solution with respect to the measurement boundary size and the distribution of noise

Analysis of the ECGI inverse problem solution with respect to the measurement boundary size and the distribution of noise

On numerical resolution of an inverse Cauchy problem modeling the airflow in the bronchial tree

Constitutive law gap functionals for solving the Cauchy problem for linear elliptic PDE

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