1. Effect of Torso Non-Homogeneities in the quasi-static inverse problems arising in electrocardiology
- Author
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Ainseba, Bedr'eddine, Bendahmane, Mostafa, Lopez Rincon, A., Afd Pharmacology, Pharmacology, Afd Pharmacology, Pharmacology, Institut de Mathématiques de Bordeaux (IMB), and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Control and Optimization ,Quantitative Biology::Tissues and Organs ,Physics::Medical Physics ,01 natural sciences ,cardiac electric field ,Bioelectric model ,medicine ,Homogeneous ,0101 mathematics ,[MATH]Mathematics [math] ,direct and inverse problems ,ComputingMilieux_MISCELLANEOUS ,Physics ,Numerical Analysis ,Applied Mathematics ,010102 general mathematics ,Mathematical analysis ,weak solution ,Inverse problem ,Torso ,non-homegeneous ,010101 applied mathematics ,medicine.anatomical_structure ,finite element ,Analysis ,Quasistatic process - Abstract
In the present paper, an homogeneous and non-homogeneous inverse problem constrained by the stationary problem in electrocardiology representing the heart, lungs surfaces, and torso model is investigated. Our goal is to reconstruct the electrical potentials on the surface of the heart from the information obtained non invasively on the torso surface. The existence and uniqueness of solution for the heart-torso problem and the related inverse problem is assessed, and the primal and dual problems are discretized using a finite element method. We present some preliminary numerical experiments using an efficient implementation of the proposed scheme in homogeneous and non-homogeneous cases. Finally, we demonstrate the effect of the non-homogeneity on the reconstructed epicardial potential and show that the inverse ECG problem cannot be solved by the classical BEM (boundary element method).
- Published
- 2020