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PSO with Tikhonov Regularization for the Inverse Problem in Electrocardiography

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Artificial Evolution (EA 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8752))

Abstract

In this paper we present a nearest neighbor particle swarm optimization (PSO) algorithm applied to the numerical analysis of the inverse problem in electrocardiography. A two-step algorithm is proposed based on the application of the modified PSO algorithm with the Tikhonov regularization method to calculate the potential distribution in the heart. The PSO improvements include the use of the neighborhood particles as a strategy to balance exploration and exploitation in order to prevent premature convergences and produce a better local search. In the literature the inverse problem in electrocardiography is solved using the minimum energy norm in a Tikhonov regularization scheme. Although this approach solves the system, the solution may not have a meaning in the physical sense. Comparing to the classical reconstruction, the two-step PSO algorithm improves the accuracy of the solution with respect to the original distribution. Finally, to validate our results, we create a distribution over the heart by using a model of electrical activity (Bidomain model) coupled with a volume conductor model for the torso. Then, using our method, we make the reconstruction of the potential distribution.

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Author information

Authors and Affiliations

  1. Institut de Mathematiques de Bordeaux, Universite Victor Segalen Bordeaux 2, Bordeaux, France

    Alejandro Lopez, Bedreddine Ainseba & Mostafa Bendahmane

  2. Departamento de Electrónica, Universidad de Guadalajara, CUCEI, Av. Revolución 1500, Guadalajara, Jal, Mexico

    Miguel Cienfuegos

Authors
  1. Alejandro Lopez
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  2. Miguel Cienfuegos
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  3. Bedreddine Ainseba
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  4. Mostafa Bendahmane
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Corresponding author

Correspondence to Alejandro Lopez .

Editor information

Editors and Affiliations

  1. INRIA Bordeaux sud-ouest, Equipe CQFD, Institut de Mathématiques de Bordeaux, Université de Bordeaux, Bordeaux, France

    Pierrick Legrand

  2. Université de Bordeaux, Bordeaux, France

    Marc-Michel Corsini

  3. Université d'Angers, Angers Cedex 01, France

    Jin-Kao Hao

  4. Laboratoire d’Informatique de l’Université de Tours, Ecole Polytechnique de l’Université de Tours, Tours, France

    Nicolas Monmarché

  5. INRA, UMR, Thirverval-Grignon, France

    Evelyne Lutton

  6. Equipe TAO, INRIA Futurs, LRI, University of Paris Sud, Orsay cedex, France

    Marc Schoenauer

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Lopez, A., Cienfuegos, M., Ainseba, B., Bendahmane, M. (2014). PSO with Tikhonov Regularization for the Inverse Problem in Electrocardiography. In: Legrand, P., Corsini, MM., Hao, JK., Monmarché, N., Lutton, E., Schoenauer, M. (eds) Artificial Evolution. EA 2013. Lecture Notes in Computer Science(), vol 8752. Springer, Cham. https://doi.org/10.1007/978-3-319-11683-9_20

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  • DOI: https://doi.org/10.1007/978-3-319-11683-9_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-11682-2

  • Online ISBN: 978-3-319-11683-9

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