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Numerical simulation of electrocardiograms

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Book cover Modeling of Physiological Flows

Part of the book series: MS&A — Modeling, Simulation and Applications ((MS&A,volume 5))

Abstract

This chapter presents a concise overview of various mathematical and numerical problems raised by the simulation of electrocardiograms (ECGs). A model for the propagation of the electrical activation in the heart and in the torso is proposed. Some of its mathematical properties are analyzed. This model is not aimed at reproducing the complex phenomena taking place at the microscopic level. It has been devised to produce realistic healthy ECGs, and some pathological ones, with a reasonable level of complexity. Rather, it relies on various assumptions that are carefully discussed through their impact on the ECGs. The coupling between the heart and the torso is a critical numerical issue which is addressed. In particular, efficient coupling strategies based on explicit algorithms are presented and analyzed. The chapter ends with some preliminary results of a reduced order model based on the Proper Orthogonal Decomposition (POD) method.

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Acknowledgements

The authors wish to thank Michel Sorine for many fruitful discussions, and Elisa Schenone for the simulations shown in Figs. 4.12 and 4.13.

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Author notes

  1. Nejib Zemzemi

    Present address: Computing laboratory, University of Oxford, Oxford, OX1 3QD, UK

Authors and Affiliations

  1. Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie-Paris 6, UMR7598, 75005, Paris, France

    Muriel Boulakia

  2. INRIA Paris-Rocquencourt, 78153, Le Chesnay Cedex, France

    Miguel A. Fernández & Jean-Frédéric Gerbeau

  3. INRIA Paris-Rocquencourt and Laboratoire de mathématiques d’Orsay, Université Paris 11, Paris, France

    Nejib Zemzemi

Authors
  1. Muriel Boulakia
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  2. Miguel A. Fernández
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  3. Jean-Frédéric Gerbeau
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  4. Nejib Zemzemi
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Editors and Affiliations

  1. MOX - Department of Mathematics, Politecnico di Milano, Italy

    Davide Ambrosi  & Alfio Quarteroni  & 

  2. Mathematics Institute of Computational Science and Engineering, École Polytechnique Fédérale de Laussane, Switzerland

    Alfio Quarteroni  & Gianluigi Rozza  & 

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Boulakia, M., Fernández, M.A., Gerbeau, JF., Zemzemi, N. (2012). Numerical simulation of electrocardiograms. In: Ambrosi, D., Quarteroni, A., Rozza, G. (eds) Modeling of Physiological Flows. MS&A — Modeling, Simulation and Applications, vol 5. Springer, Milano. https://doi.org/10.1007/978-88-470-1935-5_4

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