Towards the Numerical Simulation of Electrocardiograms

  • Muriel Boulakia
  • Miguel A. Fernández
  • Jean-Frédéric Gerbeau
  • Nejib Zemzemi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4466)


We present preliminary results of the numerical simulation of electrocardiograms (ECG). We consider the bidomain equations to model the electrical activity of the heart and a Laplace equation for the torso. The ionic activity is modeled with a Mitchell-Schaeffer dynamics. We use adaptive semi-implicit BDF schemes for the time discretization and a Neumann-Robin domain decomposition algorithm for the space discretization. The obtained ECGs, although not completely satisfactory, are promising. They allow to discuss various modelling assumptions, for example the relevance of cells heterogeneity, the fiber orientation and the coupling conditions with the torso.


Coupling Condition Transmission Condition Cell Heterogeneity Conductivity Tensor Reference Simulation 
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  1. 1.
    Boulakia, M., Fernández, M.A., Gerbeau, J.-F., Zemzemi, N.: Mathematical analysis of a coupled bidomain-torso model in electrophysiology (Submitted)Google Scholar
  2. 2.
    Colli Franzone, P., Pavarino, L.F.: A parallel solver for reaction-diffusion systems in computational electrocardiology. Math. Models Methods Appl. Sci. 6(14), 883–911 (2004)CrossRefGoogle Scholar
  3. 3.
    Colli Franzone, P., Pavarino, L.F., Taccardi, B.: Simulating patterns of excitation, repolarization and action potential duration with cardiac bidomain and monodomain models. Math. Biosci. 1(197), 35–66 (2005)CrossRefGoogle Scholar
  4. 4.
    Colli Franzone, P., Savaré, G.: Degenerate evolution systems modeling the cardiac electric field at micro- and macroscopic level. evolution equations, semigroups and functional analysis. Progr. Nonlin. Diff. Eq. Appl. 1(50), 49–78 (2002)Google Scholar
  5. 5.
    Coudière, Y., Pierre, C., Turpault, R.: Solving the fully coupled heart and torso problems of electrocardiology with a 3d discrete duality finite volume method. submitted (2006)Google Scholar
  6. 6.
    Djabella, K., Sorine, M.: Differential model of the excitation-contraction coupling in a cardiac cell for multicycle simulations. In: EMBEC’05, vol. 11, pp. 4185–4190, Prague (2005)Google Scholar
  7. 7.
    Fitzhugh, R.: Impulses and physiological states in theoretical models of nerve membrane. Biophys. J. (1), 445–465 (1961)Google Scholar
  8. 8.
    Frey, P.: Yams: A fully automatic adaptive isotropic surface remeshing procedure. Technical report 0252, Inria, Rocquencourt, France (November 2001)Google Scholar
  9. 9.
    George, P.L.: Improvement on delaunay based 3d automatic mesh generator. Finite Elements in Analysis and Design 25(3-4), 297–317 (1997)zbMATHCrossRefGoogle Scholar
  10. 10.
    George, P.L., Borouchaki, H.: ultimate robustness in meshing an arbitrary polyhedron. Int. J. Numer. Meth. Engng. 58(7), 1061–1089 (2002)CrossRefGoogle Scholar
  11. 11.
    Krassowska, W., Neu, J.C.: Effective boundary conditions for syncitial tissues. IEEE Trans. Biomed. Eng. 2(41), 137–199 (1994)Google Scholar
  12. 12.
    Lines, G.: Simulating the electrical activity in the heart. PhD thesis, Department of Informatics, University of Olso (1999)Google Scholar
  13. 13.
    Luo, C.H., Rudy, Y.: A model of the ventricular cardiac action ptentiel. depolarisation, repolarisation, and their interaction. Cir. Res. (68),1071–1096 (1994)Google Scholar
  14. 14.
    Malmivuo, J., Plonsey, R.: Bioelectromagnetism. principles and applications of bioelectric and biomagnetic fields. Oxford University Press, New York (1995)Google Scholar
  15. 15.
    Mitchell, C.C., Schaeffer, D.G.: A two-current model for the dynamics of cardiac membrane. Bulletin Math. Bio. (65),767–793 (2003)Google Scholar
  16. 16.
    Neu, J.C., Krassowska, W.: Homogenization of syncytial tissues. Crit. Rev. Biomed. Eng. 21(2), 137–199 (1993)Google Scholar
  17. 17.
    Page, E.: Cat heart muscle in vitro. part iii. the extracellular space. J. Gen. Physio. 1(46), 201–213 (1962)CrossRefGoogle Scholar
  18. 18.
    Pierre, C.: Modélisation et simulation de l’activité électrique du cœur dans le thorax, analyse numérique et méthodes de volumes finis. PhD thesis, Laboratoire J. Leray, Université de Nantes (2005)Google Scholar
  19. 19.
    Quarteroni, A., Sacco, R., Saleri, F.: Numerical mathematics. In: Texts in Applied Mathematics, 2nd edn. vol. 37, Springer, Heidelberg (2007)Google Scholar
  20. 20.
    Sachse, F.B.: Computational Cardiology: Modeling of Anatomy, Electrophysiology, and Mechanics. Springer, Heidelberg (2004)zbMATHGoogle Scholar
  21. 21.
    Sampson, K.J., Henriquez, C.S.: Electrotonic influences on action potential duration dispersion in small hearts: a simulation study. Am. J. Physiol. Heart Circ. Physiol. 289, 350–360 (2005)CrossRefGoogle Scholar
  22. 22.
    Sermesant, M., Moireau, P., Camara, O., J., S.-M., Andriantsimiavona, R., Cimrman, R., Hill, D.L., Chapelle, D., Razavi, R.: Cardiac function estimation from mri using a heart model and data assimilation: advances and difficulties. Med. Image Anal. 10(4), 642–656 (2006)CrossRefGoogle Scholar
  23. 23.
    Sundnes, J., Lines, G.T., Cai, X., Nielsen, B.F., Mardal, K.-A., Tveito, A.: Computing the electrical activity in the heart. Springer, Heidelberg (2006)zbMATHGoogle Scholar
  24. 24.
    van Capelle, F.H., Durrer, D.: Computer simulation of arrhythmias in a network of coupled excitable elements. Circ. Res. 47, 453–466 (1980)Google Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Muriel Boulakia
    • 2
  • Miguel A. Fernández
    • 1
  • Jean-Frédéric Gerbeau
    • 1
  • Nejib Zemzemi
    • 1
  1. 1.REO team, INRIA RocquencourtFrance
  2. 2.REO team, Laboratoire Jacques-Louis Lions, Université Paris 6France

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