Parallel Solution of Cardiac Reaction-Diffusion Models

  • Luca F. Pavarino
  • Piero Colli Franzone
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 40)


We present and study a parallel iterative solver for reaction-diffusion systems in three dimensions arising in computational electrocardiology, such as the Bidomain and Monodomain models. The models include intramural fiber rotation and anisotropic conductivity coefficients that can be fully orthotropic or axially symmetric around the fiber direction. These cardiac models are coupled with a membrane model for the ionic currents, consisting of a system of ordinary differential equations. The solver employs structured isoparametric Q1 finite elements in space and a semi-implicit adaptive method in time. Parallelization and portability are based on the PETSc parallel library and large-scale computations with up to O(107) unknowns have been run on parallel computers. These simulation of the full Bidomain model (without operator or variable splitting) for a full cardiac cycle are, to our knowledge, among the most complete in the available literature.


Anisotropic Conductivity Cardiac Action Potential Global Mesh Bidomain Model Iteration Matrice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. S. Balay, W. D. Gropp, L. C. McInnes, and B. F. Smith. PETSc users manual. Technical Report ANL-95/11-Revision 2.1.1, Argonne National Laboratory, 2001.Google Scholar
  2. P. Colli Franzone and L. F. Pavarino. A parallel solver for reaction-diffusion systems in computational electrocardiology. Technical report, IMATI CNR Tech. Rep. 9-PV, 2003.Google Scholar
  3. P. Colli Franzone and G. Savaré. Degenerate evolution systems modeling the cardiac electric field at micro and macroscopic level. In A. Lorenzi and B. Ruf, editors, Evolution equations, Semigroups and Functional Analysis, pages 49–78. Birkhauser, 2002.Google Scholar
  4. J. Keener and J. Sneyd. Mathematical Physiology. Springer, 1998.Google Scholar
  5. I. LeGrice and et al. Laminar structure of the heart: ventricular myocyte arrangement and connective tissue architecture in the dog. Am. J. Physiol. (Heart Circ. Physiol), 269(38):H571–H582, 1995.Google Scholar
  6. C. Luo and Y. Rudy. A model of the ventricular cardiac action potential: depolarization, repolarization, and their interaction. Circ. Res., 68(6):1501–1526, 1991.Google Scholar
  7. M. Pennacchio. The mortar finite element method for the cardiac bidomain model of extracellular potential. J. Sci. Comp., 20(2), 2004. To appear.Google Scholar
  8. A. Quarteroni and A. Valli. Numerical Approximation of Partial Differential Equations. Springer-Verlag, Berlin, 1994.Google Scholar
  9. B. F. Smith, P. E. Bjøstad, and W. Gropp. Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations. Cambridge University Press, 1996.Google Scholar
  10. D. Streeter. Gross morphology and fiber geometry in the heart. In R. Berne, editor, Handbook of Physiology, vol. 1 The Heart, pages 61–112. Williams & Wilkins, Baltimore, 1979.Google Scholar
  11. A. Victorri and et al. Numerical integration in the reconstruction of cardiac action potential using the Hodgkin-Huxley type models. Comp. Biomed. Res., 18:10–23, 1985.CrossRefGoogle Scholar
  12. R. Weber dos Santos, G. Plank, B. S., and V. E.J. Preconditioning techniques for the bidomain equations. In R. K. et al., editor, These Proceedings. LNCSE. Springer, 2004.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Luca F. Pavarino
    • 1
  • Piero Colli Franzone
    • 2
  1. 1.Dept. of MathematicsUniversità di MilanoItaly
  2. 2.Dept. of MathematicsUniversità di PaviaItaly

Personalised recommendations