Hybrid Parallelization of a Large-Scale Heart Model

  • Dorian Krause
  • Mark Potse
  • Thomas Dickopf
  • Rolf Krause
  • Angelo Auricchio
  • Frits Prinzen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7174)


The simulation of the electrophysiology of the heart is challenging due to its multiscale nature requiring the use of high spatial resolutions. Hence, it is important to efficiently utilize large parallel machines. In this article, we present a code designed to meet these scalability challenges on contemporary multicore-based massively parallel architectures. It is based on a well-established model originally designed for shared-memory systems. To improve scalability and extend support to distributed-memory architectures, we developed a hybrid OpenMP-MPI code. The new code shows excellent scalability up to 8448 cores with both explicit and implicit time discretizations. We present an in-depth analysis of the advantages of hybrid parallelization for this type of application.


Communication Time Multiple Thread Strong Scaling Bidomain Model Implicit Time Discretizations 
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.


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  1. 1.
    Bordas, R., Carpentieri, B., Fotia, G., Maggio, F., Nobes, R., Pitt-Francis, J., Southern, J.: Simulation of cardiac electrophysiology on next-generation high-performance computers. Phil. Trans. Roy. Soc. A. 367, 1951–1969 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Desplantez, T., Dupont, E., Severs, N.J., Weingart, R.: Gap junction channels and cardiac impulse propagation. J. Membrane Biol. 218, 13–28 (2007)CrossRefGoogle Scholar
  3. 3.
    Ethier, S., Tang, W.M., Lin, Z.: Gyrokinetic particle-in-cell simulations of plasma microturbulence on advanced computing platforms. J. Phys. Conf. Ser. 16(1), 1–15 (2005)CrossRefGoogle Scholar
  4. 4.
    Henriquez, C.S.: Simulating the electrical behavior of cardiac tissue using the bidomain model. CRC Crit. Rev. Biomed. Eng. 21, 1–77 (1993)MathSciNetGoogle Scholar
  5. 5.
    Hille, B.: Ion Channels of Excitable Membranes. Sinauer Associates, Inc., Sunderland (2001)Google Scholar
  6. 6.
    Hoogendijk, M.G., et al.: Mechanism of right precordial ST-segment elevation in structural heart disease: Excitation failure by current-to-load mismatch. Heart Rhythm 7, 238–248 (2010)CrossRefGoogle Scholar
  7. 7.
    Hooke, N., Henriquez, C.S., Lanzkron, P., Rose, D.: Linear algebraic transformations of the bidomain equations: Implications for numerical methods. Math. Biosci. 120(2), 127–145 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Hutter, J., Curioni, A.: Dual-level parallelism for ab initio molecular dynamics: Reaching teraflop performance with the CPMD code. Parallel Comput. 31(1), 1–17 (2005)MathSciNetCrossRefGoogle Scholar
  9. 9.
    IPM Homepage (2009),
  10. 10.
    Kaeppeli, R., Whitehouse, S.C., Scheidegger, S., Pen, U.L., Liebendörfer, M.: FISH: A 3D parallel MHD code for astrophysical applications. Technical Report arXiv:0910.2854 (2009)Google Scholar
  11. 11.
    Karypis, G., Kumar, V.: A coarse-grain parallel formulation of multilevel k-way graph partitioning algorithm. In: Parallel Processing for Scientific Computing. SIAM (1997)Google Scholar
  12. 12.
    Kléber, A., Rudy, Y.: Basic mechanisms of cardiac impulse propagation and associated arrhythmias. Physiol. Rev. 84, 431–488 (2004)CrossRefGoogle Scholar
  13. 13.
    Loft, R., Thomas, S., Dennis, J.: Terascale spectral element dynamical core for atmospheric general circulation models. In: ACM/IEEE 2001 Conference on Supercomputing (2001)Google Scholar
  14. 14.
    Mahinthakumar, G., Saied, F.: A hybrid MPI-OpenMP implementation of an implicit finite-element code on parallel architectures. Int. J. High Perform. C. 16(4), 371–393 (2002)Google Scholar
  15. 15.
    Mitchell, L., Bishop, M., Hötzl, E., Neic, A., Liebmann, M., Haase, G., Plank, G.: Modeling cardiac electrophysiology at the organ level in the peta flops computing age. In: AIP Conference Proceedings, vol. 1281(1), pp. 407–410 (2010)Google Scholar
  16. 16.
    Niederer, S., Mitchell, L., Smith, N., Plank, G.: Simulating a human heart beat with near-real time performance. Front. Physio. 2, 14 (2011)CrossRefGoogle Scholar
  17. 17.
    Noble, D., Rudy, Y.: Models of cardiac ventricular action potentials: Iterative interaction between experiment and simulation. Phil. Trans. Roy. Soc. London; Phys. Sc. 359, 1127–1142 (2001)CrossRefGoogle Scholar
  18. 18.
    PARAllel Total Energy Code,
  19. 19.
    Potse, M., Dubé, B., Richer, J., Vinet, A., Gulrajani, R.M.: A comparison of monodomain and bidomain reaction-diffusion models for action potential propagation in the human heart. IEEE Trans. Biomed. Eng. 53, 2425–2435 (2006)CrossRefGoogle Scholar
  20. 20.
    Potse, M., Dubé, B., Vinet, A.: Cardiac anisotropy in boundary-element models for the electrocardiogram. Med. Biol. Eng. Comput. 47, 719–729 (2009)CrossRefGoogle Scholar
  21. 21.
    Rabenseifner, R., Hager, G., Jost, G.: Hybrid MPI/OpenMP parallel programming on clusters of multi-core SMP nodes. In: 17th Euromicro International Conference on Parallel, Distributed and Network-based Processing, pp. 427–436 (2009)Google Scholar
  22. 22.
    Sahni, O., Zhou, M., Shephard, M.S., Jansen, K.E.: Scalable implicit finite element solver for massively parallel processing with demonstration to 160k cores. In: ACM/IEEE 2009 Conference on Supercomputing (2009)Google Scholar
  23. 23.
    ten Tusscher, K.H., Panfilov, A.V.: Alternans and spiral breakup in a human ventricular tissue model. Am. J. Physiol. 291(3), H1088–H1100 (2006)Google Scholar
  24. 24.
    Trayanova, N., Aguel, F.: Computer simulations of cardiac defibrillation: A look inside the heart. Comput. Vis. Sci. 4, 259–270 (2002)CrossRefzbMATHGoogle Scholar
  25. 25.
    Vigmond, E.J., Aguel, F., Trayanova, N.A.: Computational techniques for solving the bidomain equations in three dimensions. IEEE Trans. Biomed. Eng. 49, 1260–1269 (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Dorian Krause
    • 1
  • Mark Potse
    • 2
  • Thomas Dickopf
    • 1
  • Rolf Krause
    • 1
  • Angelo Auricchio
    • 3
  • Frits Prinzen
    • 2
  1. 1.Institute of Computational ScienceUniversity of LuganoSwitzerland
  2. 2.Cardiovascular Research InstituteMaastricht UniversityThe Netherlands
  3. 3.Fondazione Cardiocentro TicinoLuganoSwitzerland

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