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Automated Parallel Simulation of Heart Electrical Activity Using Finite Element Method

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10049))

Abstract

In this paper we present an approach to the parallel simulation of the heart electrical activity using the finite element method with the help of the FEniCS automated scientific computing framework. FEniCS allows scientific software development using the near-mathematical notation and provides automatic parallelization on MPI clusters. We implemented the ten Tusscher–Panfilov (TP06) cell model of cardiac electrical activity. The scalability testing of the implementation was performed using up to 240 CPU cores and the 95 times speedup was achieved. We evaluated various combinations of the Krylov parallel linear solvers and the preconditioners available in FEniCS. The best performance was provided by the conjugate gradient method and the biconjugate gradient stabilized method solvers with the successive over-relaxation preconditioner. Since the FEniCS-based implementation of TP06 model uses notation close to the mathematical one, it can be utilized by computational mathematicians, biophysicists, and other researchers without extensive parallel computing skills.

The work is supported by the RAS Presidium grant I.33P “Fundamental problems of mathematical modeling,” project no. 0401-2015-0025. Our study was performed using the Uran supercomputer of the Krasovskii Institute of Mathematics and Mechanics and computational cluster of the Ural Federal University.

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References

  1. Alnæs, M.S., Logg, A., Ølgaard, K.B., Rognes, M.E., Wells, G.N.: Unified form language. ACM Trans. Math. Softw. 40(2), 1–37 (2014)

    Article  MATH  Google Scholar 

  2. Geuzaine, C., Remacle, J.F.: Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities. Int. J. Numer. Methods Eng. 79(11), 1309–1331 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  3. Jansson, N.: Optimizing sparse matrix assembly in finite element solvers with one-sided communication. In: Daydé, M., Marques, O., Nakajima, K. (eds.) VECPAR 2012. LNCS, vol. 7851, pp. 128–139. Springer, Heidelberg (2013). doi:10.1007/978-3-642-38718-0_15

    Chapter  Google Scholar 

  4. Kirby, R.C., Logg, A.: A compiler for variational forms. ACM Trans. Math. Softw. 32(3), 417–444 (2006)

    Article  MathSciNet  Google Scholar 

  5. Li, Y., Chen, C.: An efficient split-operator scheme for 2-D advection-diffusion simulations using finite elements and characteristics. Appl. Math. Model. 13(4), 248–253 (1989)

    Article  MATH  Google Scholar 

  6. Logg, A., Mardal, K.A., Wells, G.: Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book. Springer Science & Business Media, Heidelberg (2012)

    Book  MATH  Google Scholar 

  7. Logg, A., Wells, G.N.: DOLFIN: automated finite element computing. ACM Trans. Math. Softw. (TOMS) 37(2), 1–28 (2010)

    Article  MathSciNet  Google Scholar 

  8. Pravdin, S.F., Berdyshev, V.I., Panfilov, A.V., Katsnelson, L.B., Solovyova, O., Markhasin, V.S.: Mathematical model of the anatomy and fibre orientation field of the left ventricle of the heart. Biomed. Eng. Online 54(12), 21 (2013)

    Google Scholar 

  9. Kerckhos, R.C.P., Healy, S.N., Usyk, T.P., McCulloch, A.D.: Computational methods for cardiac electromechanics. Proc. IEEE 94, 769–783 (2006)

    Article  Google Scholar 

  10. Ten Tusscher, K.H., Panfilov, A.V.: Alternans and spiral breakup in a human ventricular tissue model. Am. J. Physiol. Heart Circulatory Physiol. 291(3), H1088–H1100 (2006)

    Article  Google Scholar 

  11. Ten Tusscher, K.H., Panfilov, A.V., et al.: Organization of ventricular fibrillation in the human heart. Circulation Res. 100(12), e87–e101 (2007)

    Article  Google Scholar 

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Correspondence to Andrey Sozykin .

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Sozykin, A., Epanchintsev, T., Zverev, V., Khamzin, S., Bersenev, A. (2016). Automated Parallel Simulation of Heart Electrical Activity Using Finite Element Method. In: Carretero, J., et al. Algorithms and Architectures for Parallel Processing. ICA3PP 2016. Lecture Notes in Computer Science(), vol 10049. Springer, Cham. https://doi.org/10.1007/978-3-319-49956-7_29

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  • DOI: https://doi.org/10.1007/978-3-319-49956-7_29

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-49955-0

  • Online ISBN: 978-3-319-49956-7

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