Abstract
Cardiac arrhythmia is a complex and potentially fatal condition affecting millions worldwide. Computational simulations are an essential tool for understanding the mechanisms of arrhythmia and developing new treatments. However, simulating arrhythmia with high accuracy can be computationally demanding. This paper presents a second-order numerical method for simulating arrhythmia that is parallelized using OpenMP. We demonstrate the effectiveness of our method by simulating arrhythmia in a two-dimensional cardiac tissue domain. Our results show that our method is more efficient than classical methods, with significant reductions in execution times and numerical errors. Additionally, we investigate the vulnerable window, a critical period during which the heart is most susceptible to arrhythmia, and show how the new method improves the computation of this metric. In summary, our novel second-order numerical method, parallelized using OpenMP, has demonstrated significant improvements in the efficiency of simulating cardiac arrhythmia. By providing faster and more accurate simulations, this work has the potential to accelerate research and aid in the development of new treatments for this complex condition.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Tran, D.X., Yang, M.J., Weiss, J.N., Garfinkel, A., Qu, Z.: Vulnerability to re-entry in simulated two-dimensional cardiac tissue: effects of electrical restitution and stimulation sequence. Chaos Interdisc. J. Nonlinear Sci. 17(4), 043115 (2007)
Pereira, R.R.: Métodos de diferenças finitas para problemas de difusão e reação não lineares. Ph.D. thesis, Laboratório Nacional de Computação Científica, Petrópolis (2018)
OpenMP Homepage. https://www.openmp.org/. Accessed 10 Apr 2023
Keener, J., James, S. (eds.): Mathematical Physiology II: Systems Physiology, 2nd edn. Springer, New York (2009). https://doi.org/10.1007/978-0-387-79388-7
FitzHugh, R.: Impulses and physiological states in theoretical models of nerve membrane. Biophys. J. 1(6), 445–466 (1961)
Franzone, P.C., Pavarino, L.F.: A parallel solver for reaction-diffusion systems in computational electrocardiology. Math. Models Methods Appl. Sci. 14(06), 883–911 (2004)
Rogers, J.M., McCulloch, A.D.: A collocation-Galerkin finite element model of cardiac action potential propagation. IEEE Trans. Biomed. Eng. 41(8), 743–757 (1994)
Strikwerda, J.C.: Finite Difference Schemes and Partial Differential Equations. Society for Industrial and Applied Mathematics, Edition. SIAM (2004)
Sultanian, B.: Thomas algorithm for solving a tridiagonal system of linear algebraic equations. In: Gas Turbines: Internal Flow Systems Modeling. Cambridge Aerospace Series, pp. 337–339. Cambridge University Press, Cambridge (2018). https://doi.org/10.1017/9781316755686.012
Oliveira, R.S., Rocha, B.M., Burgarelli, D., Meira Jr, W., Constantinides, C., dos Santos, R.W.: Performance evaluation of GPU parallelization, space-time adaptive algorithms, and their combination for simulating cardiac electrophysiology. Int. J. Numer. Methods Biomed. Eng. 34(2), e2913 (2018)
Kaboudian, A., Cherry, E.M., Fenton, F.H.: Real-time interactive simulations of large-scale systems on personal computers and cell phones: toward patient-specific heart modeling and other applications. Sci. Adv. 5(3), eaav6019 (2019)
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)
Acknowledgements
This work has been supported by Universidade Federal de Juiz de Fora (UFJF), by a scholarship from Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) - Brazil - Finance Code 001. This research was funded by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) e Empresa Brasileira de Serviços Hospitalares (Ebserh) grant numbers 423278/2021-5, 310722/2021-7, and 315267/2020-8; by Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG) - Brazil.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Couto, G.M., Monteiro, N.Z., Rocha, B.M., dos Santos, R.W. (2023). Accelerating the Simulations of Cardiac Arrhythmia with a Second-Order Numerical Method and High-Performance Computing. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2023 Workshops. ICCSA 2023. Lecture Notes in Computer Science, vol 14112. Springer, Cham. https://doi.org/10.1007/978-3-031-37129-5_9
Download citation
DOI: https://doi.org/10.1007/978-3-031-37129-5_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-37128-8
Online ISBN: 978-3-031-37129-5
eBook Packages: Computer ScienceComputer Science (R0)