Startseite Temporally and spatially segregated discretization for a coupled electromechanical myocardium model
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Temporally and spatially segregated discretization for a coupled electromechanical myocardium model

  • Alexander A. Danilov , Alexey A. Liogky EMAIL logo und Fyodor A. Syomin
Veröffentlicht/Copyright: 31. Oktober 2024

Abstract

In this paper, we propose a novel temporally and spatially segregated numerical scheme to discretize the coupled electromechanical model of myocardium. We perform several numerical experiments with activation of a myocardial slab with structural inhomogeneity and evaluate the dependence of numerical errors on the size of spatial and temporal discretization steps. In our study, we show that the spatial step for the mechanical equations hm⩽2.5 mm yields reasonable results with noticeable errors only in the region of myocardial inhomogeneity. We also show that time step τm⩽1 ms can be used for temporal discretization of mechanical equations, and the propagation velocity of the activation and contraction fronts differs from the reference one by no more than 1.3%for such time step. Finally, we show that the increase of time discretization steps of the mechanical equations τm and the monodomain equation τe leads to phase errors with opposite signs, and we can compensate these errors by tuning the relationship between the time steps.

MSC 2010: 65M60; 74F99; 74S05

Funding statement: Funding: The study was performed at the Institute of Mechanics, Lomonosov Moscow State University, and supported by the Russian Science Foundation project No. 22-71-10007.

Acknowledgment

The parallel numerical experiments were conducted on the HPC system of the Institute for Computer Science and Mathematical Modeling, Sechenov University. Authors acknowledge colleagues from Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, and Sirius University of Science and Technology for valuable discussions about INMOST framework and numerical methods.

References

[1] R. R. Aliev and A. V. Panfilov, A simple two-variable model of cardiac excitation. Chaos, Solitons & Fractals 7 (1996), No.3, 293–301.10.1016/0960-0779(95)00089-5Suche in Google Scholar

[2] M. Bucelli, A. Zingaro, P. C. Africa, I. Fumagalli, L. Dedè, and A. Quarteroni, A mathematical model that integrates cardiac electrophysiology, mechanics, and fluid dynamics: Application to the human left heart. International Journal for Numerical Methods in Biomedical Engineering 39 (2023), No. 3, e3678.10.1002/cnm.3678Suche in Google Scholar PubMed

[3] D. Chapelle, M. A. Fernández, J.-F. Gerbeau, P. Moireau, J. Sainte-Marie, and N. Zemzemi, Numerical simulation of the electromechanical activity of the heart. In: Functional Imaging and Modeling of the Heart: 5th International Conference, FIMH 2009, Nice, France, June 3-5, 2009. Proceedings 5. Springer, 2009, pp. 357–365.10.1007/978-3-642-01932-6_39Suche in Google Scholar

[4] S. D. Cohen, A. C. Hindmarsh, and P. F. Dubois, CVODE, a stiff/nonstiff ODE solver in C. Computers in Physics 10 (1996), No. 2, 138–143.10.1063/1.4822377Suche in Google Scholar

[5] F. Del Bianco, P. C. Franzone, S. Scacchi, and L. Fassina, Electromechanical effects of concentric hypertrophy on the left ventricle: a simulation study. Computers in Biology and Medicine 99 (2018), 236–256.10.1016/j.compbiomed.2018.06.004Suche in Google Scholar PubMed

[6] A. DeSimone, B. Perthame, A. Quarteroni, L. Truskinovsky, L. Dedè, A. Gerbi, and A. Quarteroni, Segregated algorithms for the numerical simulation of cardiac electromechanics in the left human ventricle. In: The Mathematics of Mechanobiology, Cetraro, Italy 2018, 2020, pp. 81–116.10.1007/978-3-030-45197-4_3Suche in Google Scholar

[7] A. Dokuchaev, T. Chumarnaya, A. Bazhutina, S. Khamzin, V. Lebedeva, T. Lyubimtseva, S. Zubarev, D. Lebedev, and O. Solovyova, Combination of personalized computational modeling and machine learning for optimization of left ventricular pacing site in cardiac resynchronization therapy. Frontiers in Physiology 14 (2023): 1162520.10.3389/fphys.2023.1162520Suche in Google Scholar PubMed PubMed Central

[8] J. Fröhlich, T. Gerach, J. Krauß, A. Loewe, L. Stengel, and C. Wieners, Numerical evaluation of elasto-mechanical and visco-elastic electro-mechanical models of the human heart. GAMM-Mitteilungen 46 (2024), No. 3-4, e202370010.10.1002/gamm.202370010Suche in Google Scholar

[9] Y.-C. B. Fung, Biorheology of soft tissues. Biorheology 10 (1973), No. 2, 139–155.10.3233/BIR-1973-10208Suche in Google Scholar PubMed

[10] S. Godounov, A difference method for numerical calculation of discontinuous solutions of the equation of hydrodynamics. Matematicheskii Sbornik 47 (1959), No. 89-3, 271–306.Suche in Google Scholar

[11] S. Göktepe and E. Kuhl, Computational modeling of cardiac electrophysiology: A novel finite element approach. International Journal for Numerical Methods in Engineering 79 (2009), No. 2, 156–178.10.1002/nme.2571Suche in Google Scholar

[12] A. C. Hindmarsh, P. N. Brown, K. E. Grant, S. L. Lee, R. Serban, D. E. Shumaker, and C. S. Woodward, SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers. ACM Transactions on Mathematical Software (TOMS) 31 (2005), No. 3, 363–396.10.1145/1089014.1089020Suche in Google Scholar

[13] A. C. Hindmarsh, R. Serban, C. J. Balos, D. J. Gardner, D. R. Reynolds, and C. S. Woodward, User documentation for KINSOL v5.7.0 (SUNDIALS v5.7.0). Tech. Report UCRL-SM-208116, 2021.Suche in Google Scholar

[14] P. Lamata, A. Cookson, and N. Smith, Clinical diagnostic biomarkers from the personalization of computational models of cardiac physiology. Annals of Biomedical Engineering 44 (2016), 46–57.10.1007/s10439-015-1439-8Suche in Google Scholar PubMed

[15] A. A. Liogky, A. Y. Chernyshenko, A. A. Danilov, and F. A. Syomin, CarNum: parallel numerical framework for computational cardiac electromechanics. Russian Journal of Numerical Analysis and Mathematical Modelling 38 (2023), No. 3, 127–144.10.1515/rnam-2023-0011Suche in Google Scholar

[16] J. F. Marko and E. D. Siggia, Statistical mechanics of supercoiled DNA. Phys. Rev. E 52 (1995), 2912–2938.10.1103/PhysRevE.52.2912Suche in Google Scholar

[17] C. Mendonca Costa, G. Plank, C. A. Rinaldi, S. A. Niederer, and M. J. Bishop, Modeling the electrophysiological properties of the infarct border zone. Frontiers in Physiology 9 (2018), 356.10.3389/fphys.2018.00356Suche in Google Scholar PubMed PubMed Central

[18] M. P. Nash and A. V. Panfilov, Electromechanical model of excitable tissue to study reentrant cardiac arrhythmias. Progress in Biophysics and Molecular Biology 9 (2018), 356.Suche in Google Scholar

[19] D. Nickerson, N. Smith, and P. Hunter, New developments in a strongly coupled cardiac electromechanical model. EP Europace 7 (2005), No. s2, S118–S127.10.1016/j.eupc.2005.04.009Suche in Google Scholar PubMed

[20] S. A. Niederer, E. Kerfoot, A. P. Benson, M. O. Bernabeu, O. Bernus, C. Bradley, E. M. Cherry, R. Clayton, F. H. Fenton, A. Garny, E. Heidenreich, S. Land, M. Maleckar, P. Pathmanathan, G. Plank, J. F. Rodríguez, I. Roy, F. B. Sachse, G. Seemann, O. Skavhaug, and N. P. Smith, Verification of cardiac tissue electrophysiology simulators using an N-version benchmark. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 369 (2011), No. 1954, 4331–4351.10.1098/rsta.2011.0139Suche in Google Scholar PubMed PubMed Central

[21] D. Nordsletten, S. Niederer, M. Nash, P. Hunter, and N. Smith, Coupling multi-physics models to cardiac mechanics. Progress in Biophysics and Molecular Biology 104 (2011), No. 1, 77–88.10.1016/j.pbiomolbio.2009.11.001Suche in Google Scholar PubMed

[22] P. Pathmanathan and J. P. Whiteley, A numerical method for cardiac mechanoelectric simulations. Annals of Biomedical Engineering 37 (2009), No. 5, 860–873.10.1007/s10439-009-9663-8Suche in Google Scholar PubMed

[23] F. Regazzoni and A. Quarteroni, An oscillation-free fully staggered algorithm for velocity-dependent active models of cardiac mechanics. Computer Methods in Applied Mechanics and Engineering 373 (2021), 113506.10.1016/j.cma.2020.113506Suche in Google Scholar

[24] F. Regazzoni, M. Salvador, P. Africa, M. Fedele, L. Dedè, and A. Quarteroni, A cardiac electromechanical model coupled with a lumped-parameter model for closed-loop blood circulation. Journal of Computational Physics 457 (2022), 111083.10.1016/j.jcp.2022.111083Suche in Google Scholar

[25] F. B. Sachse, Computational Cardiology: Modeling of Anatomy, Electrophysiology, and Mechanics. Springer Science & Business Media, Vol. 2966, 2004.Suche in Google Scholar

[26] J. Sainte-Marie, D. Chapelle, R. Cimrman, and M. Sorine, Modeling and estimation of the cardiac electromechanical activity. Computers & Structures 84 (2006). No. 28, 1743–1759.10.1016/j.compstruc.2006.05.003Suche in Google Scholar

[27] M. Salvador, L. Dedè, and A. Quarteroni, An intergrid transfer operator using radial basis functions with application to cardiac electromechanics. Computational Mechanics 66 (2020), No. 2, 491–511.10.1007/s00466-020-01861-xSuche in Google Scholar

[28] M. Salvador, M. Fedele, P. C. Africa, E. Sung, A. Prakosa, J. Chrispin, N. Trayanova, A. Quarteroni, et al., Electromechanical modeling of human ventricles with ischemic cardiomyopathy: numerical simulations in sinus rhythm and under arrhythmia. Computers in Biology and Medicine 136 (2021), 104674.10.1016/j.compbiomed.2021.104674Suche in Google Scholar PubMed

[29] F. Syomin, A simple kinetic model of myocardium contraction: calcium-mechanics coupling. Biophysics 59 (2014), 772–779.10.1134/S0006350914050224Suche in Google Scholar

[30] F. A. Syomin and A. K. Tsaturyan, A simple model of cardiac muscle for multiscale simulation: passive mechanics, crossbridge kinetics and calcium regulation. J. Theor. Biol. 420 (2017), 105–116.10.1016/j.jtbi.2017.02.021Suche in Google Scholar PubMed

[31] F. Syomin, A. Osepyan, and A. Tsaturyan, Computationally efficient model of myocardial electromechanics for multiscale simulations. PLoS One 16 (2021), No. 7, e0255027.10.1371/journal.pone.0255027Suche in Google Scholar PubMed PubMed Central

[32] F. A. Syomin, V. A. Galushka, and A. K. Tsaturyan, Effect of strain-dependent conduction slowing on the re-entry formation and maintenance in cardiac muscle: 2D computer simulation. International Journal for Numerical Methods in Biomedical Engineering 39 (2023), No. 11, e3676.10.1002/cnm.3676Suche in Google Scholar PubMed

[33] K. M. Terekhov, A. Danilov, I. Konshin, and Y. Vassilevski, INMOST—a toolkit for distributed mathematical modeling. http://www.inmost.orgSuche in Google Scholar

[34] N. A. Trayanova, J. Constantino, and V. Gurev, Electromechanical models of the ventricles. American Journal of Physiology-Heart and Circulatory Physiology 301 (2011), No. 2, H279–H286.10.1152/ajpheart.00324.2011Suche in Google Scholar PubMed PubMed Central

[35] N. A. Trayanova and K. C. Chang, How computer simulations of the human heart can improve anti-arrhythmia therapy. The Journal of Physiology 594 (2016), No. 9, 2483–2502.10.1113/JP270532Suche in Google Scholar PubMed PubMed Central

[36] Y. Vassilevski, K. Terechov, K. Nikitin, and I. Kapyrin, Parallel Finite Volume Computation on General Meshes. Springer International Publishing, Cham, 2020.10.1007/978-3-030-47232-0Suche in Google Scholar

[37] Z. J. Wang, A. Santiago, X. Zhou, L. Wang, F. Margara, F. Levrero-Florencio, A. Das, C. Kelly, E. Dall’Armellina, M. Vazquez, et al., Human biventricular electromechanical simulations on the progression of electrocardiographic and mechanical abnormalities in post-myocardial infarction. EP Europace 23 (2021), Supplement 1, i143–i152.10.1093/europace/euaa405Suche in Google Scholar PubMed PubMed Central

Received: 2024-08-28
Revised: 2024-09-23
Accepted: 2024-09-26
Published Online: 2024-10-31
Published in Print: 2024-11-26

© 2024 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 9.9.2025 von https://www.degruyterbrill.com/document/doi/10.1515/rnam-2024-0022/pdf
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