CarNum: parallel numerical framework for computational cardiac electromechanics

References

[1] D. Ambrosi and S. Pezzuto, Active stress vs. active strain in mechanobiology: constitutive issues. J. Elast. 107 (2012), 199–212.10.1007/s10659-011-9351-4Suche in Google Scholar

[2] J. A. E. Andersson, J. Gillis, G. Horn, J. B. Rawlings, and M. Diehl, CasADi – A software framework for nonlinear optimization and optimal control. Mathematical Programming Computation 11 (2019), No. 1, 1–36.10.1007/s12532-018-0139-4Suche in Google Scholar

[3] H. Ashikaga, B. A. Coppola, K. G. Yamazaki, F. J. Villarreal, J. H. Omens, and J. W. Covell, Changes in regional myocardial volume during the cardiac cycle: implications for transmural blood flow and cardiac structure. American Journal of Physiology-Heart and Circulatory Physiology 295 (2008), No. 2, H610–H618.10.1152/ajpheart.00107.2008Suche in Google Scholar PubMed PubMed Central

[4] N. A. Balakina-Vikulova, A. Panfilov, O. Solovyova, and L. B. Katsnelson, Mechano-calcium and mechano-electric feedbacks in the human cardiomyocyte analyzed in a mathematical model. J. Physiol. Sci. 70 (2020), No. 1, 12.10.1186/s12576-020-00741-6Suche in Google Scholar PubMed PubMed Central

[5] D. M. Bers, Cardiac excitation–contraction coupling. Nature 415 (2002), 198–205.10.1038/415198aSuche in Google Scholar PubMed

[6] P. Cardiff and I. Demirdžić, Thirty years of the finite volume method for solid mechanics. Archives Comput. Meth. Engrg. 28 (2021), No. 5, 3721–3780.10.1007/s11831-020-09523-0Suche in Google Scholar

[7] R. Chabiniok, V. Y. Wang, M. Hadjicharalambous, L. Asner, J. Lee, M. Sermesant, E. Kuhl, A. A. Young, P. Moireau, M. P. Nash, et al., Multiphysics and multiscale modelling, data–model fusion and integration of organ physiology in the clinic: ventricular cardiac mechanics. Interface Focus 6 (2016), No. 2, 20150083.10.1098/rsfs.2015.0083Suche in Google Scholar PubMed PubMed Central

[8] A. Chernyshenko, A. Danilov, and V. Kramarenko, Coupling of PDE and ODE solvers in INMOST parallel platform: Application to electrophysiology. In: Communications in Computer and Information Science, Vol. 965. Springer International Publishing, 2019, 193–202.10.1007/978-3-030-36592-9_16Suche in Google Scholar

[9] A. Y. Chernyshenko, A. A. Danilov, and Y. V. Vassilevski, Numerical simulations for cardiac electrophysiology problems. In: Trends in Biomathematics: Mathematical Modeling for Health, Harvesting, and Population Dynamics. Springer International Publishing, 2019, 321–329.10.1007/978-3-030-23433-1_21Suche in Google Scholar

[10] P. G. Ciarlet, S. Kesavan, A. Ranjan, and M. Vanninathan, Lectures on the Finite Element Method, Vol. 49. Tata Institute of Fundamental Research, Bombay, 1975.Suche in Google Scholar

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

[12] K. D. Costa, J. W. Holmes, and A. D. McCulloch, Modelling cardiac mechanical properties in three dimensions. Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 359 (2001), No. 1783, 1233–1250.10.1098/rsta.2001.0828Suche in Google Scholar

[13] F. S. Costabal, F. A. Concha, D. E. Hurtado, and E. Kuhl, The importance of mechano-electrical feedback and inertia in cardiac electromechanics. Comput. Methods Appl. Mech. Engrg. 320 (2017), 352–368.10.1016/j.cma.2017.03.015Suche in Google Scholar PubMed PubMed Central

[14] P. C. Franzone and L. Guerri, Spreading of excitation in 3-D models of the anisotropic cardiac tissue. I. Validation of the eikonal model. Math. Biosci. 113 (1993), 145–209.10.1016/0025-5564(93)90001-QSuche in Google Scholar

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

[16] D. J. Gardner, D. R. Reynolds, C. S. Woodward, and C. J. Balos, Enabling new flexibility in the SUNDIALS suite of nonlinear and differential/algebraic equation solvers. ACM Transactions on Mathematical Software (TOMS), 2022.10.1145/3539801Suche in Google Scholar

[17] A. M. Gordon, E. Homsher, and M. Regnier, Regulation of contraction in striated muscle. Physiol. Rev. 80 (2000), No. 2, 853–924.10.1152/physrev.2000.80.2.853Suche in Google Scholar PubMed

[18] S. Göktepe and E. Kuhl, Electromechanics of the heart: a unified approach to the strongly coupled excitation–contraction problem. Comput. Mech. 45 (2010), No. 2, 227–243.10.1007/s00466-009-0434-zSuche in Google Scholar

[19] E. Grandi, F. S. Pasqualini, and D. M. Bers, A novel computational model of the human ventricular action potential and Ca transient. J. Molec. Cell. Cardiol. 48 (2010), 112–121.10.1016/j.yjmcc.2009.09.019Suche in Google Scholar PubMed PubMed Central

[20] E. Grandi, S. V. Pandit, N. Voigt, A. J. Workman, D. Dobrev, J. Jalife, and D. M. Bers, Human atrial action potential and Ca²⁺ model. Circulation Research 109 (2011), 1055–1066.10.1161/CIRCRESAHA.111.253955Suche in Google Scholar PubMed PubMed Central

[21] J. M. Guccione, L. K. Waldman, and A. D. McCulloch, Mechanics of active contraction in cardiac muscle: Part II. Cylindrical models of the systolic left ventricle. J. Biomech. Engrg. 115 (1993), No. 2, 82–90.10.1115/1.2895474Suche in Google Scholar PubMed

[22] C. S. Henriquez, Simulating the electrical behavior of cardiac tissue using the bidomain model. Crit. Rev. Biomed. Engrg. 21 (1993), No. 1, 1–77.Suche in Google Scholar

[23] C. S. Henriquez, A brief history of tissue models for cardiac electrophysiology. IEEE Trans. Biomed. Engrg. 61 (2014), 1457–1465.10.1109/TBME.2014.2310515Suche in Google Scholar PubMed

[24] 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

[25] 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, 2021.Suche in Google Scholar

[26] A. C. Hindmarsh, R. Serban, C. J. Balos, D. J. Gardner, D. R. Reynolds, and C. S. Woodward, User documentation for CVODE, v6.5.0. 2022.Suche in Google Scholar

[27] G. A. Holzapfel, T. C. Gasser, and R. W. Ogden, A new constitutive framework for arterial wall mechanics and a comparative study of material models. J. Elastic. Phys. Sci. Solids 61 (2000), 1–48.10.1007/0-306-48389-0_1Suche in Google Scholar

[28] J. Humphrey and F. Yin, A new constitutive formulation for characterizing the mechanical behavior of soft tissues. Biophys. J. 52 (1987), No. 4, 563–570.10.1016/S0006-3495(87)83245-9Suche in Google Scholar PubMed PubMed Central

[29] J. D. Humphrey, Continuum biomechanics of soft biological tissues. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 459 (2003), No. 2029, 3–46.10.1098/rspa.2002.1060Suche in Google Scholar

[30] P. Hunter, A. McCulloch, and H. ter Keurs, Modelling the mechanical properties of cardiac muscle. Progress in Biophysics and Molecular Biology 69 (1998), No. 2, 289–331.10.1016/S0079-6107(98)00013-3Suche in Google Scholar PubMed

[31] A. Huxley, Muscle structure and theories of contraction. Prog. Biophys. Biophys. Chem. 7 (1957), 255–318.10.1016/S0096-4174(18)30128-8Suche in Google Scholar

[32] A. F. Huxley and R. Simmons, Proposed mechanism of force generation in striated muscle. Nature 233 (1971), No. 2, 533–538.10.1038/233533a0Suche in Google Scholar PubMed

[33] B. I. Iaparov, I. Zahradnik, A. S. Moskvin, and A. Zahradníková, In silico simulations reveal that RYR distribution affects the dynamics of calcium release in cardiac myocytes. J. General Physiology 153 (2021), No. 4, e202012685.10.1085/jgp.202012685Suche in Google Scholar PubMed PubMed Central

[34] V. Jacquemet and C. S. Henriquez, Finite volume stiffness matrix for solving anisotropic cardiac propagation in 2-D and 3-D unstructured meshes. IEEE Trans. Biomed. Engrg. 52 (2005), No. 8, 1490–1492.10.1109/TBME.2005.851459Suche in Google Scholar PubMed

[35] V. Jacquemet, An eikonal approach for the initiation of reentrant cardiac propagation in reaction–diffusion models. IEEE Trans. Biomed. Engrg. 57 (2010), 2090–2098.10.1109/TBME.2010.2051156Suche in Google Scholar PubMed

[36] K. A. Kalina, L. Linden, J. Brummund, P. Metsch, and M. Kästner, Automated constitutive modeling of isotropic hyperelasticity based on artificial neural networks. Comput. Mech. 69 (2021), 213–232.10.1007/s00466-021-02090-6Suche in Google Scholar

[37] E. Karabelas, M. A. Gsell, G. Haase, G. Plank, and C. M. Augustin, An accurate, robust, and efficient finite element framework with applications to anisotropic, nearly and fully incompressible elasticity. Comput. Meth. Appl. Mech. Engrg. 394 (2022), 114887.10.1016/j.cma.2022.114887Suche in Google Scholar PubMed PubMed Central

[38] S. Land, V. Gurev, S. Arens, C. M. Augustin, L. Baron, R. Blake, C. Bradley, S. Castro, A. Crozier, M. Favino, et al., Verification of cardiac mechanics software: benchmark problems and solutions for testing active and passive material behaviour. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471 (2015), No. 2184, 20150641.10.1098/rspa.2015.0641Suche in Google Scholar PubMed PubMed Central

[39] K. Lipnikov, Y. Vassilevski, et al., Advanced numerical instruments 3D. https://sourceforge.net/projects/ani3d/, 2014.Suche in Google Scholar

[40] È. Lluch, M. De Craene, B. Bijnens, M. Sermesant, J. Noailly, O. Camara, and H. G. Morales, Breaking the state of the heart: meshless model for cardiac mechanics. Biomechanics and Modeling in Mechanobiology 18 (2019), 1549–1561.10.1007/s10237-019-01175-9Suche in Google Scholar PubMed

[41] M. M. Maleckar, J. L. Greenstein, N. A. Trayanova, and W. R. Giles, Mathematical simulations of ligand-gated and cell-type specific effects on the action potential of human atrium. Progress in Biophysics and Molecular Biology 98 (2008), 161–170.10.1016/j.pbiomolbio.2009.01.010Suche in Google Scholar PubMed PubMed Central

[42] K.-A. Mardal, O. Skavhaug, G. T. Lines, G. A. Staff, and A. Odegard, Using Python to solve partial differential equations. Comput. Sci. & Engrg. 9 (2007), No. 3, 48–51.10.1109/MCSE.2007.64Suche in Google Scholar

[43] M. P. Nash and A. V. Panfilov, Electromechanical model of excitable tissue to study reentrant cardiac arrhythmias. Progress in Biophysics and Molecular Biology 85 (2004), No. 2, 501–522.10.1016/j.pbiomolbio.2004.01.016Suche in Google Scholar PubMed

[44] J. A. Negroni and E. C. Lascano, Simulation of steady state and transient cardiac muscle response experiments with a Huxley-based contraction model. J. Molec. Cell. Cardiol. 45 (2008), No. 2, 300–312.10.1016/j.yjmcc.2008.04.012Suche in Google Scholar PubMed

[45] A. Neic, F. O. Campos, A. J. Prassl, S. A. Niederer, M. J. Bishop, E. J. Vigmond, and G. Plank, Efficient computation of electrograms and ECGs in human whole heart simulations using a reaction-eikonal model. J. Comput. Phys. 346 (2017), 191–211.10.1016/j.jcp.2017.06.020Suche in Google Scholar PubMed PubMed Central

[46] S. A. Niederer, P. J. Hunter, and N. P. Smith, A quantitative analysis of cardiac myocyte relaxation: a simulation study. Biophys. 90 (2006), No. 5, 1697–1722.10.1529/biophysj.105.069534Suche in Google Scholar PubMed PubMed Central

[47] 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), 4331–4351.10.1098/rsta.2011.0139Suche in Google Scholar PubMed PubMed Central

[48] T. O’Hara, L. Virág, A. Varró, and Y. Rudy, Simulation of the undiseased human cardiac ventricular action potential: Model formulation and experimental validation. PLoS Computational Biology 7 (2011), e1002061.10.1371/journal.pcbi.1002061Suche in Google Scholar PubMed PubMed Central

[49] P. Pathmanathan and R. A. Gray, Verification of computational models of cardiac electro-physiology. Int. J. Numer. Meth. Biomed. Engrg. 30 (2013), 525–544.10.1002/cnm.2615Suche in Google Scholar PubMed

[50] A. V. Pikunov, R. A. Syunyaev, V. Steckmeister, I. Kutschka, N. Voigt, and I. R. Efimov, Personalization of mathematical models of human atrial action potential. In: Smart Modelling For Engineering Systems. Springer Singapore, 2021, pp. 223–236.10.1007/978-981-33-4709-0_19Suche in Google Scholar

[51] E. R. Pfeiffer, A. T. Wright, A. G. Edwards, J. C. Stowe, K. McNall, J. Tan, I. Niesman, H. H. Patel, D. M. Roth, J. H. Omens, and A. D. McCulloch, Caveolae in ventricular myocytes are required for stretch-dependent conduction slowing. J. Mol. Cell. Cardiol. 76 (2014), 265–274.10.1016/j.yjmcc.2014.09.014Suche in Google Scholar PubMed PubMed Central

[52] M. Potse, B. Dube, J. Richer, A. Vinet, and R. Gulrajani, A comparison of monodomain and bidomain reaction-diffusion models for action potential propagation in the human heart. IEEE Trans. Biomed. Engrg. 53 (2006), 2425–2435.10.1109/TBME.2006.880875Suche in Google Scholar PubMed

[53] T. A. Quinn and P. Kohl, Cardiac mechano-electric coupling: Acute effects of mechanical stimulation on heart rate and rhythm. Physiol. Rev., 101 (2021), No. 1, 37–92.10.1152/physrev.00036.2019Suche in Google Scholar PubMed

[54] M. V. Razumova, A. E. Bukatina, and K. B. Campbell, Stiffness-distortion sarcomere model for muscle simulation. J. Appl. Physiol. 87 (1999), No. 5, 1861–1876.10.1152/jappl.1999.87.5.1861Suche in Google Scholar PubMed

[55] J. J. Rice, F. Wang, D. M. Bers, and P. P. de Tombe, Approximate model of cooperative activation and crossbridge cycling in cardiac muscle using ordinary differential equations. Biophys. J. 95 (2008), No. 5, 2368–2390.10.1529/biophysj.107.119487Suche in Google Scholar PubMed PubMed Central

[56] S. Rossi, R. Ruiz-Baier, L. F. Pavarino, and A. Quarteroni, Orthotropic active strain models for the numerical simulation of cardiac biomechanics. Int. J. Numer. Meth. Biomed. Engrg. 28 (2012), No. 6-7, 761–788.10.1002/cnm.2473Suche in Google Scholar PubMed

[57] V. Salamatova, Data-driven constitutive modelling via conjugate pairs and response functions. Mathematics 10 (2022), No. 23, 4447.10.3390/math10234447Suche in Google Scholar

[58] D. Smirnov, A. Pikunov, R. Syunyaev, R. Deviatiiarov, O. Gusev, K. Aras, A. Gams, A. Koppel, and I. R. Efimov, Genetic algorithm-based personalized models of human cardiac action potential. PLoS One 15 (2020), e0231695.10.1371/journal.pone.0231695Suche in Google Scholar PubMed PubMed Central

[59] S. Stella, F. Regazzoni, C. Vergara, L. Dedé, and A. Quarteroni, A fast cardiac electromechanics model coupling the eikonal and the nonlinear mechanics equations. Math. Models Meth. Appl. Sci. 32 (2022), 1531–1556.10.1142/S021820252250035XSuche in Google Scholar

[60] J. G. Stinstra, B. Hopenfeld, and R. S. MacLeod, On the passive cardiac conductivity. Ann. Biomed. Engrg. 33 (2005), 1743–1751.10.1007/s10439-005-7257-7Suche in Google Scholar PubMed

[61] 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

[62] 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

[63] K. M. Terekhov, A. Danilov, I. Konshin, and Y. Vassilevski, INMOST – a toolkit for distributed mathematical modelling. https://www.inmost.org/Suche in Google Scholar

[64] V. Timmermann, L. A. Dejgaard, K. H. Haugaa, A. G. Edwards, J. Sundnes, A. D. McCulloch, and S. T. Wall, An integrative appraisal of mechano-electric feedback mechanisms in the heart. Prog. Biophys. Mol. Biol. 130 (2017), 404–417.10.1016/j.pbiomolbio.2017.08.008Suche in Google Scholar PubMed PubMed Central

[65] K. H. ten Tusscher and A. V. Panfilov, Alternans and spiral breakup in a human ventricular tissue model. Amer. J. Physiol. Heart Circ. Physiol. 291 (2006), No. 3, H1088–H1100.10.1152/ajpheart.00109.2006Suche in Google Scholar PubMed

[66] A. Tsaturyan and V. Y. Izakov, Mathematical model of the coupling of excitation with contraction in the heart muscle. Biophysics 23 (1978), No. 5, 904–910.Suche in Google Scholar

[67] Y. Vassilevski, I. Konshin, G. Kopytov, and K. Terekhov, INMOST – a software platform and graphical environment for development of parallel numerical models on general meshes. Lomonosov Moscow State Univ. Publ., Moscow, 2013 (in Russian).Suche in Google Scholar

[68] Y. Vassilevski, A. Danilov, K. Lipnikov, and V. Chugunov Automated Technologies for Generation of Unstructured Computational Meshes, IV. Moscow, FizMatLit, 2016 (in Russian).Suche in Google Scholar

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

[70] E. Vigmond, R. W. dos Santos, A. Prassl, M. Deo, and G. Plank, Solvers for the cardiac bidomain equations. Progress in Biophysics and Molecular Biology 96 (2008), 3–18.10.1016/j.pbiomolbio.2007.07.012Suche in Google Scholar PubMed PubMed Central

[71] K. C. Wong, L. Wang, H. Zhang, H. Liu, and P. Shi, Meshfree implementation of individualized active cardiac dynamics. Computerized Medical Imaging and Graphics 34 (2010), No. 1, 91–103.10.1016/j.compmedimag.2009.05.002Suche in Google Scholar PubMed