2022
Journal article
Open Access
A fast computational model for the electrophysiology of the whole human heart
Del Corso G., Verzicco R., Viola F.
Bidomain equations Physics - Medical Physics 22/1 OA procedure Settore ING-IND/06 - FLUIDODINAMICA Medical Physics (physics.med-ph) Electrophysiology Heart modeling FOS: Physical sciences SDG 3 - Good Health and Well-being GPU computing
In this study we present a novel computational model for unprecedented simulations of the whole cardiac electrophysiology. According to the heterogeneous electrophysiologic properties of the heart, the whole cardiac geometry is decomposed into a set of coupled conductive media having different topology and electrical conductivities: (i) a network of slender bundles comprising a fast conduction atrial network, the AV-node and the ventricular bundles; (ii) the Purkinje network; and (iii) the atrial and ventricular myocardium. The propagation of the action potential in these conductive media is governed by the bidomain/monodomain equations, which are discretized in space using an in- house finite volume method and coupled to three different cell models, the Courtemanche model [1] for the atrial myocytes, the Stewart model [2] for the Purkinje Network and the ten Tusscher-Panfilov model [3] for the ventricular myocytes. The developed numerical model correctly reproduces the cardiac electrophysiology of the whole human heart in healthy and pathologic conditions and it can be tailored to study and optimize resynchronization therapies or invasive surgical procedures. Importantly, the whole solver is GPU-accelerated using CUDA Fortran providing an unprecedented speedup, thus opening the way for systematic parametric studies and uncertainty quantification analyses. (c) 2022 Elsevier Inc. All rights reserved.
Source: JOURNAL OF COMPUTATIONAL PHYSICS, vol. 457
[1] M. Courtemanche, R. J. Ramirez, S. Nattel, Ionic mechanisms underlying human atrial action potential properties: insights from a mathematical model, American Journal of Physiology-Heart and Circulatory Physiology 275 (1) (1998) H301-H321.
[2] P. Stewart, O. V. Aslanidi, D. Noble, P. J. Noble, M. R. Boyett, H. Zhang, Mathematical models of the electrical action potential of purkinje fibre cells, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 367 (1896) (2009) 2225-2255.
[3] K. Ten Tusscher, A. Panfilov, Cell model for efficient simulation of wave propagation in human ventricular tissue under normal and pathological conditions, Physics in Medicine & Biology 51 (23) (2006) 6141.
[4] A. Kaboudian, E. M. Cherry, F. H. Fenton, Real-time interactive simulations of large-scale systems on personal computers and cell phones: Toward patient-specific heart modeling and other applications, Science advances 5 (3) (2019) eaav6019.
[5] J. E. Hall, Guyton and Hall textbook of medical physiology e-Book, Elsevier Health Sciences, 2015.
[6] D. M. Harrild, C. S. Henriquez, A computer model of normal conduction in the human atria, Circulation research 87 (7) (2000) e25-e36.
[7] T. N. James, The internodal pathways of the human heart, Progress in cardiovascular diseases 43 (6) (2001) 495-535.
[8] F. Pashakhanloo, D. A. Herzka, H. Ashikaga, S. Mori, N. Gai, D. A. Bluemke, N. A. Trayanova, E. R. McVeigh, Myofiber architecture of the human atria as revealed by submillimeter diffusion tensor imaging, Circulation: arrhythmia and electrophysiology 9 (4) (2016) e004133.
[9] S. Karas Jr, R. C. Elkins, Mechanism of function of the mitral valve leaflets, chordae tendineae and left ventricular papillary muscles in dogs, Circulation research 26 (6) (1970) 689-696.
[10] R. Bordas, V. Grau, R. Burton, P. Hales, J. Schneider, D. Gavaghan, P. Kohl, B. Rodriguez, Integrated approach for the study of anatomical variability in the cardiac purkinje system: from high resolution mri to electrophysiology simulation, in: 2010 Annual International Conference of the IEEE Engineering in Medicine and Biology, IEEE, 2010, pp. 6793-6796.
[11] A. Saha, S. Roy, Papillary muscles of right ventricle - morphological variations and its clinical relevance, Cardiovascular Pathology 34 (2018) 22-27.
[12] R. A. Bergman, A. K. Afifi, et al., Atlas of microscopic anatomy.
[13] J. Tranum-Jensen, A. Wilde, J. T. Vermeulen, M. J. Janse, Morphology of electrophysiologically identified junctions between purkinje fibers and ventricular muscle in rabbit and pig hearts., Circulation research 69 (2) (1991) 429-437.
[14] O. Berenfeld, J. Jalife, Purkinje-muscle reentry as a mechanism of polymorphic ventricular arrhythmias in a 3-dimensional model of the ventricles, Circulation Research 82 (10) (1998) 1063-1077.
[15] G. A. Holzapfel, R. W. Ogden, Constitutive modelling of passive myocardium: a structurally based framework for material characterization, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 367 (1902) (2009) 3445-3475.
[16] G. Seemann, C. Höper, F. B. Sachse, O. Dössel, A. V. Holden, H. Zhang, Heterogeneous three-dimensional anatomical and electrophys-
[17] D. Nickerson, N. Smith, P. Hunter, New developments in a strongly coupled cardiac electromechanical model, EP Europace 7 (s2) (2005) S118-S127.
[18] S. G. Campbell, E. Howard, J. Aguado-Sierra, B. A. Coppola, J. H. Omens, L. J. Mulligan, A. D. McCulloch, R. C. Kerckhoffs, Effect of transmurally heterogeneous myocyte excitation-contraction coupling on canine left ventricular electromechanics, Experimental physiology 94 (5) (2009) 541-552.
[19] G. Buckberg, A. Mahajan, S. Saleh, J. I. Hoffman, C. Coghlan, Structure and function relationships of the helical ventricular myocardial band, The Journal of thoracic and cardiovascular surgery 136 (3) (2008) 578-589.
[20] R. Doste, D. Soto-Iglesias, G. Bernardino, A. Alcaine, R. Sebastian, S. Giffard-Roisin, M. Sermesant, A. Berruezo, D. Sanchez-Quintana, O. Camara, A rule-based method to model myocardial fiber orientation in cardiac biventricular geometries with outflow tracts, International journal for numerical methods in biomedical engineering 35 (4) (2019) e3185.
[21] N. A. Trayanova, Whole-heart modeling: applications to cardiac electrophysiology and electromechanics, Circulation research 108 (1) (2011) 113- 128.
[22] A. J. Pullan, K. A. Tomlinson, P. J. Hunter, A finite element method for an eikonal equation model of myocardial excitation wavefront propagation, SIAM Journal on Applied Mathematics 63 (1) (2002) 324-350.
[23] J. J. B. Jack, D. Noble, R. W. Tsien, Electric current flow in excitable cells, Clarendon Press Oxford, 1975.
[25] A. Bueno-Orovio, D. Kay, V. Grau, B. Rodriguez, K. Burrage, Fractional diffusion models of cardiac electrical propagation: role of structural heterogeneity in dispersion of repolarization, Journal of the Royal Society Interface 11 (97) (2014) 20140352.
[26] D. E. Hurtado, S. Castro, A. Gizzi, Computational modeling of non-linear diffusion in cardiac electrophysiology: A novel porous-medium approach, Computer Methods in Applied Mechanics and Engineering 300 (2016) 70- 83.
[27] N. G. Sepulveda, B. J. Roth, J. P. Wikswo Jr, Current injection into a two-dimensional anisotropic bidomain., Biophysical journal 55 (5) (1989) 987.
[28] L. Tung, A bi-domain model for describing ischemic myocardial dc potentials., Ph.D. thesis, Massachusetts Institute of Technology (1978).
[29] J. Sundnes, G. T. Lines, X. Cai, B. F. Nielsen, K.-A. Mardal, A. Tveito, Computing the electrical activity in the heart, Vol. 1, Springer Science & Business Media, 2007.
[30] E. Vigmond, R. W. Dos Santos, A. Prassl, M. Deo, G. Plank, Solvers for the cardiac bidomain equations, Progress in biophysics and molecular biology 96 (1-3) (2008) 3-18.
[31] J. P. Wikswo Jr, S.-F. Lin, R. A. Abbas, Virtual electrodes in cardiac tissue: a common mechanism for anodal and cathodal stimulation, Biophysical journal 69 (6) (1995) 2195-2210.
[35] M. Potse, B. Dubé, J. Richer, A. Vinet, R. M. Gulrajani, A comparison of monodomain and bidomain reaction-diffusion models for action potential propagation in the human heart, IEEE Transactions on Biomedical Engineering 53 (12) (2006) 2425-2435.
[36] M. Wilhelms, H. Hettmann, M. M. C. Maleckar, J. T. Koivumäki, O. Dössel, G. Seemann, Benchmarking electrophysiological models of human atrial myocytes, Frontiers in physiology 3 (2013) 487.
[37] S. Inada, J. Hancox, H. Zhang, M. Boyett, One-dimensional mathematical model of the atrioventricular node including atrio-nodal, nodal, and nodalhis cells, Biophysical journal 97 (8) (2009) 2117-2127.
[38] V. D. Corino, F. Sandberg, L. T. Mainardi, L. Sornmo, An atrioventricular node model for analysis of the ventricular response during atrial fibrillation, IEEE transactions on biomedical engineering 58 (12) (2011) 3386-3395.
[39] B. Baillargeon, N. Rebelo, D. D. Fox, R. L. Taylor, E. Kuhl, The living heart project: a robust and integrative simulator for human heart function, European Journal of Mechanics-A/Solids 48 (2014) 38-47.
[40] S. Sugiura, T. Washio, A. Hatano, J. Okada, H. Watanabe, T. Hisada, Multi-scale simulations of cardiac electrophysiology and mechanics using the university of tokyo heart simulator, Progress in biophysics and molecular biology 110 (2-3) (2012) 380-389.
[41] F. Viola, V. Meschini, R. Verzicco, Fluid-structure-electrophysiology interaction (fsei) in the left-heart: A multi-way coupled computational model, European Journal of Mechanics-B/Fluids 79 (2020) 212-232.
[43] T. Lassila, M. Lange, A. R. P. Perez, K. Lekadir, X. Albà, G. Piella, A. F. Frangi, Electrophysiology model for a human heart with ischemic scar and realistic purkinje network, in: Statistical Atlases and Computational Models of the Heart, Springer, 2015, pp. 90-97.
[44] M. Deo, P. Boyle, G. Plank, E. Vigmond, Arrhythmogenic mechanisms of the purkinje system during electric shocks: a modeling study, Heart rhythm 6 (12) (2009) 1782-1789.
[45] M. Deo, P. M. Boyle, A. M. Kim, E. J. Vigmond, Arrhythmogenesis by single ectopic beats originating in the purkinje system, American Journal of Physiology-Heart and Circulatory Physiology 299 (4) (2010) H1002-H1011.
[46] E. Behradfar, A. Nygren, E. J. Vigmond, The role of purkinje-myocardial coupling during ventricular arrhythmia: a modeling study, PloS one 9 (2).
[47] T. Ijiri, T. Ashihara, T. Yamaguchi, K. Takayama, T. Igarashi, T. Shimada, T. Namba, R. Haraguchi, K. Nakazawa, A procedural method for modeling the purkinje fibers of the heart, The journal of physiological sciences (2008) 0810170079-0810170079.
[48] A. Lopez-Perez, R. Sebastian, J. M. Ferrero, Three-dimensional cardiac computational modelling: methods, features and applications, Biomedical engineering online 14 (1) (2015) 35.
[49] C. Vergara, M. Lange, S. Palamara, T. Lassila, A. F. Frangi, A. Quarteroni, A coupled 3d-1d numerical monodomain solver for cardiac electrical activation in the myocardium with detailed purkinje network, Journal of Computational Physics 308 (2016) 218-238.
[50] P. Pathmanathan, M. O. Bernabeu, R. Bordas, J. Cooper, A. Garny, J. M. Pitt-Francis, J. P. Whiteley, D. J. Gavaghan, A numerical guide to the solution of the bidomain equations of cardiac electrophysiology, Progress in biophysics and molecular biology 102 (2) (2010) 136-155.
[51] N. A. Trayanova, J. Constantino, V. Gurev, Electromechanical models of the ventricles, American Journal of Physiology-Heart and Circulatory Physiology 301 (2) (2011) H279-H286.
[52] J. Cooper, A. Corrias, D. Gavaghan, D. Noble, Considerations for the use of cellular electrophysiology models within cardiac tissue simulations, Progress in biophysics and molecular biology 107 (1) (2011) 74-80.
[53] A. Loppini, A. Gizzi, R. Ruiz-Baier, C. Cherubini, F. H. Fenton, S. Filippi, Competing mechanisms of stress-assisted diffusivity and stretch-activated currents in cardiac electromechanics, Frontiers in physiology 9 (2018) 1714.
[54] R. H. Clayton, Y. Aboelkassem, C. D. Cantwell, C. Corrado, T. Delhaas, W. Huberts, C. L. Lei, H. Ni, A. V. Panfilov, C. Roney, et al., An audit of uncertainty in multi-scale cardiac electrophysiology models, Philosophical Transactions of the Royal Society A 378 (2173) (2020) 20190335.
[55] E. C. Vasconcellos, E. W. Clua, F. H. Fenton, M. Zamith, Accelerating simulations of cardiac electrical dynamics through a multi-gpu platform and an optimized data structure, Concurrency and Computation: Practice and Experience 32 (5) (2020) e5528.
[61] A. Saha, S. Roy, Papillary muscles of left ventricle - morphological variations and its clinical relevance, Indian heart journal 70 (6) (2018) 894-900.
[70] L. N. Trefethen, D. Bau III, Numerical linear algebra, Vol. 50, Siam, 1997.
[93] L. W.-T. Ng, M. Eldred, Multifidelity uncertainty quantification using nonintrusive polynomial chaos and stochastic collocation, in: 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference 20th AIAA/ASME/AHS Adaptive Structures Conference 14th AIAA, 2012, p. 1852.
[94] R. Molléro, X. Pennec, H. Delingette, A. Garny, N. Ayache, M. Sermesant, Multifidelity-cma: a multifidelity approach for efficient personalisation of 3d cardiac electromechanical models, Biomechanics and modeling in mechanobiology 17 (1) (2018) 285-300.
[95] C. M. Fleeter, G. Geraci, D. E. Schiavazzi, A. M. Kahn, A. L. Marsden, Multilevel and multifidelity uncertainty quantification for cardiovascular hemodynamics, Computer methods in applied mechanics and engineering 365 (2020) 113030.
[2] P. Stewart, O. V. Aslanidi, D. Noble, P. J. Noble, M. R. Boyett, H. Zhang, Mathematical models of the electrical action potential of purkinje fibre cells, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 367 (1896) (2009) 2225-2255.
[3] K. Ten Tusscher, A. Panfilov, Cell model for efficient simulation of wave propagation in human ventricular tissue under normal and pathological conditions, Physics in Medicine & Biology 51 (23) (2006) 6141.
[4] A. Kaboudian, E. M. Cherry, F. H. Fenton, Real-time interactive simulations of large-scale systems on personal computers and cell phones: Toward patient-specific heart modeling and other applications, Science advances 5 (3) (2019) eaav6019.
[5] J. E. Hall, Guyton and Hall textbook of medical physiology e-Book, Elsevier Health Sciences, 2015.
[6] D. M. Harrild, C. S. Henriquez, A computer model of normal conduction in the human atria, Circulation research 87 (7) (2000) e25-e36.
[7] T. N. James, The internodal pathways of the human heart, Progress in cardiovascular diseases 43 (6) (2001) 495-535.
[8] F. Pashakhanloo, D. A. Herzka, H. Ashikaga, S. Mori, N. Gai, D. A. Bluemke, N. A. Trayanova, E. R. McVeigh, Myofiber architecture of the human atria as revealed by submillimeter diffusion tensor imaging, Circulation: arrhythmia and electrophysiology 9 (4) (2016) e004133.
[9] S. Karas Jr, R. C. Elkins, Mechanism of function of the mitral valve leaflets, chordae tendineae and left ventricular papillary muscles in dogs, Circulation research 26 (6) (1970) 689-696.
[10] R. Bordas, V. Grau, R. Burton, P. Hales, J. Schneider, D. Gavaghan, P. Kohl, B. Rodriguez, Integrated approach for the study of anatomical variability in the cardiac purkinje system: from high resolution mri to electrophysiology simulation, in: 2010 Annual International Conference of the IEEE Engineering in Medicine and Biology, IEEE, 2010, pp. 6793-6796.
[11] A. Saha, S. Roy, Papillary muscles of right ventricle - morphological variations and its clinical relevance, Cardiovascular Pathology 34 (2018) 22-27.
[12] R. A. Bergman, A. K. Afifi, et al., Atlas of microscopic anatomy.
[13] J. Tranum-Jensen, A. Wilde, J. T. Vermeulen, M. J. Janse, Morphology of electrophysiologically identified junctions between purkinje fibers and ventricular muscle in rabbit and pig hearts., Circulation research 69 (2) (1991) 429-437.
[14] O. Berenfeld, J. Jalife, Purkinje-muscle reentry as a mechanism of polymorphic ventricular arrhythmias in a 3-dimensional model of the ventricles, Circulation Research 82 (10) (1998) 1063-1077.
[15] G. A. Holzapfel, R. W. Ogden, Constitutive modelling of passive myocardium: a structurally based framework for material characterization, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 367 (1902) (2009) 3445-3475.
[16] G. Seemann, C. Höper, F. B. Sachse, O. Dössel, A. V. Holden, H. Zhang, Heterogeneous three-dimensional anatomical and electrophys-
[17] D. Nickerson, N. Smith, P. Hunter, New developments in a strongly coupled cardiac electromechanical model, EP Europace 7 (s2) (2005) S118-S127.
[18] S. G. Campbell, E. Howard, J. Aguado-Sierra, B. A. Coppola, J. H. Omens, L. J. Mulligan, A. D. McCulloch, R. C. Kerckhoffs, Effect of transmurally heterogeneous myocyte excitation-contraction coupling on canine left ventricular electromechanics, Experimental physiology 94 (5) (2009) 541-552.
[19] G. Buckberg, A. Mahajan, S. Saleh, J. I. Hoffman, C. Coghlan, Structure and function relationships of the helical ventricular myocardial band, The Journal of thoracic and cardiovascular surgery 136 (3) (2008) 578-589.
[20] R. Doste, D. Soto-Iglesias, G. Bernardino, A. Alcaine, R. Sebastian, S. Giffard-Roisin, M. Sermesant, A. Berruezo, D. Sanchez-Quintana, O. Camara, A rule-based method to model myocardial fiber orientation in cardiac biventricular geometries with outflow tracts, International journal for numerical methods in biomedical engineering 35 (4) (2019) e3185.
[21] N. A. Trayanova, Whole-heart modeling: applications to cardiac electrophysiology and electromechanics, Circulation research 108 (1) (2011) 113- 128.
[22] A. J. Pullan, K. A. Tomlinson, P. J. Hunter, A finite element method for an eikonal equation model of myocardial excitation wavefront propagation, SIAM Journal on Applied Mathematics 63 (1) (2002) 324-350.
[23] J. J. B. Jack, D. Noble, R. W. Tsien, Electric current flow in excitable cells, Clarendon Press Oxford, 1975.
[25] A. Bueno-Orovio, D. Kay, V. Grau, B. Rodriguez, K. Burrage, Fractional diffusion models of cardiac electrical propagation: role of structural heterogeneity in dispersion of repolarization, Journal of the Royal Society Interface 11 (97) (2014) 20140352.
[26] D. E. Hurtado, S. Castro, A. Gizzi, Computational modeling of non-linear diffusion in cardiac electrophysiology: A novel porous-medium approach, Computer Methods in Applied Mechanics and Engineering 300 (2016) 70- 83.
[27] N. G. Sepulveda, B. J. Roth, J. P. Wikswo Jr, Current injection into a two-dimensional anisotropic bidomain., Biophysical journal 55 (5) (1989) 987.
[28] L. Tung, A bi-domain model for describing ischemic myocardial dc potentials., Ph.D. thesis, Massachusetts Institute of Technology (1978).
[29] J. Sundnes, G. T. Lines, X. Cai, B. F. Nielsen, K.-A. Mardal, A. Tveito, Computing the electrical activity in the heart, Vol. 1, Springer Science & Business Media, 2007.
[30] E. Vigmond, R. W. Dos Santos, A. Prassl, M. Deo, G. Plank, Solvers for the cardiac bidomain equations, Progress in biophysics and molecular biology 96 (1-3) (2008) 3-18.
[31] J. P. Wikswo Jr, S.-F. Lin, R. A. Abbas, Virtual electrodes in cardiac tissue: a common mechanism for anodal and cathodal stimulation, Biophysical journal 69 (6) (1995) 2195-2210.
[35] M. Potse, B. Dubé, J. Richer, A. Vinet, R. M. Gulrajani, A comparison of monodomain and bidomain reaction-diffusion models for action potential propagation in the human heart, IEEE Transactions on Biomedical Engineering 53 (12) (2006) 2425-2435.
[36] M. Wilhelms, H. Hettmann, M. M. C. Maleckar, J. T. Koivumäki, O. Dössel, G. Seemann, Benchmarking electrophysiological models of human atrial myocytes, Frontiers in physiology 3 (2013) 487.
[37] S. Inada, J. Hancox, H. Zhang, M. Boyett, One-dimensional mathematical model of the atrioventricular node including atrio-nodal, nodal, and nodalhis cells, Biophysical journal 97 (8) (2009) 2117-2127.
[38] V. D. Corino, F. Sandberg, L. T. Mainardi, L. Sornmo, An atrioventricular node model for analysis of the ventricular response during atrial fibrillation, IEEE transactions on biomedical engineering 58 (12) (2011) 3386-3395.
[39] B. Baillargeon, N. Rebelo, D. D. Fox, R. L. Taylor, E. Kuhl, The living heart project: a robust and integrative simulator for human heart function, European Journal of Mechanics-A/Solids 48 (2014) 38-47.
[40] S. Sugiura, T. Washio, A. Hatano, J. Okada, H. Watanabe, T. Hisada, Multi-scale simulations of cardiac electrophysiology and mechanics using the university of tokyo heart simulator, Progress in biophysics and molecular biology 110 (2-3) (2012) 380-389.
[41] F. Viola, V. Meschini, R. Verzicco, Fluid-structure-electrophysiology interaction (fsei) in the left-heart: A multi-way coupled computational model, European Journal of Mechanics-B/Fluids 79 (2020) 212-232.
[43] T. Lassila, M. Lange, A. R. P. Perez, K. Lekadir, X. Albà, G. Piella, A. F. Frangi, Electrophysiology model for a human heart with ischemic scar and realistic purkinje network, in: Statistical Atlases and Computational Models of the Heart, Springer, 2015, pp. 90-97.
[44] M. Deo, P. Boyle, G. Plank, E. Vigmond, Arrhythmogenic mechanisms of the purkinje system during electric shocks: a modeling study, Heart rhythm 6 (12) (2009) 1782-1789.
[45] M. Deo, P. M. Boyle, A. M. Kim, E. J. Vigmond, Arrhythmogenesis by single ectopic beats originating in the purkinje system, American Journal of Physiology-Heart and Circulatory Physiology 299 (4) (2010) H1002-H1011.
[46] E. Behradfar, A. Nygren, E. J. Vigmond, The role of purkinje-myocardial coupling during ventricular arrhythmia: a modeling study, PloS one 9 (2).
[47] T. Ijiri, T. Ashihara, T. Yamaguchi, K. Takayama, T. Igarashi, T. Shimada, T. Namba, R. Haraguchi, K. Nakazawa, A procedural method for modeling the purkinje fibers of the heart, The journal of physiological sciences (2008) 0810170079-0810170079.
[48] A. Lopez-Perez, R. Sebastian, J. M. Ferrero, Three-dimensional cardiac computational modelling: methods, features and applications, Biomedical engineering online 14 (1) (2015) 35.
[49] C. Vergara, M. Lange, S. Palamara, T. Lassila, A. F. Frangi, A. Quarteroni, A coupled 3d-1d numerical monodomain solver for cardiac electrical activation in the myocardium with detailed purkinje network, Journal of Computational Physics 308 (2016) 218-238.
[50] P. Pathmanathan, M. O. Bernabeu, R. Bordas, J. Cooper, A. Garny, J. M. Pitt-Francis, J. P. Whiteley, D. J. Gavaghan, A numerical guide to the solution of the bidomain equations of cardiac electrophysiology, Progress in biophysics and molecular biology 102 (2) (2010) 136-155.
[51] N. A. Trayanova, J. Constantino, V. Gurev, Electromechanical models of the ventricles, American Journal of Physiology-Heart and Circulatory Physiology 301 (2) (2011) H279-H286.
[52] J. Cooper, A. Corrias, D. Gavaghan, D. Noble, Considerations for the use of cellular electrophysiology models within cardiac tissue simulations, Progress in biophysics and molecular biology 107 (1) (2011) 74-80.
[53] A. Loppini, A. Gizzi, R. Ruiz-Baier, C. Cherubini, F. H. Fenton, S. Filippi, Competing mechanisms of stress-assisted diffusivity and stretch-activated currents in cardiac electromechanics, Frontiers in physiology 9 (2018) 1714.
[54] R. H. Clayton, Y. Aboelkassem, C. D. Cantwell, C. Corrado, T. Delhaas, W. Huberts, C. L. Lei, H. Ni, A. V. Panfilov, C. Roney, et al., An audit of uncertainty in multi-scale cardiac electrophysiology models, Philosophical Transactions of the Royal Society A 378 (2173) (2020) 20190335.
[55] E. C. Vasconcellos, E. W. Clua, F. H. Fenton, M. Zamith, Accelerating simulations of cardiac electrical dynamics through a multi-gpu platform and an optimized data structure, Concurrency and Computation: Practice and Experience 32 (5) (2020) e5528.
[61] A. Saha, S. Roy, Papillary muscles of left ventricle - morphological variations and its clinical relevance, Indian heart journal 70 (6) (2018) 894-900.
[70] L. N. Trefethen, D. Bau III, Numerical linear algebra, Vol. 50, Siam, 1997.
[93] L. W.-T. Ng, M. Eldred, Multifidelity uncertainty quantification using nonintrusive polynomial chaos and stochastic collocation, in: 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference 20th AIAA/ASME/AHS Adaptive Structures Conference 14th AIAA, 2012, p. 1852.
[94] R. Molléro, X. Pennec, H. Delingette, A. Garny, N. Ayache, M. Sermesant, Multifidelity-cma: a multifidelity approach for efficient personalisation of 3d cardiac electromechanical models, Biomechanics and modeling in mechanobiology 17 (1) (2018) 285-300.
[95] C. M. Fleeter, G. Geraci, D. E. Schiavazzi, A. M. Kahn, A. L. Marsden, Multilevel and multifidelity uncertainty quantification for cardiovascular hemodynamics, Computer methods in applied mechanics and engineering 365 (2020) 113030.
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BibTeX entry
@article{oai:it.cnr:prodotti:481750,
title = {A fast computational model for the electrophysiology of the whole human heart},
author = {Del Corso G. and Verzicco R. and Viola F.},
doi = {10.1016/j.jcp.2022.111084 and 10.2139/ssrn.3977804 and 10.48550/arxiv.2112.12854},
year = {2022}
}
0000-0003-4604-2006
