Review Article | Published:

Computational models in cardiology

Nature Reviews Cardiologyvolume 16pages100111 (2019) | Download Citation


The treatment of individual patients in cardiology practice increasingly relies on advanced imaging, genetic screening and devices. As the amount of imaging and other diagnostic data increases, paralleled by the greater capacity to personalize treatment, the difficulty of using the full array of measurements of a patient to determine an optimal treatment seems also to be paradoxically increasing. Computational models are progressively addressing this issue by providing a common framework for integrating multiple data sets from individual patients. These models, which are based on physiology and physics rather than on population statistics, enable computational simulations to reveal diagnostic information that would have otherwise remained concealed and to predict treatment outcomes for individual patients. The inherent need for patient-specific models in cardiology is clear and is driving the rapid development of tools and techniques for creating personalized methods to guide pharmaceutical therapy, deployment of devices and surgical interventions.

Key points

  • Computational models of the heart have an important and growing role in cardiology, enabling patients to be diagnosed and treated on the basis of their specific pathophysiology.

  • Simulations provide the link between the effects of genetic mutations, physiological regulations or drugs on protein function and emergent cellular and tissue function or clinical phenotypes.

  • Models representing an individual patient or a specific pathology are now used to identify the mechanisms underpinning a disease, improve patient selection and predict clinical outcomes.

  • Predictive modelling also contributes to the development of new diagnostics and devices and to the tailoring of therapies for individual patients.

  • Translational barriers remain regarding model personalization, speed and detail of the simulations and how to communicate model predictions to cardiologists within a clinical environment.

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Comprehensive In vitro Proarrhythmia Assay (CiPA):


  1. 1.

    Antman, E. M. & Loscalzo, J. Precision medicine in cardiology. Nat. Rev. Cardiol. 13, 591–602 (2016).

  2. 2.

    Loscalzo, J., Kohane, I. & Barabasi, A. L. Human disease classification in the postgenomic era: a complex systems approach to human pathobiology. Mol. Syst. Biol. 3, 124 (2007).

  3. 3.

    Lyon, A. et al. Distinct ECG phenotypes identified in hypertrophic cardiomyopathy using machine learning associate with arrhythmic risk markers. Front. Physiol. 9, 213 (2018).

  4. 4.

    Horiuchi, Y. et al. Identifying novel phenotypes of acute heart failure using cluster analysis of clinical variables. Int. J. Cardiol. 262, 57–63 (2018).

  5. 5.

    Stanley, K. Design of randomized controlled trials. Circulation 115, 1164–1169 (2007).

  6. 6.

    Gilbert, K. et al. Atlas-based computational analysis of heart shape and function in congenital heart disease. J. Cardiovasc. Transl Res. 11, 123–132 (2018).

  7. 7.

    Vadakkumpadan, F., Arevalo, H., Ceritoglu, C., Miller, M. & Trayanova, N. Image-based estimation of ventricular fiber orientations for personalized modeling of cardiac electrophysiology. IEEE Trans. Med. Imag. 31, 1051–1060 (2012).

  8. 8.

    Witzenburg, C. M. & Holmes, J. W. A. Comparison of phenomenologic growth laws for myocardial hypertrophy. J. Elast. 129, 257–281 (2017).

  9. 9.

    Arts, T., Lumens, J., Kroon, W. & Delhaas, T. Control of whole heart geometry by intramyocardial mechano-feedback: a model study. PLoS Comput. Biol. 8, e1002369 (2012).

  10. 10.

    Niederer, S. A. & Smith, N. P. Using physiologically based models for clinical translation: predictive modelling, data interpretation or something in-between? J. Physiol. 594, 6849–6863 (2016).

  11. 11.

    Trayanova, N. A., Boyle, P. M. & Nikolov, P. P. Personalized imaging and modeling strategies for arrhythmia prevention and therapy. Curr. Opin. Biomed. Eng. 5, 21–28 (2018).

  12. 12.

    Morris, P. D. et al. Computational fluid dynamics modelling in cardiovascular medicine. Heart 102, 18 (2016).

  13. 13.

    Taylor, C. A. & Figueroa, C. Patient-specific modeling of cardiovascular mechanics. Annu. Rev. Biomed. Eng. 11, 109–134 (2009).

  14. 14.

    Lamata, P. et al. Images as drivers of progress in cardiac computational modelling. Prog. Biophys. Mol. Biol. 115, 198–212 (2014).

  15. 15.

    Crozier, A. et al. Image-based personalization of cardiac anatomy for coupled eSlectromechanical modeling. Annu. Rev. Biomed. Eng. 44, 58–70 (2016).

  16. 16.

    Luo, C. & Rudy, Y. A model of the ventricular cardiac action potential. Depolarization, repolarization, and their interaction. Circ. Res. 68, 1501–1526 (1991).

  17. 17.

    Fink, M. et al. Cardiac cell modelling: observations from the heart of the cardiac physiome project. Prog. Biophys. Mol. Biol. 104, 2–21 (2011).

  18. 18.

    Heijman, J., Volders, P. G., Westra, R. L. & Rudy, Y. Local control of β-adrenergic stimulation: effects on ventricular myocyte electrophysiology and Ca2+-transient. J. Mol. Cell. Cardiol. 50, 863–871 (2011).

  19. 19.

    Lascano, E. C. et al. Role of CaMKII in post acidosis arrhythmias: a simulation study using a human myocyte model. J. Mol. Cell. Cardiol. 60, 172–183 (2013).

  20. 20.

    Fernandez-Chas, M., Curtis, M. J. & Niederer, S. A. Mechanism of doxorubicin cardiotoxicity evaluated by integrating multiple molecular effects into a biophysical model. Br. J. Pharmacol. 175, 763–781 (2017).

  21. 21.

    Fabbri, A., Fantini, M., Wilders, R. & Severi, S. Computational analysis of the human sinus node action potential: model development and effects of mutations. J. Physiol. 595, 2365–2396 (2017).

  22. 22.

    ten Tusscher, K. H. W. J. & Panfilov, A. V. Alternans and spiral breakup in a human ventricular tissue model. Am. J. Physiol. Heart Circ. Physiol. 291, H1088–H1100 (2006).

  23. 23.

    O’Hara, T., Virág, L., Varró, A. & Rudy, Y. Simulation of the undiseased human cardiac ventricular action potential: model formulation and experimental validation. PLoS Comput. Biol. 7, e1002061 (2011).

  24. 24.

    Grandi, E., Pasqualini, F. S. & Bers, D. M. A novel computational model of the human ventricular action potential and Ca transient. J. Mol. Cell. Cardiol. 48, 112–121 (2010).

  25. 25.

    Priebe, L. & Beuckelmann, D. J. Simulation study of cellular electric properties in heart failure. Circ. Res. 82, 1206–1223 (1998).

  26. 26.

    Grandi, E. et al. Human atrial action potential and Ca2+ model: sinus rhythm and chronic atrial fibrillation. Circ. Res. 109, 1055–1066 (2011).

  27. 27.

    Koivumäki, J. T., Korhonen, T. & Tavi, P. Impact of sarcoplasmic reticulum calcium release on calcium dynamics and action potential morphology in human atrial myocytes: a computational study. PLoS Comput. Biol. 7, e1001067 (2011).

  28. 28.

    Maleckar, M. M., Greenstein, J. L., Trayanova, N. A. & Giles, W. R. Mathematical simulations of ligand-gated and cell-type specific effects on the action potential of human atrium. Prog. Biophys. Mol. Biol. 98, 161–170 (2008).

  29. 29.

    Nygren, A. et al. Mathematical model of an adult human atrial cell: the role of K+ currents in repolarization. Circ. Res. 82, 63–81 (1998).

  30. 30.

    Courtemanche, M., Ramirez, R. J. & Nattel, S. Ionic mechanisms underlying human atrial action potential properties: insights from a mathematical model. Am. J. Physiol. 275, H301–H321 (1998).

  31. 31.

    Land, S. et al. A model of cardiac contraction based on novel measurements of tension development in human cardiomyocytes. J. Mol. Cell. Cardiol. 106, 68–83 (2017).

  32. 32.

    Wang, Q. et al. SCN5A mutations associated with an inherited cardiac arrhythmia, long QT syndrome. Cell 80, 805–811 (1995).

  33. 33.

    Wilde, A. A. M. & Behr, E. R. Genetic testing for inherited cardiac disease. Nat. Rev. Cardiol. 10, 571–583 (2013).

  34. 34.

    Adsit, G. S., Vaidyanathan, R., Galler, C. M., Kyle, J. W. & Makielski, J. C. Channelopathies from mutations in the cardiac sodium channel protein complex. J. Mol. Cell. Cardiol. 61, 34–43 (2013).

  35. 35.

    Clancy, C. E. & Rudy, Y. Linking a genetic defect to its cellular phenotype in a cardiac arrhythmia. Nature 400, 566–569 (1999).

  36. 36.

    Saucerman, J. J., Healy, S. N., Belik, M. E., Puglisi, J. L. & McCulloch, A. D. Proarrhythmic consequences of a KCNQ1 AKAP-binding domain mutation: computational models of whole cells and heterogeneous tissue. Circ. Res. 95, 1216–1224 (2004).

  37. 37.

    O’Hara, T. & Rudy, Y. Arrhythmia formation in subclinical (“silent”) long QT syndrome requires multiple insults: quantitative mechanistic study using the KCNQ1 mutation Q357R as example. Heart Rhythm 9, 275–282 (2012).

  38. 38.

    Ficker, E. et al. Novel characteristics of a misprocessed mutant HERG channel linked to hereditary long QT syndrome. Am. J. Physiol. Heart Circ. Physiol. 279, H1748–H1756 (2000).

  39. 39.

    Choe, C. U. et al. C-Terminal HERG (LQT2) mutations disrupt IKr channel regulation through 14-3-3ε. Hum. Mol. Genet. 15, 2888–2902 (2006).

  40. 40.

    Clancy, C. E., Tateyama, M., Liu, H., Wehrens, X. H. T. & Kass, R. S. Non-equilibrium gating in cardiac Na+ channels: an original mechanism of arrhythmia. Circulation 107, 2233–2237 (2003).

  41. 41.

    Flaim, S. N., Giles, W. R. & McCulloch, A. D. Arrhythmogenic consequences of Na+ channel mutations in the transmurally heterogeneous mammalian left ventricle: analysis of the I1768V SCN5A mutation. Heart Rhythm 4, 768–778 (2007).

  42. 42.

    Wehrens, X. H. T., Abriel, H., Cabo, C., Benhorin, J. & Kass, R. S. Arrhythmogenic mechanism of an LQT-3 mutation of the human heart Na+ channel α-subunit: a comptutational analysis. Circulation 102, 584–590 (2000).

  43. 43.

    Bankston, J. R. et al. A novel LQT-3 mutation disrupts an inactivation gate complex with distinct rate-dependent phenotypic consequences. Channels 1, 273–280 (2007).

  44. 44.

    Vecchietti, S. et al. In silico assessment of Y1795C and Y1795H SCN5A mutations: implication for inherited arrhythmogenic syndromes. Am. J. Physiol. Heart Circ. Physiol. 292, H56–H65 (2007).

  45. 45.

    Ahrens-Nicklas, R. C., Clancy, C. E. & Christini, D. J. Re-evaluating the efficacy of beta-adrenergic agonists and antagonists in long QT-3 syndrome through computational modelling. Cardiovasc. Res. 82, 439–447 (2009).

  46. 46.

    Thiel, W. H. et al. Proarrhythmic defects in Timothy syndrome require calmodulin kinase II. Circulation 118, 2225–2234 (2008).

  47. 47.

    Splawski, I. et al. Ca V 1. 2 calcium channel dysfunction causes a multisystem disorder including arrhythmia and autism. 119, 19–31 (2004).

  48. 48.

    Boczek, N. J. et al. Novel Timothy syndrome mutation leading to increase in CACNA1C window current. Heart Rhythm 12, 211–219 (2015).

  49. 49.

    Sung, R. J. et al. Beta-adrenergic modulation of arrhythmogenesis and identification of targeted sites of antiarrhythmic therapy in Timothy (LQT8) syndrome: a theoretical study. Am. J. Physiol. Heart Circ. Physiol. 298, H33–44 (2010).

  50. 50.

    Zhu, Z. I. & Clancy, C. E. L-Type Ca2+ channel mutations and T-wave alternans: a model study. Am. J. Physiol. Heart Circ. Physiol. 293, H3480–H3489 (2007).

  51. 51.

    Faber, G. M., Silva, J., Livshitz, L. & Rudy, Y. Kinetic properties of the cardiac L-type Ca2+ channel and its role in myocyte electrophysiology: a theoretical investigation. Biophys. J. 92, 1522–1543 (2007).

  52. 52.

    Fermini, B. et al. A new perspective in the field of cardiac safety testing through the comprehensive in vitro proarrhythmia assay paradigm. J. Biomol. Screen. 21, 1–11 (2016).

  53. 53.

    Verkerk, A. O. et al. Role of sequence variations in the human ether-a-go-go-related gene (HERG, KCNH2) in the Brugada syndrome. Cardiovasc. Res. 68, 441–453 (2005).

  54. 54.

    Moreno, C. et al. A new KCNQ1 mutation at the S5 segment that impairs its association with KCNE1 is responsible for short QT syndrome. Cardiovasc. Res. 107, 613–623 (2015).

  55. 55.

    Hancox, J. C., Whittaker, D. G., Du, C., Stuart, A. G. & Zhang, H. Emerging therapeutic targets in the short QT syndrome. Expert Opin. Ther. Targets 22, 439–451 (2018).

  56. 56.

    Clancy, C. E. & Rudy, Y. Na+ channel mutation that causes both Brugada and long-QT syndrome phenotypes: a simulation study of mechanism. Circulation 105, 1208–1213 (2002).

  57. 57.

    Wu, J., Kato, K., Delisle, B. P. & Horie, M. A molecular mechanism for adrenergic-induced long QT syndrome. J. Am. Coll. Cardiol. 63, 819–827 (2014).

  58. 58.

    Hu, D. et al. Dual variation in SCN5A and CACNB2b underlies the development of cardiac conduction disease without Brugada syndrome. Pacing Clin. Electrophysiol. 33, 274–285 (2010).

  59. 59.

    Priest, J. R. et al. Early somatic mosaicism is a rare cause of long-QT syndrome. Proc. Natl Acad. Sci. USA 113, 11555–11560 (2016).

  60. 60.

    Moreno, J. D. et al. Ranolazine for congenital and acquired late iNa-linked arrhythmias: In silico pharmacological screening. Circ. Res. 113, e50–e61 (2013).

  61. 61.

    Campbell, S. G., Lionetti, F. V., Campbell, K. S. & McCulloch, A. D. Coupling of adjacent tropomyosins enhances cross-bridge-mediated cooperative activation in a Markov model of the cardiac thin filament. Biophys. J. 98, 2254–2264 (2010).

  62. 62.

    Land, S. & Niederer, S. A. A spatially detailed model of isometric contraction based on competitive binding of troponin I explains cooperative interactions between tropomyosin and crossbridges. PLoS Comput. Biol. 11, e1004376 (2015).

  63. 63.

    Sewanan, L. R., Moore, J. R., Lehman, W. & Campbell, S. G. Predicting effects of tropomyosin mutations on cardiac muscle contraction through myofilament modeling. Front. Physiol. 7, 473 (2016).

  64. 64.

    Dewan, S., McCabe, K. J., Regnier, M., McCulloch, A. D. & Lindert, S. Molecular effects of cTnC DCM mutations on calcium sensitivity and myofilament activation-an integrated multiscale modeling study. J. Phys. Chem. B 120, 8264–8275 (2016).

  65. 65.

    Li, Z. et al. Improving the in silico assessment of proarrhythmia risk by combining hERG (Human Ether-à-go-go-related gene) channel–drug binding kinetics and multichannel pharmacology. Circ. Arrhythm. Electrophysiol. 10, e004628 (2017).

  66. 66.

    Sager, P. T., Gintant, G., Turner, J. R., Pettit, S. & Stockbridge, N. Rechanneling the cardiac proarrhythmia safety paradigm: a meeting report from the Cardiac Safety Research Consortium. Am. Heart J. 167, 292–300 (2014).

  67. 67.

    Johnstone, R. H. et al. Uncertainty and variability in models of the cardiac action potential: Can we build trustworthy models? J. Mol. Cell. Cardiol. 96, 49–62 (2016).

  68. 68.

    Sarkar, A. X., Christini, D. J. & Sobie, E. A. Exploiting mathematical models to illuminate electrophysiological variability between individuals. J. Physiol. 590, 2555–2567 (2012).

  69. 69.

    Mirams, G. R. et al. Simulation of multiple ion channel block provides improved early prediction of compounds’ clinical torsadogenic risk. Cardiovasc. Res. 91, 53–61 (2011).

  70. 70.

    de Oliveira, B. L. & Niederer, S. A biophysical systems approach to identifying the pathways of acute and chronic doxorubicin mitochondrial cardiotoxicity. PLoS Comput. Biol. 12, e1005214 (2016).

  71. 71.

    Mirams, G. R. et al. Prediction of thorough QT study results using action potential simulations based on ion channel screens. J. Pharmacol. Toxicol. Methods 70, 246–254 (2014).

  72. 72.

    Zipes, D. P. & Wellens, H. J. J. Sudden cardiac death. Circulation 98, 2334–2351 (1998).

  73. 73.

    Ferrero, J. M., Trenor, B. & Romero, L. Multiscale computational analysis of the bioelectric consequences of myocardial ischaemia and infarction. Europace 16, 405–415 (2014).

  74. 74.

    Morena, H. et al. Comparison of the effects of regional ischemia, hypoxia, hyperkalemia, and acidosis on intracellular and extracellular potentials and metabolism in the isolated porcine heart. Circ. Res. 46, 634–646 (1980).

  75. 75.

    Jones, D. K., Peters, C. H., Tolhurst, S. A., Claydon, T. W. & Ruben, P. C. Extracellular proton modulation of the cardiac voltage-gated sodium channel, NaV1.5. Biophys. J. 101, 2147–2156 (2011).

  76. 76.

    Du Chun, Y. U. N. et al. Acidosis impairs the protective role of hERG K+ channels against premature stimulation. J. Cardiovasc. Electrophysiol. 21, 1160–1169 (2010).

  77. 77.

    Dutta, S., Mincholé, A., Quinn, T. A. & Rodriguez, B. Electrophysiological properties of computational human ventricular cell action potential models under acute ischemic conditions. Prog. Biophys. Mol. Biol. 129, 40–52 (2017).

  78. 78.

    Dutta, S. et al. Early afterdepolarizations promote transmural reentry in ischemic human ventricles with reduced repolarization reserve. Prog. Biophys. Mol. Biol. 120, 236–248 (2016).

  79. 79.

    Potse, M., Coronel, R., Falcao, S., LeBlanc, A. R. & Vinet, A. The effect of lesion size and tissue remodeling on ST deviation in partial-thickness ischemia. Heart Rhythm 4, 200–206 (2007).

  80. 80.

    Kazbanov, I. V. et al. Effect of global cardiac ischemia on human ventricular fibrillation: insights from a multi-scale mechanistic model of the human heart. PLoS Comput. Biol. 10, e1003891 (2014).

  81. 81.

    Sanchez-Alonso, J. L. et al. Microdomain-specific modulation of L-type calcium channels leads to triggered ventricular arrhythmia in heart failure. Circ. Res. 119, 944–945 (2016).

  82. 82.

    Narayan, S. M., Bayer, J. D., Lalani, G. & Trayanova, N. A. Action potential dynamics explain arrhythmic vulnerability in human heart failure: a clinical and modeling study implicating abnormal calcium handling. J. Am. Coll. Cardiol. 52, 1782–1792 (2008).

  83. 83.

    Chang, K. C. & Trayanova, N. A. Mechanisms of arrhythmogenesis related to calcium-driven alternans in a model of human atrial fibrillation. Sci. Rep. 6, 36395 (2016).

  84. 84.

    Paci, M., Hyttinen, J., Aalto-Setala, K. & Severi, S. Computational models of ventricular- and atrial-like human induced pluripotent stem cell derived cardiomyocytes. Ann. Biomed. Eng. 41, 2334–2348 (2013).

  85. 85.

    Koivumaki, J. T. et al. Structural immaturity of human iPSC-derived cardiomyocytes: in silico investigation of effects on function and disease modeling. Front. Physiol. 9, 80 (2018).

  86. 86.

    Lei, C. L. et al. Tailoring mathematical models to stem-cell derived cardiomyocyte lines can improve predictions of drug-induced changes to their electrophysiology. Front. Physiol. 8, 986 (2017).

  87. 87.

    Paci, M., Hyttinen, J., Rodriguez, B. & Severi, S. Human induced pluripotent stem cell-derived versus adult cardiomyocytes: an in silico electrophysiological study on effects of ionic current block. Br. J. Pharmacol. 172, 5147–5160 (2015).

  88. 88.

    Harding, S. E. Large stem cell-derived cardiomyocyte grafts: cellular ventricular assist devices? Mol. Ther. 22, 1240–1242 (2014).

  89. 89.

    Ukwatta, E. et al. Myocardial infarct segmentation from magnetic resonance images for personalized modeling of cardiac electrophysiology. IEEE Trans. Med. Imag. 35, 1408–1419 (2015).

  90. 90.

    Ukwatta, E. et al. Image-based reconstruction of three-dimensional myocardial infarct geometry for patient-specific modeling of cardiac electrophysiology. Med. Phys. 42, 4579–4590 (2015).

  91. 91.

    Suinesiaputra, A., McCulloch, A. D., Nash, M. P., Pontre, B. & Young, A. A. Cardiac image modelling: breadth and depth in heart disease. Med. Image Anal. 33, 38–43 (2016).

  92. 92.

    Zhang, X. et al. Information maximizing component analysis of left ventricular remodeling due to myocardial infarction. J. Transl Med. 13, 343 (2015).

  93. 93.

    Ringenberg, J. et al. Corrigendum to “effects of fibrosis morphology on reentrant ventricular tachycardia inducibility and simulation fidelity in patient-derived models”. Clin. Med. Insights Cardiol. 8, 51 (2014).

  94. 94.

    Bayer, J. D., Blake, R. C., Plank, G. & Trayanova, N. A. A novel rule-based algorithm for assigning myocardial fiber orientation to computational heart models. Ann. Biomed. Eng. 40, 2243–2254 (2012).

  95. 95.

    Arevalo, H. J. et al. Arrhythmia risk stratification of patients after myocardial infarction using personalized heart models. Nat. Commun. 7, 11437 (2016).

  96. 96.

    Deng, D., Arevalo, H. J., Prakosa, A., Callans, D. J. & Trayanova, N. A. A feasibility study of arrhythmia risk prediction in patients with myocardial infarction and preserved ejection fraction. Europace 18, iv60–iv66 (2016).

  97. 97.

    Sanchez, C. et al. Sensitivity analysis of ventricular activation and electrocardiogram in tailored models of heart-failure patients. Med. Biol. Eng. Comput. 56, 491–504 (2018).

  98. 98.

    Ranjan, R. et al. Personalized MRI-based modeling predicts ventricular tachycardia vulnerability in patients receiving primary prevention ICDs [abstract 16247]. Circulation 134, A16247–A16247 (2016).

  99. 99.

    Relan, J. et al. Coupled personalization of cardiac electrophysiology models for prediction of ischaemic ventricular tachycardia. Interface Focus 1, 396–407 (2011).

  100. 100.

    Corrado, C. et al. Personalized models of human atrial electrophysiology derived from endocardial electrograms. IEEE Trans. Biomed. Eng. 64, 735–742 (2016).

  101. 101.

    Vigmond, E. J., Ruckdeschel, R. & Trayanova, N. Reentry in a morphologically realistic atrial model. J. Cardiovasc. Electrophysiol. 12, 1046–1054 (2001).

  102. 102.

    Virag, N. et al. Study of atrial arrhythmias in a computer model based on magnetic resonance images of human atria. Chaos 12, 754–763 (2002).

  103. 103.

    Dang, L. et al. Evaluation of ablation patterns using a biophysical model of atrial fibrillation. Ann. Biomed. Eng. 33, 465–474 (2005).

  104. 104.

    Vigmond, E. J. et al. The effect of vagally induced dispersion of action potential duration on atrial arrhythmogenesis. Heart Rhythm 1, 334–344 (2004).

  105. 105.

    Freudenberg, J., Schiemann, T., Tiede, U. & Hohne, K. H. Simulation of cardiac excitation patterns in a three-dimensional anatomical heart atlas. Comput. Biol. Med. 30, 191–205 (2000).

  106. 106.

    Harrild, D. & Henriquez, C. A computer model of normal conduction in the human atria. Circ. Res. 87, 25–36 (2000).

  107. 107.

    Seemann, G. et al. Heterogeneous three-dimensional anatomical and electrophysiological model of human atria. Phil. Trans. A Math. Phys. Eng. Sci. 364, 1465–1481 (2006).

  108. 108.

    Reumann, M., Bohnert, J., Seemann, G., Osswald, B. & Dossel, O. Preventive ablation strategies in a biophysical model of atrial fibrillation based on realistic anatomical data. IEEE Trans. Biomed. Eng. 55, 399–406 (2008).

  109. 109.

    Aslanidi, O. V. et al. 3D virtual human atria: a computational platform for studying clinical atrial fibrillation. Prog. Biophys. Mol. Biol. 107, 156–168 (2011).

  110. 110.

    McDowell, K. S. et al. Mechanistic inquiry into the role of tissue remodeling in fibrotic lesions in human atrial fibrillation. Biophys. J. 104, 2764–2773 (2013).

  111. 111.

    McDowell, K. S. et al. Methodology for patient-specific modeling of atrial fibrosis as a substrate for atrial fibrillation. J. Electrocardiol. 45, 640–645 (2012).

  112. 112.

    Dossel, O., Krueger, M. W., Weber, F. M., Wilhelms, M. & Seemann, G. Computational modeling of the human atrial anatomy and electrophysiology. Med. Biol. Eng. Comput. 50, 773–799 (2012).

  113. 113.

    Fastl, T. E. et al. Personalized computational modeling of left atrial geometry and transmural myofiber architecture. Med. Image Anal. 47, 180–190 (2018).

  114. 114.

    Pashakhanloo, F. et al. Myofiber architecture of the human atria as revealed by submillimeter diffusion tensor imaging. Circ. Arrhythm. Electrophysiol. 9, e004133 (2016).

  115. 115.

    Corrado, C. et al. A work flow to build and validate patient specific left atrium electrophysiology models from catheter measurements. Med. Image Anal. 47, 153–163 (2018).

  116. 116.

    Trayanova, N. A. Mathematical approaches to understanding and imaging atrial fibrillation: significance for mechanisms and management. Circ. Res. 114, 1516–1531 (2014).

  117. 117.

    Ten Tusscher, K. H., Hren, R. & Panfilov, A. V. Organization of ventricular fibrillation in the human heart. Circ. Res. 100, e87–101 (2007).

  118. 118.

    Keldermann, R. H. et al. Effect of heterogeneous APD restitution on VF organization in a model of the human ventricles. Am. J. Physiol. Heart Circ. Physiol. 294, H764–H774 (2008).

  119. 119.

    Bayer, J. D., Lalani, G. G., Vigmond, E. J., Narayan, S. M. & Trayanova, N. A. Mechanisms linking electrical alternans and clinical ventricular arrhythmia in human heart failure. Heart Rhythm 13, 1922–1931 (2016).

  120. 120.

    Van Nieuwenhuyse, E., Seemann, G., Panfilov, A. V. & Vandersickel, N. Effects of early afterdepolarizations on excitation patterns in an accurate model of the human ventricles. PLoS ONE 12, e0188867 (2017).

  121. 121.

    Vandersickel, N., de Boer, T. P., Vos, M. A. & Panfilov, A. V. Perpetuation of torsade de pointes in heterogeneous hearts: competing foci or re-entry? J. Physiol. 594, 6865–6878 (2016).

  122. 122.

    Sadrieh, A. et al. Multiscale cardiac modelling reveals the origins of notched T waves in long QT syndrome type 2. Nat. Commun. 5, 5069 (2014).

  123. 123.

    Potse, M. et al. Similarities and differences between electrocardiogram signs of left bundle-branch block and left-ventricular uncoupling. Europace 14, v33–v39 (2012). Suppl. 5.

  124. 124.

    Keller, D. U., Weiss, D. L., Dossel, O. & Seemann, G. Influence of I(Ks) heterogeneities on the genesis of the T-wave: a computational evaluation. IEEE Trans. Biomed. Eng. 59, 311–322 (2012).

  125. 125.

    Chen, X., Hu, Y., Fetics, B. J., Berger, R. D. & Trayanova, N. A. Unstable QT interval dynamics precedes ventricular tachycardia onset in patients with acute myocardial infarction: a novel approach to detect instability in QT interval dynamics from clinical ECG. Circ. Arrhythm. Electrophysiol. 4, 858–866 (2011).

  126. 126.

    Nguyen, U. C. et al. An in-silico analysis of the effect of heart position and orientation on the ECG morphology and vectorcardiogram parameters in patients with heart failure and intraventricular conduction defects. J. Electrocardiol. 48, 617–625 (2015).

  127. 127.

    Bacharova, L. et al. The effect of reduced intercellular coupling on electrocardiographic signs of left ventricular hypertrophy. J. Electrocardiol. 44, 571–576 (2011).

  128. 128.

    Zhu, X., Wei, D. & Okazaki, O. Computer simulation of clinical electrophysiological study. Pacing Clin. Electrophysiol. 35, 718–729 (2012).

  129. 129.

    Ashikaga, H. et al. Feasibility of image-based simulation to estimate ablation target in human ventricular arrhythmia. Heart Rhythm 10, 1109–1116 (2013).

  130. 130.

    Rantner, L. J., Vadakkumpadan, F., Spevak, P. J., Crosson, J. E. & Trayanova, N. A. Placement of implantable cardioverter-defibrillators in paediatric and congenital heart defect patients: a pipeline for model generation and simulation prediction of optimal configurations. J. Physiol. 591, 4321–4334 (2013).

  131. 131.

    Heijman, J., Erfanian Abdoust, P., Voigt, N., Nattel, S. & Dobrev, D. Computational models of atrial cellular electrophysiology and calcium handling, and their role in atrial fibrillation. J. Physiol. 594, 537–553 (2016).

  132. 132.

    Krummen, D. E. et al. Mechanisms of human atrial fibrillation initiation: clinical and computational studies of repolarization restitution and activation latency. Circ. Arrhythm. Electrophysiol. 5, 1149–1159 (2012).

  133. 133.

    Zhao, J., Trew, M. L., Legrice, I. J., Smaill, B. H. & Pullan, A. J. A tissue-specific model of reentry in the right atrial appendage. J. Cardiovasc. Electrophysiol. 20, 675–684 (2009).

  134. 134.

    Aslanidi, O. V., Boyett, M. R., Dobrzynski, H., Li, J. & Zhang, H. Mechanisms of transition from normal to reentrant electrical activity in a model of rabbit atrial tissue: interaction of tissue heterogeneity and anisotropy. Biophys. J. 96, 798–817 (2009).

  135. 135.

    Wu, T. J. et al. Role of pectinate muscle bundles in the generation and maintenance of intra-atrial reentry: potential implications for the mechanism of conversion between atrial fibrillation and atrial flutter. Circ. Res. 83, 448–462 (1998).

  136. 136.

    Gong, Y. et al. Mechanism underlying initiation of paroxysmal atrial flutter/atrial fibrillation by ectopic foci: a simulation study. Circulation 115, 2094–2102 (2007).

  137. 137.

    Cherry, E. M., Ehrlich, J. R., Nattel, S. & Fenton, F. H. Pulmonary vein reentry — properties and size matter: insights from a computational analysis. Heart Rhythm 4, 1553–1562 (2007).

  138. 138.

    Chang, K. C., Bayer, J. D. & Trayanova, N. A. Disrupted calcium release as a mechanism for atrial alternans associated with human atrial fibrillation. PLoS Comput. Biol. 10, e1004011 (2014).

  139. 139.

    Hwang, M. et al. Ganglionated plexi stimulation induces pulmonary vein triggers and promotes atrial arrhythmogenecity: In silico modeling study. PLoS ONE 12, e0172931 (2017).

  140. 140.

    Gharaviri, A. et al. How disruption of endo-epicardial electrical connections enhances endo-epicardial conduction during atrial fibrillation. Europace 19, 308–318 (2017).

  141. 141.

    Roney, C. H. et al. Modelling methodology of atrial fibrosis affects rotor dynamics and electrograms. Europace 18, iv146–iv155 (2016).

  142. 142.

    Vigmond, E., Pashaei, A., Amraoui, S., Cochet, H. & Hassaguerre, M. Percolation as a mechanism to explain atrial fractionated electrograms and reentry in a fibrosis model based on imaging data. Heart Rhythm 13, 1536–1543 (2016).

  143. 143.

    Roney, C. H. et al. Spatial resolution requirements for accurate identification of drivers of atrial fibrillation. Circ. Arrhythm. Electrophysiol. 10, e004899 (2017).

  144. 144.

    Uldry, L., Virag, N., Jacquemet, V., Vesin, J. M. & Kappenberger, L. Optimizing local capture of atrial fibrillation by rapid pacing: study of the influence of tissue dynamics. Ann. Biomed. Eng. 38, 3664–3673 (2010).

  145. 145.

    Uldry, L., Virag, N., Lindemans, F., Vesin, J. M. & Kappenberger, L. Atrial septal pacing for the termination of atrial fibrillation: study in a biophysical model of human atria. Europace 14, 112–120 (2012).

  146. 146.

    Ruchat, P. et al. A biophysical model of atrial fibrillation to define the appropriate ablation pattern in modified maze. Eur. J. Cardiothorac. Surg. 31, 65–69 (2007).

  147. 147.

    Li, C. et al. The spatiotemporal stability of dominant frequency sites in in-silico modeling of 3-dimensional left atrial mapping of atrial fibrillation. PLoS ONE 11, e0160017 (2016).

  148. 148.

    Zahid, S. et al. Patient-derived models link re-entrant driver localization in atrial fibrillation to fibrosis spatial pattern. Cardiovasc. Res. 110, 443–454 (2016).

  149. 149.

    Zahid, S. et al. Feasibility of using patient-specific models and the “minimum cut” algorithm to predict optimal ablation targets for left atrial flutter. Heart Rhythm 13, 1687–1698 (2016).

  150. 150.

    McDowell, K. S. et al. Virtual electrophysiological study of atrial fibrillation in fibrotic remodeling. PLoS ONE 10, e0117110 (2015).

  151. 151.

    Dhamala, J. et al. Quantifying the uncertainty in model parameters using Gaussian process-based Markov chain Monte Carlo in cardiac electrophysiology. Med. Image Anal. 48, 43–57 (2018).

  152. 152.

    Konukoglu, E. et al. Efficient probabilistic model personalization integrating uncertainty on data and parameters: Application to eikonal-diffusion models in cardiac electrophysiology. Prog. Biophys. Mol. Biol. 107, 134–146 (2011).

  153. 153.

    Wallman, M., Smith, N. P. & Rodriguez, B. Computational methods to reduce uncertainty in the estimation of cardiac conduction properties from electroanatomical recordings. Med. Image Anal. 18, 228–240 (2014).

  154. 154.

    Pathmanathan, P., Shotwell, M. S., Gavaghan, D. J., Cordeiro, J. M. & Gray, R. A. Uncertainty quantification of fast sodium current steady-state inactivation for multi-scale models of cardiac electrophysiology. Prog. Biophys, Mol. Biol. 117, 4–18 (2015).

  155. 155.

    Shotwell, M. S. & Gray, R. A. Estimability analysis and optimal design in dynamic multi-scale models of cardiac electrophysiology. J. Agr. Biol. Environ. Stat. 21, 261–276 (2016).

  156. 156.

    Dhamala, J. et al. Spatially adaptive multi-scale optimization for local parameter estimation in cardiac electrophysiology. IEEE Trans. Med. Imag. 36, 1966–1978 (2017).

  157. 157.

    Johnston, B. M., Coveney, S., Chang, E. T. Y., Johnston, P. R. & Clayton, R. H. Quantifying the effect of uncertainty in input parameters in a simplified bidomain model of partial thickness ischaemia. Med. Biol. Eng. Comput. 56, 761–780 (2018).

  158. 158.

    Chang, E. T., Strong, M. & Clayton, R. H. Bayesian Sensitivity Analysis of a cardiac cell model using a gaussian process emulator. PLoS ONE 10, e0130252 (2015).

  159. 159.

    Mullens, W. et al. Insights from a cardiac resynchronization optimization clinic as part of a heart failure disease management program. J. Am. Coll. Cardiol. 53, 765–773 (2009).

  160. 160.

    Auricchio, A. & Prinzen, F. W. Enhancing response in the cardiac resynchronization therapy patient: the 3B perspective — bench, bits, and bedside. JACC Clin. Electrophysiol. 3, 1203–1219 (2017).

  161. 161.

    Auricchio, A., Lumens, J. & Prinzen, F. W. Does cardiac resynchronization therapy benefit patients with right bundle branch block: cardiac resynchronization therapy has a role in patients with right bundle branch block. Circ. Arrhythm. Electrophysiol. 7, 532–542 (2014).

  162. 162.

    Kerckhoffs, R. C. et al. Cardiac resynchronization: insight from experimental and computational models. Prog. Biophys. Mol. Biol. 97, 543–561 (2008).

  163. 163.

    Leenders, G. E. et al. Septal deformation patterns delineate mechanical dyssynchrony and regional differences in contractility: analysis of patient data using a computer model. Circ. Heart Fail. 5, 87–96 (2012).

  164. 164.

    Lumens, J. et al. Differentiating electromechanical from non-electrical substrates of mechanical discoordination to identify responders to cardiac resynchronization therapy. Circ. Cardiovasc. Imag. 8, e003744 (2015).

  165. 165.

    Bishop, M. et al. Three-dimensional atrial wall thickness maps to inform catheter ablation procedures for atrial fibrillation. Europace 18, 376–383 (2016).

  166. 166.

    Tracy, C. M. et al. 2012 ACCF/AHA/HRS focused update of the 2008 guidelines for device-based therapy of cardiac rhythm abnormalities: a report of the American College of Cardiology Foundation/American Heart Association Task Force on Practice Guidelines and the Heart Rhythm Society. [corrected]. Circulation 126, 1784–1800 (2012).

  167. 167.

    Jones, S. et al. Cardiac resynchronization therapy: mechanisms of action and scope for further improvement in cardiac function. Europace 19, 1178–1186 (2017).

  168. 168.

    Huntjens, P. R. et al. Influence of left ventricular lead position relative to scar location on response to cardiac resynchronization therapy: a model study. Europace 16 (Suppl. 4), iv62–iv68 (2014).

  169. 169.

    Kerckhoffs, R. C., McCulloch, A. D., Omens, J. H. & Mulligan, L. J. Effects of biventricular pacing and scar size in a computational model of the failing heart with left bundle branch block. Med. Image Anal. 13, 362–369 (2009).

  170. 170.

    ter Keurs, H. E., Rijnsburger, W. H., van Heuningen, R. & Nagelsmit, M. J. Tension development and sarcomere length in rat cardiac trabeculae. Evidence of length-dependent activation. . Circ. Res. 46, 703–714 (1980).

  171. 171.

    Niederer, S. A. et al. Length-dependent tension in the failing heart and the efficacy of cardiac resynchronization therapy. Cardiovasc. Res. 89, 336–343 (2011).

  172. 172.

    Lumens, J. et al. Comparative electromechanical and hemodynamic effects of left ventricular and biventricular pacing in dyssynchronous heart failure: electrical resynchronization versus left-right ventricular interaction. J. Am. Coll. Cardiol. 62, 2395–2403 (2013).

  173. 173.

    van Everdingen, W. M. et al. Echocardiographic prediction of cardiac resynchronization therapy response requires analysis of both mechanical dyssynchrony and right ventricular function: a combined analysis of patient data and computer simulations. J. Am. Soc. Echocardiogr. 30, 1012–1020 (2017).

  174. 174.

    Constantino, J., Hu, Y. & Trayanova, N. A. A computational approach to understanding the cardiac electromechanical activation sequence in the normal and failing heart, with translation to the clinical practice of CRT. Prog. Biophys. Mol. Biol. 110, 372–379 (2012).

  175. 175.

    Crozier, A. et al. The relative role of patient physiology and device optimisation in cardiac resynchronisation therapy: a computational modelling study. J. Mol. Cell Cardiol. 96, 93–100 (2016).

  176. 176.

    Lee, A. W. et al. Biophysical modeling to determine the optimization of left ventricular pacing site and AV/VV delays in the acute and chronic phase of cardiac resynchronization therapy. J. Cardiovasc. Electrophysiol. 28, 208–215 (2017).

  177. 177.

    Okada, J. I. et al. Multi-scale, tailor-made heart simulation can predict the effect of cardiac resynchronization therapy. J. Mol. Cell Cardiol. 108, 17–23 (2017).

  178. 178.

    Pluijmert, M. et al. New insights from a computational model on the relation between pacing site and CRT response. Europace 18, iv94–iv103 (2016).

  179. 179.

    Niederer, S. A. et al. Biophysical modeling to simulate the response to multisite left ventricular stimulation using a quadripolar pacing lead. Pacing Clin. Electrophysiol. 35, 204–214 (2012).

  180. 180.

    Hyde, E. R. et al. Beneficial effect on cardiac resynchronization from left ventricular endocardial pacing is mediated by early access to high conduction velocity tissue: electrophysiological simulation study. Circ. Arrhythm. Electrophysiol. 8, 1164–1172 (2015).

  181. 181.

    Hu, Y., Gurev, V., Constantino, J. & Trayanova, N. Efficient preloading of the ventricles by a properly timed atrial contraction underlies stroke work improvement in the acute response to cardiac resynchronization therapy. Heart Rhythm 10, 1800–1806 (2013).

  182. 182.

    Reumann, M. et al. Computer model for the optimization of AV and VV delay in cardiac resynchronization therapy. Med. Biol. Eng. Comput. 45, 845–854 (2007).

  183. 183.

    Hu, Y., Gurev, V., Constantino, J. & Trayanova, N. Optimizing cardiac resynchronization therapy to minimize ATP consumption heterogeneity throughout the left ventricle: a simulation analysis using a canine heart failure model. Heart Rhythm 11, 1063–1069 (2014).

  184. 184.

    Sermesant, M. et al. Patient-specific electromechanical models of the heart for the prediction of pacing acute effects in CRT: a preliminary clinical validation. Med. Image Anal. 16, 201–215 (2012).

  185. 185.

    Kayvanpour, E. et al. Towards personalized cardiology: multi-scale modeling of the failing heart. PLoS ONE 10, e0134869 (2015).

  186. 186.

    Krishnamurthy, A. et al. Patient-specific models of cardiac biomechanics. J. Comput. Phys. 244, 4–21 (2013).

  187. 187.

    Huntjens, P. R. et al. Electrical substrates driving response to cardiac resynchronization therapy: a combined clinical-computational evaluation. Circ. Arrhythm. Electrophysiol. 11, e005647 (2018).

  188. 188.

    Augustin, C. M. et al. Anatomically accurate high resolution modeling of human whole heart electromechanics: a strongly scalable algebraic multigrid solver method for nonlinear deformation. J. Comput. Phys. 305, 622–646 (2016).

  189. 189.

    Viceconti, M., Henney, A. & Morley-Fletcher, E. In silico clinical trials: how computer simulation will transform the biomedical industry. Int. J. Clin. Trials 3, 37–46 (2016).

  190. 190.

    Prinzen, F. W. et al. Innovation in cardiovascular disease in Europe with focus on arrhythmias: current status, opportunities, roadblocks, and the role of multiple stakeholders. Europace 20, 733–738 (2017).

  191. 191.

    Niederer, S. A., Fink, M., Noble, D. & Smith, N. P. A meta-analysis of cardiac electrophysiology computational models. Exp. Physiol. 94, 486–495 (2009).

  192. 192.

    Holmes, J. W. & Lumens, J. Clinical applications of patient-specific models: the case for a simple approach. J. Cardiovasc. Transl Res. 11, 71–79 (2018).

  193. 193.

    Richter, Y., Lind, P. G. & Maass, P. Modeling specific action potentials in the human atria based on a minimal single-cell model. PLoS ONE 13, e0190448 (2018).

  194. 194.

    Bueno-Orovio, A., Cherry, E. M. & Fenton, F. H. Minimal model for human ventricular action potentials in tissue. J. Theor. Biol. 253, 544–560 (2008).

  195. 195.

    Corrado, C. & Niederer, S. A. A two-variable model robust to pacemaker behaviour for the dynamics of the cardiac action potential. Math. Biosci. 281, 46–54 (2016).

  196. 196.

    Neic, A. et al. Efficient computation of electrograms and ECGs in human whole heart simulations using a reaction-eikonal model. J. Comput. Phys. 346, 191–211 (2017).

  197. 197.

    Gurev, V. et al. A high-resolution computational model of the deforming human heart. Biomech. Model. Mechanobiol. 14, 829–849 (2015).

  198. 198.

    Niederer, S., Mitchell, L., Smith, N. & Plank, G. Simulating human cardiac electrophysiology on clinical time-scales. Frontiers Physiol. 2, 14 (2011).

  199. 199.

    Niederer, S. A. et al. Verification of cardiac tissue electrophysiology simulators using an N-version benchmark. Phil. Trans. A Math. Phys. Eng. Sci. 369, 4331–4351 (2011).

  200. 200.

    Land, S. et al. Verification of cardiac mechanics software: benchmark problems and solutions for testing active and passive material behaviour. Proc. Math. Phys. Eng. Sci. 471, 20150641 (2015).

  201. 201.

    Smith, L. P. et al. SBML Level 3 package: hierarchical model composition, version 1 release 3. J. Integr. Bioinform. 12, 603–659 (2015).

  202. 202.

    Cuellar, A. et al. The CellML 1.1 specification. J. Integr. Bioinform. 12, 259 (2015).

  203. 203.

    Kerckhoffs, R. C., Omens, J. H. & McCulloch, A. D. Mechanical discoordination increases continuously after the onset of left bundle branch block despite constant electrical dyssynchrony in a computational model of cardiac electromechanics and growth. Europace 14 (Suppl. 5), v65–v72 (2012).

  204. 204.

    Nolden, M. et al. The medical imaging interaction toolkit: challenges and advances: 10 years of open-source development. Int. J. Comput. Assist. Radiol. Surg. 8, 607–620 (2013).

  205. 205.

    Ayachit, U. The Paraview Guide: A Parallel Visualization Application (Kitware Inc, 2015).

  206. 206.

    Rhode, K. S. et al. A system for real-time XMR guided cardiovascular intervention. IEEE Trans. Med. Imag. 24, 1428–1440 (2005).

  207. 207.

    Razavi, R. et al. Cardiac catheterisation guided by MRI in children and adults with congenital heart disease. Lancet 362, 1877–1882 (2003).

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S.A.N. acknowledges support from the UK Engineering and Physical Sciences Research Council (EP/M012492/1, NS/A000049/1 and EP/P01268X/1), the British Heart Foundation (PG/15/91/31812 and PG/13/37/30280) and King’s Health Partners London National Institute for Health Research (NIHR) Biomedical Research Centre. J.L. acknowledges support from the Dr. Dekker Program of the Dutch Heart Foundation (grant 2015T082) and the Netherlands Organisation for Scientific Research (NWO-ZonMw, VIDI grant 016.176.340). N.A.T. acknowledges support from Leducq Foundation and from the NIH (grants DP1-HL123271 and R01HL116280). M. Strocchi (King’s College London, UK) provided assistance with creating the four-chamber heart images in figure 3.

Reviewer information

Nature Reviews Cardiology thanks B. Rodriguez and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Author information


  1. Department of Biomedical Engineering, School of Biomedical Engineering and Imaging Sciences, King’s College London, London, UK

    • Steven A. Niederer
  2. Department of Biomedical Engineering, Cardiovascular Research Institute Maastricht (CARIM), Maastricht University Medical Center, Maastricht, Netherlands

    • Joost Lumens
  3. IHU LIRYC, Electrophysiology and Heart Modeling Institute, Fondation Bordeaux Université, Pessac, France

    • Joost Lumens
  4. Department of Biomedical Engineering and the Institute for Computational Medicine, Johns Hopkins University, Baltimore, MD, USA

    • Natalia A. Trayanova


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All the authors researched data for the article, contributed substantially to the discussion of the content, and wrote, reviewed and edited the manuscript before submission.

Competing interests

S.A.N. has received support from Abbott, Boston Scientific, Edwards Lifesciences, Pfizer, Roche and Siemens. J.L. has received support from Medtronic. N.A.T. declares no competing interests.

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Correspondence to Steven A. Niederer.

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