Free Access
Math. Model. Nat. Phenom.
Volume 12, Number 5, 2017
Mathematical models in physiology
Page(s) 208 - 239
Published online 13 October 2017
  1. S. Abboud, O. Berenfeld, D. Sadeh. Simulation of high-resolution qrs complex using a ventricular model with a fractal conduction system. effects of ischemia on high-frequency qrs potentials. Circulation research, 68 (1991), pp. 1751–1760. [CrossRef] [PubMed]
  2. R. R. Aliev, A. V. Panfilov. A simple two-variable model of cardiac excitation. Chaos, Solitons & Fractals, 7 (1996), pp. 293–301. [CrossRef]
  3. A. Azzouzi, Y. Coudière, R. Turpault, N. Zemzemi. A mathematical model of the purkinje-muscle junctions. Mathematical biosciences and engineering: MBE, 8 (2011), pp. 915–930. [CrossRef] [MathSciNet]
  4. G. W. Beeler, H. Reuter. Reconstruction of the action potential of ventricular myocardial fibres. The Journal of physiology, 268 (1977), p. 177. [CrossRef] [PubMed]
  5. 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 (1998), pp. 1063–1077. [CrossRef] [PubMed]
  6. R. M. Bordas, K. Gillow, D. Gavaghan, B. Rodriguez, D. Kay. A bidomain model of the ventricular specialized conduction system of the heart. SIAM Journal on Applied Mathematics, 72 (2012), pp. 1618–1643. [CrossRef] [MathSciNet]
  7. M. Cerrone, S.F. Noujaim, E.G. Tolkacheva, A. Talkachou, R.O. Connell, O. Berenfeld, J. Anumonwo, S.V. Pandit, K. Vikstrom, C. Napolitano, S. G. Priori, J. Jalife, Arrhythmogenic mechanisms in a mouse model of catecholaminergic polymorphic ventricular tachycardia, Circulation research, 101 (2007), pp. 1039–1048. [CrossRef] [PubMed]
  8. Y. Coudière, C. Pierre. Stability and convergence of a finite volume method for two systems of reaction-diffusion equations in electro-cardiology. Nonlinear analysis: real world applications, 7 (2006), pp. 916–935. [CrossRef] [MathSciNet]
  9. C. Dángelo, A. Quarteroni. On the coupling of 1d and 3d diffusion-reaction equations: Application to tissue perfusion problems. Mathematical Models and Methods in Applied Sciences, 18 (2008), pp. 1481–1504. [CrossRef] [MathSciNet]
  10. D. DiFrancesco, D. Noble. Amodel of cardiac electrical activity in corporating ionic pumps and concentration changes. Philosophical Transactions of the Royal Society of London B: Biological Sciences, 307 (1985), pp. 353–398. [CrossRef]
  11. M. Ethier, Y. Bourgault. Semi-implicit time-discretization schemes for the bidomain model. SIAM Journal on Numerical Analysis, 46 (2008), pp. 2443–2468. [CrossRef] [MathSciNet]
  12. C. Fantoni, M. Kawabata, R. Massaro, F. Regoli, S. Raffa, V. Arora, J. A. Salverino-Uriarte, H. U. Klein, A. Auricchio. Right and left ventricular activation sequence in patients with heart failure and right bundle branch block: a detailed analysis using three-dimensional non-fluoroscopic electroanatomic mapping system. Journal of cardiovascular electrophysiology, 16 (2005), pp. 112–119. [CrossRef] [PubMed]
  13. M. A. Fernández, N. Zemzemi. Decoupled time-marching schemes in computational cardiac electrophysiology and ecg numerical simulation. Mathematical biosciences, 226 (2010), pp. 58–75. [CrossRef] [MathSciNet] [PubMed]
  14. R. FitzHugh. Impulses and physiological states in theoretical models of nerve membrane. Biophysical journal, 1 (1961), p. 445. [CrossRef] [PubMed]
  15. M. Haissaguerre, E. Vigmond, B. Stuyvers, M. Hocini, O. Bernus. Ventricular arrhythmias and the his-purkinje system. Nature Reviews Cardiology, (2016).
  16. M. Hanslien, K. H. Karlsen, A. Tveito. On a finite difference scheme for a beeler-reuter based model of cardiac electrical activity International Journal of Numerical Analysis and Modelling, 3 (2006), pp. 395–412.
  17. J. G. Heywood, R. Rannacher. Finite-element approximation of the nonstationary navier-stokes problem. part IV: Error analysis for second-order time discretization. SIAM Journal on Numerical Analysis, 27 (1990), pp. 353–384. [CrossRef] [MathSciNet]
  18. R. Imanishi, S. Seto, S. Ichimaru, E. Nakashima, K. Yano, M. Akahoshi. Prognostic significance of incident complete left bundle branch block observed over a 40-year period. The American journal of cardiology, 98 (2006), pp. 644–648. 62 [CrossRef] [PubMed]
  19. K. Kunisch, A. Marica. Well-posedness for the mitchell-schaeffer model of the cardiac membrane SFB-Report No, 18 (2013), p. 2013.
  20. G. Lopera, W. G. Stevenson, K. Soejima, W. H. Maisel, B. Koplan, J. L. Sapp, S. D. Satti, L. M. Epstein. Identification and ablation of three types of ventricular tachycardia involving the his-purkinje system in patients with heart disease. Journal of cardiovascular electrophysiology, 15 (2004), pp. 52–58. [CrossRef] [PubMed]
  21. M. Lorange, R. M. Gulrajani. A computer heart model incorporating anisotropic propagation: I. model construction and simulation of normal activation. Journal of electrocardiology, 26 (1993), pp. 245–261. [CrossRef] [PubMed]
  22. C-H. Luo, Y. Rudy. A model of the ventricular cardiac action potential. depolarization, repolarization, and their interaction. Circulation research, 68 (1991), pp. 1501–1526. [CrossRef] [PubMed]
  23. C-H. Luo, Y. Rudy. A dynamic model of the cardiac ventricular action potential. I. simulations of ionic currents and concentration changes. Circulation research, 74 (1994), pp. 1071–1096. [CrossRef] [PubMed]
  24. M. E. Marsh, S. T. Ziaratgahi, R. J. Spiteri. The secrets to the success of the rush-larsen method and its generalizations. IEEE Transactions on Biomedical Engineering, 59 (2012), pp. 2506–2515. [CrossRef]
  25. C. C. Mitchell, D. G. Schaeffer. A two-current model for the dynamics of cardiac membrane. Bulletin of mathematical biology, 65 (2003), pp. 767–793. [CrossRef] [PubMed]
  26. J. Nagumo, S. Arimoto, S. Yoshizawa. An active pulse transmission line simulating nerve axon. Proceedings of the IRE, 50 (1962), pp. 2061–2070. [CrossRef]
  27. H.-X. Niu, W. Hua, S. Zhang, X. Sun, F. -Z. Wang, K.-P. Chen, H. Wang, X. Chen. Assessment of cardiac function and synchronicity in subjects with isolated bundle branch block using doppler imaging. Chinese medical journal, 119 (2006), pp. 795–800. [PubMed]
  28. D. Noble. A modification of the hodgkin-huxley equations applicable to purkinje fibre action and pacemaker potentials. The Journal of Physiology, 160 (1962), p. 317. [CrossRef] [PubMed]
  29. D. Notaro, L. Cattaneo, L. Formaggia, A. Scotti, P. Zunino A Mixed Finite Element Method for Modeling the Fluid Exchange Between Microcirculation and Tissue Interstitium. Advances in Discretization Methods. Springer International Publishing, 2016. 3–25. [CrossRef]
  30. M. Perego, A. Veneziani. An efficient generalization of the rush-larsen method for solving electro-physiology membrane equations. Electronic Transactions on Numerical Analysis, 35 (2009), pp. 234–256. [MathSciNet]
  31. J.M. Rogers, A.D. McCulloch. A collocation-galerkin finite element model of cardiac action potential propagation. IEEE Transactions on Biomedical Engineering, 41 (1994), pp. 743–757. [CrossRef] [PubMed]
  32. K. Simelius, J. Nenonen, M. Horacek. Modeling cardiac ventricular activation. International Journal of Bioelectromagnetism, 3 (2001), pp. 51–58.
  33. J. Smoller, Shock waves and reaction-diffusion equations. vol. 258, Springer Science & Business Media, 2012
  34. K. Ten Tusscher, D. Noble, P.-J. Noble, A. V. Panfilov. A model for human ventricular tissue. American Journal of Physiology Heart and Circulatory Physiology, 286 (2004), pp. H1573–H1589.
  35. K. Ten Tusscher, A. V. Panfilov. Modelling of the ventricular conduction system. Progress in biophysics and molecular biology, 96 (2008), pp. 152–170. [CrossRef] [EDP Sciences] [PubMed]
  36. V. Thomeé. Galerkin finite element methods for parabolic problems. Second edition, Springer Series in Computational Mmathematics, 25 (2006).
  37. E. J. Vigmond, C. Clements. Construction of a computer model to investigate sawtooth effects in the purkinje system. Biomedical Engineering, IEEE Transactions on, 54 (2007), pp. 389–399. [CrossRef]
  38. L. Wolff, J. Parkinson, P. White. Bundle-branch block with short p-r interval in healthy young people prone to paroxysmal tachycardia. Annals of noninvasive electrocardiology, 11 (2006), pp. 340–353. [CrossRef]

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