Electro-mechanical coupling in a one-dimensional model of heart muscle fiber

Russian Journal of Numerical Analysis and Mathematical Modelling

Volumn 29, Issue 5, 2014, Pages 275-284

  Katsnelson, Leonid B ^a   Vikulova, Natalia A ^a   Kursanov, Alexander G ^a,b   Solovyova, Olga E ^a,b   Markhasin, Vladimir S ^a,b  

^a INSTITUTE OF IMMUNOLOGY AND PHYSIOLOGY   (Russian Federation)

^b URAL FEDERAL UNIVERSITY   (Russian Federation)

Author keywords

Cardiac mechano electric feedback; heterogeneous myocardium; mathematical modelling

Indexed keywords

COUPLINGS; MATHEMATICAL MODELS;

BILATERAL RELATIONS; CONTINUOUS MEDIUM; ELECTRICAL EXCITATION; GENERIC MODELING; HETEROGENEOUS MYOCARDIUM; MECHANO-ELECTRIC FEEDBACK; MUSCLE CONTRACTIONS; ONE-DIMENSIONAL MODEL;

MUSCLE;

EID: 84908116405     PISSN: 09276467     EISSN: 15693988     Source Type: Journal    
DOI: 10.1515/rnam-2014-0022     Document Type: Article

References (16)

1. R. H. Clayton, O. Bernus, E. M. Cherry, H. Dierckx, F. H. Fenton, L. Mirabella, A. V. Panfilov, F. B. Sachse, G. Seemann, and H. Zhang, Models of cardiac tissue electrophysiology: progress, challenges and open questions. Prog. Biophys. Mol. Biol. 104 (2011), No. 1-3, 22-48.
2. G. Iribe, C. W. Ward, P. Camelliti, C. Bollensdorfi, F. Mason, R. A. Burton, A. Garny, M. K. Morphew, A. Hoenger, W. J. Lederer, and P. Kohl, Axial stretch of rat single ventricular cardiomyocytes causes an acute and transient increase in Ca2+ spark rate. Circ. Res. 104 (2009), 787-795.
3. V. Izakov, L. B. Katsnelson, F. A. Blyakhman, V. S. Markhasin,and T. F. Shklyar, Cooperative effects due to calcium binding by troponin and their consequences for contraction and relaxation of cardiac muscle under various conditions of mechanical loading. Circ. Res. 69 (1991), No. 5, 1171-1184.
4. T. Jahnke and C. Lubich, Error bounds for exponential operator splittings. BIT Numer. Math. 40 (2000), No. 4, 735-744.
5. L. B. Katsnelson, T. Sulman, O. Solovyova, and V. S. Markhasin, Role of myocardial viscoelasticity in disturbances of electrical and mechanical activity in calcium overloaded cardiomyocytes: mathematical modelling. J. Theor. Biol. 272 (2011), No. 1, 83-95.
6. L. B. Katsnelson, T. B. Sulman, O. E. Solovyova, and V. S. Markhasin, Cooperative mechanisms of thin filament activation and their contribution to the myocardial contractile function. Assessment in a mathematical model. Biophys. 54 (2009), No. 1, 39-46.
7. J. P. Keener and J. Sneyd, Mathematical Physiology: I: Cellular Physiology. Springer, 2008.
8. R. C. P. Kerckhofis, S. N. Healy, T. P. Usyk, and A. D. McCulloch, Computational methods for cardiac electromechanics. Proceedings of the IEEE 94 (2006), No. 4, 769-782.
9. P. Kohl, C. Bollensdorfi, and A. Garny, Effects of mechanosensitive ion channels on ventricular electrophysiology: experimental and theoretical models. Exp. Physiol. 91 (2006), 307-321.
10. P. Kohl, F. Sachs, and M. R. Franz, Cardiac mechano-electric coupling and arrhythmias. OUP Oxford, 2011.
11. V. S. Markhasin, A. A. Balakin, L. B. Katsnelson, P. Konovalov, O. N. Lookin, Y. Protsenko, and O. Solovyova, Slow force response and auto-regulation of contractility in heterogeneous myocardium. Prog. Biophys. Mol. Biol. 110 (2012), No. 2-3, 305-318.
12. D. Noble, A. Varghese, P. Kohl, and P. Noble, Improved guinea-pig ventricular cell model incorporating a diadic space, IKr and IKs, and length- and tension-dependent processes. Can. J. Cardiol. 14 (1998), No. 1, 123-134.
13. R. M. Shaw and Y. Rudy, Ionic mechanisms of propagation in cardiac tissue. Roles of the sodium and L-type calcium currents during reduced excitability and decreased gap junction coupling. Circ. Res. 81 (1997), No. 5, 727-741.
14. O. Solovyova, L. B. Katsnelson, P. Konovalov, O. Lookin, A. S. Moskvin, Y. L. Protsenko, N. Vikulova, P. Kohl, and V. S. Markhasin, Activation sequence as a key factor in spatio-temporal optimization of myocardial function. Philos. Transact. A Math. Phys. Eng. Sci. 364 (2006), No. 1843, 1367-1383.
15. O. Solovyova, N. Vikulova, L. B. Katsnelson, V. S. Markhasin, P. J. Noble, A. Garny, P. Kohl, and D. Noble, Mechanical interaction of heterogeneous cardiac muscle segments in silico: effects on Ca2+ handling and action potential. I JBC 13 (2003), No. 12, 3757-3782.
16. N. A. Trayanova, Whole-heart modelling: applications to cardiac electrophysiology and electromechanics. Circ. Res. 108 (2011), No. 1, 113-128.