A method for analyzing the stability of the resting state for a model of pacemaker cells surrounded by stable cells

Mathematical Biosciences and Engineering

Volumn 7, Issue 3, 2010, Pages 505-526

  Artebrant, Robert ^a   Tveito, Aslak ^b   Lines, Glenn T ^b  

^a SIMULA RESEARCH LABORATORY   (Norway)

^b UNIVERSITY OF OSLO   (Norway)

Author keywords

Ectopic waves; Partial differential equations; Stability

Indexed keywords

ACTION POTENTIAL; ARTICLE; BIOLOGICAL MODEL; BIOLOGICAL RHYTHM; HEART CONTRACTION; HEART MUSCLE CELL; HUMAN; MATHEMATICAL COMPUTING; PHYSIOLOGY; STATISTICAL MODEL;

ACTION POTENTIALS; BIOLOGICAL CLOCKS; HUMANS; LINEAR MODELS; MODELS, CARDIOVASCULAR; MYOCARDIAL CONTRACTION; MYOCYTES, CARDIAC; NUMERICAL ANALYSIS, COMPUTER-ASSISTED;

EID: 77954591691     PISSN: 15471063     EISSN: 15510018     Source Type: Journal    
DOI: 10.3934/mbe.2010.7.505     Document Type: Article

References (15)

1. R. A. FitzHugh, Impulses and physiological states in theoretical models of nerve membrane, Biophys. J., 1 (1961), 445.
2. V. Jacquemet, Pacemaker activity resulting from the coupling with nonexcitable cells, Phys. Rev. E, 74 (2006), 011908-1-7.
3. J. Keener and J. Sneyd, "Mathematical Physiology I: Cellular Physiology," Springer, New York, 2008.
4. J. Keener and J. Sneyd, "Mathematical Physiology II: Systems Physiology," Springer, New York, 2008.
5. R. Khan, Identifying and understanding the role of pulmonary vein activity in atrial fibrillation, Cardiovasc. Res., 64 (2004), 387-394.
6. R. L. Liboff, "Introductory Quantum Mechanics," Pearson Education, San Fransisco, 2003.
7. S. O. Linge, G. T. Lines, J. Sundnes and A. Tveito, On the frequency of automaticity during ischemia in simulations based on stochastic perturbations of the Luo-Rudy I model, Comput. Biol. Med., 38 (2008), 1218-1227.
8. C. H. Luo and Y. Rudy, A model of the ventricular cardiac action potential: Depolarisation, repolarisation, and their interaction, Circ. Res., 68 (1991), 1501-1526.
9. D. Noble, Modeling the heart, Physiology, 19 (2004), 191-197.
10. A Pumir, A. Arutunyan, V. Krinsky and N. Sarvazyan, Genesis of ectopic waves: Role of coupling, automaticity, and heterogeneity, Biophys. J., 89 (2005), 2332-2349.
11. Y. Rudy and J. R. Silva, Computational biology in the study of cardiac ion channels and cell electrophysiology, Q. Rev. Biophys., 39 (2006), 57-116.
12. A. Tveito and G. T. Lines, A condition for setting off ectopic waves in computational models of excitable cells, Math. Biosci., 213 (2008), 141-150.
13. J. N. Weiss, A. Karma, Y. Shiferaw, P-S. Chen, A. Garfinkel and Z. Qu, From pulsus to pulseless: The saga of cardiac alternans, Circ. Res., 98 (2006), 1244-1253.
14. J. N. Weiss, Z. Qu, P-S. Chen, S-F. Lin, H. S. Karagueuzian, H. Hayashi, A. Garfinkel and A. Karma, The dynamics of cardiac fibrillation, Circulation, 112 (2005), 1232-1240.
15. www.cellml.org