Modeling cardiac pacemakers with relaxation oscillators

Physica A: Statistical Mechanics and its Applications

Volumn 336, Issue 1-2, 2004, Pages 153-162

  Grudziński, Krzysztof ^a   Zebrowski, Jan J ^a  

^a WARSAW UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Action potentials; Modeling; Relaxation oscillator

Indexed keywords

CARDIOVASCULAR SYSTEM; COMPUTER SIMULATION; MATHEMATICAL MODELS; NEUROLOGY; PACEMAKERS; PHYSIOLOGY;

ACTION POTENTIALS; NERVOUS SYSTEMS;

RELAXATION OSCILLATORS;

EID: 17644433215     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2004.01.020     Document Type: Conference Paper

References (15)

1. Bub G., Glass L. Bifurcations in a discontinuous circle map. a theory for a chaotic cardiac arrythmia Int. J. Bifurcations Chaos. 5(2):1995;359-371.
2. Thompson J.M.T., Steward H.B. Nonlinear Dynamics and Chaos. 2nd Edition:2002;Wiley, New York.
3. van der Pol B., van der Mark J. The heartbeat considered as a relaxation oscillation and an electrical model of the heart. Philos. Mag. 6:1928;763-775.
4. FitzHugh R. Impulses and physiological states in theoretical models of nerve membrane. Biophys. J. 1:1961;445-466.
5. Hodgkin A.L., Huxley A.F. A quantitative description of membrane current and its applications to conduction and excitation in nerve. J. Physiol. (London). 117:1952;500-544.
6. Katholi C.R., Urthaler F., Macy J. Jr., James T.N. A mathematical model of automaticity in the sinus node and the AV junction based on weakly coupled relaxation oscillators. Comput. Biomed. Res. 10:1977;529-543.
7. West B.J., Goldberger A.L., Rovner G., Bhargava V. Nonlinear dynamics of the heartbeat, The AV junction: passive conduict or active oscillator? Physica D. 17:1985;198-206.
8. di Bernardo D., Signorini M.G., Cerutti S. A model of two nonlinear coupled oscillators for the study of heartbeat dynamics. Int. J. Bifurcations Chaos. 8(10):1998;1975-1985.
9. L. Glass, P. Hunter, A. McCulloch (Eds.), Theory of Heart, Springer, New York, 1990.
10. P.D. Zipes, J. Jalife (Eds.), Cardiac Electrophysiology: From Cell to Bedside, 3rd Edition, W.B. Saunders, Philadelphia, 2000.
11. Hoffman B.F., CraneField P.F. Electrophysiology of the Heart. 1960;McGraw-Hill, New York.
12. A. Bayés da Luna, Clinical Electrocardiography: a Textbook, 2nd updated Edition, Futura Publishing, New York, 1998.
13. Postnov D., Seung Kee H., Hyungtae K. Synchronization of diffusively coupled oscillators near the homoclinic bifurcation. Phys. Rev. E. 60(3):1999;2799-2807.
14. Morris C., Lecar H. Voltage oscillations in the barnacle giant muscle fiber. Biophys. J. 35(1):1981;193-213.
15. All numerical calculations were done by means of the Dynamics Solver program by Juan M. Aguirregabiria ( http://tc.lc.ehu.es/jma.html ), using the Runge-Kutta method of order 4.