Model of bidirectional interaction between myocardial pacemakers based on the phase response curve

As a basis for the study of sinus rhythm determination, a model is proposed of bidirectionally-coupled oscillators as a system of difference equations based on the phase response curve of sinoatrial pacemaker cells. Solutions corresponding to the one-to-one synchronization of the two pacemakers are obtained, and the relation among those solutions is examined: It is revealed that two different solutions with different cycle length coexist, and the synchronized frequency can be higher or lower than the original intrinsic frequencies of the two pacemaker cells. The experimental results of the cultured cells of cardiac pacemakers are interpreted by the analytical result of the model.

[1]  J. Nagumo,et al.  On a response characteristic of a mathematical neuron model , 1972, Kybernetik.

[2]  Robert L. DeHaan,et al.  Synchronization of pulsation rates in isolated cardiac myocytes , 1972 .

[3]  J Jalife,et al.  Effects of current flow on pacemaker activity of the isolated kitten sinoatrial node. , 1980, The American journal of physiology.

[4]  I. Harary,et al.  In vitro studies on single beating rat heart cells. I. Growth and organization. , 1963, Experimental cell research.

[5]  T Sano,et al.  Mechanism of rhythm determination among pacemaker cells of the mammalian sinus node. , 1978, The American journal of physiology.

[6]  T. Kawahara.  Coupled Van der Pol oscillators — A model of excitatory and inhibitory neural interactions , 1980, Biological Cybernetics.

[7]  D A Linkens.  The stability of entrainment conditions for RLC coupled Van der Pol oscillators used as a model for intestinal electrical rhythms. , 1977, Bulletin of mathematical biology.

[8]  J Jalife,et al.  Effect of Electrotonic Potentials on Pacemaker Activity of Canine Purkinje Fibers in Relation to Parasystole , 1976, Circulation research.

[9]  M. Kawato,et al.  Two coupled neural oscillators as a model of the circadian pacemaker. , 1980, Journal of theoretical biology.

[10]  S. Daan,et al.  Two coupled oscillators: simulations of the circadian pacemaker in mammalian activity rhythms. , 1978, Journal of theoretical biology.

[11]  Harukazu Tsuruta,et al.  Difference equation model of the entrainment of myocardial pacemaker cells based on the phase response curve , 2004, Biological Cybernetics.

[12]  G E Mark,et al.  Pacemaker activity and mitosis in cultures of newborn rat heart ventricle cells. , 1966, Experimental cell research.

[13]  K. Goshima,et al.  Synchronized beating of and electrotonic transmission between myocardial cells mediated by heterotypic strain cells in monolayer culture. , 1969, Experimental cell research.

[14]  I HARARY,et al.  In vitro studies on single beating rat heart cells. II. Intercellular communication. , 1963, Experimental cell research.