Methods Inf Med 1994; 33(01): 116-119
DOI: 10.1055/s-0038-1634966
Original Article
Schattauer GmbH

Bonhoeffer-van der Pol Oscillator Model of the Sino-Atrial Node: A Possible Mechanism of Heart Rate Regulation

S. Sato
1   Department of Biophysical Engineering, Faculty of Engineering Science Osaka University, Japan
,
S. Doi
1   Department of Biophysical Engineering, Faculty of Engineering Science Osaka University, Japan
,
T. Nomura
1   Department of Biophysical Engineering, Faculty of Engineering Science Osaka University, Japan
› Author Affiliations
Further Information

Publication History

Publication Date:
08 February 2018 (online)

Abstract:

A Bonhoeffer-van der Pol equation with a stable limit cycle is proposed as a model of the pacemaker in the sino-atrial node to exptain heart rate regulation. Standard tools, such as the phase transition curve in nonlinear dynamic system theory, are used to analyze the model and results are compared with other studies on experiments with dogs.

 
  • REFERENCES

  • 1 Dong E, Reite BA. Effect of timing of vagal stimulation on heart rate in the dog. Circ Res 1970; 27: 635-46.
  • 2 DiFrancesco D, Noble D. A model of cardiac electrical activity incorporating ionic pumps and concentration changes. Phil Trans R Soc Loud 1985; B307: 353-98.
  • 3 FitzHugh R. Impulses and physiological states in theoretical models of nerve membrane. Biophys J 1961; 01: 445-66.
  • 4 Bonhoeffer KF. Activation of passive iron as a model for the excitation of nerve. J Gen Physiol 1948; 32: 69-91.
  • 5 Sato S, Doi S. Response characteristics of the 8VP neuron model to periodic pulse inputs. Math Biosci 1992; 112: 243-59.
  • 6 Kawato M. Transient and steady state phase response curve of limit cycle oscillators. J Math Biol 1981; 12: 13-30.
  • 7 Wmfree AT. Biological rhythms and the behavior of population of coupled oscillator. J Theor Biol 1967; 16: 15-2.
  • 8 Nomura T, Sato S, Doi S. et al. A Bonhoeffer-van der Pol model of locked and non-locked behaviors of living pacemaker neurons. Biol Cybern 1993; 69: 429-37.