Atrial fibrillation is a common cardiac arrhythmia in which there is an irregular heartbeat. This paper develops a theoretical model for the intervals between successive heartbeats during atrial fibrillation based on the following ideas. There is an irregular pattern of activation of the upper chambers (atria) of the heart. Excitation travels from the atria through the specialized conducting tissue called the atrioventricular node to the lower chamber of the heart (ventricles). We model this situation by a stochastic map. If the map is linear, then it is possible to compute analytically the probability density for the timings between ventricular activations. Numerical simulations of nonlinear maps show correspondences with clinical data. Thus this work casts a clinical medical problem in the context of stochastic maps. \textcopyright{} 1996 The American Physical Society.
[1]
Laurence A. Baxter,et al.
Chaos, Fractals, and Noise: Stochastic Aspects of Dynamics, Second Edition , 1994, by Andrzej Lasota and Michael C. Mackey, Applied Mathematical Sciences, vol. 97 (New York: Springer-Verlag), xiv + 472 pp.
,
1996,
Probability in the Engineering and Informational Sciences.
[2]
Mark E. Josephson,et al.
Clinical cardiac electrophysiology ; techniques and interpretations
,
2001
.
[3]
Philip J. Podrid,et al.
Atrial fibrillation : mechanisms and management
,
1992
.
[4]
P. McClintock,et al.
Noise in nonlinear dynamical systems: Preface
,
1989
.
[5]
L. Glass,et al.
Theory of heart : biomechanics, biophysics, and nonlinear dynamics of cardiac function
,
1991
.