Stochastic model for heart-rate fluctuations.
A normal human heart rate shows complex fluctuations in time, which is natural, because the heart rate is controlled by a large number of different feedback control loops. These unpredictable fluctuations have been shown to display fractal dynamics, long-term correlations, and 1/f noise. These characterizations are statistical and they have been widely studied and used, but much less is known about the detailed time evolution (dynamics) of the heart-rate control mechanism. Here we show that a simple one-dimensional Langevin-type stochastic difference equation can accurately model the heart-rate fluctuations in a time scale from minutes to hours. The model consists of a deterministic nonlinear part and a stochastic part typical to Gaussian noise, and both parts can be directly determined from the measured heart-rate data. Studies of 27 healthy subjects reveal that in most cases, the deterministic part has a form typically seen in bistable systems: there are two stable fixed points and one unstable one.
Kuusela
Tom
T
Department of Physics, University of Turku, Finland. tom.kuusela@utu.fi
Shepherd
Tony
T
Hietarinta
Jarmo
J
D002319:Cardiovascular System; D003198:Computer Simulation; D017709:Fractals; D006339:Heart Rate; D006801:Humans; D008954:Models, Biological; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D016011:Normal Distribution; D012815:Signal Processing, Computer-Assisted; D013269:Stochastic Processes; D013997:Time Factors