Abstract
We study the statistics of return intervals between large heartbeat intervals (above a certain threshold Q) in 24 h records obtained from healthy subjects. We find that both the linear and the nonlinear long-term memory inherent in the heartbeat intervals lead to power-laws in the probability density function PQ(r) of the return intervals. As a consequence, the probability WQ(t; Δt) that at least one large heartbeat interval will occur within the next Δt heartbeat intervals, with an increasing elapsed number of intervals t after the last large heartbeat interval, follows a power-law. Based on these results, we suggest a method of obtaining a priori information about the occurrence of the next large heartbeat interval, and thus to predict it. We show explicitly that the proposed method, which exploits long-term memory, is superior to the conventional precursory pattern recognition technique, which focuses solely on short-term memory. We believe that our results can be straightforwardly extended to obtain more reliable predictions in other physiological signals like blood pressure, as well as in other complex records exhibiting multifractal behaviour, e.g. turbulent flow, precipitation, river flows and network traffic.
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GENERAL SCIENTIFIC SUMMARY Introduction and background. Physiological signals like heartbeat intervals, blood pressure or breathing as outputs of the human complex system typically employ complicated nonlinear behaviour with significant information underlying the dynamics of their fluctuations. Investigation of laws governing this dynamics plays an important role in better understanding the development of autonomic disorders. In the last decade, the scaling behaviour of the fluctuations in physiological signals has been investigated intensively. It was shown that physiological signals exhibit multifractal features which are reminiscent of turbulence and can be effectively modelled by multiplicative cascades.
Main results. We employ the return interval statistics, which is known to be a powerful tool for extracting information about nonlinear memory in time series, in order to make predictions of the next occurrences of large heartbeat intervals. We show that such important quantities as the probability density of return intervals and conditional return period exhibit power-law behaviour. Based on these results, we suggest a method to predict the occurrence of the next large heartbeat interval. We show explicitly that the proposed method which exploits long-term memory is superior to the conventional precursory pattern recognition technique which focuses on short-term memory.
Wider implications. Due to the validity of our theoretical results for a wide class of processes exhibiting multifractal behaviour, we believe that they can be straightforwardly extended to make more reliable predictions also in other complex systems exhibiting multifractal behaviour, such as turbulent flow, precipitation, river flows and network traffic.