Quantifying Heartbeat Dynamics by Magnitude and Sign Correlations

We review a recently developed approach for analyzing time series with long-range correlations by decomposing the signal increment series into magnitude and sign series and analyzing their scaling properties. We show that time series with identical long-range correlations can exhibit different time organization for the magnitude and sign. We apply our approach to series of time intervals between consecutive heartbeats. Using the detrended fluctuation analysis method we find that the magnitude series is long-range correlated, while the sign series is anticorrelated and that both magnitude and sign series may have clinical applications. Further, we study the heartbeat magnitude and sign series during different sleep stages — light sleep, deep sleep, and REM sleep. For the heartbeat sign time series we find short-range anticorrelations, which are strong during deep sleep, weaker during light sleep and even weaker during REM sleep. In contrast, for the heartbeat magnitude time series we find long-range positive correlations, which are strong during REM sleep and weaker during light sleep. Thus, the sign and the magnitude series provide information which is also useful for distinguishing between different sleep stages. A broad class of physical and biological systems exhibits complex dynamics, associated with the presence of many components interacting over a wide range of time or space scales. These often-competing interactions may generate an output signal with fluctuations that appear “noisy” and “erratic” but reveal scale-invariant structure. One general approach to study these systems is to analyze the ways that such fluctuations obey scaling laws [1, 2, 3]. We consider the time series formed by consecutive cardiac interbeat intervals (Fig. 1a) and focus on the correlations in the time increments between consecutive beats. This time series is of general interest, in part because it is the output of a complex integrated control system, including competing stimuli from the neuroautonomic nervous system [4]. These stimuli modulate the rhythmicity of the heart’s intrinsic pacemaker, leading to complex fluctuations. Previous reports indicate that these fluctuations exhibit scaleinvariant properties [5, 6, 7], and are anticorrelated over a broad range of time scales (i.e., the power spectrum follows a power-law where the amplitudes of the higher frequencies are dominant) [8]. By long-range anticorrelations we also mean that the root mean square fluctuations function of the integrated series is proportional to nα where n is the window scale and the scaling exponentα is smaller than 0.5. In contrast, for uncorrelated behavior α 0 5, while for correlated behavior α 0 5. The time series of the fluctuations in heartbeat intervals can be “decomposed” into Downloaded 28 Aug 2007 to 128.197.27.5. Redistribution subject to AIP license or copyright, see http://proceedings.aip.org/proceedings/cpcr.jsp 118