Quantifying Heartbeat Dynamics by Magnitude and Sign Correlations

Abstract

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.