Scaling behaviour of heartbeat intervals obtained by wavelet-based time-series analysis

• Published in: Nature (London) Vol. 383; no. 6598; pp. 323 - 327
• Main Authors: Ivanov, Plamen Ch, Rosenblum, Michael G., Peng, C.-K., Mietus, Joseph, Havlin, Shlomo, Stanley, H. Eugene, Goldberger, Ary L.
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 26.09.1996; Nature Publishing; Nature Publishing Group
• Subjects: Adult; Algorithms; Anatomy & physiology; Biological; Biological and medical sciences; Electrocardiography; Electrocardiography. Vectocardiography; Electrodiagnosis. Electric activity recording; Female; Fourier Analysis; Heart; Heart function; Heart Rate - physiology; Humanities and Social Sciences; Humans; Instability; Intervals; Investigative techniques, diagnostic techniques (general aspects); letter; Male; Mathematical analysis; Medical sciences; Middle Aged; Models, Cardiovascular; Models, Statistical; multidisciplinary; Reference Values; Science; Science (multidisciplinary); Sleep; Sleep Apnea Syndromes - physiopathology; Stability; Statistical analysis; Time; Time series; Wavelet transforms; Human; Heart rate; Electrodiagnosis; Wavelet transformation; Time series; Electrocardiography; Signal analysis
• ISSN: 0028-0836; 1476-4687
• DOI: 10.1038/383323a0

BIOLOGICAL time-series analysis is used to identify hidden dynamical patterns which could yield important insights into underlying physiological mechanisms. Such analysis is complicated by the fact that biological signals are typically both highly irregular and non-stationary, that is, their statistical character changes slowly or intermittently as a result of variations in background influences 1–3 . Previous statistical analyses of heartbeat dynamics 4–6 have identified long-range correlations and power-law scaling in the normal heartbeat, but not the phase interactions between the different frequency components of the signal. Here we introduce a new approach, based on the wavelet transform and an analytic signal approach, which can characterize non-stationary behaviour and elucidate such phase interactions. We find that, when suitably rescaled, the distributions of the variations in the beat-to-beat intervals for all healthy subjects are described by a single function stable over a wide range of timescales. However, a similar scaling function does not exist for a group with cardiopulmonary instability caused by sleep apnoea. We attribute the functional form of the scaling observed in the healthy subjects to underlying nonlinear dynamics, which seem to be essential to normal heart function. The approach introduced here should be useful in the analysis of other nonstationary biological signals.