Fractal dimension of heart rate time series: an effective measure of autonomic function

Previous studies suggested that heart rate (HR) time series may be more appropriately analyzed by nonlinear techniques because of the nonlinear nature of these data. In this study, we quantified the complexity of the HR time series, using fractal dimension, a previously described measure developed to study axonal growth, which quantifies the space-filling propensity and convolutedness of a waveform, and compared these results with another recently used measure, approximate entropy. Fractal dimension and approximate entropy of HR time series (unfiltered) correlate highly with each other and also with the high-frequency power (0.2-0.5 Hz) and, hence, appear to reflect vagal modulation of HR variability. These measures were also statistically more consistent and effective than measures of spectral analysis. Fractal dimension of the midfrequency time series of HR (filtered with a pass band of 0.05-0.15 Hz) also appears to be a statistically effective measure of relative sympathetic activity, especially in the standing posture.