DEMONSTRATION OF 1/f FLUCTUATIONS AND WHITE NOISE IN THE HUMAN HEART RATE BY THE VARIANCE-TIME-CURVE: IMPLICATIONS FOR SELF-SIMILARITY

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Abstract
Spectral analysis of heart rate variability is usually performed by Fast Fourier Transform. Here we demonstrate the self-affine properties of the human heart rate using a spectral analysis based on counting statistics. Each QRS complex is considered to be a point event and from the number of events N(Δt) in consecutive time windows Δt the variance is calculated. From the finding that the variance of N(Δt) follows a power law proportional to (Δt)1+b in case of 1/fb noise, it is shown that the variance of the heart rate as determined for windows of length Δt, i.e., N(Δt)/Δt, is proportional to (Δt)b−1. From a 12-day Holter recording, the scaling region could be determined to cover 0.16 to 0.000136 Hz. A function X(t) is self-affine if X(t) and X(rt)/rH have the same distribution functions. From the variance-time-curve, it can be shown that the exponent H is dependent on b with b=2H−1. In young healthy men, the parameter b fluctuates between 0.2 and 1.0 during 24 h and thus determines the self-affine scaling factor H=(b−1)/2 for the amplitude of heart rate, if the time axis is scaled by r. Thus, during periods of 1/f noise, the heart rate scales with H=0, and for periods of almost white noise, with H close to .

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