The scaling exponent of the correlation sum in human heart rate reflects short-time variability and is influenced by finite-size effects and mean heart rate dynamics.
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Caution in interpreting heart rate correlation-sum scaling as complexity marker; leaves open refined nonlinear analyses after finite-size correction.
It is shown that in the case of human heart rate, the scaling behavior of the correlation sum (calculated by the Grassberger-Procaccia algorithm) is a result of the interplay of various factors: finite resolution of the apparatus (finite-size effects), a wide dynamic range of mean heart rate, the amplitude of short-time variability being a decreasing function of the mean heart rate. This is done via constructing a simple model of heart rhythm: a signal with functionally modulated Gaussian noise. This model reproduces the scaling behavior of the correlation sum of real medical data. The value of the scaling exponent depends on all the above-mentioned factors, and is a certain measure of short-time variability of the signal.
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Säkki et al. (2003) studied this question.
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