The local effective Holder exponent has been applied to evaluate the variability of heart rate locally at an arbitrary position (time) and resolution (scale). The local effective Holder exponent [1,2] used is effectively insensitive to local polynomial trends in heartbeat rate due to the use of the Wavelet Transform Modulus Maxima technique. Also the variability so obtained is compatible in the sense of distribution to the Multifractal Spectra of the analysed heart rate time series. This provides the possibility of standardising the variability estimation for comparison between different patients and between different recordings for one patient. The previously reported global correlation behaviour [3] is captured in the effective Holder exponent based, local variability estimate. This includes discriminating healthy and sick (congestive heart failure patients) on the basis of both the central (Hurst) exponent and the width of the multifractal spectra. In addition to this, we observed intriguing patterns of individual response in variability records to daily activities. A moving average filtering of Holder exponent based variability estimates was used to enhance these fluctuations. We find that this way of local presentation of scaling properties may be of clinical importance.

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Struzik, Z.R. (2001). Revealing Local Variablity Properties of Human Heartbeat Intervals with the Local Effective Hölder Exponent. Fractals, 9(1), 77–93.