Multifractal and Multiscale Detrended Fluctuation Analysis of Cardiovascular Signals: how the Estimation Bias Affects ShortTerm Coefficients and a Way to mitigate this Error

The Detrended Fluctuation Analysis (DFA) is a popular method for quantifying the self-similarity of the heart rate that may reveal complexity aspects in cardiovascular regulation. However, the self-similarity coefficients provided by DFA may be affected by an overestimation error associated with the shortest scales. Recently, the DFA has been extended to calculate the multifractal-multiscale self-similarity and some evidence suggests that overestimation errors may affect different multifractal orders. If this is the case, the error might alter substantially the multifractal-multiscale representation of the cardiovascular self-similarity. The aim of this work is 1) to describe how this error depends on the multifractal orders and scales and 2) to propose a way to mitigate this error applicable to real cardiovascular series.Clinical Relevance— The proposed correction method may extend the multifractal analysis at the shortest scales, thus allowing to better assess complexity alterations in the cardiac autonomic regulation and to increase the clinical value of DFA.