Multiscale assessment of the degree of multifractality for physiological time series.

Recent advancements in detrended fluctuation analysis (DFA) allow evaluating multifractal coefficients scale-by-scale, a promising approach for assessing the complexity of biomedical signals. The multifractality degree is typically quantified by the singularity spectrum width (WSS), a method that is critically unstable in multiscale applications. Thus, we aim to propose a robust multiscale index of multifractality, compare it with WSS and illustrate its performance on real biosignals. The proposed index is the cumulative function of squared increments between consecutive DFA coefficients at each scale n: αCF(n). We compared it with WSS calculated scale-by-scale considering monofractal/monoscale, monofractal/multiscale, multifractal/monoscale and multifractal/multiscale random processes. The two indices provided qualitatively similar descriptions of multifractality, but αCF(n) differentiated better the multifractal components from artefacts due to crossovers or detrending overfitting. Applied on 24 h heart rate recordings of 14 participants, the singularity spectrum failed to always satisfy the concavity requirement for providing meaningful WSS, while αCF(n) demonstrated a statistically significant heart rate multifractality at night in the scale ranges 16-100 and 256-680 s. Furthermore, αCF(n) did not reject the hypothesis of monofractality at daytime, coherently with previous reports of lower nonlinearity and monoscale multifractality during the day. Thus, αCF(n) appears a robust index of multiscale multifractality that is useful for quantifying complexity alterations of physiological series. This article is part of the theme issue 'Advanced computation in cardiovascular physiology: new challenges and opportunities'.