Sensitivity Estimations in Favor of Using Inter-fractal Angle in Detrended Fluctuation Analysis

Background. It has become common in research with detrended fluctuation analysis (DFA) to use slopes of regression lines (alpha(1) and alpha(2)) and their ratio as measures of fractal properties of dynamical processes such as physiological rhythm fluctuations. In this study, instead of the ratio (alpha(1)/alpha(2)) in DFA of ECG RR intervals and respiratory signals, we propose the use of a new measure: the inter-fractal angle (0) - angle that DFA regression lines form between each other. Methods. Angle 0 was obtained by means of graphical-analytical calculation. Using one way-Anova test, sensitivity of 0 on the influence of slow breathing and orthostasis was compared in respect to ratio alpha(1)/alpha(2) Results. Comparisons revealed that changes of 0 were statistically more significant than changes of alpha(1)/alpha(2). Conclusion. Inter-fractal angle is an elegant new measure of DFA that is more sensitive to perturbations such as changes in body posture and breathing regime than alpha(1)/alpha(2).

Automated summary

This study introduces a new measure, the inter-fractal angle (θ), which is more sensitive to perturbations like slow breathing and orthostasis compared to the traditional alpha(1)/alpha(2) ratio in detrended fluctuation analysis of physiological rhythm fluctuations.