Comparing adaptive fractal and detrended fluctuation analyses of stride time variability: Tests of equivalence

Fractal analyses quantify self-similarities in stride-to-stride fluctuations over different time scales. Fractal exponents can be measured with adaptive fractal analysis (AFA) or detrended fluctuation analysis (DFA), though measurements obtained with the algorithms have not been directly compared.

Are stride time fractal exponents measured with AFA and DFA algorithms equivalent?

Data from 50 participants with Parkinson's Disease (n = 15), age-similar healthy adults (n = 15) and healthy young adults (n = 20) were analyzed in this cross-sectional, observational study. Participants completed 6-min walks at self-selected speeds overground on a straight walkway and on a treadmill. Stride times were measured with inertial measurement units. Fractal exponents in stride time data were processed using AFA and DFA algorithms and compared with two one-sided tests of equivalence. Mixed ANOVAs were used to compare exponents between groups and conditions.

Fractal exponents computed with AFA and DFA were equivalent neither in the overground (0.796 & 0.830, respectively, p = .587) nor treadmill conditions (0.806 & 0.882, respectively, p = .122). Fractal exponents measured with DFA were higher than when measured with AFA. Standard errors were 22% lower when measured with AFA. Additionally, a group × condition interaction was statistically significant when fractal exponents were processed with the AFA algorithm (F(2,47) = 11.696, p < .001), whereas the group × condition interaction was not statistically significant when DFA exponents were compared (F(2, 47) = 2.144, p = .129).

AFA and DFA do not produce equivalent estimates of the fractal exponent α in stride time dynamics. Estimates of the fractal exponent α obtained with AFA or DFA algorithms therefore should not be used interchangeably. Standard errors were lower when derived with AFA. Fractal exponents calculated with AFA may be more sensitive to conditions that influence stride time fractal dynamics than are measures calculated with DFA.