Evidence of an upper entrainment limit for walking with fractal auditory stimuli

Abstract

Background: Variability exists in all biological signals, and in human gait research it has been found to be an indicator of neuromuscular system functioning. Detrended fluctuation analysis (DFA), a nonlinear method used to quantify the strength of long-range correlations in the temporal structure of stride-to-stride gait variability, has revealed gait differences in certain populations that are not observed with traditional linear measures like standard deviation. Previous research suggests that humans can adapt gait patterns to match different variability structures through sensory cues, such as auditory metronomes. However, the upper limits of adaptability and the strength of long-term correlations in gait variability remain unclear. Exploring these limits not only deepens our understanding of neuromuscular control mechanisms but could also inform the design of targeted interventions, such as rehabilitation strategies, to enhance motor control in clinical populations. The aim of this study was to investigate the possible upper limits of long-term correlations in stride-to-stride gait variability, characterized by the fractal scaling index (FSI) using DFA.

Methods: Fourteen healthy young adults (age 25 ± 3 years; seven females) completed seven treadmill walking trials at a fixed, self-selected speed. The first trial was uncued, and during the remaining six trials participants timed their steps to an auditory metronome with FSI ranging between 1.00 and 1.25. Gait FSI, velocity, stride time, cadence, and the time difference between heel contact and the associated metronome "tones" were calculated.

Results: Uncued gait FSI averaged 0.76 (±0.1). As the metronome FSI increased from 1.00 to 1.15, gait FSI approximated 1.00. Beyond 1.15 (metronome FSI values of 1.20 and 1.25), gait FSI dropped below 0.70, resembling uncued walking. Other gait measures remained unchanged. These findings suggest an upper gait FSI limit of approximately 1.00 during entrainment to metronome FSI values <1.20, beyond which adaptability diminishes.

Conclusions: This study establishes the upper entrainment limit for gait FSI during synchronization with fractal auditory stimuli, with implications for designing effective gait rehabilitation interventions targeting specific variability patterns.

Keywords: Auditory metronome; Detrended fluctuation analysis; Entrainment; Fractal entrainment threshold; Fractal scaling index; Gait adaptability; Gait analysis; Gait variability; Nonlinear analysis.

Figure 1. Marker name and corresponding anatomic location of each marker for use with 3D motion capture.

Figure 2. Procedural sequence flow chart.

Sequence occurs numerically beginning with block 1 and ending with block 5. Rest periods were given between each block, between each walking trial, and whenever otherwise needed by the participant. The asterisk (*) in blocks 3 and 5 indicate motion capture collection. Stimuli (represented by their FSI values) used individually for each trial within block 5 were performed in random order.

Figure 3. Gait fractal scaling index (FSI) in response to varying stimulus FSI values.

A total of 4 outliers were excluded based on box and whisker plots constructed per each trial. Baseline, uncued gait FSI measurements are represented by dashed lines. Standard deviation bars are included for cued gait FSI. Star (⋆) indicates statistically significant differences.