Impact of series length on statistical precision and sensitivity of autocorrelation assessment in human locomotion.

Long-range autocorrelations (LRA) are a robust feature of rhythmic movements, which may provide important information about neural control and potentially constitute a powerful marker of dysfunction. A clear difficulty associated with the assessment of LRA is that it requires a large number of cycles to generate reliable results. Here we investigate how series length impacts the reliability of LRA assessment. A total of 94 time series extracted from walking or cycling tasks were re-assessed with series length varying from 64 to 512 data points. LRA were assessed using an approach combining the rescaled range analysis or the detrended fluctuation analysis (Hurst exponent, H), along with the shape of the power spectral density (α exponent). The statistical precision was defined as the ability to obtain estimates for H and α that are consistent with their theoretical relationship, irrespective of the series length. The sensitivity consisted of testing whether significant differences between experimental conditions found in the original studies when considering 512 data points persisted with shorter series. We also investigate the use of evenly-spaced diffusion plots as a methodological improvement of original version of methods for short series. Our results show that the reliable assessment of LRA requires 512 data points, or no shorter than 256 data points provided that more robust methods are considered such as the evenly-spaced algorithms. Such series can be reasonably obtained in clinical populations with moderate, or even more severe, gait impairments and open the perspective to extend the use of LRA assessment as a marker of gait stability applicable to a broad range of locomotor disorders.

Effects of age and walking speed on long-range autocorrelations and fluctuation magnitude of stride duration.

Stride duration variability is considered a marker of gait balance and can be investigated in at least two different ways. Fluctuation magnitude can be addressed by classical mathematical methods, whereas fluctuation dynamics between strides can be characterized using the autocorrelation function. Although each approach has revealed changes of these parameters in different age-groups, most studies have focused on spontaneous walking speeds, which vary across groups and is described as a possible confounder in the assessment of stride duration variability. In the present study, the influence of speed on stride duration fluctuations was first analyzed in six young adults walking at six different speeds on a treadmill. Second, the results of 18 subjects from three different age-groups (≈5, 25, and 75 years old) were compared to assess the effect of age on the same variables at three different speeds. Fluctuation dynamics was evaluated, thanks to combined mathematical methods recently validated in the context of physiological time series, to increase the level of confidence in the results. Fluctuation magnitude was assessed by coefficients of variation (CV) on the same and large number of 512 gait strides, to enhance the validity of comparisons between both parameters. Long-range autocorrelations were highlighted in all time series, and characteristics were not influenced by gait speed and age of the participants. This suggests that the dynamics of variability is efficient for comparing subjects presenting with different spontaneous speed, and supports the hypothesis that long-range variability of human gait reflects a centrally controlled behavior. In contrast, CV was inversely related to walking speed and the age of the subjects. Slower speeds increased CV values, and fluctuation magnitude was also significantly larger for children compared with young and old adults. This confirms that fluctuation magnitude and dynamics could be complementary tools for more complete gait characterization.

Towards a "gold-standard" approach to address the presence of long-range auto-correlation in physiological time series.

Series of motor outputs generated by cyclic movements are typically complex, suggesting that the correlation function of the time series spans over a large number of consecutive samples. Famous examples include inter-stride intervals, heartbeat variability, spontaneous neural firing patterns or motor synchronization with external pacing. Long-range correlations are potentially important for fundamental research, as the neural and biomechanical mechanisms generating these correlations remain unknown, and for clinical applications, given that the loss of long-range correlation may be a marker of disease. However, no systematic approach or robust analysis methods have yet been used to support the study of correlation functions in physiological series. This study investigates four selected methods (the Hurst exponent, the power spectral density analysis, the rate of moment convergence and the multiscale entropy methods). We present the result of each analysis performed on artificial computer-generated series in which the auto-correlation function is known, and then on time series extracted from gait and upper limb rhythmic movements. Our results suggest that combined analysis using the Hurst exponent and the power spectral density is suitable for rather short series (512 points). The rate of moment convergence directly supports the power spectral density analysis, and the multiscale entropy further confirms the presence of long-range correlation, although this method seems more appropriate for longer series. The proposed methodology increases the level of confidence in the hypothesis that physiological series are long-memory processes, which is of prime importance for future fundamental and clinical research.