To test these possibilities, we first measured the stride interval in healthy young adult men as they walked continuously on level ground at their self-determined, usual rate for about nine minutes . To measure the stride interval in health and disease, ultra-thin, force sensitive switches were placed inside the shoe. We recorded the footswitch force on an ambulatory recorder and then determined heelstrike timing . This recently devised, inexpensive and portable technique enables, for the first time, continuous and relatively long-term measurement of gait, and is roughly analogous to the use of Holter monitoring for recording continuous heartbeat activity.
A representative stride interval time series from a healthy subject is shown in Fig. 9 (top). Of note is the stability of the stride interval; during a nine-minute walk, the coefficient of variation is only 4%. Thus, as in Fig. 8, a reasonable first approximation of the dynamics of the stride interval would be a constant. Nonetheless, the stride interval, like the healthy heartbeat, does vary irregularly, raising the intriguing possibility of some underlying complex temporal ``structure.'' Further, this complicated pattern changes after random shuffling of the data points (Fig. 9), demonstrating that the original temporal pattern is related to the sequential ordering of the stride intervals, and is not simply a result of the distribution of the data points. Fig. 9 (bottom left) shows the DFA plots for the original time series and the shuffled time series. The slope of the line relating log F(n) to log n is .83 for the original time series and .50 after random shuffling. Thus, fluctuations in the stride interval scale as indicating long-range correlations, while the shuffled data set behaves as uncorrelated (white) noise; = .50. Fig. 9 (bottom right) displays the power spectrum of the original time series. The spectrum is broadband and scales as with .92. The two scaling exponents are consistent with each other within statistical error due to finite data length , and both and are consistent with long-range (fractal) correlations (compare with Fig. 5.
Figure: Representative stride interval time series before and after random shuffling of the data points (above) and the detrended fluctuation analysis (DFA) and power spectrum analysis (below). The structure in the original time series disappears after random shuffling of the data. DFA indicates that this structure represents a fractal process with long-range correlations ( = .83). Adapted from .
For a group of ten healthy adults, we confirmed that the scaling exponents and both indicated the presence of long-range correlations consistent with a fractal gait rhythm. After random shuffling of the original stride interval time series, approaches the value of a completely uncorrelated process (.50). The shuffled time series has the same mean and standard deviation as the original time series, indicating that this fractal property of healthy human gait is related to the sequential ordering of the stride interval time series, but not to the first or second moments of the time series.