Gait dynamics, fractals and falls: finding meaning in the stride-to-stride fluctuations of human walking

Abstract

Until recently, quantitative studies of walking have typically focused on properties of a typical or average stride, ignoring the stride-to-stride fluctuations and considering these fluctuations to be noise. Work over the past two decades has demonstrated, however, that the alleged noise actually conveys important information. The magnitude of the stride-to-stride fluctuations and their changes over time during a walk - gait dynamics - may be useful in understanding the physiology of gait, in quantifying age-related and pathologic alterations in the locomotor control system, and in augmenting objective measurement of mobility and functional status. Indeed, alterations in gait dynamics may help to determine disease severity, medication utility, and fall risk, and to objectively document improvements in response to therapeutic interventions, above and beyond what can be gleaned from measures based on the average, typical stride. This review discusses support for the idea that gait dynamics has meaning and may be useful in providing insight into the neural control of locomotion and for enhancing functional assessment of aging, chronic disease, and their impact on mobility.

Fig. 1

Example of the stride-to-stride fluctuations in the stride interval (i.e., the stride time or gait cycle duration). The stride time fluctuates around its mean (the horizontal line) in an apparently noisy, random fashion.

Fig. 2

Detrended fluctuation analysis (DFA) applied to time series of stride time from a healthy young adult. The slope of the line relating the size of the fluctuations to the window size, n, is defined as the fractal scaling exponent, a. For this participant, the slope is .83, indicating long-range, fractal correlations in the original data. When the data is randomly re-ordered (shuffled), the slope becomes .5, reflecting white noise and an absence of fractal scaling. Adapted from Hausdorff, Peng et al. (1995).

Fig. 3

Effects of gait speed on long-range correlations and fractal dynamics. A) Example of time series of stride time during 1 hour of walking in a healthy young adult at slow, normal and fast walking rates, and below, after the fast data set is randomly shuffled. B) While there are subtle effects of gait speed, DFA shows that there is fractal scaling at all 3 gait speed. Adapted from (Hausdorff et al., 1996)

Fig. 4

Effects of healthy aging on gait: sensitivity of fractal dynamics. The average stride time, stride time variability, Timed Up and Go performance are similar in this group of healthy older adults and healthy young adults, while the fractal scaling index is reduced with aging. Adapted from Hausdorff, Mitchell et al. (1997).

Fig. 5

Among community-living older adults, gait speed was similar in fallers and non-fallers, while measures of stride variability were significantly increased in fallers. Adapted from Hausdorff, Edelberg et al. (1997).

Fig. 6

Stride-to-stride fluctuations in the stride, as measured at baseline, were much larger in this participant who experienced a fall during the 12 month follow-up period, as compared to the non-fallers. Group results were similar. Adapted from Hausdorff, Rios et al. (2001).

Fig. 7

a Example of swing time series from a patient with PD and a control, under usual walking conditions and when performing serial 7 subtractions. Under usual walking conditions, variability is larger in the patient with PD (CV = 2.7%), compared to the control (CV = 1.3%). Variability increases during dual tasking in the participant with PD (CV = 6.5%), but not in the control (CV = 1.2%). b) For all levels of dual tasking difficulty, gait variability values among the PD participants were significantly increased compared to the controls. In PD, but not in controls, variability increased with the level of difficulty of the dual task. In contrast, gait speed (not shown) responded similarly in both groups. Adapted from Yogev et al. (2005).

Fig. 7

a Example of swing time series from a patient with PD and a control, under usual walking conditions and when performing serial 7 subtractions. Under usual walking conditions, variability is larger in the patient with PD (CV = 2.7%), compared to the control (CV = 1.3%). Variability increases during dual tasking in the participant with PD (CV = 6.5%), but not in the control (CV = 1.2%). b) For all levels of dual tasking difficulty, gait variability values among the PD participants were significantly increased compared to the controls. In PD, but not in controls, variability increased with the level of difficulty of the dual task. In contrast, gait speed (not shown) responded similarly in both groups. Adapted from Yogev et al. (2005).

Fig. 8

Among older adults, a) measures of gait variability are associated with executive function (EF), but not with memory b). Adapted from Hausdorff et al. (2005).

Fig. 9

Effects of treadmill walking on stride time variability of patients with PD. During treadmill walking, stride-to-stride variability was significantly lower compared to usual walking (at the same gait speed). * p < .001. Adapted from Frenkel-Toledo et al. (2005b).

Fig. 10

Simplified block diagram depicting some of the factors that contribute to gait stability and fall risk. Adapted from Hausdorff, Nelson et al. (2001).

Fig. 11

Example of the effects of MPH (MPH) on stride time variability during usual walking in a child with ADHD. Above: baseline (72 hours off MPH). Below: after treatment with MPH. Note how the stride-to-stride fluctuations are reduced in response to MPH. Adapted from (Leitner et al. (2007).

Fig. 12

Representative swing time series from a patient with major depressive disorder (38 yr old male; swing time CV = 3.2%), and a healthy control participant (25 yr old male; swing time CV = 1.6%). Note the relatively large stride-to-stride fluctuations in the participant with major depressive disorder. CV: coefficient of variation. Adapted from Hausdorff, Peng et al. (2004).