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Alterations of Fractal Dynamics with Aging and Disease

These findings indicate that fractal gait dynamics depend on central nervous system function. Therefore, we hypothesized that just as aging and cardiovascular disease may alter the fractal nature of the heartbeat, so too changes in central nervous system function might alter the fractal gait pattern. To test this hypothesis, we have begun to systematically study the effects of advanced age and neurodegenerative disorders on fractal gait rhythm [36].

Effects of Aging

We compared the gait of a group of very healthy elderly adults (ages 76 tex2html_wrap_inline1255 3 yrs) to healthy young adults (ages 25 tex2html_wrap_inline1255 2 yrs). Interestingly, both groups had identical mean stride intervals (elderly: 1.05 sec; young: 1.05 sec), and required almost identical amounts of time to perform a standardized functional test of gait and balance. The magnitude of stride-to-stride variability (i.e., stride interval coefficient of variation) was also very similar in the two groups (elderly: 2.0%; young: 1.9 %). Fig. 11 ( left) compares the stride interval time series for a young and an elderly subject. Visual inspection suggests a possible subtle difference in the dynamics of the two time series (the data from the young subject appearing more ``patchy''). Fluctuation analysis reveals a marked distinction in how the fluctuations change with time scale for these subjects. The stride interval fluctuations are more random (less correlated) for the elderly subject than for the young subject, a difference not detectable by comparing the first and second moments.

Similar results were obtained for other subjects in these groups, indicating a subtle, previously undetected alteration in the fractal scaling of gait with healthy aging. Even among healthy elderly adults who have otherwise normal measures of gait and lower extremity function, the fractal scaling pattern is significantly altered when compared with young adults.

From a practical clinical perspective, the breakdown of long-range correlations of gait with aging is of interest for a number of reasons. An exciting prospect is that quantitative assessment of fractal properties of locomotion may provide a simple, inexpensive way to obtain important information about gait instability among the elderly. Falls are a major cause of disability and death in this age group [37]. The ability to identify individuals at greatest risk, as well as to assess interventions designed to restore gait stability (e.g., exercise, footwear), could have major public health implications. From a more basic physiologic viewpoint, realistic models of gait dynamics must account not only for the unexpected long-range correlations in stride interval in health, but also for their breakdown with aging and disease [15].

Figure: Left: Example of the effects of aging. Stride interval time series are shown (above) and DFA (below) for a 71-year-old elderly subject and a 23-year-old young adult. For illustrative purposes, each time series is normalized by subtracting its mean and dividing by its standard deviation. This normalization process highlights any temporal ``structure'' in the time series, but does not affect the fluctuation analysis. Therefore, in this figure, stride interval is unitless. For the elderly subject, DFA indicates a more random and less correlated time series. Indeed, tex2html_wrap_inline1001 is 0.56 (tex2html_wrap_inline1295 white noise) for the elderly subject and 1.04 (tex2html_wrap_inline1327 noise) for the young adult. Right: Example of the effects of Huntington's disease (HD). For the subject with Huntington's disease (age: 41 years old), as compared with a healthy control, the stride interval fluctuations, F(n), increase more slowly with time scale, n. This indicates a more random and less correlated time series. Indeed, tex2html_wrap_inline1001 is 0.40 for this subject with Huntington's disease and 0.92 for this healthy control subject. Adapted from [36].

Effects of Neurodegenerative Disease

We further hypothesized that impaired central nervous system control might also alter the fractal property of gait. To test this hypothesis, we have compared the stride interval time series of subjects with Huntington's disease and Parkinson's disease, two major neurodegenerative disorders of the basal ganglia (a part of the brain responsible for regulating motor control), with data from healthy controls. The time series and fluctuation analysis for a subject with Huntington's disease and a control subject are shown in Fig. 11 (right panel). For the subject with Huntington's disease, stride interval fluctuations, F(n), increase slowly with time scale, n, compared to a healthy control. This finding indicates increased randomness and reduced stride interval correlations as compared with the control subject. In general, compared to healthy control subjects, fractal scaling was reduced in the subjects with Parkinson's disease and reduced further in subjects with Huntington's disease. Interestingly, while tex2html_wrap_inline1001 was lowest in subjects with Huntington's and intermediate in subjects with Parkinson's disease, subjects with Parkinson's disease walked more slowly compared to subjects with Huntington's disease, further confirming that the mechanisms responsible for the generation of gait speed are apparently independent of those regulating fractal scaling (Fig. 10A).

Among the subjects with Huntington's disease, the fractal scaling index tex2html_wrap_inline1001 was inversely correlated with disease severity (see Figure 12). Moreover, tex2html_wrap_inline1001 was significantly lower in subjects with the most advanced stages of Huntington's disease as compared with subjects in the early stages of the disease, indicative of more random stride interval fluctuations. Interestingly, in a few subjects with the most severe impairment, tex2html_wrap_inline1001 was less than 0.5, suggesting the presence of a qualitatively different type of dynamical behavior (namely, anti-correlations) in the gait rhythm.

Figure: Among subjects with Huntington's disease, disease severity score (0=most impairment; 13=no impairment), measured using an index that correlates with positron emission tomography (PET) scan indices of caudate metabolism [38], is strongly (p < .0005) associated with fractal scaling of gait. Adapted from [36].

These results indicate that with both Parkinson's and Huntington's disease, there is a breakdown of the normal fractal, long-range correlations in the stride interval, especially apparent in subjects with advanced Huntington's disease. Step-to-step fluctuations are more random (i.e., more like white noise), suggesting that the fractal property of gait is modulated in part by central nervous system (i.e., basal ganglia) function. Although fractal scaling is altered both with aging and certain diseases, the magnitude of these changes varies in different conditions, and other measures of gait dynamics may also distinguish among different disease states and aging [39], adding specificity to these new dynamical measures (compare with Fig. 6).

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Next: General Conclusions Up: Fractal Dynamics of Human Previous: Mechanisms of Fractal Gait