In the previous section, we described the fractal fluctuations in the healthy human heartbeat, as well as alterations of these normal scale-invariant patterns with both aging and disease. In this section, we turn our attention from the dynamics of the involuntary (autonomic) nervous system to the voluntary nervous system.
Figure: Top: The gait cycle duration is termed the stride interval and is typically measured as the time
between consecutive heelstrikes of the same foot.
Bottom: Stride interval time series of a healthy subject while walking
under constant environmental conditions. Although the stride interval
is fairly stable (varying only between 1.1 to 1.4 sec), it fluctuates about its mean (solid line) in an apparently unpredictable manner. A key question is whether these fluctuations represent uncorrelated randomness or whether there is a hidden fractal temporal structure, like that seen for the heartbeat. Adapted from [15].
Our focus here is on the step-to-step fluctuations in walking rhythm, that is, the duration of the gait cycle, also referred to as the stride interval (see Figure 8). The stride interval is analogous to the cardiac interbeat interval, and, like the heartbeat, it was traditionally thought to be quite regular under healthy conditions. However, as shown in Fig. 8, subtle and complex fluctuations are apparent in the duration of the stride interval. While this ``noise'' had been previously observed [32, 33], until recently these fluctuations had not been characterized and their origin was largely unknown. Our goal is to analyze these step-to-step fluctuations in gait in order to gain insight into the neural control of locomotion in health and disease.
The simplest explanation for these step-to-step variations in walking rhythm is that they trivially represent uncorrelated (white) noise superimposed on a basically regular process -- random fluctuations riding on top of the normal, constant walking rhythm. A second possibility is that these fluctuations have short-range correlations (``memory'') as one might expect to see in a Markov process or a biological system where there is exponential decay of the system ``memory.'' In that case, the current value of the stride interval would be influenced by only the most recent stride intervals, but over the long term, fluctuations would vary randomly. A third, less intuitive possibility is that the fluctuations in the stride interval could exhibit the type of long-range correlations seen in the healthy human heartbeat (see above), as well as other scale-free, fractal phenomena [7, 3]. If this were the case, the stride interval at any instant would depend (at least in a statistical sense) on the intervals at relatively remote times, and this dependence (``memory effect'') would decay in a power-law fashion.