The relationship between variability and stability of movement is not well understood. Traditional gait analyses often assume that the stride-to-stride variations in walking kinematics are the result of noise. Gait data are collected for a number of isolated and independent strides, normalized to a standard length (100%), then averaged across strides to form a picture of a “typical” stride. However, the spatio-temporal structure of the stride-to-stride variability in the gait pattern is lost in this process. It was anticipated that techniques used to study and model nonlinear dynamical systems might prove valuable for quantifying the complexity and dynamic stability of continuous locomotion. The goal of this study was to examine the variability and nonlinear dynamics of continuous walking and to understand how this process was affected by walking on a motorized treadmill and by the loss of sensory feedback that occurs in peripheral neuropathy.

A portable "DataLogger" device was built to collect kinematic data during continuous walking. The DataLogger was based on the Tattletale Model 8 (Onset Computer, Inc., Pocasset, MA), consisting of a programmable microprocessor and an 8-channel, 12-bit A/D converter, interfaced to a 15Mb Persistor CF8 Compact Flash RAM card (Peripheral Issues, Inc., Mashpee, MA). Three electrogoniometers measured the sagittal plane joint angles of the hip, knee, and ankle joints and a tri-axial accelerometer positioned at the base of the sternum measured the movements of the upper body. The DataLogger was attached to a backpack-style harness that was lightweight (less than 2.5 kg), self-contained, and did not interfere with the subject's ability to walk in a normal manner. The DataLogger was used to collect ten minutes of continuous data for each trial.

Average walking velocities, stride lengths, and stride times, and standard deviations of stride times were quantified to examine overall gait motions. Stride-to-stride mean and maximum standard deviations were computed for each set of time series data to quantify stride-to-stride variability. Slopes of log-log power spectral density (PSD) distributions of stride interval data were computed to examine long-range correlations in these data. Correlation dimensions (Grassberger and Procaccia, 1983) were computed for each time series to examine differences in the complexity of these signals. Short-term and long-term maximum local divergence rates (Lyapunov exponents) were computed for each time series to quantify the dynamic stability of these movements (Rosenstein et al., 1993). Surrogate data were generated by replacing the mean-stride-removed fluctuations in each of the original time series with phase-randomized fluctuations. The short-term and long-term divergence rates of these surrogate time series were compared to those from the original data to determine if the fluctuations in the original time series could be adequately modeled as correlated Gaussian noise.

The first study examined the differences in locomotor kinematics between overground and treadmill walking. Ten young healthy subjects (five men and five women) with no history orthopedic or neurological disorders, and taking no medications that might have affected their balance or locomotion participated. Subjects walked around an open indoor walking track (OG) at a comfortable pace for 10 minutes while their walking kinematics and average walking speeds were recorded. These subjects then walked on a motorized treadmill (TM) at the same average speed.

Walking on a motorized treadmill reduced the stride-to-stride variability exhibited during overground walking, particularly at the distal extremities. Long-range correlations in the stride intervals were significantly reduced during TM walking relative to OG walking. There were no differences in the correlation dimensions calculated for either OG or TM walking. There were significant reductions in both short-term and long-term divergence exponents for TM walking compared to OG walking. These results suggested that walking on the motorized treadmill was associated with reductions in both the stride-to-stride variability and the instability of walking. However, these different variability and stability measures were not strongly correlated to each other, and were most likely quantifying different aspects of locomotor behavior. A comparison of the local divergence trajectories for the original and surrogate data revealed that stride-to-stride fluctuations could not be adequately modeled by linear stochastic noise. This suggested that important information about the neuromuscular control of walking might be reflected in the spatio- temporal structure of these fluctuations.

The second study was a comparison of overground locomotor kinematics in fourteen patients with severe peripheral neuropathy (NP) compared to twelve gender-, age-, height-, and weight-matched non-diabetic controls (CO). Severe peripheral neuropathy was defined as “Loss of Protective Sensation” (LOPS), or the inability to feel a 5.07 Semmes-Weinstein monofilament under at least one of four regions of either foot. Subjects were asked to walk at their own self-selected comfortable pace around an open indoor walking track for a period of 10 minutes. During this time, their walking kinematics and average walking speeds were recorded.

NP subjects walked slower and with shorter stride lengths than CO subjects did. NP subjects were more variable than CO subjects were;​ however, these differences were concentrated at the most distal joints. Sensory status was a significant predictor of mean stride-to-stride variability at the ankle joint, even after accounting for differences in range of motion, lower extremity strength, and walking velocity. There were no differences in slopes of log-log PSD functions of the stride time data;​ however, both NP subjects and healthy CO subjects showed a decrease in these slopes relative to young healthy subjects. NP subjects exhibited more complex movement patterns (i.e. greater correlation dimensions) than did CO subjects, particularly at the hip and knee. Sensory status was a significant predictor of the increase in the complexity of knee joint motions, after accounting for differences in walking velocity, range of motion, and lower extremity strength.

NP subjects exhibited greater long-term dynamic stability than CO subjects for upper body movements in the horizontal plane did. These differences in dynamic stability were significantly predicted by differences in walking velocity. These results support the hypothesis that the reduction in walking velocity was a compensatory strategy used by NP subjects to maintain the dynamic stability of the upper body (Courtemanche et al., 1996). These measures of variability and dynamic stability were not strongly correlated to each other. Finally, the local divergence trajectories of the phase-randomized surrogate data were significantly different than those of the original data. Therefore, the stride-to-stride fluctuations were significantly nonlinear and could not be adequately modeled by an optimal linear stochastic process. These results further support the findings of the OG/TM study that there might be important information regarding the control of locomotion within these fluctuations.

The nonlinear time series analysis methods used in this study were able to reveal a number of unique insights into the nature of locomotion under the various conditions examined. These results point to the potential improved understanding of neuromuscular control that these techniques might bring to the study of locomotion. This research has contributed to the study of locomotion in several ways. First, a new level of technology was developed to examine gait as a continuous cyclic process under ecologically valid conditions. Second, this research has shed new light on the nature of locomotor control when viewed as a nonlinear dynamical system. Finally, the effects of the loss of afferent feedback on the control of locomotion are now better understood and it is anticipated that these findings will eventually have a clinically meaningful impact on the care of these patients.