Figure 1.
An unimpaired human subject wearing Anklebot while walking on a treadmill.
Figure 2.
Typical plot of knee angle as measured by Anklebot vs. phase (% of gait cycle).
The miniature icons of a walker illustrate the corresponding phases of a gait cycle. Four extrema were identified from zero crossings of the knee angular velocity: (1) maximum knee flexion during stance phase, (2) maximum knee extension during terminal stance phase, (3) maximum knee flexion during swing phase and (4) maximum knee extension adjacent to heel strike.
Figure 3.
Phase of perturbation torque pulse vs. stride number plotted for three different trials.
Entrainment was determined by linear regression of phase of perturbation onto stride number for the last 15 strides during perturbation: in A, the regression slope is significantly negative—a non-entrained gait with a fast perturbation; in B, the regression slope is not significantly different from zero—an entrained gait; in C, the regression slope is significantly positive—a non-entrained gait with a slow perturbation.
Figure 4.
Typical results of a gait that did not entrain to “fast” perturbation (τP<τ0).
The box plot shows the distribution of walking periods of the last 15 strides before perturbation, the last 15 strides during perturbation and the first 15 strides after the end of perturbation. The knee angle and the torque pulse imposed by Anklebot during the last 15 perturbation periods are plotted next to the box plot; each row indicates knee angle (the dotted blue curve) and Anklebot torque profile (the solid red curve) during one perturbation cycle. For each cycle, the phase of maximum knee flexion is identified (the black circle) and the trend of the maximum knee flexion phase is visualized by a green arrow. Stride duration (shown in the box plot) did not change significantly due to the mechanical perturbations, and the phase of maximum knee flexion drifted continuously relative to the perturbation.
Figure 5.
Typical results of a gait that did not entrain to “slow” perturbation (τP>τ0).
Stride duration (shown in the box plot) did not change significantly due to the mechanical perturbations, and the phase of maximum knee flexion drifted continuously relative to the perturbation. The direction of drift is opposite to Figure 4.
Figure 6.
Typical results of a gait that entrained to perturbation.
Stride duration (shown in the box plot) approximated τP with a statistically significant difference from the walking period before perturbation. The subject's cadence changed from the originally preferred value to synchronize with the periodic perturbation. Maximum knee flexion maintained a constant phase difference from the perturbation pulse instead of drifting relative to the perturbation pulse.
Table 1.
Subjects' preferred speeds, walking periods and normalized stride lengths.
Table 2.
Basin of entrainment normalized by walking cadence and its variability.
Figure 7.
Transient behavior under perturbation.
A shows the knee angle (the dotted blue curve), Anklebot torque profile (the solid red curve), and maximum knee flexion phase (the green circle and arrow) during the last 15 perturbation cycles, and B shows knee angle and Anklebot torque profile with the onset of torque pulse marked (the dotted brown arrow) during the last 15 gait cycles under perturbation. In A, the maximum knee flexion which should occupy an almost constant phase of gait cycle drifted initially but converged on a specific phase of the perturbation cycle. The convergence is also shown in B; the onset of torque pulse drifted initially, but converged on a specific phase of the gait cycle, which is close to 50%.
Figure 8.
Histograms of the phase, φP at which the perturbation torque pulses occurred in phase-locked strides.
Purple bars in A, B and C show the distribution of φP in the last 15 strides of all entrained trials of 11 subjects who only performed experiment 1. Superimposed on this histogram in A is the distribution of φP of phase-locked strides in experiment 2 (dark blue bars), in B with auditory input masked (green bars), and in C with auditory input masked and a distracting task (light blue bars). A polar (“rose”) plot of the histogram of all entrained trails of all 19 subjects in experiment 1 is shown in D showing that the distribution occupied a narrow region of the gait cycle. Statistical analysis indicated no significant difference between these distributions in mean or standard deviation.
Figure 9.
In A, there is significant difference between stride duration before and during perturbation, but no significant difference between during and after perturbation; in B, there is significant difference between stride duration before, during and after perturbation. For all trials classified into B, the mean stride duration after perturbation lay between its during-perturbation and pre-perturbation values.
Figure 10.
Phase of perturbation torque pulse vs. stride number in experiment 2.
A illustrates typical phase locking of one subject; σ is the standard deviation of the gait phases at which the torque pulse occurred in the last 15 strides during perturbation of all entrained trials of the subject in experiment 1. The phase of convergence and onset of phase locking were determined as explained in Data Analysis. The miniature icons of a walker illustrate the corresponding phases of a gait cycle. The initial perturbation pulse was applied just before the beginning of a double stance phase (−5% gait cycle). Over 70 subsequent strides (140 steps) taking approximately 100 seconds, the subject gradually changed cadence to phase lock with the perturbation at 50% gait cycle, approximately the maximum ankle-actuation phase of normal human walking. B shows the phase locking of all 7 subjects who participated in experiment 2.