Measurement of passive ankle stiffness in subjects with chronic hemiparesis using a novel ankle robot

Abstract

Our objective in this study was to assess passive mechanical stiffness in the ankle of chronic hemiparetic stroke survivors and to compare it with those of healthy young and older (age-matched) individuals. Given the importance of the ankle during locomotion, an accurate estimate of passive ankle stiffness would be valuable for locomotor rehabilitation, potentially providing a measure of recovery and a quantitative basis to design treatment protocols. Using a novel ankle robot, we characterized passive ankle stiffness both in sagittal and in frontal planes by applying perturbations to the ankle joint over the entire range of motion with subjects in a relaxed state. We found that passive stiffness of the affected ankle joint was significantly higher in chronic stroke survivors than in healthy adults of a similar cohort, both in the sagittal as well as frontal plane of movement, in three out of four directions tested with indistinguishable stiffness values in plantarflexion direction. Our findings are comparable to the literature, thus indicating its plausibility, and, to our knowledge, report for the first time passive stiffness in the frontal plane for persons with chronic stroke and older healthy adults.

Fig. 1.

Photograph of the anklebot applying torques to move the ankle joint in dorsiflexion (toe up) (left) and plantarflexion (toe down) (right). The subject (not shown here) is seated with the knee flexed at 45° and leg partly suspended from a custom-made barber chair.

Fig. 2.

Measurement of passive stiffness using the anklebot. Top, left: commanded ramp-and-hold displacement perturbation (θ_command) of 15° in dorsiflexion (DF) with constant velocity (v) of 5°/s and hold time (t_hold) of 1 s. Top, right: raw traces of ankle angle and torque from a single representative control subject shown with initial (θ₀, τ₀) and final conditions (θ_∞, τ_∞). Bottom, left: steady-state torque (τ_static) and angle (θ_static) data obtained by perturbing the subject's ankle over the entire range of commanded perturbations in the sagittal plane (right positive: dorsiflexion, left negative: plantarflexion, PF). Bottom, right: each data point is obtained by perturbing the ankle to a commanded angle and measuring the resultant net torque (τ_∞−τ₀) and angular displacement (θ_∞−θ₀) under static conditions.

Fig. 3.

Top and top, middle: sample electromyogram (EMG) data (in mV) from the tibialis anterior (TA) and gastrocnemius (GAS) muscles in a single stroke subject when undergoing a commanded ankle perturbation of 15° in eversion. The data show three distinct phases: background activity before onset of perturbation (gray), muscle activity during movement until the hold phase (black), and finally, the return of the ankle to its neutral position (to the right of the vertical dashed line); Bottom and bottom, middle: box and whisker plots of electromyographic activity (in mV) from TA and GAS muscles in stroke subjects, averaged over the entire range of commanded perturbations in the sagittal and frontal planes. In each direction of movement, the mean EMG from each muscle is shown separately for background (Bck) and movement (Mvt) phases. In each box plot, the upper and lower ends of each box correspond to the first and third quartiles of the data set, respectively, with the median value shown inside the box; the length of each whisker is 1.5 times the interquartile value; each whisker extends from the edge of the box to the nearest data points within the length of whisker.

Fig. 4.

Linear regressors showing the mean ± SD of passive stiffness estimates across the entire sample of subjects within all three groups (YH: young healthy, AC: age-matched controls, ST: stroke) in both the sagittal (left) and frontal (right) planes. Passive stiffness is estimated as the slope of the least-squares linear regressor between applied torque τ (sagittal: τ_dp, frontal: τ_ie) and angular displacement θ (sagittal: θ_dp, frontal: θ_ie) for each subject. Each regressor is drawn as a mean (dashed line) with 1 SD above and below (solid lines). Separate regressors are computed for estimating ankle stiffness in each direction within a degree of freedom: dorsiflexion (toe up, positive angle) and plantarflexion (toe down, negative angle) in the sagittal plane, and eversion (heel away from midline, positive angle) and inversion (heel toward midline, negative angle) in the frontal plane. The linear regressors are shown with the offset values of robot torque subtracted and are thus forced through the origin. The estimates are shown only for the range of commanded perturbations in each group.

Fig. 5.

Comparison of passive stiffness between healthy (YH and AC) and stroke (ST) groups in (counterclockwise from top left) dorsiflexion (K_dorsi), plantarflexion (K_plantar), inversion (K_inversion), and eversion (K_eversion). The error bars represent variability across all subjects tested within a group. Statistical significance between YH or AC vs. ST groups is *P < 0.05.

Fig. 6.

Logarithm of the stiffness ratio in the frontal vs. sagittal plane for all 3 groups (YH, ST, and AC). The figure shows minimum-area, 99%-confidence ellipses (with corresponding centers of the data set ×) in the frontal-sagittal plane for each group. Notice the overlap between the 3 groups in the sagittal plane but a null intersection between healthy (YH, AC) and stroke groups (ST) in the frontal plane.