Conservation of Reactive Stabilization Strategies in the Presence of Step Length Asymmetries During Walking

Abstract

The ability to maintain dynamic balance in response to unexpected perturbations during walking is largely mediated by reactive control strategies. Reactive control during perturbed walking can be characterized by multiple metrics such as measures of whole-body angular momentum (WBAM), which capture the rotational dynamics of the body, and through Floquet analysis which captures the orbital stability of a limit cycle attractor. Recent studies have demonstrated that people with spatiotemporal asymmetries during gait have impaired control of whole-body dynamics as evidenced by higher peak-to-peak ranges of WBAM over the gait cycle. While this may suggest that spatiotemporal asymmetries could impair stability, no studies have quantified how direct modification of asymmetry influences reactive balance control. Here, we used a biofeedback paradigm that allows participants to systematically adopt different levels of step length asymmetry to test the hypothesis that walking asymmetrically impairs the reactive control of balance. In addition, we tested the hypothesis that perturbations to the non-dominant leg would cause less whole-body rotation due to its hypothesized role in weight support during walking. We characterized reactive control strategies in two ways. We first computed integrated angular momentum to characterize changes in whole-body configuration during multi-step responses to perturbations. We also computed the maximum Floquet multipliers (FMs) across the gait cycle, which represent the rate of convergence back to limit cycle behavior. Our results show that integrated angular momentum during the perturbation step and subsequent recovery steps, as well as the magnitude of maximum FMs over the gait cycle, do not change across levels of asymmetry. However, our results showed both limb-dependent and limb-independent responses to unexpected perturbations. Overall, our findings suggest that there is no causal relationship between step length asymmetry and impaired reactive control of balance in the absence of neuromotor impairments. Our approach could be used in future studies to determine if reducing asymmetries in populations with neuromotor impairments, such people post-stroke or amputees improves dynamic stability.

Keywords: angular momentum; asymmetry; locomotion; reactive control; stability.

Figure 1

(A) Experiment protocol. Participants completed a total of six trials. Participant’s Baseline step length asymmetry was collected during the first 3-min baseline trial without visual feedback. Then, they were instructed to complete a randomized sequence of five 6-min trials with target step length asymmetries of 0%, ±10% and ±15%. During each visual feedback trial, the participant first practiced with feedback for 1 min, then 10 perturbations were randomly applied at foot strike on each side. (B) Visual feedback for three of the five trials of step length asymmetry are shown. (C) Experimental setup. Participant were instructed to walk on the split-belt treadmill. A “success” message would appear on the screen when step length was within the three standard deviations of the desired target.

Figure 2

Example of time series data from an unperturbed and perturbed step. (A) Treadmill belt velocity, (B) vertical ground reaction force and (C–E) whole-body angular momentum (WBAM) for a representative perturbation step and recovery stride. The gray traces indicate the time series data for an unperturbed stride while the black traces indicate a perturbation stride. Each stride begins at heel strike. Black vertical lines correspond to the time of foot strike and gray vertical lines correspond to time of toe-off. Solid lines and dashed lines represent contralateral legs.

Figure 3

(A) Example of a 3D projection of the angular momentum trajectory recorded during baseline walking for one representative participant. (B) Illustration of a hypothetical perpendicular slice of the angular momentum trajectory as a Poincare section. S* represents the fixed point which is the average of pre-perturbation strides.

Figure 4

(A) Raw step length asymmetry data for one representative participant. Each data point represents the step length asymmetry. The target asymmetries for this example followed the order of 10%, −10%, 0, 15%, −15%. Each target asymmetry is represented by a different color. BSL: baseline step; PTB: perturbation step; REC: recovery step. (B) Achieved step length asymmetry vs. target step length asymmetry for all participants (N = 19). Achieved step length asymmetry is calculated as the average of all pre-perturbation strides and tends to undershoot the target at 15% and −15%. The green dots represent individual data. Horizontal bars indicate the median across all participants.

Figure 5

Averaged integrated angular momentum over the step cycle for all participants about the (A) pitch, (B) roll and (C) yaw axes for perturbations that occurred on the non-dominant (left column) and dominant side (right column). These results represent the 0% asymmetry condition (N = 19). The first step (B1) corresponds to the non-dominant limb for the left column and the dominant limb for the right column. Subsequent steps alternate between non-dominant and dominant. B: Baseline; PTB: Perturbation; R: Recovery. The horizontal bars and corresponding stars indicated whether the difference in integrated angular momentum between two steps was significant (**p < 0.001, *p < 0.05). The data are represented as boxplots such that the lower and upper edges of the box indicate the 25th and 75th percentile of the data, respectively. The horizontal line within each box indicates the median. The whiskers extend to the furthest data point beyond the lower or upper edges of the box that is within a distance of 1.5 times the middle 50th percentile of the data. Points that lie beyond the whiskers denote outliers.

Figure 6

Box plot of integrated angular momentum about the (A) pitch, (B) roll and (C) yaw axes at baseline step (B2), perturbation step (PTB) and recovery steps (R1 and R2) across each level of achieved asymmetry (N = 19) for perturbations on the non-dominant (left column) and dominant (right column) sides.

Figure 7

(A) Variation in the magnitude of the maximum Floquet multiplier (FM) across the gait cycle for five levels of target asymmetry (N = 17). The shaded area indicates the 95% confidence interval. (B) FM_Max across all levels of asymmetry for (N = 17) participants.