Robot-Aided Training of Propulsion: Eﬀects of Torque Pulses Applied to the Hip and Knee Joint Under User-Driven Treadmill Control

,

by the hip and foot landmark defined segment, relative to the vertical laboratory axis, commonly assessed at the moment of peak propulsive force [7], [9]- [14].As such, propulsion can increase by applying a greater plantarflexor moment while keeping TLA constant, or by increasing TLA while applying the same plantarflexor moment.Due to the association between GS and propulsion, training methods that modulate the components of propulsion during walking are attractive for rehabilitation of individuals with neuromotor impairment [3].
Multiple methods have been developed for modulating propulsion mechanics during walking practice, such as wearable exoskeletons [15], [16], functional electrical stimulation combined with high-speed walking [12], challenge-based paradigms based on resistive forces applied by tethers to the pelvis [17] or arising from belt accelerations [11], and real-time biofeedback [18], [19].Specifically, exoskeletons have been used to deliver torque to the hip and knee joint during stance, resulting in modulation of both components of propulsion in healthy participants [15].Also, a soft exo-suit [20] has been developed to apply dorsiflexion and plantarflexion assistance during training to increase peak propulsive force, TLA, and therefore GS, in a hemiparetic subject [16].Many other approaches based on exoskeletons, while not directly targeting propulsion mechanics, indirectly modulated propulsion mechanics while the exoskeleton controller was being optimized to minimize the cost of transport [21]- [23].Functional electrical stimulation has been used to modulate propulsion mechanics extensively also in clinical popluations.As an example, patients post-stroke participating in a 12-week training protocol incorporating functional electric stimulation of paretic ankle dorsiflexor and plantarflexor musculature learned to generate clinically meaningful improvements in peak paretic propulsive force and increase TLA [12].Finally, real-time biofeedback has been used to target changes in propulsion mechanics in healthy young and older adults [18], and a similar approach has been applied in post-stroke individuals, demonstrating the ability of post-stroke participants to increase paretic peak propulsive force through the two contributors of TLA and plantarflexor moment [24]- [26].
While most of the previous approaches demonstrated the ability of modulating propulsion mechanics during training, the ultimate goal of gait rehabilitation intervention is for beneficial effects to persist beyond training.However, the mechanisms of neuromuscular control involved in responding to interventions modulating propulsion mechanics are not well understood.Therefore, the effects of a training method on propulsion mechanics during and following training need to be both assessed and analyzed quantitatively.
A specific challenge for studies targeting after-effects in propulsion mechanics is that these after-effects can not be quantified accurately in a standard treadmill setup based on fixed speed treadmill walking.For example, in our previous work, we applied torque pulses to the hip and knee joint during stance, and quantified the effects of pulsed torque application on propulsion mechanics both during and after exposure [15].
After exposure, the treadmill speed was fixed and equal to the one identified by the participant at baseline.Our previous setup was limited in studying after-effects of training on propulsion mechanics, as any intended effects on propulsion mechanics may be "cancelled" by the the constraint of walking at a constant, predetermined speed.In fact, hypothetical increases in propulsive force induced by training may not be "useful" for walking at that predetermined gait speed, which is identified in absence of any exoskeleton action.To properly evaluate the effects of exoskeletons on propulsion mechanics, it would be important to perform an evaluation during overground walking, or on a treadmill setup equipped to adjust the speed based on the intended speed of the participant [27].
In this work, we applied pulses of torque in consecutive strides to the knee and hip joints during stance while using a user-driven treadmill controller such that GS may change in response to changes in walking mechanics.We quantified propulsion kinematics with hip extension (HE), as measured by the robotic exoskeleton, and TLA as assessed by motion capture.Also, we quantified propulsion kinetics using NPI.
We quantified effects during and after training in terms of the three outcome measures, plus GS resulting from the interaction between user, exoskeleton, and treadmill controller.
We tested the primary hypothesis that any of the twelve pulse conditions modulate propulsion mechanics significantly during and after training relative to baseline.Moreover, we conducted secondary analyses to determine which parameters of the pulse conditions (i.e., joint torque, direction, timing) drove the effects during and after training, and to determine whether propulsion mechanics measured during pulsed torque training was associated with effects measured after training.

A. Study Participants & Pulse Conditions
We performed an a priori power analysis based on our previous study results [15] to determine sample size.We set α equal to 0.05/48 (corrected for 12 pulse conditions x 4 time point comparisons to baseline), β beta equal to 0.85, utilized two tailed statistics, and an effect size of 1.08 taken from the NPI outcome measure for pulse condition eight at the late assessment of after-effects that followed training.This analysis predicted a minimum sample size of 22 healthy participants to detect the targeted pre-post change in walking mechanics.
A subset of 12 pulse conditions were selected for testing to allow for a full factorial statistical assessment of pulse factors.However, exposing participants to all selected 12 pulse conditions would require more experimentation time than could reasonably be expected.As such, we divided participants into two groups and assigned two overlapping subsets of 8 pulses to each group (Fig. 1).

68
Data collections were conducted on an instrumented split-69 belt treadmill (Bertec Corp., Columbus OH, USA) that mea-70 sured analog force/torque data.The ALEX II robot [28], a 71 powered unilateral lower extremity exoskeleton, as seen in 72 Fig. 2, was utilized to apply torque pulses about the right knee 73 and hip joints of participants.The exoskeleton is suspended 74 by a mobile carriage over the instrumented split-belt treadmill 75 and secured from moving during experimentation by locking 76 casters.Participants were protected from falling through the 77 use of an overhead track and harness system (Solo-Step Inc., 78 North Sioux City, SD, USA   torque pulse condition (Fig. 1).

C. User-driven Treadmill Controller
During experimentation, the speed of the treadmill belts were determined by the antero-posterior coordinate of the ALEX II suspension system.A T8-5805 rotary encoder (Kuebler Inc., NC, USA), located on one of the joints of four-bar mechanism of the ALEX II suspension system was read in real time by the Simulink control software.The software translated the real time encoder angle (θ k ) to a lunge position (D k ) quantified in meters via a calibration function with constant k g .A proportional controller (gain G k ) was used to convert lunge distance (D k ) into to an increment in desired belt speed (V k+1 ) at each iteration (k), at a rate of 1000 Hz.
The neutral lunge angle (θ 0 ) was calculated as the average 7 of lunge encoder angle of eleven right and left gait cycles of 8 walking at self-selected GS (ssGS).The current lunge angle 9 (θ k ) was determined as the average lunge encoder angle over the past four strides.If the current lunge position (D k ) was anterior/greater or posterior/less than the neutral position/zero, the treadmill belt accelerated or decelerated, respectively.The treadmill belt velocities were controlled in real time by the Simulink program through a USB TCP/IP protocol connection with the treadmill control hardware.

D. Motion Capture
A ten camera T40-S (Vicon Motion Systems Ltd, Oxford, UK) system with Vicon Tracker 3.3 software was used to track the real time trajectories of two retroflective markers located on anatomical and robot landmarks.These two landmarks were the right malleoli and right hip joint center on the exterior of the exoskeleton hip linkage (inline with the shaft of the hip motor gearbox).The trajectories of these two markers were streamed in real time to Simulink with Vicon DataStream SDK 1.6 for logging and offline calculation of right TLA.

E. Experimental Procedures
1) Assessment Session: After fitting the exoskeleton to the participant, a first walking session was conducted to familiarize the participant with the exoskeleton, and with the assessment of ssGS and of the neutral lunge position.At the beginning of this session, the participant walked in the exoskeleton to assess the fit and alignment of the mechanism, followed by a couple of minutes for the participant to familiarize with the exoskeleton.Then, a second session was conducted to determine the participant's maximum safe GS while wearing the exoskeleton -up to the limit of 1.45 m/s.Next, the participant's ssGS was determined: three rampup (starting at 0.70 m/s and increased in increments of 0.05 m/s) and three ramp-down trials (starting at maximum safe GS and decreased in increments of 0.05 m/s) were performed, and each ended when the subject indicated having reached a comfortable speed.The average of these six trials, which we considered to be the ssGS, was set as the starting treadmill speed for all pulse training sessions.After determining ssGS, the neutral lunge position of the participant was assessed.Utilizing the acquired neutral lunge position, the participant was given 200 strides to explore the behavior of the userdriven treadmill speed controller via antero-posterior lunge.

2) Pulse Training Sessions:
In the first visit, the participant proceeded to perform the first two training sessions.Training sessions were performed entirely under user-driven treadmill control and consisted of 100 or 150 strides of transparent control for baseline assessment, 300 strides of pulsed-torque training (utilizing one of the eight pulse conditions), and 200 strides of after-effect assessment.The first 9 participants and last 13 participants were exposed to 100 and 150 strides of baseline, respectively.The number of strides at baseline were increased after seeing inconsistent convergence across the first 9 participants to a steady state value after 100 strides.Each session lasted for approximately 15 minutes and all sessions within the same visit were separated by a minimum of 10 minutes of rest outside of the exoskeleton to reduce the effects of fatigue.The second and third visits each consisted  1) Outcome Measures: Four outcome measures were selected to describe the effects of the intervention on propulsion mechanics, defined consistent with our previous work [15] (when applicable).Gait speed (GS) was defined as the velocity of the two treadmill belts, as determined by the response of user-driven treadmill controller.Right hip extension angle (HE) was defined as the angle of the hip of the right (robotassisted) leg as measured by the hip motor encoder at the instant of peak anterior ground reaction force (aGRF).Normalized propulsive impulse (NPI) of the right leg was defined as the integral of the antero-posterior component of GRF over the time interval that the component is positive, normalized by the participant's body weight (in N).Trailing limb angle of the right leg (TLA) was defined as the angle formed by the line connecting the hip marker and ankle marker (V Leg ), relative to the global vertical axis, at the instant (t P ) of peak aGRF, i.e., as: The experiment was divided into three sections: 100 strides 16 before pulse application (baseline), 300 strides of pulse appli-  AE-L) -last 20 strides of no pulse condition after intervention (581-600).At each of these time points, we obtained the outcome measure as the mean for the designated strides.
2) Effects of torque pulses on propulsion mechanics: We performed pairwise tests to establish whether any pulse condition significantly modulated the outcome measures during pulse application (2 paired tests per pulse pairing P-E with BL and P-L with BL), and after pulse application (2 paired tests per pulse pairing AE-E with BL and AE-L with BL).The Shapiro-Wilk test was used to detect normality of the paired samples.If the samples were normally distributed, a ttest was performed, otherwise a Wilcoxon signed-rank test was performed.For either test, a false-positive rate of α = 0.05/48 was selected, using a Bonferroni correction to account for 48 comparisons (4 comparisons per pulse x 12 pulses).Since the Bonferroni correction leads to a conservative statistical threshold, we also report the significance of pulse-specific Dunnett's tests for comparison of outcomes at each Time Point relative to baseline, within each pulse condition of each measure, given a false-positive rate of α = 0.05/4.

3) Effects of torque pulse parameters on propulsion mechanics:
We performed linear mixed effect models to determine how factors of the pulses modulated the outcomes at different time points.We utilized JMP Pro Version 16 (SAS Institute Inc., Cary, NC, USA) to fit a linear mixed model to each of the four outcome measure data sets consisting of 880 data points.Each data set consisted of 2 groups, 11 participants per group, 8 pulse conditions per participant group (of the 12 total pulse conditions), 5 evaluation time points per pulse condition, and one outcome per time point.The linear mixed model effects were participant (1 through 22), phase of gait cycle (Early or Late Stance), hip torque (-15 N•m or 15 N•m, respectively), knee torque (-10 N•m, 0 N•m, or 10 N•m), and time point of measurement (BL, P-E, P-L, AE-E, or AE-L).The fixed effects included the main, two-way, threeway, and four-way effects of stance, knee torque, hip torque, and time point.The random effects included the main effect of participant and two-way interaction of participant and the four main effects.Fixed effects tests and statistical contrasts were conducted with a false positive rate of α = 0.05.

4) Association between propulsion mechanics during and after torque pulse application:
Stepwise regressions were performed on the measured data to establish the association between the change in measured effects from baseline (BL) to late after training (AE-L) (dependent variable) and the change in effects measured between BL and training (P-E & P-L) across all pulse condition and participants (set of independent variables).Given the multi-collinearity problem in the multiple metrics of propulsion mechanics quantified during training, we used a stepwise regression method to identify a minimal set of explanatory variables for each outcome measure [29], and ran separate models for each of the four outcomes.The initial terms considered for each model included the difference in effects of all four outcome measures assessed between BL and training (P-E & P-L).For each of the four models, we performed a stepwise regression with backward elimination, utilizing an automatic exclusion rule of p < 0.05 to remove explanatory variables from the models.The backwards elimi-1 nation procedure was given freedom to select terms regardless 2 of broken hierarchy.

4
The stride by stride group means, with the BL Time Point

B. Effects of torque pulse parameters on propulsion mechanics
The linear mixed effect models had an adjusted R 2 of 0.70, 0.71, 0.86, and 0.76 for GS, HE, NPI, and TLA, respectively, which indicates a high goodness of fit.The fixed effects are reported in Table II.Given the interest in analyzing training effects, the significant fixed effects that include TP are presented in detail below, together with a list of relevant post-hoc tests that are useful to interpret the size and direction of each effect.
1) Gait Speed: Time Point was a significant main effect for GS, as GS was greater at P-L (0.034±0.012 m/s, p = 0.043), AE-E (0.034±0.012 m/s, p = 0.039), and AE-L (0.047±0.012 m/s, p = 0.002) than BL, across all pulse conditions.Also, the model revealed a significant interaction of Time Point and Hip Torque, shown in Fig. 5, driven by an increase in GS at P-L (0.067±0.016 m/s, p = 0.001) and AE-L (0.062±0.016 m/s, p = 0.005) from BL, under the application of Hip Flexion Torque.A contrast analysis of this two-way interaction shows that the change in GS between P-L and BL was greater under Hip Flexion Torque than under Hip Extension Torque (0.067±0.010 m/s, p = 0.001).
The three-way interaction of Time Point, Phase, and Knee Torque was significant for HE (Fig. 6).For Knee Flexion Torque pulses at Early Stance, HE increased at several Time Points compared to BL (P-L: 3.93±0.93     The three-way interaction of Time Point, Phase, and Hip

8
Torque was significant for HE (Fig. 7).For Hip Flexion Torque A contrast analysis of the three-way interaction of Time Point, Phase, and Hip Torque revealed that for Hip Flexion   Torque (Fig. 8).This was driven by a greater increase of NPI 11

B L P -E P -L A E -E A E -L
from BL, at P-E and P-L, under Hip Extension Torque pulses 12 relative to Hip Flexion Torque (P-E: 2.51±0.46ms, p = 0.007; 13 P-L: 2.34±0.46ms, p = 0.011). 14 The three-way interaction of Time Point, Phase, and Knee

4) Trailing Limb Angle:
The two-way interaction between Time Point and Knee Torque was significant for TLA.A contrast analysis reveals that the change in TLA with respect to BL under Knee Flexion Torque is greater than the one measured under Knee Extension Torque at two time points (P-E: 0.822±0.177deg, p = 0.021); P-L: 0.982±0.177deg, p = 0.006).

C. Association between propulsion mechanics during and after torque pulse application
The stepwise regression models identified robust associations between changes in propulsion mechanics during and after torque pulse application, with R 2 values of 0.46, 0.51, 0.26, and 0.38 for GS, HE, NPI, and TLA, respectively.For GS, only two terms remained in the model after backwards elimination, while three terms remained in the models for HE, NPI, and TLA, a large reduction from the initial set of 8 explanatory variables.Measurements of the same outcome during pulse application were consistently retained by the backwards elimination procedure, for all outcomes.Specifically, a consistent positive association between the measurement of a specific outcome at P-L and the measurement of the same outcome at AE-L was detected in all models as the term with the highest level of significance.This association can be interpreted as a retention of the effects of training, where for GS, 70% of the changes measured at P-L were retained at AE-L (parameter estimate: 0.701, t-ratio: 143.36); for PE, 79% of the changes measured at P-L were retained at AE-L (parameter estimate: 0.787, t-ratio: 165.00); for NPI, 38% of the changes measured at P-L were retained at AE-L (parameter estimate: 0.378, tratio: 43.81); for TLA, 55% of the changes measured at P-L were retained at AE-L (parameter estimate: 0.547, t-ratio: 84.66) (S5, column one).
Secondary to the retention effects, the model also identified a negative association between changes in propulsion mechanics during early pulse application and after-effects (S5, column two).Specifically, 40% of the changes in HE at P-E were reflected in the opposite direction at AE-L (parameter estimate: -0.392, t Ratio: 25.69), 16% of the changes in NPI at P-E were reflected in the opposite direction at AE-L (parameter estimate: -0.160, t Ratio: 9.05), and 23% of the changes in TLA at P-  The main objective of this experiment was to quantify the 37 effects on propulsion mechanics of torque pulses applied to the 38 hip and knee joint during the stance phase of walking, when 39 participants walk on a user-driven treadmill.We collected 40 data on 22 healthy participants, exposed to twelve different 41 combinations of torque pulses, applied to the hip and/or knee 42 joint during early or late stance, and quantified the effects 43 on propulsion mechanics, specifically gait speed (GS), hip 44 extension (HE), normalized propulsive impulse (NPI), and 45 trailing limb angle (TLA).

46
Overall, our experiment indicates that pulses of torque 47 applied to the hip and knee joint during user-driven treadmill 48 control can induce significant changes in propulsion mechan-

42
For NPI, a kinetic measure of propulsion, pulse application significant effects during pulse application and after-effects were positive in direction.In general, conditions exhibiting the largest positive changes in HE, and not NPI, during or after training resulted in increased GS after training.For example, for pulse 13, despite the positive after-effects in NPI, no significant effects were measured on GS.Instead, the largest positive after-effect in GS were measured for pulse conditions 4, 8, 14, 16. 4, 8, and 14 are conditions where HE was significantly increased during pulse application, while 16 is a condition where HE changed initially in a negative direction, but then exhibited large positive after-effects.Looking more closely at the dynamics of GS evolution over the course of an experiment (Fig. S1), GS appears to increase through out the progression of the walking conditions for many of the pulse conditions on the group level.While many of the changes are not statistically significant at the individual pulse level (4), and so potential "drift" effects are smaller than the ones induced by specific torque pulse condition, the main effect of time point on GS indicates the that P-L, AE-E, and AE-L are all greater than baseline.This effect may be due in part to the participants not having reached a steady state walking speed on the userdriven treadmill, within the 100-150 strides of baseline..
Overall, the stepwise regression models indicate that the effects in propulsion mechanics measured after torque pulse application are associated with changes measured during pulse application, and that the nature of such an association is primarily of retention of training effects.Such retention seems to be primarily limited to the specific component of propulsion mechanics, whereby changes in HE after training are most strongly predicted by changes in HE during training, and so for NPI, TLA, and GS.Some of the measured effects are in alignment with those measured previously in an experiment conducted at fixed walking speed [15].In our previous work, we measured increased HE during training in conjunction with early stance extension and with late stance flexion torques, while a reversal in these torque directions led to decreased HE.In the user-driven treadmill training presented here, early pulse application effects were relatively attenuated but late application effects and aftereffects were larger in magnitude and only positive.As per NPI, it had increased during training for flexion torques applied at late stance, and increased after training in conjunction with flexion torque pulses applied at early stance.In the userdriven treadmill training, only early stance extension torques, particularly at the knee, and late stance hip extension and knee flexion torques, exhibited strong positive effects in NPI during early pulse application.In agreement with the previous experiment, early stance flexion torques (pulse 8), particularly that which included the knee, exhibited significant positive after-effects in NPI.In addition, the user-driven treadmill experiment indicated has significant positive after-effects in NPI for late stance extension torques.
This study did have some limitations, that should be considered for future research in this topic.First, all participants held to the left handrail during the experiment.While this was consistent across all participants and pulse conditions, this factor may have introduced biomechanical constraints and/or effects to propulsive forces that have not been captured in the presented analyses.Moreover, the accuracy of the user-driven treadmill controller in identifying the participant's desired speed has not been quantified prior to this experiment.Specifically, the effect of several factors, such as the personal preference in being at the front or back of the treadmill, subject preference for a more/less responsive controller, effect of delay with respect to the lunge measurement, on the resultant behavior of the user-driven treadmill controller are likely complex.For both reasons, the results of this study are meaningful in a relative sense (comparison between torque conditions and different phased of torque pulse application within a gait cycle), but likely not in an absolute sense (i.e., change in GS, HE, NPI) when comparing to other studies using different experimental setups.

Fig. 1 :
Fig. 1: Pulses corresponding to the two separate groups, each consisting of 11 participants.

Fig. 2 :
Fig. 2: Experimental setup consisting of a participant in the Active Leg EXoskeleton II (ALEX II) and wearing a safety harness while on the instrumented split-belt treadmill.

Fig. 3 : 2 conditions to training sessions were pseudo-randomized across 3 participants. 4 F. Data Analysis 5 For 13 (
Fig. 3: Visual representation of a training session, consisting of 100 (or 150) strides of baseline, 300 strides of pulse application, followed by 200 strides for after-effect assessment. of 3 additional pulse training sessions, for a total of eight 1

5
value subtracted, of the four outcome measures for all twelve 6 pulses are visualized in Figs S1 -S4.The results of statistical 7 analysis conducted using the selected outcome measures is 8 reported below.

Fig. 4 : 3 the 6 ( 3 .
Fig. 4: Breakdown of GS, HE, NPI, and TLA by factor for the twelve tested pulses.Circles indicate measured group means, whiskers indicate s.e.m., asterisks indicate statistically significant Dunnett's test comparison to respective baseline.

Fig. 5 : 1 HE (- 3 . 2 Conversely, for Hip Extension Torque pulses, a change from 3 4 p
Fig. 5: Least square means and S.E.M. of the two-way interaction between Time Point and Hip Torque of the linear mixed model for GS.

6 3 ) 8 BL ( 1 .
Normalized Propulsive Impulse: Time Point was a sig-7 nificant main effect for NPI, as NPI was greater at AE-L than 32±0.44 ms, p = 0.025) across all conditions.The 9 model revealed a significant interaction of Time Point and Hip10

16 shows 18 BFig. 6 :Fig. 7 :
Fig. 6: Least square means and S.E.M. of the three-way interaction between Time Point, Phase, and Knee Torque of the linear mixed model for HE.

Fig. 8 :Fig. 9 :
Fig. 8: Least square means and S.E.M. of the two-way interaction between Time Point and Hip Torque of the linear mixed model for NPI.

Fig. 10 :
Fig. 10: Least square means and S.E.M. of the two-way interaction between Time Point and Knee Torque of the linear mixed model for TLA.

1
ics in a group of healthy individuals.The most consistent 2 effects were measured for the outcome measure of HE.HE 3 increased significantly during pulse application in eleven out 4 of twelve conditions, and decreased relative to baseline in 5 two conditions during early pulse application.Moreover, HE 6 increased after training relative to baseline in eleven out of 7 twelve pulse conditions.Significant effects during and after 8 pulse application were detected also for NPI, with significant 9 positive or negative changes measured during pulse application 10 (five out of twelve conditions), and significant increases in 11 NPI measured in three of twelve conditions after torque pulse 12 application.Effects on GS were present in a smaller number 13 of conditions than in HE (positive effect in eight out of twelve 14 conditions at late pulse application), but changes in GS were 15 positively associated with changes in HE at all time points (r 16 regression coefficient at PE-E: 0.41, PE-L: 0.22, AE-E: 0.35, 17 AE-L: 0.40), more so than with changes in NPI (r regression 18 coefficient at PE-E: 0.09, PE-L: 0.00, AE-E: 0.17, AE-L: 19 0.11).Effects on TLA were also associated with the effects on 20 HE (r regression coefficient at PE-E: 0.63, PE-L: 0.43, AE-E: 21 0.37, AE-L: 0.48), but the magnitude of the effects on TLA 22 was much smaller than on HE (significantly increased relative 23 to baseline only in one pulse condition during training, no 24 significant changes in TLA were detected after training).25 Phase was the most important factor in modulating HE 26 effects during and after training, relative to baseline, as knee 27 torque and hip torque modulated HE differently, and often in 28 opposite directions, depending on the timing of the applied 29 pulse.For example, at P-L, knee torque applied in flexion or 30 extension exhibited an opposite change in HE with respect 31 to BL, depending on whether the torque was applied during 32 early or late stance.Similarly, at each hip torque condition, 33 a reversal in phase condition lead to a different directional 34 change in HE with respect to BL.Ultimately, the kinematic 35 measure of interest for propulsion is TLA.Our analysis 36 indicates that pulses of torque to the hip and knee have 37 only a limited effect on modulating TLA, suggesting likely 38 compensations occurring with the ankle joint and possibly with 39 the timing of push-off.This observation is consistent with the 40 literature that HE angle is not directly related to propulsion 41 mechanics [30].

Fig. S1 :
Fig.S1: Group mean and 95% confidence interval for GS data by stride, with the average measurement at the BL time point subtracted for all twelve pulse conditions.Shaded region of each condition indicates strides during which pulses are applied and non-shaded regions indicate strides for baseline or after-effect assessment.

Fig. S2 :
Fig. S2: Group mean and 95% confidence interval for HE data by stride, with the BL time point measure subtracted for all twelve pulse conditions.Shaded region of each condition indicates strides during which pulses are applied and non-shaded regions indicate strides for baseline or after-effect assessment.

Fig. S3 :
Fig.S3: Group mean and 95% confidence interval for NPI data by stride, with the BL time point measure subtracted for all twelve pulse conditions.Shaded region of each condition indicates strides during which pulses are applied and non-shaded regions indicate strides for baseline or after-effect assessment.

Fig. S4 :
Fig.S4: Group mean and 95% confidence interval for TLA data by stride, with the BL time point measure subtracted for all twelve pulse conditions.Shaded region of each condition indicates strides during which pulses are applied and non-shaded regions indicate strides for baseline or after-effect assessment.

Fig. S5 :
Fig.S5: Prediction profiles for changes in GS, HE, NPI, and TLA at late after-effects given the main effects during early or late pulse application identified by stepwise regression.
).A custom real-time controller 79 written in MATLAB & Simulink (MathWorks Inc., Natick 80 MA, USA) acquired signals from the instrumented split-belt 81 treadmill and ALEX II and sent command signals to the two 82 motors at a frequency of 1000 Hz.Dell Precision 3620 with a Windows 7 OS 87 (Dell Inc., Round Rock, TX, USA).The ALEX II contains 88 two Kollmorgen ACM22C rotary motors with integrated Smart 89 Feedback Devices (Danaher Corporation, Washington D.C., 90 USA).These provide an emulated encoder resolution of 4096 91 pulses per revolution providing an effective hip and knee angle 92 For Knee Extension Torque pulses at Early Stance, HE was greater at AE-L than BL (4.37±0.93deg, p = 0.001) and similarly for Knee Flexion Torque at Late Stance, HE was greater at AE-L than BL (4.28±0.93deg, p = 0.002).Lastly, in conditions Zero Knee Torque pulses at Early Stance conditions (grouping conditions where only hip torque is applied at Early Stance, i.e. Pulses 3 and 4), HE was greater at AE-L than BL (5.32±1.15deg, p = 0.002).

TABLE I :
Effect sizes for all pairwise comparisons between baseline and each following time points for all twelve conditions.Values are bolded if statistically significant using a Bonferroni correction across all pulses, and marked with an asterisk if significant for a pulse-specific Dunnett's test.

TABLE II :
Fixed effect test results for the linear mixed effect models: GS, HE, NPI, and TLA GS Fixed Effects Tests Nparm DFNum DFDen F Ratio Prob >F

TABLE III :
Fixed effects test results for the stepwise regression models: GS, HE, NPI, and TLA