Twenty-nine participants at least six months post-stroke completed a single session of paretic propulsion biofeedback training. Participants were recruited from the community and the Registry for Aging and Rehabilitation Evaluation database at the University of Southern California. Participants were included if they could walk independently for five minutes on a treadmill, had paresis confined to one side, were aged 18–80, and had no exercise contraindications. Participants were excluded if they had damage to the pons, basal ganglia, or cerebellum on an MRI, signs of cerebellar involvement or extrapyramidal symptoms, uncontrolled hypertension, orthopedic or pain conditions, or Montreal Cognitive Assessment five-minute protocol score less than nineteen. If a participant regularly wore an ankle–foot orthosis for community ambulation, they wore it during the study.

We assessed motor impairment using the lower-extremity Fugl-Meyer scale [17] and balance using the Berg Balance Test [18]. We measured cardiovascular endurance using the six-minute walk test [19] and determined overground self-selected gait speed using the ten-meter walk test [20].

This protocol is described in detail in the text of Supplemental Methods. Briefly, we collected kinematic and kinetic data while participants walked on an instrumented treadmill at their self-selected speed. First, participants walked for two minutes without biofeedback. Then, they completed four five-minute biofeedback trials (see Supplemental Fig. 1A, for experimental paradigm). During the biofeedback trials, participants walked with paretic propulsion biofeedback, which provided the paretic limb's real-time anterior ground reaction force during stance. After each stride, participants were also given feedback of their peak paretic propulsion. The biofeedback goal was the midpoint between peak paretic and non-paretic propulsion at baseline [7], with a ± 5N goal zone. Please see Supplemental Fig. 1C for a schematic of the biofeedback paradigm. Some participants used the handrails (light touch) during the experiment for balance aid (n = 11).

Kinematic data were acquired using a ten-camera motion capture system (Qualisys AB, Goteborg, Sweden; 100 Hz), and kinetic data using a dual-belt instrumented treadmill (Bertec Corporation, Columbus, OH, USA; 1000 Hz). Participants wore a harness for safety; however, the harness did not provide body weight support. Markers were placed bilaterally on the iliac crest, greater trochanter, lateral femoral epicondyle, lateral malleolus, and fifth metatarsal head.

All data were processed and analyzed in MATLAB R2020a (MathWorks, Natick, MA). Kinematic data were low-pass filtered with a 6 Hz cutoff, and kinetic data were low-pass filtered with a 20 Hz cutoff [21]. Foot-strike and toe-off were estimated as the most anterior and posterior positions of the lateral malleoli markers, respectively.

We first calculated peak propulsion (P) as the most positive value of the anterior/posterior ground reaction force during the stance phase for both limbs. Positive values corresponded to anteriorly directed ground reaction forces. Then, we calculated propulsion asymmetry magnitude (|PA|; Eq. 1). [22]

$$|\text| = \frac_-_)}_+_}$$

(1)

We then calculated the change in propulsion asymmetry magnitude (Δ |PA|) from baseline for each stride taken during the biofeedback trials. To do this, we averaged propulsion asymmetry magnitude across the final thirty strides of the baseline trial. Then, we subtracted this value from propulsion asymmetry magnitude for each stride taken during the biofeedback trials, reflecting how much participants changed propulsion asymmetry compared to baseline.

The CGAM is an overall gait asymmetry measure that allows for the inclusion of any lateralized biomechanical measures of interest and provides a single measure of overall gait asymmetry between 0 (no asymmetry) and 200 (completely asymmetric) [15]. First, a symmetry index (si) is calculated for each biomechanical impairment of interest (M) using Eq. 2. Then, the symmetry indices (si) are combined into a single symmetry matrix for each participant (S), with m columns (number of metrics) and n rows (number of strides). Finally, the symmetry matrix and the covariance of the symmetry matrix (KS) are used to calculate CGAM for each stride (Eq. 3).

$$_=100* \frac_-_)}_+_)}$$

(2)

$$CGAM= \sqrt_\right)*S}_)}}$$

(3)

We had eight candidate variables to include in the CGAM calculation: single-limb support time, double-limb support time, stance time, step length, peak swing knee flexion, peak hip flexion, trailing limb angle, and circumduction. Before calculating CGAM using these variables, we checked for collinearity using a variance inflation factor (VIF) cutoff of ten [23] to ensure we were not including variables that were closely related. We found that stance time and single-limb support time had VIF values greater than ten. After removing stance time, the remaining variables had a VIF of less than ten. Therefore, we included the following seven variables in the CGAM calculation: double-limb support time, single-limb support time, step length, peak swing knee flexion, peak hip flexion, trailing limb angle, and circumduction. Definitions for the variables included in the CGAM calculation are described in the following section. We chose not to include propulsion in the CGAM calculation to understand the effect of manipulating propulsion asymmetry on overall gait asymmetry outside of what the biofeedback was designed to change.

Finally, we calculated the change in CGAM (Δ CGAM) from baseline for each stride. To do this, we averaged the CGAM values from the final thirty strides of the baseline trial and subtracted this value from the CGAM of each stride taken during the biofeedback trials.

Step length was defined as the anterior–posterior distance between the lateral malleoli markers at heel strike. Knee flexion was defined as the angle between the thigh segment (between lateral tibial epicondyle to greater trochanter markers) and shank segment (between lateral malleolus and lateral tibial epicondyle) in the sagittal plane. Hip flexion was defined as the sagittal plane angle between the thigh and pelvis segments (between greater trochanter and iliac crest markers). Circumduction was the maximal lateral difference between the ankle marker during swing and the same ankle marker during stance. Trailing limb angle was defined as the angle between the vertical lab axis and the vector created by the greater trochanter and lateral malleoli markers in the sagittal plane. Double-limb support time was the time from contralateral heel strike to ipsilateral toe off. Single-limb support time was the time from the contralateral toe-off to the contralateral heel strike.

All statistical analyses were performed in R (4.2.2) [24]. First, we confirmed that all participants had propulsion asymmetry at baseline. Participants with a baseline propulsion asymmetry < 0.11 (minimal detectable change for propulsion asymmetry in our data), were removed from all analyses. Then, we wanted to establish that participants used biofeedback to increase paretic propulsion as intended. To do this, we first normalized paretic propulsion to body weight and then averaged it over the final thirty strides of each trial. Then, we fit a linear mixed effects model with average paretic propulsion as the outcome, a fixed effect for trial, and a random intercept using the lme4 package [25].

Next, we determined how increasing paretic propulsion influenced propulsion asymmetry by fitting a linear mixed-effects model with Δ |PA| as the outcome, a fixed effect for change in paretic propulsion, and a random intercept for each participant. We also included a random slope because it improved the model fit (determined using the Bayesian information criterion score). We fit the model to the final 113 strides of each biofeedback trial for each participant, which matched the minimum number of strides per biofeedback trial taken in the cohort, ensuring that each participant had data from the same number of strides included in the analyses. The final 113 strides were included regardless of whether each stride was within the provided biofeedback goal. After fitting the model, the residuals did not meet regression assumptions (checked using the performance package [26]); therefore, we ran robust mixed-effects models to account for those violations [27] and report those results.

Next, we investigated the relationship between propulsion asymmetry magnitude and CGAM at baseline. To do this, we fit a robust linear mixed-effects model with CGAM as the outcome, a fixed effect for propulsion asymmetry magnitude, and a random intercept for each participant. We fit the model to the final 42 strides of the baseline trial for each participant, which matched the minimum number of strides taken during the baseline trial in the cohort.

To test our primary hypothesis, we examined the relationship between Δ |PA| and the corresponding Δ CGAM. To do this, we fit a robust linear mixed-effects model with Δ CGAM as the outcome, a fixed effect for Δ |PA|, and a random intercept for each participant. We also included a random slope because it improved the model fit. We fit the model to the last 113 strides of each biofeedback trial for each participant, which matched the minimum number of strides per biofeedback trial taken in the cohort. The final 113 strides were included regardless of whether each stride was within the provided biofeedback goal.