Large propulsion demands increase locomotor learning at the expense of step length symmetry

There is a clinical interest in increasing the extent of locomotor learning induced by split-belt treadmills that move each leg at different speeds. However, factors facilitating locomotor learning are poorly understood. We hypothesized that augmenting the braking forces, rather than propulsion forces, experienced at the feet would increase locomotor adaptation and learning. To test this, forces were modulated during split-belt walking with distinct slopes: inclined (larger propulsion than braking), declined (larger braking than propulsion), and flat (similar propulsion and braking). These groups were compared using step length asymmetry, which is a clinically relevant measure robustly adapted on split-belt treadmills. Unexpectedly, the group with larger propulsion demands (i.e., the incline group) adapted faster and more, and had larger after-effects when the split-belt perturbation was removed. We also found that subjects who propelled more during baseline and experienced larger disruptions of propulsion forces in early adaptation exhibited greater after-effects, which further highlights the catalytic role of propulsion on locomotor learning. The relevance of mechanical demands on shaping our movements was also indicated by the steady state split-belt behavior, during which each group recovered their baseline leg orientation to meet leg-specific force demands at the expense of step length symmetry. Notably, the flat group was nearly symmetric, whereas the incline and decline group overshot and undershot symmetry, respectively. Taken together, our results indicate that forces propelling the body facilitate gait adaptation during split-belt walking. Therefore, interventions that increase propulsion demands may be a viable strategy for augmenting locomotor learning in individuals with hemiparesis. Key Points Summary Split-belt walking (i.e., legs moving at different speeds) can induce locomotor learning and even improve hemiparetic gait, but little is known about how to facilitate this process. We investigated the effect of braking and propulsion forces on locomotor learning by testing young unimpaired subjects on the split-belt condition at different slopes (i.e., flat, decline, and incline), which distinctively modified these forces. Propulsion forces facilitated locomotor learning indicated by 1) greater adaptation and after-effects following split-belt walking of the inclined group, which experienced larger propulsion demands and 2) a positive correlation between individual after-effects and subject-specific propulsion during regular walking and initial steps in the split condition. Interestingly, incline and decline groups self-selected asymmetric step lengths at steady state in the split condition, challenging the prominent view that step length asymmetry is a biomarker for inefficient gait. Our results suggest that interventions augmenting propulsion demands could correct hemiparetic gait more effectively.

• Split-belt walking (i.e., legs moving at different speeds) can induce locomotor learning 23 and even improve hemiparetic gait, but little is known about how to facilitate this 24 process. 25 26 • We investigated the effect of braking and propulsion forces on locomotor learning by 27 testing young unimpaired subjects on the split-belt condition at different slopes (i.e., 28 flat, decline, and incline), which distinctively modified these forces. 29 30 • Propulsion forces facilitated locomotor learning indicated by 1) greater adaptation and 31 after-effects following split-belt walking of the inclined group, which experienced larger 32 propulsion demands and 2) a positive correlation between individual after-effects and 33 subject-specific propulsion during regular walking and initial steps in the split condition. 34 35 • Interestingly, incline and decline groups self-selected asymmetric step lengths at steady 36 state in the split condition, challenging the prominent view that step length asymmetry 37 is a biomarker for inefficient gait. 38 39 • Our results suggest that interventions augmenting propulsion demands could correct 40 hemiparetic gait more effectively. 41

Introduction 42
There is an interest in increasing the extent of locomotor adaptation and learning 43 induced by split-belt walking because it can correct the step length asymmetry of individuals 44 with hemiparesis, such as stroke survivors. Post-stroke rehabilitation targets step length 45 asymmetry because it impairs mobility by augmenting the effort to walk (Waters & Mulroy, 46 1999), reducing walking speed (Balasubramanian et al., 2007), compromising balance (Lewek et 47 al., 2014), and if not corrected, step length asymmetry leads to other comorbidities such as 48 musculoskeletal injuries (Jørgensen et al., 2000) and joint pain (Patterson et al., 2012). 49 Promising studies have shown that walking with the legs moving at different speeds (i.e., split-50 belt walking) results in long-lasting reduction of step length asymmetry post-stroke when 51 walking overground (Reisman et al., 2009(Reisman et al., , 2013. However, split-belt walking is not always 52 effective even after repeated exposure to the split-belt experience (Reisman et al., 2013;Lewek 53 et al., 2017) and it is still unclear why some stroke survivors re-learn to walk symmetrically but 54 others do not. Thus, it is fundamental to identify factors facilitating split-belt adaptation to 55 augment them for increasing motor learning in all individuals. 56 The increased mechanical work (Selgrade et al., 2017), step length asymmetry (Reisman 57 et al., 2005), and hence metabolic effort , upon introducing the split-belt 58 environment are thought to drive locomotor adaptation. Notably, these three factors are large 59 during the initial steps of split-belt walking and are minimized as subjects learn to walk in the 60 split-belt context Selgrade et al., 2017). Thus, modulating anterior-posterior 61 forces applied at the feet during split-belt walking could facilitate locomotor adaptation given 62 their direct impact on mechanical work and step lengths in regular gait (Donelan et al., 2002). In 63 particular, we hypothesize that altering braking forces could modulate the adaptation of gait 64 based on prior studies showing that braking forces are critical for gait stability (Beschorner et al.,65 proxy for the body's position, was estimated as the mean instantaneous position across hip 159 markers. α-distances were positive because the foot usually lands in front of the hips, whereas 160 X-distances were negative because the trailing leg is behind the hips at foot landing. Note that 161 the summation of the magnitudes of α and X equals the leading leg's step length. Dashed lines indicate when the resting breaks occurred (B) The decomposition of step length 169 into leading (α) and trailing (X) leg positions with respect to the body are illustrated. This 170 decomposition was done because it is known that inclination affects these aspects of step 171 length differently (Leroux, et al 2002;Dewolf et al 2017). Also note that when taking a step, the 172 step length will depend on the position of the leading and trailing leg, which are generating a 173 braking and propulsion force, respectively. (C) Anterior-posterior forces are plotted for sample 174 subjects walking at the baseline epoch in each inclination condition. The filtered forces (un-175 shifted panels) clearly illustrate the effect of inclination on braking and propulsion forces: the  176  incline group reduced braking and accentuated propulsion, the flat group experienced similar  177  braking and propulsion, and the decline group accentuated braking and reduced propulsion. To  178 facilitate the identification of peak braking (maximum negative value) and peak propulsion 179 forces (maximum positive value) in all conditions, we removed the slope-specific projection of 180 subjects' weight on the AP direction (shifted panels). This procedure also allowed us to 181 characterize the magnitude of kinetic outcome measures for each condition beyond those due 182 to the slope-specific bias. (D) We used the peak braking and peak propulsion force for each 183 step to compute outcome measures of interest, such as the ΔAdapt measure. This measure was 184 computed to quantify increments or reductions in magnitude within the adaptation epoch of 185 each specific parameter. Note that increases in magnitude were defined as positive changes, 186 whereas decreases in magnitude were defined as negative changes. 187 188 Kinetic Data Analysis: 189 We characterized how ground reaction forces were modulated by inclination. The kinetic 190 analysis was focused on forces in the anterior-posterior direction since these are modulated by 191 inclination (e.g., Lay et al., 2006) and they are adapted during split-belt walking (Ogawa et al., 192 2014). The anterior-posterior ground reaction forces (AP forces) where normalized by each 193 subject's body weight to account for inter-subject differences in weight. The quiet stance forces 194 for the incline and decline groups were subtracted in order to facilitate the identification of both 195 positive (propulsion) and negative (braking) features of the AP forces at all slopes and to 196 characterize the magnitude of these force for each condition beyond those due to the slope-197 specific bias. The removal of the quiet stance forces is illustrated for a representative subject at 198 each inclination in Figure 1C. Note that at quiet stance (i.e., when subjects are just standing), 199 there is an anterior-posterior ground reaction force due to the projection of subjects' weight on 200 the surface of the treadmill. This quiet stance force is zero for the flat group since AP forces are 201 negligible during quiet stance on a level surface. However, this quiet stance force was 202 substantial for the inclined and declined group. Thus, we calculated the quiet stance force based 203 on the inclination of the treadmill and subtracted it from AP forces during gait (Eq. 1). 204 The shifted AP forces were further decomposed into braking and propulsion forces for each 206 stride. The braking force was defined as the component of the shifted AP force with negative 207 values. The braking forces were computed independently for the slow (BS) and fast legs (BF). 208 On the other hand, the propulsion force was defined as the component of the shifted AP force 209 with positive values that followed the braking phase ( Figure 1D). The propulsion forces were 210 also computed independently for the slow (PS) and fast legs (PF). We focused our analysis on 211 the peak braking and propulsion forces for each leg and for each stride ( Figure 1D Table 1. Medium baseline behavior was used as a reference 219 in all outcome measures computed with kinematic parameters (e.g., step length asymmetry and 220 step lengths), whereas speed-specific baselines were used for kinetic parameters (e.g., braking 221 and propulsion forces). In other words, fast baseline was used as a reference for the leg walking 222 fast during adaptation and the slow baseline was used as a reference for the leg walking slow 223 during adaptation, whereas medium baseline was used as a reference for both legs when they 224 walked at the same medium speed in post-adaptation. This methodology is consistent with 225 prior split-belt studies indicating that kinetic parameters plateau near values similar to those of 226 the speed-specific baseline . Outcome measures of interest were Early 227 Adaptation, Late Adaptation, After-Effects, ΔAdapt, and ΔPost. Early Adaptation (EarlyA) was 228 defined as the difference between the averaged behavior of the first 5 strides of the split-belt 229 condition (strides 1-5) and the speed-specific baseline values as indicated earlier. This outcome 230 measure characterized the extent to which subjects were perturbed by the split-belt condition. 231 Note that we did not exclude any strides of adaptation because all subjects experienced a short 232 split condition before the adaptation period to minimize startle effects. Late Adaptation (LateA) 233 was defined as the average of the last 40 strides of adaptation for all parameters. This outcome 234 measure indicated the steady state behavior reached at the end of the adaptation period. After-235 Effects were defined as the average of the first 5 strides of Post-Adaptation relative to medium 236 baseline such that increments and reductions in magnitude of a specific parameter with respect 237 to medium baseline were marked as positive or negative, respectively. We also characterized 238 the behavioral changes within the adaptation and post-adaptation with indices ΔAdapt and 239 ΔPost, respectively. ΔAdapt and ΔPost were computed as the difference between Late and Early 240 Adaptation for ΔAdapt and late and early post-adaptation for ΔPost (i.e., average of the last 40 241 strides or 5 strides for late and early, respectively). This was done such that an increase in the 242 magnitude of a parameter during either adaptation or post-adaptation resulted in positive 243 values and a reduction of the parameter was marked as negative values. For example, we 244 illustrate ΔAdapt for braking and propulsion forces in Figure 1D. Note that the braking force 245 decreased during the adaptation period (negative value), whereas the propulsion force 246 increased during the same period (positive value). Lastly, the effect of slope on the rate of 247 adaptation was determined by fitting the averaged step length asymmetry for each inclination 248 group with a single exponential (y=a*exp((-1/τ)*x)+c) using a non-linear least squares method. 249 The 95% confidence intervals of the Tau coefficient were used to compare the adaptation rates 250 across groups. 251

Post-Hoc Data Analysis 252
Following our planned analysis, it was clear that propulsion forces were more important 253 for locomotor adaptation and learning processes than anticipated. Thus, features characterizing 254 each subject's propulsion forces were used as predictors in a statistical model to determine 255 after-effects of step length asymmetry at an individual level. In this propulsion-based model, we 256 hypothesized that perturbation of the propulsion forces per leg (i.e., propulsion during early 257 adaptation) would be predictive of step length asymmetry after-effects. We also considered that 258 each individual's magnitude of baseline propulsion could influence after-effects because we 259 reasoned that those with larger propelling tendencies maybe more prone to correcting 260 reductions to their propulsion forces. Additionally, we included subject-specific propulsion 261 asymmetries during baseline in our model because we thought that those who are naturally 262 more asymmetric could be less resistant to update their movements for achieving the large 263 propulsion asymmetry required for split-belt walking. In sum, a multiple regression analysis was 264 performed with step length asymmetry after-effects as a dependent variable and 6 regressors: We also perform two additional analyses to evaluate the predictive power of the propulsion-277 based model on after-effects of step length asymmetry at an individual level. First, we applied 278 the same procedure described above using step length, rather than propulsion force, to 279 determine if any information about the behavior of individual legs was predictive of the inter-280 subject variability of after-effects in step length asymmetry. Second we used a mean-based 281 model that only included the categorical factor as a regressor to test if the propulsion-based 282 model accounted for more inter-subject variability on step length asymmetry after-effects than 283 the group mean behavior. The explanatory power between models was contrasted with Bayes 284 Factor Analysis (Kass et al., 1995) using the Bayesian Information Criteria approximation 285 (Wagenmakers, 2007). Lastly, several multiple linear regressions between kinetic and kinematic 286 variables were performed within and across epochs to investigate the association between 287 propulsion forces and after-effects in step length asymmetry. Of note, the regression of 288 propulsion forces across epochs (i.e., between ΔAdapt and after-effects) was done with 289 contralateral legs to be consistent with the post-hoc observation that adaptation of step length 290 on one side led to after-effects on the other side (see Figure 3). 291

Table1: Outcome Measures 292
Outcome Measure Meaning Early Adaptation (EarlyA) Quantifies how perturbing split-belt walking is for a given parameter. This parameter is reported in reference to medium baseline for symmetry parameters, and in reference to speed specific baseline for leg-specific parameters. Late Adaptation (LateA) Quantifies the amount that the split-belt perturbation was counteracted for step length asymmetry only. This parameter is reported in reference to medium baseline for symmetry parameters.

After-Effects
Quantifies how much motor learning, or how much of the split-belt walking pattern subjects use following adaptation relative to medium baseline behavior. Positive values indicate that the post-adaptation is larger in magnitude than if was during baseline, except for individual step lengths where positive values indicate that the step length is increased in the Post-Adaptation Epoch.

ΔAdapt & ΔPost
Quantifies the change in a parameter during adaptation and post-adaption, respectively. Therefore, ΔAdapt and ΔPost enabled us to determine if changes during adaptation led to comparable changes during post-adaptation. Positive means there was an increase in magnitude of a parameter within an epoch and vice versa.

Rate of Adaptation
Quantified the group mean rate of adaptation of step length asymmetry for during adaptation assuming a single exponential.

Baseline Propulsion Magnitude
Quantifies subject's baseline propulsion force magnitude characteristic for each leg during medium baseline, which is the average walking speed during adaptation.

Baseline Propulsion Asymmetry
Quantifies subject's propulsion force laterality in the most demanding baseline condition (i.e., fast baseline). 293

Statistical Analysis 294
One-way ANOVAs were used to test the effects of inclination condition on kinetic and kinematic 295 outcome measures (e.g., ΔAdapt, After-Effects, etc.). Outcome measures with significant 296 ANOVAs were further analyzed with Tukey post-hoc testing. We compared the time constants 297 estimated from single exponential fits of group averages of step length asymmetry using the 298 95% confidence intervals for each rate coefficient. Time constants were determined to be 299 significantly different when the confidence intervals were not overlapping. We additionally 300 wished to know if each group's step length asymmetry steady state was different from zero, 301 therefore we performed a two-sided t-tests on each group's late adaptation values. A three-way 302 ANOVA was also performed to determine the effect of leg and inclination condition on the 303 changes of step length that occurred during adaptation and post-adaptation. As such, the 304 dependent variables were changes of step length that occurred during these epochs (i.e., 305 ΔAdapt and ΔPost); the independent variables were slope (i.e., incline, flat, decline), leg (i.e., 306 fast or slow leg), epoch (i.e., adaptation or post-adaptation), and the interactions between these 307 independent variables. Lastly, two multiple regressions were performed for step length 308 asymmetry to assess the association between 1) the perturbation (EarlyA) vs. adaptation 309 (ΔAdapt) of this parameter and 2) its adaptation vs. its after-effects. In these regressions group 310 was used as a categorical factor only if it was found to be independent of the continuous 311 variable (i.e., EarlyA for regression 1 and ΔAdapt for regression 2) as indicated by a non-312 significant Pearson Coefficient. Should a strong correlation between the categorical and 313 continuous regressor was found, a linear regression was performed and the confounding 314 influence of group was noted. For visualization purposes only, we displayed the results of a 315 linear regression when the continuous variable of the multiple regression analysis was a 316 significant factor. A significance level of α=0.05 was used for all statistical tests. MATLAB was 317 used for all statistical analysis (The MathWorks, Inc., Natick, Massachusetts, United States). 318

RESULTS 319
Inclination regulated the adaptation and after-effects of step length asymmetry. 320 Step length symmetry was not recovered in the sloped split-belt conditions. All groups were 321 perturbed by split-belt walking and subsequently adapted ( Figure 2A). However, each group 322 reached a different step length asymmetry by Late Adaptation (p<0.001) such that the flat group 323 plateaued near symmetric step lengths (SLA_LateA=0, p=0.08), whereas the decline group 324 undershot step length symmetry (SLA_LateA<0, p<0.001) and the incline group overshot step 325 length symmetry (SLA_LateA >0, p<0.001) ( Figure 2B). Interestingly, while both sloped groups 326 were perturbed more than the flat group (SLA_EarlyA: group main effect p=0.003; incline vs. flat 327 p=0.036; decline vs. flat p=0.002), only the incline group adapted more than the other two 328 groups (SLA_ΔAdapt: group main effects p<0.001; incline vs. flat p<0.001; incline vs. decline 329 p=0.002) and faster (Figure 2A; inlayed plot). Importantly, groups were not only distinct in their 330 adaptation, but also in their after-effects (p=0.002) such that the incline group had greater after-331 effect than the decline (p=0.03) and flat groups (p=0.002). Our regression analyses on individual 332 subjects revealed that larger perturbations led to more adaptation (pmdl<0.001, R 2 =89, 333 SLA_EarlyA: p<0.001) and greater adaptation resulted in more after-effects (R 2 =46; p<0.001). 334 However, these associations were likely driven by group differences since group was either a 335 significant categorical predictor of adaptation (Group: p<0.001) or group was strongly correlated 336 to the continuous predictor of after-effects (p=0.004). In other words, the larger perturbation 337 and adaptation of the inclined condition presumably resulted in greater after-effects in this 338 group compared to others. Therefore, contrary to our hypothesis, the slope condition 339 augmenting propulsion (i.e., incline walking) rather than braking led to more and faster 340 adaptation and greater after-effects. It was also unexpectedly found that the sloped groups 341 plateaued at values that were distinct from their baseline step length symmetry, begging the 342 questions of whether inclination had a different effect across individual step lengths (addressed 343 in Figure 3) and why this would happen (addressed in Figure 4). Each data point represents the average of 5 consecutive strides and shaded regions indicate the 349 standard error for each group. Note that the incline group adapted more quickly than the other 350 sloped conditions as indicated by the time constants found by fitting the group data with a 351 single exponential (R 2 >=0.86). The time constants are plotted with 95% confidence intervals 352 during the adaptation phase and the inlayed axis shows the fits of the adaptation timecourses 353 scaled between 0 (Early Adaptation) and 1 (Late Adaptation) for each group. (B) Bar plots 354 indicate the averaged step length asymmetry for each group during Late Adaptation ± standard 355 errors and horizontal lines indicate statistical differences between groups according to post-hoc 356 testing. Note that each group plateaued at different step length asymmetry values that were 357 statistically different from symmetry (zero value) as indicated by individual t-tests reported 358 below the x-axis. Individual subject behavior is indicated with grey dots for each group. (C) 359 Results from multiple regression analysis between ΔAdapt and two uncorrelated regressors: 360 slope condition and step length asymmetry during early adaptation. The regression model was 361 significant pmdl<0.001, R 2 =0.89 and both regressors were significant predictors. In panel C and 362 D, values for individual subjects are illustrated with colored dots and mean values for the group 363 are illustrated with colored squares. Lines on the squares represent standard error bars. p anova 364 parallel to either the x-axis or y-axis indicates the effect of inclination condition on the outcome 365 measure plotted on the respective axis. For example, panel C shows a significant group effect on 366 step length asymmetry during Early Adaptation (p anova =0.003) and delta (p anova <0.001). In 367 addition, significant post-hoc differences between groups are illustrated with lines connecting 368 colored squares. For example, panel C also illustrates that although the decline (red square) and 369 incline groups (green square) were more perturbed by split-belt walking than the flat group 370 (yellows square), only the incline group (green square) adapted more than the other two 371 groups. (D) Linear regression between ΔAdapt and After-Effects for step length asymmetry was 372 significant (p<0.001, R 2 =0.46). This indicated that the more step length asymmetry was adapted 373 (large ΔAdapt values), the greater the after-effects. However, this association was strongly 374 influenced by group differences. Specifically, the incline group who adapted the most, had the 375 largest step length asymmetry after-effects. 376 377 Inclination accentuates the adaptation of step lengths on the fast leg and subsequent after-378 effects on the slow leg.  Leg orientation mediated by inclination and walking speed underlay the distinct step length 420 asymmetries across sloped conditions. More specifically, subjects oriented their legs to 421 prioritize slope-specific demands on AP forces to walk at the speed imposed under each leg at 422 the expense of step length symmetry during adaptation. This is shown in Figure 4 illustrating the 423 top view of ankle positions relative to the body ( Figure 4A) and the step lengths to which these 424 positions contribute ( Figure 4B) at baseline walking (slow and fast speeds) and late adaptation 425 under each sloped condition ( Figure 4C). Note that in slow baseline walking (Fig. 4C 1  for each leg during Early Adaptation forces ± standard errors. We observed that the braking and 520 propulsion forces were more perturbed in the decline and incline groups, respectively, 521 compared to the flat group. In panels B through D, positive and negative values respectively 522 indicate increments or reduction in force relative to speed-specific baselines. Thin horizontal 523 lines between groups illustrate significant differences (p<0.05) based on post-hoc analysis and 524 gray dots indicate values for individual subjects. (C) ΔAdapt: The height of the bars indicates 525 group averages for the adaptation of braking and propulsion forces for each leg during split-belt 526 walking ± standard errors. We observed that the adaptation of braking was significantly greater 527 in the decline than the flat group, whereas the adaptation of propulsion was significantly larger 528 in the incline than the flat group. (D) After-Effects: The height of the bars indicates group 529 averages After-Effects during early post-adaptation relative to medium baseline ± standard 530 errors. The preferential impact of decline walking on braking forces and incline walking on 531 propulsion ones was also observed in the after-effects. Namely, the flat group had smaller after-532 effects in braking than the decline group and in propulsion than the incline group. 533 534 A propulsion-based model predicted subject-specific after-effects in step length asymmetry 535 While braking and propulsion forces were both altered with inclination during and after split-536 belt walking, the adaptation of movements only increased in the incline group who experienced 537 greater propulsion demands. This suggested that propulsion forces, rather than braking ones, 538 played an important role in the adaptation and after-effects of walking movements. 539 Consistently, we found that a propulsion-based model could predict individual after-effects in 540 step length asymmetry (F(4, 20)=17.5, R 2 =0.73, p<0.001) ( Figure 6A). In particular, we observed 541 a significant association between after-effects in step length asymmetry and the perturbation of 542 the slow leg's propulsion (t=-2.42, p=0.028), the slow leg's baseline propulsion (t=2.38, p=0.030), 543 and baseline's propulsion asymmetry (t=2.88, p=0.011). These significant coefficients in the 544 multiple regression equation indicated that subjects exhibiting greater after-effects in step 545 length asymmetry were 1) those who were more perturbed during split-belt walking, 2) those 546 who naturally had higher propulsion tendencies during baseline walking, and 3) those who 547 naturally had larger propulsion asymmetries (i.e., larger propulsion with their dominant than 548 non-dominant leg) during baseline walking. Interestingly, these associations were exclusive to 549 the non-dominant (i.e., slow) leg given that propulsion features of the dominant (i.e., fast) leg 550 during baseline (t=-0.47, p=0.64) or early adaptation (t=1.20, p=0.25) were not significant 551 predictors of after-effects in step length asymmetry. Importantly, inclination (categorical factor) 552 was also not a significant predictor (t<0.28, p>0.78) in the multiple regression analysis, 553 indicating that the propulsion-based model was not simply reflecting the differences in after-554 effects across groups (reported in Figure 2). The non-significant predictive power of the sloped 555 condition was reiterated by the Bayes Factor of 925 indicating that the propulsion-based model 556 had "very strong" predictive power (Kass Raftery, 2007) compared to a model that only included 557 the mean after-effect values for each group. This larger predictive power of the propulsion-558 based model was maintained, but to a lesser extent when using more strides to characterize 559 after-effects (1:10 strides, BF=97.3) as in prior work (Malone et al., 2012). Lastly, the propulsion-560 based model was still a better predictor of subject-specific step length asymmetries than a 561 multiple regression model based on individual step lengths (F(2, 22)=6.04, R 2 =0.21, p=0.02; 562 Bayes Factor of 11.9*10^3), in which only the disturbance of the slow step length was a 563 significant factor (SLs_EarlyA: t=-2.26 p=0.038; SLf_EarlyA: t=-2.05, p=0.057; SLs_base: t=-0.20, 564 p=0.84; SLf_base: t=-0.47, p=0.65; SLasym: t=-0.06, p=0.95). This indicated that subject-specific 565 propulsion forces during baseline and adaptation provided more information about inter-566 subject variability of after-effects than step lengths of individual legs, which is remarkable given 567 that step lengths were used to directly compute step length asymmetry. Therefore, each 568 participant's tendencies to regulate propulsion forces during baseline and adaptation epochs 569 were a strong indicator of individual after-effects in step length asymmetry, which represent 570 subject-specific learning during split-belt walking. 571 Finally, we observed that this association between unilateral disturbance of slow leg's 572 propulsion and after-effects in step length asymmetry can be explained by the impact of 573 propulsion forces on the slow step length during post-adaptation. This was indicated by 574 regression analyses between kinetic and kinematic variables within and across adaptation and 575 post-adaptation epochs ( Figure 6B-F). These regressions revealed that large perturbations of the 576 slow leg's propulsion led to large adaptation of this parameter ( Figure 6B; pmdl<0.001, R 2 =0.82), 577 such that subjects that were perturbed the most were also those that adapted the slow leg's 578 propulsion the most. In addition, the adaptation of the slow leg's propulsion force was positively 579 associated with after-effects on the other leg's propulsion ( Figure 6C; p=0.020, R 2 =0.38). In 580 other words, larger adaptation of the slow leg's propulsion was related to greater after-effects 581 on the propulsion of the fast side and not on the slow side (data not shown). This is consistent 582 with the post-hoc observation that adaptation of step length on one side led to after-effects on 583 the other side (see Figure 3). Importantly, there was a strong association between the fast leg's 584 propulsion after-effects and those of the trailing position of this leg (fast X-position) ( Figure 6D; 585 R 2 =0.80) when taking a step with the leg that walked slow in the split condition. Consistently, 586 the after-effects of the fast leg's X-position were associated to those of the slow leg's step 587 length ( Figure 6E; p<0.001, R 2 =0.84), which was strongly associated with step length asymmetry 588 after-effects ( Figure 6F; R 2 =0.89). It is worth pointing out that group was a factor in all these 589 regressions since it was either a significant categorical predictor in the multiple regressions (6B: after-effects in step length asymmetry (SLA_after-effect) and step lengths of the leg that walked 633 slow during the split condition (SLs_after-effect). This is consistent with results indicating that 634 step length asymmetries during post-adaptation are mostly attributed to the slow leg's step 635 length after-effects. 636 637

DISCUSSION 638
We investigated the influence of anterior-posterior forces on gait adaptation and learning 639 induced by split-belt walking at different slopes, which naturally altered leg orientation and 640 forces when feet were in contact with the ground. To our surprise, each inclination group 641 recovered their baseline leg orientation at the expense of step length symmetry, which was a 642 profound finding given that step length asymmetry is considered a biomarker of inefficient gait 643 Bhounsule et al., 2014;Awad et al., 2015;Finley & Bastian, 2017). These 644 distinct leg orientations were likely self-selected to generate the forces for walking at the 645 specific speed and slope set by each split-belt task. This was achieved by distinct adaptation 646 between the leading and trailing legs' orientation at foot landing, suggesting the involvement of 647 different physiological mechanisms in the control of leg orientation over the course of the 648 stance phase. It was also unexpected that propulsion forces, rather than braking ones, 649 influenced locomotor learning, which was indicated by the larger adaptation and after-effects of 650 the sloped group with larger propulsion demands compared to the one with larger braking 651 demands. The key role of propulsion forces was further supported by the fact that subject-652 specific propulsion tendencies during baseline and early adaptation were predictive of individual 653 after-effects. Taken together, our findings suggest that altering propulsion forces during split-654 belt walking facilitates locomotor learning. Therefore, interventions augmenting propulsion 655 demands could be more efficacious in the rehabilitation of hemiparetic gait. 656 657 658 The motor system prioritizes the control of leg orientation over step length symmetry 659 660 All groups recovered their baseline leg orientation at the expense of step length symmetry, 661 which indicated that speed-specific leg orientation was prioritized over symmetric step lengths. 662 This has two key implications. First, step length symmetry is a gait feature that is not as valued 663 by the motor system as previously considered. Specifically, step length symmetry is thought to 664 be tightly controlled because subjects self-select symmetric step lengths even in asymmetric 665 environments (e.g., Reisman et al., 2005;Savin et al., 2014) and those with more symmetric step 666 lengths in these environments are also those spending less metabolic energy (Finley et al., 667 2013). Thus, we surprisingly found that subjects in the incline and decline split-belt groups 668 respectively overshot and undershot step length symmetry to recover baseline leg orientations. 669 However, this finding can be explained by the impact of kinetic demands in shaping our 670 movements, which is the second implication of our result. Notably, inverted pendulum models 671 of walking suggest that subjects orient their legs to maintain a constant speed by equalizing 672 positive and negative work over the gait cycle (Kajita et al., 2001;Donelan et al., 2002;Kuo, 673 2002; Kuo et al., 2005). Consistently, we observed that subjects oriented their legs in the incline 674 and decline groups to generate the forces counteracting the distinct effect of gravity on the 675 center of mass at the different slopes (Lay et al., 2006). Thus, leg orientation is closely regulated 676 in order to walk at the distinct speeds and inclination (Leroux et al., 2002;Orendurff et al., 2008) 677 imposed on each group. We particularly observed a strong effect of slope on leg orientation 678 when walking slow, but this is also observed at fast speeds when using a coordinate frame 679 aligned with gravity (Leroux et al., 2002), rather than aligned with walking surface as done in this 680 study. Given that humans have least-effort tendencies (Margaria, 1976 The self-selected leg orientation also led to a contralateral relation between adaptation and 688 post-adaptation. In other words, the disruption to forces and movements of individual legs led 689 to more ipsilateral adaptation, but it did not result in larger ipsilateral after-effects. In fact, more 690 adaptation of one leg changed the gait of the other leg as indicated by after-effects in kinetic 691 and kinematic measures (e.g., propulsion forces, step length, and trailing position). This is in 692 contrast to sensorimotor adaptation of other motor behaviors such as reaching, in which 693 adaptation and de-adaptation effects are mostly constrained to a single effector (Nozaki et  length value for the leg walking slow during adaptation. This is exclusively observed during split 706 and not tied conditions, indicating that this might be task-constraint of split-belt walking, which 707 will be the subject of future work. In sum, split-belt walking at different slopes predominantly 708 altered the adaptation of one leg and let to subsequent after-effects on the other leg, 709 highlighting the bilateral nature of sensorimotor adaptation in walking. 710

711
Physiological mechanisms for controlling leg orientation. 712 713 Our results suggest distinct control between the leading and trailing legs' orientation when 714 taking a step because they transition differently upon sudden changes in the walking 715 environment. More specifically, the leading leg's orientation at foot landing (α position) exhibits 716 smooth and continuous changes when transitioning from the split to tied situations in all our 717 inclination conditions and other perturbation magnitudes (Malone et al., 2012), whereas the 718 trailing leg's orientation (X position) is discontinuous. This suggests that the leading leg's 719 orientation at foot landing is controlled in a feedforward manner -that is, it is planned before 720 the movement is executed based on an a slowly updated internal representation of the 721 environment. This is supported by the fact that sensory information about leg orientation at 722 foot landing is sent to cerebellar structures (Bosco & Poppele, 2001), housing the feedforward 723 control of movements (Herzfeld et al., 2015) and the fact that spinalized cats cannot adapt the 724 orientation of the leading leg during split-belt walking (Frigon et al., 2017). On the other hand, 725 the trailing leg's orientation when taking a step could be determined by a combination of 726 feedback and feedforward control. Consider that feedback mechanisms adjust our movements 727 by transforming delayed sensory information into actions in real-time (Jordan & Rumelhart, 728 1992;Bhushan & Shadmehr, 1999). Accordingly, the trailing leg's orientation is immediately 729 regulated upon manipulations to ipsilateral sensory information from spindles in hip muscles, 730 load sensors and cutaneous information (Grillner & Rossignol, 1978 Here we find that individuals biased to propel more or asymmetrically during 779 baseline walking exhibit larger after-effects. We speculate that these baseline features possibly 780 led to more adaptation and consequently larger after-effects. Consider that the split 781 perturbation disrupts propulsion away from the baseline behavior and subjects adapt towards 782 their original bias, as observed in other gait features (Malone & Bastian, 2014). Therefore, 783 individuals with greater biases need to adapt more to approach their larger baseline bias. In 784 addition, we observed that the asymmetric bias was in the same direction as the one observed 785 during late adaptation. Thus, subjects that were more asymmetric might adapt more because 786 they are more prone to adopt the asymmetric pattern needed to walk in the split condition. Of 787 note, we observed a large range of propulsion forces during baseline and early adaptation 788 across individuals, which might be needed to identify the reported association between 789 propulsion forces and after-effects. In sum, our findings indicate that augmenting propulsion 790 demands during split-belt walking facilitates gait adaptation and locomotor learning, suggesting 791 that altering propulsion forces could be used as a training stimulus for gait rehabilitation. 792

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Clinical implications 794 795 There is an interest in modulating the extent of split-belt adaptation and learning as stroke 796 subjects tend to only adapt to their baseline asymmetry during adaptation (Malone & Bastian,797