Step width and frequency to modulate: Active foot placement control ensures stable gait

Step width and frequency to modulate: 1 Active foot placement control ensures stable gait 2 3 A.M. van Leeuwen1,2, J.H. van Dieën1, A. Daffertshofer1,2, S.M. Bruijn1,2,3* 4 5 1Department of Human Movement Sciences, Faculty of Behavioural and Movement Sciences, Vrije 6 Universiteit Amsterdam, Amsterdam Movement Sciences, Amsterdam, The Netherlands 7 2Institute of Brain and Behavior Amsterdam 8 3Biomechanics Laboratory, Fujian Medical University, Quanzhou, Fujian, PR China 9


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In healthy individuals, ankle, hip and push-off strategies complement foot placement in 49 maintaining stability [2,6]. Coordinated recruitment of these control strategies may 50 guarantee stability throughout the gait cycle [7,8]. For example, the ankle strategy allows for 51 an early response to a perturbation, before the foot placement strategy becomes effective 52 following heel strike [9]. In elderly, pathological, or prosthetic gait, an impairment in one 53 strategy may require individuals to rely more on another one [10,11]. When aiming for 54 stability improvements, it is hence important to understand the details of these control 55 strategies as well as their interplay. In the current study, we focused on the foot placement 56 strategy in healthy individuals during steady-state treadmill walking. Following Wang and 57 Srinivasan [4], we expected that mediolateral foot placement can be predicted by CoM state, 58 reflective of a step-by-step control strategy (E1). And, in line with Rankin et al. [12], we 59 expected mediolateral foot placement to correlate with hip ab-and adductor muscle activity 60 during the preceding swing phase (E2), supporting the active nature of this control 61 mechanism. We tested these two expectations during normal and slow walking. We chose 62 two speeds because the implementation of the foot placement strategy has been shown to 63 be speed-dependent [13]. Further experimental conditions served to challenge the degree of 64 (active) foot placement control; see below. 65 66 Degree of control 67 The degree of foot placement control can be inferred from its predictability based on the CoM 68 state. The mid-swing CoM state is a better predictor of foot placement than the swing foot 69 state itself, although this prediction is not entirely accurate [4]. Eventual inaccuracies could 70 be attributed to motor noise or task constraints. In certain contexts, a high degree of foot 71 placement control might not be necessary. As an example, we note that foot placement seems 72 to correlate less with CoM state in externally stabilized gait and at slower speeds. Apparently, 73 its control is less important in these conditions [5,13]. In addition, the necessary degree of 74 foot placement control may depend on the availability of alternative control strategies. 75 Arguably, foot placement is most effective in shifting the CoP, though adapting ankle moments 76 allows for a complementary shift during stance. As mentioned above, this can enable early 77 stabilizing responses [9] and/or corrections of inaccurate foot placements [11]. According to 78 Fettrow et al. [8], foot placement and ankle moments are interdependent, i.e. one may 79 compensate for the other. In this context, we hypothesized foot placement to compensate for 80 a limited possibility to shift the CoP underneath the stance foot, through constrained ankle 81 moments (H1). If true, this will be in line with the findings of Hof et al. [11], who demonstrated 82 that more lateral foot placement compensated for the impossibility to induce a CoP shift 83 under a prosthetic leg. Conversely, a lesser degree of foot placement control might be 84 compensated for by ankle moments. Such compensation could facilitate adaptation of foot 85 placement to environmental or task constraints without threatening stability. Accordingly, we 86 hypothesized that constraining the foot placement by stepping onto projected lines will yield 87 diminished foot placement control (H2

Ankle moment constrained
Walking with shoes with a narrow ridge (1 cm) underneath the soles (LesSchuh, Fig 1), constraining mediolateral displacement of the CoP underneath the foot in a straight line.

Foot placement constrained
Walking with bilateral foot placement constraints (projected lines on treadmill indicating mediolateral target locations for foot placement). 147 We randomized the order of the conditions across participants and speeds. Before beginning 148 the experiment, participants performed a five-minutes familiarization (two minutes at normal 149 walking speed, three minutes at slow walking speed) without imposing further constraints; cf. 150 below. Additionally, participants familiarized with ankle moment constraining shoes (Fig 1)  151 prior to data collection. To ensure that all trials contained at least 200 consecutive strides, 152 trials at normal walking speed lasted five and trials at slow walking speed ten minutes.
(2) 247 We quantified the degree of foot placement control via the relative explained variance (R 2 ) of 248 model 1 and the active contribution to step-by-step variability in foot placement via the R 2 of 249 model 2. 250

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Step-by-step foot placement control in steady-state walking 260 The regression coefficients (β) of model (1) were tested against zero in a Bayesian one-sample 261 t-test, to infer whether mediolateral foot placement can be predicted by CoM state during 262 steady-state walking (E1) III . And, to assess whether mediolateral foot placement correlates 263 with hip ab-and adductor muscle activity of the preceding swing phase during steady-state 264 walking (E2), we tested the regression coefficients of model (2)  Step-by-step foot placement control with ankle moment constraints 268 We performed a Fisher transformation on the R 2 values prior to statistical testing. Bayesian 269 equivalents of a 2´2 repeated measures ANOVA with factors Condition (levels: ankle moment 270 constrained/foot placement constrained versus steady-state walking) and Speed (levels: 271 normal versus slow) served to test the effects of the constraints and walking speed, as well as 272 their interaction, on degree of (active) step-by-step foot placement control; relative explained 273 variance of models (1) and (2). Moreover, to test the constrained conditions against the 274 steady-state walking condition, we used Bayesian planned post-hoc assessments. 275

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We tested the R 2 values of models (1) and (2) in the ankle moment constrained condition 277 against the steady-state walking condition. By this we could estimate whether constraining 278 the ankle moment led to compensation in the degree of foot placement control. That is, this 279 allowed for testing the hypotheses that compensation will encompass tighter control (H1) 280 driven by compensatory muscle activation (H3). 281

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Step-by-step foot placement control with foot placement constraints Step-by-step foot placement control in steady-state walking  Rankin et al. [12] for the relation between foot placement 320 and gluteus medius (hip abductor) activity. More lateral steps were associated with higher 321 bursts in gluteus medius activity during early swing (60-80% of the stride cycle). Conversely, 322 as shown in Fig 4, higher adductor longus activity was associated with more medial steps. Median gluteus medius activity across legs and participants. Panels A and B show the results for respectively normal and slow walking speed. For each participant strides were divided over medial and lateral steps, of which the median was taken respectively. For the median lateral step, there was a higher burst in gluteus medius activity during early swing (60-80%) of the gait cycle. The depicted EMG traces are normalized to average stride peak activity for each speed respectively. Median adductor longus activity across legs and participants. Panels A and B represent the results for respectively normal and slow walking speed. For each participant strides were divided over medial and lateral steps, of which the median was taken respectively. Higher EMG activity during early swing (60-80% of the stride cycle) appears to be associated with more medial steps. The depicted EMG traces are normalized to average stride peak activity for each speed, respectively.
Our results show that, in the steady-state walking condition, m. gluteus medius and m. 327 adductor longus activity predicted foot placement. At normal walking speed, we found 328 extreme (BF10_gm = 50281.309) and moderate evidence (BF10_al = 6.050) when testing the 329 muscle model's (model 2) regression coefficients against zero (Fig 5, panel A). At slow walking 330 speed, extreme evidence was found for both muscles' regression coefficients (BF10_gm = 331 535.867, BF10_al =4984.586, Fig 5, panel B). The sign of the regression coefficients was as 332 expected, with more gluteus medius activity corresponding to more lateral foot placement 333 (positive sign) and more medial foot placement corresponding to more adductor longus 334 activity (negative sign). Although the mean R 2 was low for both speeds (see also Fig 7, below), 335 the moderate to extreme evidence for the regression coefficients supports the idea that 336 mediolateral foot placement is determined by hip ab-and adductor muscle activity during the 337 preceding swing phase (E2).

A B
Step-by-step foot placement control with ankle moment constraints Step-by-step foot placement control with foot placement constraints 366 367 Model 1: Foot placement model

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The Bayesian repeated measures ANOVA of the relative explained variance (R 2 ) of the foot 369 placement model (model 1, Fig 8) revealed that the best model included the factors condition 370 and speed, when testing for mid-swing. There was extreme evidence for this model as We investigated the degree of (active) foot placement control during steady-state treadmill 390 walking. We successfully replicated the findings of Wang and Srinivasan [4] and Rankin et al. 391 [12] and can support that during steady-state walking foot placement is coordinated to CoM 392 state and is associated with hip ab-/adductor muscle activity. The degree of foot placement 393 control did not tighten when constraining the ankle moments. However, we found that the 394 control strategy can be adapted, achieving less tight foot placement control when constraining 395 foot placement at a slow walking speed, whereas at a normal walking speed the degree of 396 foot placement control was upheld. Overall, we can underwrite the growing body of literature 397 [3,7,8,12,15,16,24] and confirm that the foot placement model as introduced by Wang and 398 Srinivasan [4] reflects an active control strategy, related to mediolateral stability [5]. 399 400 Ankle moment constrained walking

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The ankle moments were constrained by narrowing the surface area underneath the shoe. As 402 a result, the CoP shift was limited to the width of a narrow beam (see S1 for illustration). We 403 hypothesized that foot placement would compensate for the imposed constraint, by 404 tightening control. However, for both normal and slow walking, no difference was found in 405 the relative explained variance of the foot placement model as compared to steady-state 406 walking. The degree of foot placement control was not tightened for compensation. 407 Admittedly, we focused on steady-state gait control, while related studies mostly studied 408 reactive gait control. Yet, this finding was unexpected given previous ones in the literature [7, 409 8, 11, 25]. For example, Hof et al. [11] demonstrated more lateral steps in prosthetic legs to 410 accommodate for a limited CoP shift. Similarly, Vlutters et al. [25], showed foot placement 411 adjustments in response to anteroposterior perturbations when wearing CoP-shift-limiting 412 'pin shoes'. Reimann et al. [7] reported that in response to vestibular stimulation execution of 413 the foot placement and ankle strategy was serially coordinated as a balance response. This 414 suggests that without complementary ankle moments, a wider step might have been required 415 to accommodate illusory falls, in line with their modelling results. And, Fettrow et al. [8] 416 showed an inverse relationship between the execution of the ankle strategy and foot 417 placement strategy during steady-state walking. Together these studies suggest that in 418 response to natural variations or perturbations, foot placement control can accommodate for 419 limited ankle moments. Here we would like to add that this does not necessarily imply more 420 accurate control. 421 422 An important difference between the aforementioned studies and the current one is that their 423 main outcome measure was based on average adjustments, i.e. on increases in step width or 424 gain, whereas our R 2 outcome measure reflects foot placement accuracy in accommodating 425 variations in CoM state. A limitation of our approach is that information provided by the 426 intercept of the model is lost, i.e. the average step width. We hence explored differences in 427 step width between the ankle moment constrained conditions and the steady-state walking 428 conditions. Indeed, extreme evidence (BF > 100) demonstrated increased step width when 429 participants walked with LesSchuh at both speeds (see S2). While this is likely to reflect a 430 compensatory strategy, a limitation of our study could be that with LesSchuh participants 431 should avoid to step into the middle of the split belt treadmill (as the surface area of the shoes 432 was narrow enough to fit between the two belts). Participants might have increased their step 433 width as a precaution, and these findings should hence be interpreted with care. Nevertheless, 434 increasing step width may be considered an appropriate response to the sustained (and 435 invariable) perturbation of LesSchuh. Given the lower R 2 in the ankle moment constrained 436 condition at normal walking speed (Fig 6), this perturbation may not only have perturbed the 437 ankle moments, but foot placement as well. Probably, LesSchuh perturbed stance leg control 438 during swing and consequently led to less accurate foot placement. This suggests that learning 439 how to adapt to this perturbation may improve the degree of foot placement control, similar 440 to earlier findings related to continuous foot placement perturbations [24]. 441 442 An increased step width has earlier been considered as a general stabilizing strategy, 443 characterizing cautious gait in an unpredictable situation [26,27]. An increase in step width is 444 a possible temporary compensatory strategy that seems to be used until one is able to develop 445 tighter control of foot placement. The duration of our trials (5 minutes at normal walking 446 speed and 10 minutes at slow walking speed) might have been too short to adapt the degree 447 of control. Recently, it has been shown that repeated exposure to a perturbing force field 448 yielded an adaptation in foot placement control [24]. During later exposures tighter control 449 was manifested as compared to the first 5-minute-perturbed trial. The initial increase in step 450 widths was diminished in these later exposures. We conjecture that longer or multiple trials 451 with LesSchuh can lead to an increased R 2 of the foot placement model. An increased degree 452 of control may allow for a reduction of the average step width while maintaining stability. 453 Walking with wider steps has been associated with a higher energy cost, and in normal walking 454 individuals tend to select the step width that minimizes metabolic costs [28]. That is, 455 adaptation over time and reduced step width may lead to a more economic compensatory 456 strategy. Alternatively, increasing step width compared to normal walking might be a more 457 economic strategy when walking with limited ankle moments. An additional energy cost 458 related to actively increasing step-by-step control, might prevent participants to select 459 narrower steps [29]. 460 461 Further exploratory analysis in slow walking revealed that the imposed ankle moment 462 constraint coincided with increased stride frequency, besides average step width, in spite of 463 the metronome-imposed frequency (see S3). Increasing stride frequency has already been 464 identified as a strategy to improve gait stability [30][31][32]. The use of an ankle strategy appears 465 less prominent when walking with high as compared to low stride frequency [33]. By 466 modulating stride frequency and increasing average step width, the need for more accurate 467 foot placement control (as reflected by our outcome measure R 2 ) might have been 468 circumvented. In future studies, it is worth looking into the hip and push-off strategies [2, 6, 469 8, 34, 35] to see whether they worked as compensatory strategies as well. 470 471 Whether compensatory hip ab-/adductor muscle activity does play a role in the compensatory 472 response or not still remains inconclusive. We did not find a compensatory increase in step-473 by-step foot placement accuracy. Thus, it seems likely that hip ab-/adductor activity does not 474 have a higher contribution to the variation in foot placement. However, the average increase 475 in step width could have been driven by increased gluteus medius activity. This may explain 476 why our analysis provided anecdotal (i.e. inconclusive) evidence rather than support for the 477 null hypothesis. 478

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Foot placement constrained walking 480 The foot placement constraint (lines projected on the treadmill) reduced step width variability 481 in both slow and normal walking (see S4), denoting that the constraint was effective. The 482 projected line appeared following toe-off. Therefore, we prevented preplanning a CoM 483 trajectory during the preceding step [19,36] in relation to the projection. Consequently, foot 484 placement adjustments had to be realized during swing, which we expected to undermine the 485 relationship between foot placement and CoM state. Evidence exists that rapid foot 486 placement adjustments are feasible during a stepping task [37], although stability constraints 487 appear to negatively affect responses to large jumps of foot placement targets [38]. In our 488 study, foot placement appeared to be more effectively constrained by the projections during 489 slow walking as compared to normal walking, as reflected by a lower step width variability at 490 the slower speed (see S4). Regarding the degree of foot placement control, we found a 491 condition ´ speed interaction effect on the R 2 of the foot placement model (model 1). The 492 reduction in step width variability caused a diminished degree of foot placement control 493 according to the foot placement model at a slow walking speed. At a normal walking speed 494 this effect was less pronounced, and R 2 remained higher than during slow walking (Fig 8). In 495 other words, at normal walking speed, the relationship between foot placement and CoM 496 state was largely retained. This suggests that at a normal walking speed, stability constraints 497 outweighed the task instruction. We interpret this to indicate that tight foot placement 498 control is more important at normal as compared to slow walking speed. We would like to 499 note that this agrees with previous findings that the R 2 of the foot placement model is lower 500 at slower speeds [13]. Yet, our results showed that foot placement remains actively controlled 501 during slow steady-state walking, despite the lower degree of foot placement control. 502 503 Conclusion 504 505 We found muscle driven step-by-step foot placement control during steady-state walking. This 506 control appears to be more important at normal as compared to slow walking speed, based 507 on the degree of foot placement control and adaptability to a foot placement constraint. 508 When compensating for constrained ankle moments, average step width and stride 509 frequency, rather than the degree of foot placement control were adjusted. Blue and red bars represent respectively the steady-state walking and ankle moment constrained conditions. The grey lines connect the individual data points. An exploratory Bayesian repeated measures ANOVA, including the steady-state walking and ankle moment constrained condition at both speeds, revealed that the best model included only the factor "Condition" with extreme evidence as compared to the Null model (BF10 = 1.610 * 10 15 ). Post-hoc analysis provided extreme evidence supporting an increase in step width at both speeds to compensate for the ankle moment constraint (BF10 = 1.064*10 13 ). Blue and red bars represent respectively the steady-state walking and ankle moment constrained conditions. The grey lines connect the individual data points. As an exploratory analysis, as well as a protocol check, Bayesian repeated measures ANOVA, including the steady-state walking and ankle moment constrained condition at both speeds, revealed that the best model included the factors "Condition" and "Speed". Post-hoc analysis provided extreme evidence (BF10 = 7.959*10 42 ) indicating that stride frequency increased in the ankle moment constrained conditions as compared to steady-state walking. S4 Effectiveness of the foot placement constraint: step width variability 630 631 S4 Fig. Mean step width variability during the steady-state walking and foot placement constrained conditions. Blue and black bars represent respectively the steady-state walking and foot placement constrained conditions. The grey lines connect the individual data points. Bayesian repeated measures ANOVA, including the steady-state walking and foot placement strategy constrained condition at both speeds, revealed that the best model included the factors "Condition" and "Speed", with extreme evidence as compared to the Null model (BF10 = 590646.967). Post-hoc analysis provided extreme evidence for a lower step width variability in the foot placement constrained condition as compared to steady-state walking (BF10 = 55714.494). When comparing between speeds, a two-tailed Bayesian paired samples t-test provided extreme evidence demonstrated that in the foot placement constrained condition, the step width variability remained higher at a normal walking speed as compared to the slow walking speed (BF10 = 2091.388). 632 633 634