The Role of Entrainment in Human Walking: Energy Minimization in 1 Oscillating Environments

21 During locomotion, humans often entrain (i.e. their Previous studies have discussed the role of nonlinear oscillators (e.g. central pattern generators) 24 in facilitating entrainment. However, the underlying benefits of entrainment are unknown. 25 Given substantial evidence that humans prioritize economy during locomotion, we tested 26 whether reduced metabolic expenditure accompanies human entrainment to vertical force 27 oscillations, where frequency and amplitude were prescribed via a custom mechatronics system 28 during walking. Although metabolic cost was not significantly reduced during entrainment, 29 individuals who experienced negative work from oscillations had a higher cost than those who 30 experienced positive work, and subjects generally selected phase relationships indicating the 31 latter. It is possible that individuals use mechanical cues to infer energy cost and inform 32 effective gait strategies. If so, an accurate prediction may rely on the relative stability of 33 interactions with the environment. Our results suggest that entrainment is preferred over a 34 wide range of oscillation parameters, though not as a direct priority for minimizing metabolic 35 cost. Instead, entrainment may act to stabilize interactions with the environment, thus 36 increasing predictability for the effective implementation of internal models that guide energy 37 minimization. 38 39


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Human walking is an oscillating system where the body moves in cyclic patterns to traverse a 47

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Subjects entrain to external oscillations 115 Figure 3 shows the median step frequency normalized to baseline preferred (magenta) as well 116 as 25% and 75% quartiles (grey shaded region) for individuals who entrained their steps with 117 external oscillations at least once during the indicated trial condition. Subjects generally 118 preferred entrainment, overall. However, the level of entrainment varied between individuals; 119 e.g. some only entrained in two trials while others entrained in five out of six total trials. The 120 likelihood of subject entrainment largely depended on the oscillation parameters prescribed: 121 frequency, Δ , expressed as a percent difference from subject baseline and amplitude; , 122 expressed as a percentage of subject body weight (BW) force (see Methods for details). For 123 example, all ten subjects entrained when Δ = −6, 0% and = 30% (Fig. 3b,d). 124 Conversely, no subjects entrained when Δ = 6% and = 10% , thus only individual 125 subject data are shown (Fig. 3e). In general, entrainment in conditions with higher motor 126 frequencies and lower amplitudes was less stable and more transient. Note, the data for Δ = 127 0 end earlier than other trials since there was no metronome used (the oscillation frequency 128 already matched baseline preferred, so was deemed unnecessary; Fig. 3c,d). However, 129 individuals largely followed the metronome in other trials, as the median data quickly converged 130 on a relative frequency of one at approximately 300 s into the trial. During 300 ≤ ≤ 600 , subjects were directed to follow the cadence of the metronome 140 at their predetermined baseline step frequency ("frequency clamping") even as the oscillations 141 continued at a different frequency. There was no metronome used in trials where Δ = 0, 142 since frequencies were already matched. As a result, these experiments ended after around 143 = 300 . Note, median data are only shown for individuals who entrained at least once 144 throughout the trial. In the trial condition where Δ = 6% and = 10% , individual 145 subject data are shown instead since no entrainment occurred. 146 8 In many instances, subjects exhibited transient entrainment -meaning their step frequency 147 drifted in and out of the oscillation frequency throughout the trial (Fig. 4a). To better 148 characterize how well subjects entrained their gait in the various trial conditions, two metrics 149 were considered: entrainment step ratio ( , Fig. 4b) and average entrainment duration (Δ ̅ , 150  off (subject allowed to entrain) versus with the metronome turned on (not allowed to entrain). 183 Metabolic expenditure increased by 25.8% ( < 0.001*) when subjects walked on the treadmill 184 wearing the harness but with no active oscillations versus when they walked on the treadmill 185 without the harness (Baselines 2 and 1, respectively; Fig. 5). When comparing trials with active 186 oscillations, no significant differences were found, with the exception of one parameter 187 combination: Δ = −6% and = 30% . This condition was more costly without the 188 metronome compared to all other trials and baseline conditions. Still, metabolic cost did not 189 differ significantly depending on the presence of the metronome (blue vs. green in Fig. 5) for any 190 of the trial conditions tested. All in all, the metronome -and thus, the freedom of subjects to 191 entrain -had no statistical effect on metabolic power. Importantly, this result did not change 192 when controlling for the level of entrainment (e.g. ) in each trial condition. given: ̅ = 94 ± 55 o . This means that peak current is prescribed to the motor pulling up just 227 after a quarter through the step cycle (approximately at toe off of the trailing leg). Due to 228 system dynamics, this current peak shows up as a spike in tension force slightly later as the 229 "active force peak". 230 The preferred motor phase seems to imply a strategy of receiving positive power from the 231 active oscillations, given peak active force approximately aligns with peak vertical CoM velocity 232 ( Fig. 6d). Despite this alignment, negative power still greatly outweighs any positive power 233 received from the system. Since the resistive forces largely responsible for excess negative 234 power relate to motion of the CoM (damping relates to velocity, inertial forces to acceleration), 235 a 90% increase in vertical velocity amplitude may help to explain why net negative power still 236 dominates subjects during entrainment, despite a preferred phase indicating the opposite. term between motor frequency and oscillation amplitude was found to be insignificant after 301 controlling for multiple hypothesis testing (see Table S1  Step frequency adaptations 322 Step frequency adaptations in the current study (±6%) are comparable to those of previous 323 reports: approximately ±2-8% of preferred step frequency 13-15,17 . Even so, some subjects 324 struggled to entrain with the oscillator system even in the most favorable conditions (e.g. If the preferred strategy uses oscillation forces to replace positive muscle work, then the extent 365 to which this strategy is energetically favorable likely relies on an individual downregulating leg 366 work and associated muscle activity 19 . Yet subjects substantially increased the vertical excursion 367 of their CoM when they entrained to motor oscillations compared to at baseline (an increase of 368 58.2% or 125.5% for = 10% or 30% , respectively). The increased body oscillation is 369 likely evidence that subjects did not downregulate their push off during entrainment. Instead, it 370 seems that subjects preferred to increase positive power from the system by aligning active 371 force peaks approximately with toe off in the step cycle (Fig. 6b, 8a). Furthermore, subjects that 372 leveraged the most positive power from the oscillations had the lowest metabolic cost (local 373 minimum at ≈ 90 o ). These results, however, should be treated with caution. Experiments 374 presented here did not explicitly control or manipulate the motor phase, but rather, the phase 375 variation depicted in Figure 8a  The experiments presented in the current study describe subject interactions that can be 430 relatively volatile, at least before subjects converge on entrainment. In particular, inexperience 431 with the oscillation system may require a prerequisite to the dual-part control of locomotion 432 described previous: a stabilization phase. Here, stability does not necessarily refer to fall 433 avoidance or balance, but rather to a state of relative consistency, where interactions with the 434 environment are sufficiently repeatable over subsequent steps. A relatively stable interaction 435 may be required before feedforward or feedback control can be successfully implemented, and 436 entrainment could provide that stability. 437 21 Koban et al. 36 explained a similar perspective in a slightly different context, with regards to 438 individuals that entrain gait when walking side by side (i.e. interpersonal synchronization). They 439 described a process by which entrainment occurs to reduce the perceived mismatch between an 440 expectation about their companion's motor behavior based on their own. An analogous 441 principle could be adapted to the expectation of mechanical interactions with the environment, 442 as mediated by the entrainment opportunities associated with the oscillator system described in 443 this manuscript. In lieu of a direct metabolic motivation for entrainment, it may be possible that 444 the motor control system prefers a relatively stable interaction with the environment so as to 445 make feedforward predictions more precise and actionable. 446

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Participants 448 A convenience sample of ten healthy university students (five males, five females) were 449 recruited. The mean [± 1 standard deviation (SD)] subject height was 1.71 ± 0.07 m, leg length 450 was 0.91 ± 0.06 m, weight was 65.7 ± 12.2 kg and age was 26.2 ± 2. Pulse signals were recorded in LabVIEW to mark the timing of peak current sent to the motors 490 relative to the start time of a given step cycle (Δ ). In addition to data synchronization, the 491 pulse signals were used to calculate the phase lag of peak current relative to the step cycle ( ). 492

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(2) 493 Due to dynamics of the system, there was a slight delay from when peak current was driven to 494 the motors to when tension spiked in the harness. The average delay, Δ , was calculated for all 495 subjects and trials and phase data were shifted as appropriate: * = + Δ . 496 Oxygen consumption and carbon dioxide elimination rates were measured using a commercial 497 metabolic analysis system (TrueMax 2400, ParvoMedics, Salt Lake City, UT, USA). All trials lasted 498 longer than five minutes, which allowed metabolic data to reach steady state conditions before 499 mean and SD values were calculated (typically the remaining 2-3 minutes of each trial). Oxygen 500 consumption rates in 2 −1 were multiplied by a factor of 20.1 to convert to Watts. Gross 501 metabolic rate was converted to net metabolic rate by subtracting baseline values during quiet 502 standing. Net metabolic power was non-dimensionalized by dividing belt speed and subject BW 503 (sometimes referred to as non-dimensional cost of transport). During all metabolics testing, the 504 data were deemed acceptable if the respiratory exchange ratio remained below a value of 1.0. 505 Test protocol 506 During Baseline 1, subjects walked on the treadmill freely (i.e. without the body harness; Fig. 2b) 507 for a five-minute duration. The treadmill speed ( = 1.19 −1 on average) was programmed 508 such that non-dimensional speed, ̃, equaled 0.4 during all testing. 509

=̃√
(3) 510 where is the subject's hip height measured from the ground while standing. Speed was 511 rounded to the nearest tenth of a km/hour, per the treadmill's available resolution. 512 During Baseline 2, subjects walked while wearing the body harness connected to the pulley-513 cable system (Fig. 2b) for a ten-minute duration. Both actuators provided a constant nominal 514 tension (approximately 10% BW) to reduce slack in the system, but the average net force on the 515 body was zero since one cable pulled up while the others pulled down. Subjects also 516 experienced added inertia from the motors and associated hardware connected in the system, 517 as well as friction and damping. Each subject's baseline preferred step frequency ( ) was 518 assessed and motor frequencies prescribed in testing conditions were determined relative to 519 this baseline. 520 During experiments, subjects walked in the harness for two minutes with nominal motor current 521 to avoid cable slack. Next, current oscillations were commanded to the motors at a constant 522 frequency and amplitude, and the subject was instructed to respond freely (Fig. 2a). Five 523 minutes later, subjects were asked to step to the beep of a metronome (matched to their 524 baseline frequency, i.e. "frequency clamping"; Fig. 2a) even as oscillations continued at a 525 different frequency. After another five minutes, the oscillations and metronome ceased, and the 526 subject prepared to end the trial. Metabolic data was collected throughout this test to compare 527 oxygen consumption while responding freely in the system (allowed to entrain) versus walking 528 to the metronome (not allowed to entrain). This test was performed with various oscillation 529 amplitudes ( = 10, 30% ) and motor frequencies relative to baseline step frequency 530 (Δ = 0, ±6%; see Fig. 2b). 531 In the case of trial conditions where Δ = 0%, no metronome was played and the trial ended 533 after five minutes of oscillations. Trial conditions were randomized to minimize any ordering 534 effects. 535 During experiments, a curtain was used to blind subjects from any motion of the pulleys or 536 motors (Fig. 1b). Ambient noise was played through headphones to help block out rhythmic 537 sounds of the system. During trials, subjects were asked to walk in any manner that felt most 538 natural or extracted minimal effort. However, subjects were encouraged to explore different 539 aspects of their gait, including stride length. Note, a more detailed description of the oscillator 540 system design and operation can be found in the Supplementary Materials. 541 Defining entrainment 542 Entrainment was defined with arbitrary thresholds: any step frequencies within ±3 SDs 543 (~±0.02 Hz) of the prescribed motor frequency for at least sixteen out of twenty (80%) 544 consecutive steps. The SD of subjects was determined from the last minute of data from 545 Baseline 2 (treadmill walking with the harness). Two metrics quantified the level of entrainment 546 for a subject in each trial. The entrainment step ratio ( ) is the ratio of entrained steps to 547 total steps taken during experiment (without the metronome) while the average duration of 548 25 entrainment (Δ ̅ ) was used to estimate entrainment durations since subjects sometimes drifted 549 in and out of the motor's frequency. 550 Statistical analysis 551 Filtered relative step frequency data were interpolated at equal time intervals matching the 552 data acquisition rate. Median values of the interpolated data were taken across all subjects who 553 entrained at least once in the trial and at each time point, to represent skewed distributions 554 more appropriately. Quartiles characterized the spread of the distribution for each time point at 555 25% and 75% levels. 556 Linear mixed models were used to assess various outcomes during experiments. The mixed 557 model was chosen to control for repeated measurements among subjects participating in 558 multiple trials each; subject was included in the models as a random effect. All statistical models 559 were developed and evaluated in JMP (SAS Institute Inc., Cary, NC USA, version 14.1.0) using the 560 restricted maximum likelihood method for parameter estimation and a compound symmetric 561 covariance structure. 562 In three models, motor frequency (Δ ) and amplitude ( ) as well as an interaction between 563 the two (Δ ) were added as fixed effects to test if the oscillation parameters contributed 564 significantly to the various outcomes. The first two models tested the effect of oscillation 565 parameters on the level of entrainment via and Δ ̅ . 566 In order to assess metabolic power, a linear mixed model was stratified by trial condition, 567 baseline type (wearing or not wearing the harness) and the metronome's status (i.e. active or 568 inactive) during data collection. A post hoc Tukey's Honestly Significant Difference test was used 569 to detect differences in estimates of metabolic power ( = 0.05), while controlling for multiple 570 hypothesis testing. Given the metronome's status only indicates whether an individual has the 571 capacity to entrain and not whether they actually did entrain, a separate model was used to test 572 for the effect of entrainment level (via entrainment step ratio, ) as a covariate for metabolic 573 power. Δ ̅ was not included to avoid collinearity. Mechanical work done by the harness tension 574 was also included to assess any effect of the mechanical interaction on cost. 575 The significance of fixed model effects was evaluated with 95% confidence limits and post hoc During 300 ≤ ≤ 600 , subjects were directed to follow the cadence of the metronome 725 at their predetermined baseline step frequency ("frequency clamping") even as the oscillations 726 continued at a different frequency. There was no metronome used in trials where Δ = 0, 727 since frequencies were already matched. As a result, these experiments ended after around 728 = 300 . Note, median data are only shown for individuals who entrained at least once 729 throughout the trial. In the trial condition where Δ = 6% and = 10% , individual 730 subject data are shown instead since no entrainment occurred. 731