ABSTRACT The unstable nature of our bipedal posture requires continuous feedback to maintain internal estimates of self-motion and generate appropriate balance-correcting responses. This

feedback control process involves the integration of multisensory information, including vestibular cues of head motion. Minimizing head motion variability may optimize the information

transmitted by vestibular signals that are important for balance control and consequently drive vestibular contributions to locomotion which decrease as we move faster. In this study,

participants walked outdoors at 40% to 140% of their preferred step cadence while we characterized head kinematic variability and vestibular-evoked balance responses to electrical vestibular

preferred step cadences, near previously established minima for the metabolic cost of locomotion. The relationship between head kinematic variability and vestibular-evoked balance responses,

however, was inconsistent across all step cadences, suggesting that head kinematic variability did not drive vestibular-evoked balance response magnitude. The observed reduction in the

variability of head motion signals at the preferred locomotor cadence/speed may serve to improve our self-motion estimates and reduce information processing requirements to ensure effective

navigation, thereby potentially contributing to the well-established minimum in metabolic cost near preferred cadence. SIMILAR CONTENT BEING VIEWED BY OTHERS STABILIZATION DEMANDS OF WALKING

MODULATE THE VESTIBULAR CONTRIBUTIONS TO GAIT Article Open access 02 July 2021 NO EVIDENCE FOR STOCHASTIC RESONANCE EFFECTS ON STANDING BALANCE WHEN APPLYING NOISY GALVANIC VESTIBULAR

STIMULATION IN YOUNG HEALTHY ADULTS Article Open access 10 June 2021 ALTERED ACTIVE CONTROL OF STEP WIDTH IN RESPONSE TO MEDIOLATERAL LEG PERTURBATIONS WHILE WALKING Article Open access 22

July 2020 INTRODUCTION Uncertainty is always present in the sensory information that we receive, worsening confidence in our self-motion estimates. The vestibular system, responsible for

detecting head motion in space, provides movement information to our brain, but the certainty of this information is diminished by the inherent noisiness and delays of the neural pathways

associated with the encoding of head self-motion cues1. As our internal estimate of head motion in space contributes to whole-body balance responses for maintaining our bipedal posture2,3,

it is critical we maximize the reliability of the vestibular signals of head motion when navigating our environment. Similar to how we walk at speeds that minimize our energy

expenditure4,5,6, it may be beneficial to reduce the uncertainty of the vestibular information given that sensory noise increases the metabolic cost of neuronal information processing7.

There is evidence that humans minimize head movement variability during locomotion and other complex movements8,9,10,11. It is not clear, however, if this relates to the task-dependent

modulation in the vestibular control of balance during locomotion, an important consideration given the vestibular contributions to maintaining our upright posture as we move. Clinical and

experimental studies have shown that vestibular contributions to balance decrease as locomotor speed and step cadence increase12,13,14,15. MacNeilage & Glasauer16 developed a model based

on an index of head kinematic variability across strides (\({V}_{res}\)) that they proposed represents a ratio between motor efference copy noise and vestibular information noise to predict

the context-dependent attenuation in the measured vestibular control of balance during locomotion. Their model was inspired by observations in tadpoles and juvenile frogs where

contributions of vestibular gaze stabilizing mechanisms decrease and are replaced by feedforward control from the motor efference copy as locomotor speed increases17,18,19. For example, as

vestibular noise increases relative to motor noise (i.e., decreased \({V}_{res}\)), it is predicted that vestibular signals would be downregulated for self-motion estimation, and the

magnitude of vestibular balance responses would decrease. Recently, Mackrous and colleagues20 found no difference in vestibular afferent signals encoding head motion between locomotor speeds

in adult nonhuman primates, questioning the presence of peripheral feedforward mechanisms to regulate the vestibular contributions to balance during locomotion in mammals. While human

experimental results have shown that \({V}_{res}\) decreases concurrently with the magnitude of vestibular-evoked balance responses21,22, this has only been characterized at locomotor speeds

(0.4 and 0.8 m/s) and step cadences (52 and 78 steps/minute) slower than our preferred locomotor speed and cadence. Thus, it is critical that we investigate head kinematics and vestibular

balance control across a wide range of speeds and cadences given that this relationship may change as speed and cadence increase beyond our preferred movement parameters. The objective of

this study was to characterize the relationship between head kinematic variability and vestibular-evoked balance responses across step cadences representing 40% to 140% of participants’

preferred step cadences. Here, we defined head kinematic variability as a ratio of the variability around a stride-cycle attractor representing the average stride head kinematics (residual

variability) and the variability around the total average head kinematics within and across strides (i.e., the near zero offset; total variability)16. To do so, we used a portable, inertial

measurement unit (IMU)-based system (Fig. 1) that can simultaneously apply electrical vestibular stimulation (EVS; a common technique to elicit vestibular-evoked balance responses) and

measure kinematics to characterize head movement during locomotion and quantify the magnitude of the EVS-evoked balance responses22. Given previous observations, we hypothesized that

vestibular-evoked balance responses would decrease as cadence increased past the participants’ preferred cadence. It was unclear, however, how head kinematic variability would change for

these larger locomotor speeds and cadences. If head variability is minimal at the preferred locomotor cadence, we would expect \({V}_{res}\) to decrease up to a participant’s preferred

cadence but to increase beyond the preferred cadence (minima hypothesis). Alternatively, \({V}_{res}\) may continue to decrease beyond the preferred cadence (monotonic decrease hypothesis).

A monotonic decrease in \({V}_{res}\) would support the hypothesis by MacNeilage and colleagues16 that changes to \({V}_{res}\) explain the modulation in vestibular-evoked responses. RESULTS

Twelve healthy young participants completed bouts of walking at 40%, 60%, 80%, 100%, 120%, and 140% of their preferred step cadence. To capture participants’ natural locomotor patterns, all

walking trials were completed outdoors on a paved surface. We first recorded 30 s of natural walking without EVS to determine the natural step cadence of each participant. At each cadence

condition, participants completed 85 strides without EVS followed by 215 strides while experiencing EVS (Methods). EVS modulates the firing rate of primary vestibular nerve afferents via the

application of a small electrical current to the mastoid processes, thus eliciting whole-body balance responses of vestibular origin23. We estimated head kinematic variability using

\({V}_{res}\), which is a ratio between the residual variability and total variability of head kinematics across strides (see insets of Figs. 2 and 3 for illustrations of \({V}_{res}\)

calculations, and Eqs. 7–9 in Methods)16. Given that the changes to \({V}_{res}\) across step cadences were similar in the EVS and non-EVS conditions (although the \({V}_{res}\) was

generally ~ 11–23% higher in the trials with EVS; see Supplementary Materials), only the \({V}_{res}\) data from the trials with EVS are presented here to allow for direct comparison with

the vestibular-evoked balance responses. Gait events (heel strike and toe off) were determined using IMUs on each ankle (Methods). Across participants, the preferred step cadence was 107.3 ±

 9.1 steps/minute with a resulting gait speed of 1.4 ± 0.3 m/s. From 40 to 140% of the participants’ preferred step cadence, step cadence and gait speed increased (43.8 ± 3.8 to 149.4 ± 13.2

steps/min and 0.4 ± 0.1 to 2.1 ± 0.4 m/s, respectively), while the proportion of double leg stance (i.e., the time between right heel strike and left toe-off and the time between left heel

strike and right toe-off) decreased, similar to previous observations24,25,26 (see Supplementary Materials for complete gait characteristics table). Head orientation, measured with an IMU

fixed to a mouthguard (Methods), changed slightly across the different conditions, with the average head pitch ranging from the lowest at the 40% condition (Reid’s plane 4.0 ± 6.1° up from

horizontal) to the highest at the 100% condition (8.8 ± 6.4°). HEAD KINEMATICS ACROSS CADENCES To determine stride-by-stride head kinematic variability, we calculated \({V}_{res}\) using the

gravity-corrected and transformed net linear acceleration (\({V}_{res}\) \({a}_{NET}\)), mediolateral linear acceleration (\({V}_{res}\) \({a}_{ML}\); Fig. 2), net angular velocity

(\({V}_{res}\) \({\omega }_{NET}\)), and roll angular velocity (\({V}_{res}\) \({\omega }_{roll}\); Fig. 3) from a mouthguard-fixed IMU (see Methods; similar to previous work from MacNeilage

and Glasauer16). \({V}_{res}\) \({a}_{NET}\) and \({V}_{res}\) \({\omega }_{NET}\) provide indices of the overall head variability as they are calculated from the linear accelerations and

angular velocities from all three axes, respectively. \({V}_{res}\) \({a}_{ML}\) and \({V}_{res}\) \({\omega }_{roll}\) are calculated from mediolateral linear acceleration and roll angular

velocity, respectively, which correspond to the plane in which the EVS-evoked balance responses occur. We generally observed four peaks of variable amplitude within the stride cycle,

corresponding to the approximate locations of heel strikes and toe-offs from both feet. From the 40% to 100% cadence conditions, the mean \({V}_{res}\) decreased for all participants in all

measures except \({V}_{res}\) \({a}_{ML}\) (observed in 10/12 participants). From the 100% to 140% conditions, the mean \({V}_{res}\) generally increased (\({V}_{res} {a}_{NET}\): 9/12

participants; \({V}_{res} {a}_{ML}\): 9/12 participants; \({{V}_{res} \omega }_{NET}\): 6/12 participants; \({V}_{res} {\omega }_{roll}\): 6/12 participants). We performed repeated measures

analysis of variance (rmANOVA) to determine if there was a main effect of step cadence on each measure of head kinematic variability (\({V}_{res}\); Table 1 and Fig. 4). Post-hoc paired

Student t-tests (\(\alpha\) = 0.05) were performed between the following step cadence conditions: 40–100% to confirm that \({V}_{res}\) decreased21,22 up to the preferred cadence

(one-tailed), and 100–120% and 100–140% to characterize how head kinematic variability changed beyond the preferred cadence (two-tailed). To correct for multiple comparisons, we used the

Holm method. For all \({V}_{res}\) measures, we observed significant main effects and a significant decrease from the 40% to 100% step cadence condition (0.24–0.72 × ; Table 1). In contrast,

we observed significant increases from the 100% to 140% condition in the mean \({V}_{res} {a}_{NET}\) (1.59 × ; Table 1), and from 100 to 120% and 140% in the mean \({V}_{res} {a}_{ML}\)

(1.22–1.37 × ; Table 1). There were no significant changes in the \({V}_{res}\) \({\omega }_{NET}\) or \({V}_{res}\) \({\omega }_{roll}\) beyond the 100% step cadence condition. VESTIBULAR

RESPONSES ACROSS CADENCES We also calculated the time-dependent coherence between EVS and kinematic signals (i.e., a measure of relation between two signals; see Methods) for each individual

participant and across all participants to quantify the magnitude of vestibular-evoked balance responses27,28. Larger coherence values indicate stronger relation between vestibular input

and balance responses, thus calculating coherence across cadences allowed us to quantify changes in vestibular-evoked responses as a function of step cadence. Gain was also calculated (see

Supplementary Materials), but only coherence is presented here as the changes in gain between step cadences were similar to and supported the coherence results. Time-dependent coherence was

calculated between the EVS and the gravity-corrected and transformed mediolateral (ML) linear accelerations from IMUs placed on the low back and each ankle. This allowed us to characterize

the vestibular-evoked balance responses at the approximate centre of mass and in the lower limbs, respectively. We observed regions of significant coherence (based on a 99% confidence limit)

in all participants and IMUs in the 40–100% cadence conditions (see Fig. 5 for representative participant). Significant coherence was generally observed between 0–10 Hz during single-leg

stance in the back and during stance phases in the corresponding ankles, similar to previous findings22. All participants exhibited significant coherence in the 120% condition for all IMUs,

except for one participant’s left ankle ML accelerations. For the 140% cadence condition, we observed significant coherence in 9/12 participants for the back ML acceleration and 11/12

participants for the right and left ankle ML accelerations. We extracted the peak coherence from across the stride cycle and frequencies and performed rmANOVAs to determine if there was a

main effect of step cadence on peak coherence (Table 2 and Fig. 6). To confirm that the vestibular-evoked responses decreased in magnitude with increasing step cadence, the following

post-hoc, one-sided paired Student t-tests were performed: 40–100% to confirm previous findings, and 100–120% and 100–140% to verify that the vestibular responses decreased in magnitude

beyond the preferred step cadence. We observed significant main effects for all coherence measures (back, right ankle, and left ankle ML linear accelerations). Additionally, we observed

significant decreases in all post-hoc t-tests (40–100%: 0.27–0.34 × , 100–120%: 0.59–0.64 × , 100–140%: 0.31–0.46 × ; Table 2), except from the 100% to 120% condition in the back ML linear

acceleration peak coherence. To directly relate \({V}_{res}\) and coherence, we determined linear fits and calculated the coefficient of determination (R2) of the linear fits between each

combination of mean \({V}_{res}\) and peak coherence measures. This was calculated for all step cadence conditions, 40% to 100% step cadence conditions, and the 100% to 140% step cadence

conditions. While there was a positive relationship between \({V}_{res}\) and coherence from 40 to 100%, the relationship was negative or zero from 100 to 140%. Furthermore, in all cases

(except the linear fits between \({V}_{res}\) \({\omega }_{roll}\) and left ankle peak coherence), the R2 decreased when fitting data from the 40% to 100% conditions compared to data from

all step cadences. Consequently, the linear fits worsened when the faster step cadences were added. We presented only the linear fits with the peak back coherence in Fig. 4 because all

coherence measures yielded similar results. The linear fits with all other coherence measures are included in the Supplementary Materials. FITTING HEAD KINEMATICS AND VESTIBULAR CHANGES

ACROSS STEP CADENCE AND GAIT SPEED To establish the relationship between head kinematic variability and vestibular-evoked balance responses with step cadence and gait speed, we fitted

functions to mean \({V}_{res}\) and peak coherence, respectively. HEAD KINEMATIC VARIABILITY We fitted both 2nd degree polynomial (minima hypothesis) and exponential decay (monotonic

decrease hypothesis) functions to the mean \({V}_{res}\) measures from all participants. The difference in the Akaike information criterion (AIC) between the polynomial and decay fits

(\(\Delta AIC\) = polynomial – exponential decay) was calculated to identify the most appropriate fit (a lower AIC indicates a more appropriate model; see Methods). If \(\Delta AIC>0,\)

the exponential decay was the most appropriate fit and if \(\Delta AIC<0\), the polynomial was the most appropriate fit. Using the fitting method that best represented the group data, we

then fitted each participant’s individual data and calculated the adjusted coefficient of determinations (\({\overline{R} }^{2}\)). The AIC was lower in the polynomial fits compared to the

exponential decay fits for head kinematic variability across step cadences (\({V}_{res} {a}_{NET}{:} \Delta AIC\) = −78.5, polynomial \({\overline{R} }^{2}\) = 0.94 ± 0.05; \({V}_{res}

{a}_{ML}\): \(\Delta AIC\) = −40.2, polynomial \({\overline{R} }^{2}\) = 0.35 ± 0.65; \({V}_{res}\) \({\omega }_{NET}\): \(\Delta AIC\) = −41.3, polynomial \({\overline{R} }^{2}\) = 0.83 ± 

0.19; \({V}_{res}\) \({\omega }_{roll}\): \(\Delta AIC\) = −13.6, polynomial \({\overline{R} }^{2}\) = 0.78 ± 0.19; Fig. 7A) and gait speeds (\({V}_{res} {a}_{NET}\): \(\Delta AIC\) = −69.3,

polynomial \({\overline{R} }^{2}\) = 0.86 ± 0.20; \({V}_{res} {a}_{ML}\): \(\Delta AIC\) = −39.9, polynomial \({\overline{R} }^{2}\) = 0.20 ± 0.67; \({V}_{res}\) \({\omega }_{NET}\):

\(\Delta AIC\) = −64.9, polynomial \({\overline{R} }^{2}\) = 0.71 ± 0.32; \({V}_{res}\) \({\omega }_{roll}\): \(\Delta AIC\) = −38.4, polynomial \({\overline{R} }^{2}\) = 0.71 ± 0.25; Fig. 

7B). To determine the locomotor cadence and speed at which head kinematic variability was minimal, we extracted the minimum value for each participant’s 2nd degree polynomial function. The

locations of the minima varied between 90–126 steps/min across step cadences (\({V}_{res} {a}_{NET}\) at 117 ± 9 steps/min; \({V}_{res} {a}_{ML}\) at 90 ± 17 steps/min; \({V}_{res}\)

\({\omega }_{NET}\) at 126 ± 16 steps/min; \({V}_{res}\) \({\omega }_{roll}\) at 125 ± 25 steps/min; Fig. 7A) and 1.1–1.7 m/s across gait speeds (\({V}_{res} {a}_{NET}\) at 1.5 ± 0.2 m/s;

\({V}_{res} {a}_{ML}\) at 1.1 ± 0.3 m/s; \({V}_{res}\) \({\omega }_{NET}\) at 1.7 ± 0.2 m/s; \({V}_{res}\) \({\omega }_{roll}\) at 1.7 ± 0.3 m/s; Fig. 7B). VESTIBULAR-EVOKED BALANCE

RESPONSES To confirm that vestibular-evoked balance responses decreased with step cadence, we fitted exponential decay functions to each individual participant’s peak coherences from the

three IMU measurements. In general, the exponential decay functions were well fitted to the data as demonstrated by the large \({\overline{R} }^{2}\) values (back: 0.90 ± 0.06; right ankle:

0.85 ± 0.14; left ankle: 0.86 ± 0.18; Fig. 8A). We found similar results when fitting the peak coherences across gait speeds (back: 0.89 ± 0.07; right ankle: 0.84 ± 0.15; left ankle: 0.87 ± 

0.17; Fig. 8B). DISCUSSION We found that, contrary to the model proposed by MacNeilage and colleagues, head kinematic variability did not predict vestibular modulations at step cadences

faster than 100% of preferred cadence. To determine this, we measured \({V}_{res}\), a metric of head kinematic variability across strides, and EVS-evoked balance responses from participants

as they walked at cadences ranging from 40 to 140% of their natural step cadence in the real-world. Across all the \({V}_{res}\) measures computed, a 2nd degree polynomial function, with

the minimum near the preferred step cadences, fitted the data better than an exponential decay function. In contrast, the peak magnitude of the vestibular-evoked balance responses decreased

as step cadence increased and was well fitted to an exponential decay function as hypothesized. These results suggest that head kinematic variability is minimal near our preferred locomotor

cadences and is not the driving factor in the cadence and speed induced modulation of vestibular balance control. HEAD KINEMATIC VARIABILITY IS MINIMAL NEAR PREFERRED STEP CADENCES The

changes to head kinematic variability (\({V}_{res}\)) across step cadences and gait speeds were best fitted to 2nd degree polynomial curves. The local minima in polynomials fitted to the

mean \({V}_{res}\) were located at 90–126 steps/min and 1.1–1.7 m/s across step cadence and gait speed, respectively. These correspond with the range of step cadences (96–126 steps/min) and

gait speeds (0.9–1.8 m/s) that we identified during the preferred cadence condition and is similar to what has previously been measured as preferred step cadences and gait

speeds29,30,31,32,33,34. Hirasaki et al.9 found that within the gait speed range of 1.2–1.8 m/s (and step cadences of 108–132 steps/min), head and body coordination was optimized, and the

bandwidth around the predominant frequency of the vertical translation spectral density was minimized. This speed range is also optimal for minimizing energetic cost during locomotion35,36.

Furthermore, other authors have observed that the symmetry of head movement is optimized at preferred step cadences and speeds, which they argued reflects head stability30,31; although we

note that this interpretation has been criticized37,38. MacNeilage and Glasauer16 proposed that \({V}_{res}\), which is calculated as the ratio of residual to total head kinematic

variability over a stride cycle, represents a ratio of the motor noise to the proportion of sensory (vestibular) noise. However, an alternative interpretation of \({V}_{res}\) is that it

represents a “noise-to-signal” ratio of the head kinematics, rather than a predictor of vestibular-evoked balance responses. In this view, the variance of the head movement signals around

the mean across stride cycles (i.e., the numerator of the \({V}_{res}\) equation) is considered the sensory noise which is then compared to the overall signal amplitude (as measured by the

total sum of squares, i.e., the denominator of the \({V}_{res}\) equation). Unlike the previous interpretation, this does not depend on the assumption of Weber’s law that signal amplitude is

proportional to sensory noise39, which may not be followed for vestibular cues of self-motion40,41. Given this interpretation, our results suggest that the vestibular “noise-to-signal”

ratio is minimal near our preferred cadences and gait speeds. There is evidence that greater noise in sensory signals increases the metabolic cost of neuronal information processing7 and

that this information processing is optimized to reduce metabolic cost42. Thus, reducing the variability of our head movement may serve to minimize the energy requirements of processing

vestibular information. Given the large energy demands of the central nervous system and evolutionary pressures to optimize energy expenditure and the quality of sensory information

encoded43,44, our preferred movement patterns may have evolved to balance between the energetic costs of our motor commands and the central sensory information processing pressures of signal

quality, metabolic cost, and number of neurons required. For example, it has been shown that humans choose locomotor patterns that are not energetically optimal when step length and width

are constrained45, suggesting that other factors – possibly head kinematic variability – are important considerations for how we choose our locomotor patterns. Alternatively, given that that

blood gas receptors do not sense energetic cost during locomotion46, it is possible that our head kinematics provide partial (and indirect) information to facilitate energetic optimization

during locomotion. These results open the door to future work exploring how the metabolic costs of our motor actions and sensory processing demands are balanced as we navigate our

environment. HEAD KINEMATIC VARIABILITY DOES NOT MODULATE VESTIBULAR-EVOKED BALANCE RESPONSES We also characterized the changes to head kinematic variability and vestibular-evoked balance

responses at faster step cadences. For the \({V}_{res}\) measures using the linear head accelerations (\({V}_{res}\) \({a}_{NET}\) and \({V}_{res} {a}_{ML}\)), we generally observed that the

participant mean \({V}_{res}\) values increased beyond the 100% cadence condition (except in the 100–120% \({V}_{res}\) \({a}_{NET}\) comparison). These increases in mean \({V}_{res}\)

ranged from 17–35% between the 100% and 120% conditions, and 39–77% between the 100% and 140% cadence conditions. Given that increased \({V}_{res}\) was suggested to indicate that sensory

noise has decreased relative to motor noise16, the magnitude of vestibular-evoked balance responses should consequently increase. However, we observed significant decreases (51–60% decrease)

in the extracted peak coherences between the 100% and 140% step cadence conditions. While there were no differences detected in the \({V}_{res}\) measures driven by the angular velocity of

the head (\({V}_{res}\) \({\omega }_{NET}\) and \({V}_{res}\) \({\omega }_{roll}\)), possibly due to the greater variance in the mean \({V}_{res}\) values extracted for these measures, these

measures did not decrease with the vestibular-evoked balance responses. We also observed that the \({V}_{res}\)-coherence correlations from the 40–100% cadence conditions and the 100–140%

conditions were near orthogonal, especially in the linear acceleration \({V}_{res}\) measures. Furthermore, the correlations between \({V}_{res}\) and coherence were positive from the

40–100% cadence conditions but not for the 100–140% conditions, indicating that the relationship between \({V}_{res}\) and coherence was not consistent across step cadences. Previous studies

at slower step cadences and gait speeds have observed mean \({V}_{res}\) decrease 14–51% as step cadence and gait speed increased (at 52 steps/min and 0.4 m/s to 78 steps/min and 0.8 

m/s)21,22. At the same step cadences and speeds, decreases in the peak coherence between EVS and muscle activity (17–31%)13, centre of pressure displacement (47%)21, and linear accelerations

(34–38%)22 have been reported. In accordance with ths previous observations, we found the mean \({V}_{res}\) decreased by 14–45% between the 40% and 60% step cadence conditions, which

corresponded to average step cadences of 44 and 65 steps/min, respectively. Concurrently, we observed decreases (25–32%) in the peak coherence from the back and ankle ML linear acceleration

coherence, which approximate respectively the vestibular-evoked responses of the whole-body body centre of mass and individual lower limbs. To characterize the overall change in vestibular

balance control across step cadences and gait speeds, we fitted exponential decay curves to the participant peak coherences. For all IMUs, the exponential decay curve was well suited to

represent the decreased magnitude of vestibular-evoked balance responses as a function of step cadence and gait speed. Given that both the paired t-tests and the fitted the exponential decay

functions indicated a continued decrease in vestibular-evoked responses, these results complement previous studies measuring vestibular balance responses at slower locomotor cadences while

also extending these findings to preferred and faster walking. This supports our hypothesis, as well as observations in clinical studies12, that the vestibular-evoked balance responses would

decrease as step cadence (and gait speed) increased beyond our preferred step cadence. However, the increasing (linear accelerations) or unchanging (angular velocities) \({V}_{res}\) at

faster cadences contradicts the prediction that changes to \({V}_{res}\) will reflect vestibular balance response modulations at faster step cadences, suggesting that the vestibular control

of balance during locomotion is not modulated by the ratio of motor to sensory noise as quantified by \({V}_{res}\). The increased head kinematic variability at faster cadences/speeds does

not preclude the proposal by MacNeilage and colleagues that the reduction in vestibular-evoked balance responses at faster step cadences/speeds may be related to a relative increase in the

feedforward control of locomotion. Although Mackrous et al.20 revealed no attenuation of vestibular primary afferents in adult primates during locomotion, suppression of vestibular signals

may occur in the vestibular nuclei (see review by Cullen47) and be influenced by factors not captured by \({V}_{res}\). Alternatively, this modulation of vestibular-evoked balance responses

could arise from body stability demands, as providing external pelvis stabilization or increasing step width have been shown to decrease vestibular balance responses during locomotion48.

Additionally, when walking on a split-belt treadmill, the modulation of the vestibular-evoked responses is consistent with the kinematics from each limb49. A direct relation between these

vestibular modulations and changes in head kinematic variability, however, cannot be determined given that head kinematics were not recorded in these studies. Another possible explanation

for the attenuation of vestibular balance as cadence increases may be related to non-linearities in vestibular afferent encoding of head motion20,50 and bi-linear vestibular nuclei gains51,

resulting in saturation of head motion signals. To test if non-linear processes in vestibular pathways contributed to the attenuation of the vestibular evoked balance responses, we modelled

the vestibular afferent responses to head motion and electrical stimuli20,50,52,53 as well as the known vestibular peripheral (sigmoid function to maintain firing rates between 0 and 250 

Hz)20,50 and central (bi-linear gains)51 non-linearities (see Supplementary Materials). In summary, we found that the predicted vestibular afferent responses generally did not saturate (less

than 2% of predicted firing rates occurred outside the 50–200 Hz range), even at the higher step cadences. Consequently, when we calculated coherence between the body kinematics and the

simulated central vestibular nuclei firing rates, it was not different than when using the true EVS signal. Thus, it is unlikely that vestibular afferent non-linearities and bi-linear

vestibular nuclei gains are responsible for the attenuation of vestibular-evoked balance responses as locomotor cadence and speed increase. LIMITATIONS As we did not restrict head

orientation during trials, participants walked with their head more flexed (pitched down) as their step cadence deviated from the preferred rate (both slower and faster). The observed

changes in mean head pitch angle, however, were modest (8.8° to 4.0° up from horizontal). These small head angle changes would be expected to alter the vestibular-evoked responses by 2% if

we assume a net EVS vector pointing 17–19° up from Reid’s plane23. Given that we observed changes ranging from 25–60% between locomotor cadences/speeds, it is unlikely that any head

orientation induced change to the EVS-evoked responses had any noticeable effect on our results. Caution should be exercised when interpreting the lower peak coherence values that we

measured at the fastest step cadences. Many of the peak coherence values we extracted at the cadence conditions of 100% and beyond were just higher than the minimum threshold for the

individual participant coherence (0.0212). For example, if the coherence confidence limit was increased to 99.9% (increasing the significance threshold by ~ 50%), a larger number of

participants would exhibit no coherence at the faster cadences (back: 2 at 100%, 3 at 120%, and 7 at 140%; right ankle: 1 at 120% and 7 at 140%; left ankle: 1 at 100%, 2 at 120%, and 8 at

140%) compared to the confidence interval of 99% that we used (back: 3 at 140%, right ankle: 1 at 140%; left ankle: 1 at 120% and 1 at 140%). Upon further inspection, we observed that many

of the coherence peaks in the 120% and 140% cadence conditions occurred outside of the typical timing (stance phase) and frequency (0–10 Hz) where coherence was observed. However, it is

unlikely that this affected the results and interpretation of our data, given that peak coherences we observed for these conditions were low and would be unlikely to influence the fit of the

exponential decay functions. CONCLUSION In summary, we observed that \({V}_{res}\) was minimal near our preferred cadences and gait speeds while the magnitude of the vestibular-evoked

balance responses decreased as step cadence increased. This demonstrates that \({V}_{res}\) does not predict vestibular responses at faster step cadences and speeds. Furthermore, our results

show that head kinematic variability is reduced at preferred step cadences to potentially minimize the cost of processing noisy information in our vestibular sensing. We propose that

optimizing sensory information during locomotion decreases the metabolic cost of information processing while improving our internal and perceptual self-motion estimates, making us more

effective in navigating our environment. METHODS PARTICIPANTS We recruited 14 healthy young adult participants with no neurological or musculoskeletal impairments to participate in this

study. However, two were unable to complete the experiment due to discomfort with the EVS so the final sample size consisted of 12 participants. To determine an appropriate sample size, we

performed power analyses given effect sizes (1.403–3.009) between the magnitude of vestibular responses observed at 52 steps/min and 78 steps/min22. We determined that the minimal sample

size for a two-sided paired sample t-test with a desired α = 0.05 and power = 0.9 was 8 participants and we added an additional 4 to account for the smaller differences between step cadences

for a total of 12 participants (6 females, 6 males; age = 24.3 ± 2.5 years; height = 171.8 ± 13.4 cm; mass = 71.1 ± 17.0 kg). This experiment was reviewed by the University of British

Columbia Clinical Research Ethics Board (H22-01776) and participants provided written informed consent prior to enrolling in the study. All research was performed in accordance with relevant

guidelines/regulations and conformed to the declaration of Helsinki, with the exception of registration to a database. SET-UP Participants were instructed to wear athletic clothing and

comfortable running shoes for walking, to replicate their natural walking behaviour. We attached four inertial measurement units (IMUs; MPU 6050; accelerometer range =  ± 16 g; gyroscope

range =  ± 2000˚/s) to the participant for the duration of the experiment (Fig. 1). The first IMU was mounted to a custom-made mouthguard that was prepared for each participant using a vinyl

polyciliate putty to form a dental impression and ethylene vinyl acetate to vacuum form the mouthguard. The IMU was mounted on a small cast acrylic tab attached to the mouthguard so that it

sat outside the mouth. By fixing the IMU directly to the skull via the upper dentition, we can record head kinematics without skin motion artefact54. The second IMU was placed on the low

back at the third lumbar spinous process and the height was measured for each participant (105.3 ± 9.6 cm SD). This placement was chosen to approximate the body centre of mass accelerations

which we have previously used to characterize whole-body vestibular responses during locomotion22. The remaining two IMUs were placed just above each lateral malleolus to detect heel strike

and toe-off55 and characterize lower limb vestibular responses22,56. IMU CALIBRATION Each IMU was first calibrated to correct the sensitivity and bias of the accelerometer and the bias in

the gyroscopes57. We performed IMU-to-body calibration prior to the experimental trials to align the IMUs to a body reference frame with x: forward, y: right, and z: down (Fig. 1). After

being attached to the participant, we recorded two 5 s calibration poses for each IMU58. The first calibration pose was performed with the participant standing upright, to define the true

z-axis. For the head IMU, this involved levelling the head so that Reid’s plane was perpendicular to gravity to orient the head IMU with respect to the vestibular apparatus. Then, the

participant pitched each respective body segment ~ 90 degrees forward to define an approximate x-axis for the second calibration position. The approximate x-axis and true z-axis were defined

as opposite to the net acceleration vector caused by the gravitational field. The true y-axis was calculated as the cross-product of the true z-axis and the approximate x-axis. Finally, the

true x-axis was calculated as the cross-product between the true y-axis and the true z-axis. PORTABLE SYSTEM We previously devised a portable system for concurrent kinematic measurement and

electrical stimulation, employing a reconfigurable I/O device (myRIO-1900, National Instruments) equipped with a field-programmable gate-array running LabVIEW 2019b (National

Instruments)22. In this setup, the microcontroller communicated to each of the IMUs with I2C protocol via a wired connection. An analog output was interfaced with a constant current

stimulator to administer the electrical stimuli (see _Stimulus_ section). Data acquisition occurred directly on the myRIO-1900 at a sampling rate of 200 Hz. Both the microcontroller and

stimulator were powered by a 12-V battery (TalentCell, China), and the participants wore all components within a compact backpack. A wireless connection facilitated communication between a

laptop (ThinkPad X1 Nano, Lenovo) and the myRIO-1900, enabling system control and real-time data visualization. The myRIO-1900 has a storage capacity of 256 megabytes, so the data were

transferred to the laptop halfway through the data collection to avoid data corruption due to insufficient memory storage. STIMULUS We applied binaural bipolar electrical vestibular

stimulation to the participants via carbon rubber electrodes (9 cm2) coated with conductive gel. The electrodes were affixed to the participant’s mastoid processes with hypoallergenic tape.

The electrical vestibular stimuli were generated as stochastic waveforms (stochastic EVS; 0–20 Hz, amplitude peak ± 4.5 mA, root mean square 1.25 mA) using LabVIEW 2019b (National

Instruments) and were delivered by a constant current isolated linear stimulator (STIMSOLA, Biopac Systems Inc.). We selected these parameters because they have previously been shown to

elicit EVS-evoked balance responses in the lower limbs and whole body, with kinematic responses occurring at frequencies between 0–10 Hz during locomotion22. Ten unique EVS waveforms were

generated for this study, and one was randomly selected for each trial. EVS modulates the firing rate of the primary otolith and semicircular canal vestibular afferents52,59,60 to generate

craniocentric virtual head movement signals61,62. In a binaural bipolar configuration, the EVS-evoked net motion includes a virtual angular velocity signal, oriented around an axis

positioned approximately 17–19 degrees above Reid’s plane23,53,63 accompanied by an inference of interaural linear acceleration during a head forward orientation64. The choice of stochastic

EVS as the stimulus was based on its advantageous characteristics, as it enables the examination of vestibular responses throughout the entire stride cycle27. Importantly, stochastic EVS

minimizes testing duration when compared to conventional square wave stimuli27. PROTOCOL The protocol for this study was completed outdoors on pavement at the University of British Columbia

Vancouver campus. We chose this outdoor setting because there are differences in head kinematics between treadmill and above ground locomotion9,65,66, so it was important to study head

kinematic variability in real-world environments to characterize natural locomotor behaviour. To minimize any possible effects of different locations or ground types, all trials were

completed within the same 500-m stretch of walking path. All trials were completed without any precipitation present. Firstly, to determine their natural walking speed and cadence,

participants walked without stimulation for 30 s continuously. The participants were all told to “walk at a normal, comfortable speed” to avoid any possible variation due to different

instructions29. Additionally, for all trials, we instructed participants to look towards the horizon while walking. While participants are generally instructed to pitch their head at ~ 

17–19° from horizontal during studies involving EVS23, here we were interested in observing natural head kinematics so we chose not to rigidly constrain head pitch during the experiment (see

Discussion). Once the participant’s natural locomotor cadence was determined, they completed the following six locomotor cadence conditions in a randomized order: 40%, 60%, 80%, 100%, 120%,

and 140% of their natural cadence. The cadences were guided by a metronome played to the participants using earbud headphones and verbal feedback from the experimenter was provided if the

participant was not maintaining the desired cadence. We calculated the distance covered from the start to the end of each trial by utilizing global positioning system measurements from a

smartphone app (phyphox, RWTH Aachen University). This allowed us to estimate the average gait speed (distance travelled divided by trial duration). For each condition, participants

completed 85 strides without any stimulation followed by 215 strides with EVS which was split over three trials. As trial duration was determined by the number of strides and step cadence,

it ranged from 65 to 325 s. Trials began when the participant reached the required cadence. While 250 strides has previously been shown to be an appropriate number of strides to characterize

time-dependent coherence for lower limb muscles27, our recent work suggests that fewer strides (up to 120 strides) are needed to estimate vestibular-evoked responses with body mounted IMUs

for slow cadences (52 and 78 steps/min) and speeds (~ 0.4 and ~ 0.8 m/s)22. Breaks were provided whenever necessary to avoid fatigue and a forced break was taken at the halfway point of the

experiment. Prior to and after each trial, the experimenters confirmed that the EVS electrodes and IMUs were secured. SIGNAL ANALYSIS After data collection, the signals were linearly

interpolated to correct for any possible missed samples during data recording. On average, 2.4 samples recorded by the portable system were dropped each trial (range = 0–46 samples), which

is approximately one sample dropped for every 22,900 samples, or 115 s. Following the IMU calibration, we filtered the IMU data with a dual pass lowpass fourth order Butterworth filter at 80

 Hz. The stochastic EVS data were filtered at 20 Hz with a dual pass lowpass fourth order Butterworth filter. IMU ORIENTATION ESTIMATION To determine the orientation of the various body

segments, we used a complementary filter67 to calculate the tilt orientation of the IMUs along the pitch (around Y-axis) and roll (around X-axis) axes (Eq. 1).

$${{\varvec{\theta}}}_{{\varvec{i}}}=\left({{\varvec{\theta}}}_{{\varvec{i}}-1}+\boldsymbol{

}{{\varvec{\omega}}}_{{\varvec{i}},{\varvec{r}}}\boldsymbol{*}{\varvec{d}}{\varvec{t}}\right){\varvec{G}}+\left({{\varvec{a}}{\varvec{c}}{\varvec{c}}}_{{\varvec{i}}}\right)\left(1-{\varvec{G}}\right)$$

(1) Here, \({{\varvec{\theta}}}_{{\varvec{i}}}\) represents the orientation estimate (pitch or roll) at the ith sample point with respect to the vertical axis in one dimension.

\({{\varvec{\omega}}}_{{\varvec{i}},{\varvec{r}}}\) is the rotated angular velocity around the same axis obtained from the gyroscope (see Eq. 4), \({\varvec{d}}{\varvec{t}}\) is the time

step between samples (5 ms), \({\varvec{G}}\) is a weighting factor balancing gyroscope and accelerometer estimates (set to 0.995), and

\({{\varvec{a}}{\varvec{c}}{\varvec{c}}}_{{\varvec{i}}}\) represents the orientation estimate derived from accelerometer data. If the net acceleration deviated by 10% or more from 9.81 m/s2,

only gyroscope information was used for orientation estimation at that specific sample point. The equations for calculating accelerometer orientation estimates in pitch and roll, with

reference to the IMU body frame and the recorded accelerations (\({\varvec{a}}=\left[\begin{array}{ccc}\ddot{{\varvec{x}}}& \ddot{{\varvec{y}}}&

\ddot{{\varvec{z}}}\end{array}\right]\)) were as follows (Eqs. 2 and 3):

$${{\varvec{p}}{\varvec{i}}{\varvec{t}}{\varvec{c}}{\varvec{h}}={\varvec{a}}{\varvec{c}}{\varvec{c}}}_{{\varvec{i}}}={\varvec{a}}{\varvec{t}}{\varvec{a}}{\varvec{n}}2{\varvec{d}}({\ddot{{\varvec{x}}}}_{{\varvec{i}}},{\ddot{{\varvec{z}}}}_{{\varvec{i}}})$$

(2) $${{\varvec{r}}{\varvec{o}}{\varvec{l}}{\varvec{l}}=\boldsymbol{

}{\varvec{a}}{\varvec{c}}{\varvec{c}}}_{{\varvec{i}}}=-{\varvec{a}}{\varvec{t}}{\varvec{a}}{\varvec{n}}2{\varvec{d}}({\ddot{{\varvec{y}}}}_{{\varvec{i}}},\sqrt{{\ddot{{\varvec{x}}}}_{{\varvec{i}}}^{2}+\boldsymbol{

}{\ddot{{\varvec{z}}}}_{{\varvec{i}}}^{2}})$$ (3) Additionally, we rotated the raw angular velocities (\({{\varvec{\omega}}}_{{\varvec{i}}}\)) with the previous estimated rotation matrix

(\({{\varvec{R}}}_{{\varvec{i}}-1}\), calculated from pitch and roll orientations, assuming no yaw) prior to the complementary filter integration (Eq. 4). This was done to account for the

rotating frame during the integration of angular velocity to position. $${{\varvec{\omega}}}_{{\varvec{i}},{\varvec{r}}}=\boldsymbol{

}{{\varvec{\omega}}}_{{\varvec{i}}}{{\varvec{R}}}_{{\varvec{i}}-1}$$ (4) IMU LINEAR ACCELERATION GRAVITY CORRECTION Linear accelerometers cannot distinguish between gravitational and

inertial accelerations. To isolate the true inertial component of linear accelerations at each timestep (\({{\varvec{a}}}_{{\varvec{i}}}^{\boldsymbol{*}}\)), we removed the gravitational

component (Eq. 5). Using the estimated orientation rotation matrix from the current iteration (\({{\varvec{R}}}_{{\varvec{i}}}\)), we rotated and subtracted the gravitational components

(\({\varvec{g}}= \left[\begin{array}{ccc}0& 0& -9.81\end{array}\right]\)) from the current timestep accelerometer data (\({{\varvec{a}}}_{{\varvec{i}}}\)). Subsequently, we low pass

filtered the IMU data at 20 Hz using a dual pass 4th order Butterworth filter.

$${{\varvec{a}}}_{{\varvec{i}}}^{\boldsymbol{*}}=({{\varvec{a}}}_{{\varvec{i}}}-{\varvec{g}}{{\varvec{R}}}_{{\varvec{i}}})$$ (5) HEAD IMU LINEAR ACCELERATION TRANSFORMATION Finally, to

accurately represent linear accelerations experienced by the vestibular system, the linear accelerations were transformed to the location of the vestibular system (approximated as the

mid-point between the external acoustic meati) with the following rigid body vector relationship54,68 (Eq. 6): $${{\varvec{a}}}_{{\varvec{B}},{\varvec{i}}}=\boldsymbol{

}{{\varvec{a}}}_{{\varvec{A}},{\varvec{i}}}+{\boldsymbol{\alpha }}_{{\varvec{i}}}\boldsymbol{ }\times

{{\varvec{r}}}_{{\varvec{B}}-{\varvec{A}}}+{{\varvec{\omega}}}_{{\varvec{i}}}\boldsymbol{ }\times ({{\varvec{\omega}}}_{{\varvec{i}}}\times {{\varvec{r}}}_{{\varvec{B}}-{\varvec{A}}})$$ (6)

where \({{\varvec{a}}}_{{\varvec{B}},{\varvec{i}}}\) represents the gravity-removed linear acceleration at the approximate location of the vestibular system,

\({{\varvec{a}}}_{{\varvec{A}},{\varvec{i}}}\) is the gravity-removed linear acceleration at the mouthguard, \({\boldsymbol{\alpha }}_{{\varvec{i}}}\) denotes angular acceleration,

\({{\varvec{r}}}_{{\varvec{B}}-{\varvec{A}}}\) signifies the position vector from the mouthguard to the approximate location of the vestibular system, and

\({{\varvec{\omega}}}_{{\varvec{i}}}\) represents the body-fixed angular velocity. STEP DETECTION We segmented the data into strides by identifying heel strike and toe-off events using both

the right and left ankle IMUs. We determined heel strikes as the local minima of the y-axis angular velocity (mediolateral) following the prominent mid-swing peaks, while we estimated

toe-offs as the zero-crossing points of y-axis angular velocity before the mid-swing peaks55. We defined a stride as the interval between right heel contact and the sample just before the

subsequent right heel contact. Strides were not included if they contained a stumble or trip. We also had a provision to remove strides if they were either 50% longer or shorter than the

participant’s average stride duration. This resulted in the removal of two total strides across all participants and conditions (both in the same participant at the slowest cadence condition

during the EVS trials). QUANTIFICATION OF HEAD KINEMATIC VARIABILITY To assess the variability in head movement during locomotion, we calculated the proportion of residual variance

(\({V}_{res}\)) for both head linear accelerations and angular velocities. This measure was developed to predict the magnitude of vestibular-evoked balance responses during locomotion16,21.

MacNeilage and Glasauer16 proposed that the ratio between the residual and total variability of the head kinematics across strides represents the ratio between motor efference copy noise and

vestibular information noise, respectively. Based on the Maximum-likelihood model of cue-integration69,70, they predicted that as vestibular noise increases relative to motor noise,

vestibular head motion signals would be downregulated and the vestibular-evoked balance responses would decrease in magnitude. We computed \({V}_{res}\) for the net head linear acceleration

(\({a}_{NET})\) and net head angular velocity (\({\omega }_{NET}\)) from the stride-normalized, gravity-corrected, and transformed data from the head IMU. Additionally, we calculated the

\({V}_{res}\) for ML head linear acceleration (\({a}_{ML})\) and roll head angular velocity (\({\omega }_{roll}\)) because EVS elicits virtual signals in the frontal plane when walking and

looking forward71,72. $${{\varvec{V}}({\varvec{t}})}_{{\varvec{r}}{\varvec{e}}{\varvec{s}}}=\boldsymbol{

}{{\varvec{S}}{\varvec{S}}({\varvec{t}})}_{{\varvec{r}}{\varvec{e}}{\varvec{s}}}/{{\varvec{S}}{\varvec{S}}({\varvec{t}})}_{{\varvec{t}}{\varvec{o}}{\varvec{t}}}$$ (7)

$${{\varvec{S}}{\varvec{S}}({\varvec{t}})}_{{\varvec{r}}{\varvec{e}}{\varvec{s}}}=\boldsymbol{

}\frac{1}{{\varvec{N}}}\sum_{{\varvec{i}}=1}^{{\varvec{N}}}\sum_{{\varvec{d}}}({{\varvec{m}}\left({\varvec{t}}\right)}_{{\varvec{d}},{\varvec{i}}}-{{\varvec{f}}\left({\varvec{t}}\right)}_{{\varvec{d}}}{)}^{2}$$

(8) $${{\varvec{S}}{\varvec{S}}({\varvec{t}})}_{{\varvec{t}}{\varvec{o}}{\varvec{t}}}=\boldsymbol{

}\frac{1}{{\varvec{N}}}\sum_{{\varvec{i}}=1}^{{\varvec{N}}}\sum_{{\varvec{d}}}({{\varvec{m}}\left({\varvec{t}}\right)}_{{\varvec{d}},{\varvec{i}}}-{\overline{{\varvec{m}}}

}_{{\varvec{d}}}{)}^{2}$$ (9) where \({{\varvec{V}}({\varvec{t}})}_{{\varvec{r}}{\varvec{e}}{\varvec{s}}}\) is the \({V}_{res}\) across the stride cycle (Eq. 7),

\({{\varvec{S}}{\varvec{S}}({\varvec{t}})}_{{\varvec{r}}{\varvec{e}}{\varvec{s}}}\) is the residual sum of squares representing the deviation from the average stride cycle (i.e.,

stride-cycle attractor; Eq. 8) and \({{\varvec{S}}{\varvec{S}}({\varvec{t}})}_{{\varvec{t}}{\varvec{o}}{\varvec{t}}}\) is the total signal magnitude from the total stride cycle mean (Eq. 9).

We calculated these measures across the normalized stride cycle between the total number of strides (\({\varvec{N}}\)). \({\varvec{d}}\) represents the dimension (axes x, y, z) of the head

motion. For the \({V}_{res}\) \({a}_{NET}\) and \({V}_{res}\) \({\omega }_{NET}\), \(d=[x y z]\) and the components

(\({{\varvec{S}}{\varvec{S}}({\varvec{t}})}_{{\varvec{r}}{\varvec{e}}{\varvec{s}}}\) and \({{\varvec{S}}{\varvec{S}}({\varvec{t}})}_{{\varvec{t}}{\varvec{o}}{\varvec{t}}}\)) were calculated

by summing the squared error across all three dimensions. Whereas for the \({V}_{res}\) \({a}_{ML}\), \(d=y\) and for the \({V}_{res}\) \({\omega }_{roll}\), \(d=x\).

\({{\varvec{m}}\left({\varvec{t}}\right)}_{{\varvec{d}},{\varvec{i}}}\) is the head motion at the normalized stride time \(t\), for stride \(i\) and in dimension \(d\).

\({{\varvec{f}}\left({\varvec{t}}\right)}_{{\varvec{d}}}\) is the average head motion (stride-cycle attractor) at time \(t\) and dimension \(d\). \({\overline{{\varvec{m}}}

}_{{\varvec{d}}}\) is the average head motion along the dimension \(d\). We calculated \({V}_{res}\) for both the trials with and without the applied EVS. While the average \({V}_{res}\) was

 ~ 11–23% higher in the trials with the applied EVS, the changes in \({V}_{res}\) across step cadences were similar between conditions. Thus, only the \({V}_{res}\) measures from trials with

EVS are shown in the results. The EVS-induced increase in average \({V}_{res}\) was mainly driven by larger (~ 10–48%) residual variability around the average stride cycle kinematics. The

\({V}_{res}\) measures from the trials without EVS are included in the Supplementary Materials. TIME-DEPENDENT FREQUENCY ANALYSES To assess the phasic modulation of vestibular-evoked balance

responses during locomotion, we computed time-dependent coherence, gain, and spectral output power between the EVS and body kinematics (gravity-corrected ML acceleration from the low back

and ankle IMUs, each calculated individually). Coherence was not calculated using the head kinematics, because these will be affected by both whole-body movements as well as head specific

vestibular reflexes (i.e., vestibulocolic reflex) which can occur at frequencies much higher than the applied EVS (up to 300 Hz)73. Coherence is a metric for assessing the linear association

between an input and output signal across various frequencies. It can be likened to time-domain correlation analyses, wherein a coherence value of 0 indicates no similarity, while a value

of 1 indicates a perfect correlation with no noise, irrespective of scaling, between two signals at a specific frequency28,74. The coherence between the EVS and low back ML acceleration

represents the vestibular response evoked at the body centre of mass, whereas the coherences between the EVS and the ankle ML accelerations represent the vestibular responses evoked in the

lower limbs. Gain quantifies the scaling factor between the two signals at a particular frequency while spectral output power characterizes the squared magnitude of the output signal

(gravity-corrected ML acceleration from the low back and ankle IMUs) across different frequencies. We employed Morlet wavelet decomposition spanning from 0.5 Hz to 20 Hz, to extract

time-dependent cross-spectra and auto-spectra of EVS and body segment kinematics27,28,75. Wavelets were defined in 0.5 Hz intervals, but still have power outside of their peak frequency due

to frequency smoothing that occurs when defining the wavelets76. The data were divided into strides and padded with 50% additional data from preceding and subsequent strides to prevent

distortions at the edge of a window. To maximize coherence between applied EVS and evoked balance responses, we shifted the EVS signal 200 ms later in time62,77,78 prior to the frequency

analyses. Following the Morlet decomposition, we resampled the data from each stride to facilitate stride-by-stride coherence, gain, and spectral power output calculations. For individual

participant results, we normalized stride durations and gait event timings (right heel strike, left toe-off, left heel strike, right toe-off) to each participant’s individual averages for

the given cadence condition. For between cadence comparisons, normalization was carried out with respect to total means across participants and cadences. This allowed for comparisons

throughout the stride cycle while maintaining alignment with gait events. The time-dependent coherence [\({\varvec{C}}\left({\varvec{\tau}},{\varvec{f}}\right)\)], gain

[\({\varvec{G}}\left({\varvec{\tau}},{\varvec{f}}\right)\)], and body kinematics spectral output power [\({\varvec{S}}\left({\varvec{\tau}},{\varvec{f}}\right)\)] were calculated using the

following Eqs. (10–12): $${\varvec{C}}\left({\varvec{\tau}},{\varvec{f}}\right)=\boldsymbol{

}\frac{|{{\varvec{P}}}_{{\varvec{x}}{\varvec{y}}}\left({\varvec{\tau}},{\varvec{f}}\right){|}^{2}}{{{\varvec{P}}}_{{\varvec{x}}{\varvec{x}}}\left({\varvec{\tau}},{\varvec{f}}\right){{\varvec{P}}}_{{\varvec{y}}{\varvec{y}}}\left({\varvec{\tau}},{\varvec{f}}\right)}$$

(10) $${\varvec{G}}\left({\varvec{\tau}},{\varvec{f}}\right)=\boldsymbol{

}\left|\frac{{{\varvec{P}}}_{{\varvec{x}}{\varvec{y}}}\left({\varvec{\tau}},{\varvec{f}}\right)}{{{\varvec{P}}}_{{\varvec{x}}{\varvec{x}}}\left({\varvec{\tau}},{\varvec{f}}\right)}\right|$$

(11) $${\varvec{S}}\left({\varvec{\tau}},{\varvec{f}}\right)=\boldsymbol{ }{{\varvec{P}}}_{{\varvec{y}}{\varvec{y}}}\left({\varvec{\tau}},{\varvec{f}}\right)$$ (12) where \({\varvec{\tau}}\)

represents the specific time point within the stride cycle, and \({\varvec{f}}\) is the frequency. \({{\varvec{P}}}_{{\varvec{x}}{\varvec{y}}}\left({\varvec{\tau}},{\varvec{f}}\right)\)

represents the time-normalized time-dependent cross-spectrum between EVS and body kinematics (low back or ankle ML linear acceleration),

\({{\varvec{P}}}_{{\varvec{x}}{\varvec{x}}}\left({\varvec{\tau}},{\varvec{f}}\right)\) is the time-normalized time-dependent auto-spectrum of the EVS signal, and

\({{\varvec{P}}}_{{\varvec{y}}{\varvec{y}}}\left({\varvec{\tau}},{\varvec{f}}\right)\) is the time-normalized time-dependent auto-spectrum of body kinematic measurements (low back or ankle

ML linear acceleration) obtained from the IMU. DATA REDUCTION & STATISTICAL ANALYSIS We reported summary statistics as mean ± SD. To address the main objectives of this study, we

performed the following analyses to examine the changes in the \({V}_{res}\) and vestibular-evoked balance responses across cadences spanning 40–140% of each participant’s preferred cadence.

DETERMINING COHERENCE SIGNIFICANCE For each participant, we determined time-dependent coherence to be significant if it crossed a 99% confidence limit (\({\varvec{C}}{\varvec{L}}\) = 0.01)

threshold which is equivalent to an alpha-level of 0.05 due to the two-dimensional (time and frequency) nature of the data27. Based on the number of strides (\({\varvec{n}}\) = 215) used to

calculate coherence, we determined the threshold for each participant was 0.0212 (99%; Eq. 13).

$${\varvec{t}}{\varvec{h}}{\varvec{r}}{\varvec{e}}{\varvec{s}}{\varvec{h}}{\varvec{o}}{\varvec{l}}{\varvec{d}}=1-{{\varvec{C}}{\varvec{L}}}^{1/{\varvec{n}}}$$ (13) We performed similar

calculations for the pooled time-dependent coherence; however, pooled time-dependent coherence was calculated by using the sum of all the cross- and auto-spectra, consequently the

significance threshold was determined by the total number of strides summed across the participants (\({\varvec{n}}\) = 2580). This resulted in a significance threshold for the pooled

time-dependent coherence of 0.0018 (99%). COMPARISON OF HEAD KINEMATIC VARIABILITY AND VESTIBULAR CONTROL ACROSS CADENCES To compare changes to head kinematic variability, we extracted mean

\({V}_{res}\) across the stride cycle (for all four measures calculated) from each participant and cadence. This approach has previously been used to compare the attenuation of

vestibular-evoked balance responses and \({V}_{res}\) between different cadences and speeds21,22. Similarly, we extracted peak coherence (across time and frequency) from each participant and

cadence for the back, right ankle and left ankle ML acceleration to quantify vestibular-evoked balance responses across the cadences. To correct for the non-normality of these values, we

applied a Fisher transformation79. While coherence and gain have been used in tandem to quantify vestibular-evoked balance responses27, gain is unreliable at low and non-significant

coherences. Given that we observed low (or non-significant) coherence at the higher step cadence conditions, we only used coherence to quantify the vestibular-evoked balance responses but

present power and gain estimates in Fig. 5 (see Results) as well as bootstrapped differences in the Supplementary Materials. To determine the main effects of step cadence on \({V}_{res}\)

and coherence, we performed independent rmANOVAs (\(\alpha\) = 0.05) for all four \({V}_{res}\) measures and all three coherence measures80. When the assumption of sphericity was violated, a

Greenhouse–Geisser correction was performed. We then performed post-hoc paired Student t-tests to compare between specific step cadence conditions. To confirm previous observations, that

both \({V}_{res}\) and coherence decrease from slow step cadences (below preferred step cadence) up to preferred step cadences21,22, one-sided Student t-tests were performed between the 40%

and 100% step cadence condition. Similarly, to confirm that coherence continued to decrease at step cadences faster than preferred cadence, we performed one-sided Student t-tests between the

100% and 120% as well as 100% and 140% step cadence conditions. Given that it was not clear how \({V}_{res}\) would change at faster step cadences, we performed two-sided Student t-tests to

compare the 100% to the 120% and to the 140% conditions. The Holm method was used to correct for the multiple comparisons81. To directly compare the relationship between \({V}_{res}\) and

coherence, we calculated the coefficient of determination (R2) of a linear fit between each combination of mean \({V}_{res}\) and peak coherence measures. This was calculated for the 40% to

100% step cadence conditions, the 100% to 140% step cadence conditions, and all step cadence conditions. Thus, we compared the linear fits and the R2 values between fits to determine how the

relationship between \({V}_{res}\) and coherence changed across step cadences. _CURVE FITTING MEAN _ \({V}_{RES}\) _ AND PEAK COHERENCE ACROSS CADENCES AND SPEEDS_ To model the changes in

mean \({V}_{res}\) and peak coherence across cadences, we performed curve fitting to both the group and individual participant responses to characterize how these measures changed as a

function of step cadence. Even though participants walked at a wide range of cadences, we did not normalize the cadences relative to the preferred cadence to facilitate comparisons with

existing literature on average preferred step cadences30,31,32. As the \({V}_{res}\) measures were variable between participants, we normalized each participant’s average mean \({V}_{res}\)

to the overall average mean \({V}_{res}\) across participants for each measure. Given that we expected coherence to decrease as step cadence increases, we fitted an exponential decay

function to the extracted peak coherences for each participant and the three coherence measures calculated. We also fitted an exponential decay to the mean \({V}_{res}\) measures across

cadences to test if \({V}_{res}\) would similarly decrease (Eq. 14), given that MacNeilage & Glasauer (2017) proposed it as a measure to predict changes to vestibular balance responses.

$${\varvec{y}}={\varvec{a}}{{\varvec{e}}}^{{\varvec{b}}{\varvec{x}}}$$ (14) where \({\varvec{a}}\) and \({\varvec{b}}\) were evaluated using a non-linear least squares fitting method,

\({\varvec{b}}<0\) in order to model a decay function, \({\varvec{x}}\) is the cadence, and \({\varvec{y}}\) is the predicted measure (peak coherence or mean \({V}_{res}\)). We then

calculated the adjusted coefficient of determination (\({\overline{R} }^{2}\)) for each of the individual participant fits. In order to determine whether \({V}_{res}\) was minimal near

preferred cadences and could better be modelled as a polynomial function, we also fit a 2nd degree polynomial to the extracted values (Eq. 15). This was only performed for the \({V}_{res}\)

given that previous work suggest that vestibular-evoked balance responses will decrease with increased step cadence and speed and thus it was not expected to increase above the preferred

step cadence13,15,21,22. $${\varvec{y}}=\boldsymbol{ }{{\varvec{a}}{\varvec{x}}}^{2}+{\varvec{b}}{\varvec{x}}+{\varvec{c}}$$ (15) where \({\varvec{a}}\), \({\varvec{b}}\), and

\({\varvec{c}}\) were fitted with least squares, \({\varvec{x}}\) is the cadence, and \({\varvec{y}}\) is the predicted measure (mean \({V}_{res}\)). To compare the fits for mean

\({V}_{res}\), we calculated the Akaike information criterion (AIC) for the group exponential decay and polynomial fits82. Given that a lower AIC value indicates a better fit, accounting for

the number of parameters, we calculated the difference in the AIC (\(\Delta AIC\)) as the AIC from the polynomial subtracted by the AIC from the exponential decay. Similar to step cadence,

we also performed the same curve fitting for the mean \({V}_{res}\) and peak coherence across average gait speed, which we calculated using the distance travelled and trial duration. We

performed these additional analyses to facilitate comparisons with the existing locomotor energetics literature4,5, which quantified changes to metabolic cost across gait speeds. While step

cadence and gait speed are strongly related83, the relationship between step cadence and gait speed was not perfectly linear because we did not control step length. DATA AVAILABILITY Data

and code to replicate the figures in this manuscript can be found in the Borealis data repository (https://doi.org/10.5683/SP3/LLLEF8). REFERENCES * Faisal, A. A., Selen, L. P. &

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Robotics, and Rehabilitation_ (MIT Press, 2021). Google Scholar  Download references ACKNOWLEDGEMENTS We would like to thank Aidan Della Siega and Matthew Galassi for their help with data

collection as well as Drs. Chris Dakin and Patrick Forbes for their comments on the manuscript. AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * School of Kinesiology, University of British

Columbia, Vancouver, BC, Canada Liam H. Foulger, Romeo Chua & Jean-Sébastien Blouin * School of Biomedical Engineering, University of British Columbia, Vancouver, BC, Canada Calvin Kuo *

Centre for Hip Health and Mobility, University of British Columbia, Vancouver, BC, Canada Calvin Kuo * Djavad Mowafaghian Centre for Brain Health, University of British Columbia, Vancouver,

BC, Canada Jean-Sébastien Blouin * Institute for Computing, Information and Cognitive Systems, University of British Columbia, Vancouver, BC, Canada Jean-Sébastien Blouin Authors * Liam H.

Foulger View author publications You can also search for this author inPubMed Google Scholar * Calvin Kuo View author publications You can also search for this author inPubMed Google Scholar

* Romeo Chua View author publications You can also search for this author inPubMed Google Scholar * Jean-Sébastien Blouin View author publications You can also search for this author

inPubMed Google Scholar CONTRIBUTIONS LHF—Conceptualization, Methodology, Formal analysis, Investigation, Writing—Original Draft, Writing—Review & Editing; CK—Methodology, Writing—Review

& Editing; RC—Writing—Review & Editing; JSB—Conceptualization, Methodology, Resources, Writing—Review & Editing, Supervision, Funding acquisition. CORRESPONDING AUTHOR

Correspondence to Jean-Sébastien Blouin. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no competing interests. ADDITIONAL INFORMATION PUBLISHER’S NOTE Springer Nature remains

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variability is minimal near preferred cadence and independent of the vestibular control of locomotion. _Sci Rep_ 15, 18670 (2025). https://doi.org/10.1038/s41598-025-99878-w Download

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