Part of the data presented in this study were reported earlier by Li et al. (Li et al. 2024). Here, we briefly summarize the procedures.

Sixteen healthy participants (7 male, 9 female) were recruited (age: 23.5 ± 3.4 years, height: 1.71 ± 0.07 m, weight: 64.5 ± 13.2 kg). Participants were recruited only if they did not have any diagnosed orthopedic or neurological disorders and did not use medication that can cause dizziness. Participants were instructed not to engage in intense physical exercise and to refrain from alcohol consumption 24 h prior to the experiment. Two participants were excluded due to technical problems in the signal synchronization. Participants provided written informed consent. The experimental design and procedures were approved by the VU Amsterdam Research Ethics Committee (VCWE-2022-126) and conformed to the Declaration of Helsinki, except for pre-registration.

Participants were exposed to a zero-mean stochastic EVS signal with a bandwidth from 0 to 25 Hz, peak amplitude of ± 5.0 mA, and duration of 8 min (Dakin et al. 2010) This signal was applied as an analogue signal through a digital-to-analogue converter (National Instruments Corp., Austin, USA) to an isolated constant-current stimulator (BIOPAC System Inc., Goleta, USA), which was connected to carbon rubber electrodes (9 cm2). The electrodes were coated with electrode gel (SonoGel, Bad Camberg, Germany) and were placed over the mastoid processes behind the ears.

Ground reaction forces were measured at 1000 samples/s by force plates embedded within the split-belt treadmill (ForceLink b.v., Culemborg, the Netherlands). Kinematic data were collected using a 3D motion capture system (Northern Digital Inc, Waterloo Ont, Canada) at a sampling rate of 50 samples/s. Cluster markers were attached to the feet, shanks, thighs, pelvis, trunk, head, upper arms and forearms. Corresponding anatomical landmarks were digitized using a six-marker probe based on the model as Kingma et al. (1996).

A 64-channel REFA amplifier (TMSi, Oldenzaal, The Netherlands, CMRR: > 90 dB, input impedance: > 100 MΩ, gain: 26.55) was used to record the bipolar surface electromyography (EMG) at 2048 samples/s. After shaving, abrading, and cleaning the skin with alcohol, paired disposable self-adhesive Ag/AgCl surface electrodes (Ambu blue sensor, Ballerup, Denmark) were placed 2–3 cm lateral to the spinous processes at eight vertebral levels bilaterally, including the seventh cervical vertebra (C7), the third, fifth, seventh, ninth and twelfth thoracic vertebra (T3, T5, T7, T9, T12) and the second and fourth lumbar vertebra (L2, L4). A reference electrode was placed over the acromion process.

Before the experiment, participants were exposed to vestibular stimulation in a 3 min walk at 2.8 km/h and were instructed to align their steps to the beat of a metronome at 78 steps/min for familiarization. The metronome was used to control the participants’ cadence and to avoid large differences in cadence between the conditions. During the experiment, participants walked with eyes open on the dual-belt treadmill at 2.8 km/h with a cadence of 78 steps/min for 8 min in six conditions. The conditions were defined by the presence of EVS (EVS and no-EVS), by head orientation: head forward (HF) or head leftward (HL) and by step width (preferred step width: PSW and narrow step width: NSW). In the head forward condition, participants were asked to look straight ahead to a target fixed on the wall. In the head facing leftward condition, participants were asked to turn their head to the maximal comfortable position to the left. The order of the conditions was randomized for each participant. Participants received repeated verbal instruction to maintain their cadence and head orientation during the trials. Data from narrow step width conditions were not used in this study.

The global coordinate system was defined as positive x laterally to the right, positive y-axis forward, positive z-axis vertically upward. To measure if, and how well participants performed the task of controlling head orientation, cadence and step width, the time series of the head orientation was first calculated using Euler decomposition (z-y-x sequence) in the global coordinate system, then averaged over gait cycles at each normalized time point for each participant. To remove any offset in the local joint coordinate systems, orientations in the head leftward (HL) condition were corrected by subtracting the averaged orientation in walking with head forward without EVS for each participant. In the rest of this paper, we define the head orientation as 0° when head facing forward, positive angles as facing leftward, and negative angles as facing rightward.

The electromyography, force plate and vestibular stimulation signals were synchronized based on trigger signals. Gait events (i.e., heel strikes and toe-offs) were calculated based on the center of pressure (Roerdink et al. 2008). Cadence was calculated from the time between subsequent heel strikes of the same leg.

Step width was calculated as the distance between the second toe tip markers during heel strikes in the mediolateral direction. EMG signals (sampled at 2048 Hz) were resampled to 1000 Hz to align with the sampling rate of the force plate and EVS signals. To remove EVS artifacts, a sixth-order Butterworth high pass filter with a cutoff frequency of 100 Hz was applied on bipolar EMG signals, followed by rectification of the filtered EMG signals (Blouin et al. 2011; Forbes et al. 2014; Li et al. 2024). For each vertebral level and participant, rectified EMG was normalized to the maximum amplitude of the EMG signal of the averaged gait cycle during walking with preferred step width, while facing forward and without EVS. Then, based on right heel strikes, the EVS and normalized EMG signals were sliced into gait cycles. To avoid distortion in the coherence and gain calculation, each gait cycle was padded with data from the previous (50%) and subsequent (50%) cycle. The coherence and frequency response function (FRF) between EVS and EMG were calculated based on the continuous Morlet wavelet decomposition as described in Li et al (2024). The gain (1/milliampere, mA−1) and phase estimates (radian, rad) between EVS and EMG were defined as the modulus and the angle of frequency response function, respectively. Phase estimates were transformed into time lags (millisecond, ms) by dividing by their corresponding frequencies. The gain and delay were defined as the median of the gains and time lags across the frequencies and gait phases at peak coherence for each vertebral level and each participant.

To test whether the instructions were followed, repeated-measures ANOVAs with two factors: head orientation (HO: head forward (HF) and head left (HL)) × the presence of EVS (EVS and No EVS) were performed on head orientation (yaw) and cadence. To determine the differences in average muscle activity between conditions, one-dimensional statistical parametric mapping-based repeated-measures ANOVAs were performed with two factors: head orientation × presence of EVS (Pataky et al., 2016). To identify any substantial effects on muscle activity, significance was set as p value < 0.01.

Since coherence is naturally bounded between 0 and 1, the modified Fisher-Z transform was applied on coherence values before statistical analysis. For each participant, coherence exceeding 0.015, (i.e., p < 0.01), was defined as significant (Zhan et al. 2006). To identify whether the coupling between EVS and EMG significantly differed between head orientations, cluster-based permutation tests, using t-statistics and 2000 permutations, were applied to the coherence (Maris et al. 2007). The effects of head orientation, vertebral level, and side (L: left and R: right side of the trunk), and their interactions on delays and gains were tested with repeated-measures ANOVAs. Sphericity for repeated-measures ANOVAs was verified by Mauchly’s test (p > 0.05). Greenhouse–Geisser corrections were applied when the assumption of sphericity was rejected. A Bonferroni correction was applied for the post hoc tests. A p value less than 0.05 was defined as significant. Statistical analyses were performed in MATLAB (2019a, The MathWorks, Natick, US).