Perception of roll-tilt during physical motions systematically depends on GVS waveforms and physical motion profiles

We empirically examined roll tilt perceptions during GVS and passive whole-body roll tilt in the absence of other sensory cues (Fig 1A). This empirical assessment enabled both the characterization and quantification of GVS effects in the presence of naturalistic physical motion (0.07–0.36Hz), across comparable frequencies of GVS current at tolerable current amplitudes (+/-4mA peak current). GVS current was directionally coupled either a) positively (anticipating an amplification of roll-tilt perceptions) or b) negatively (anticipating an attenuation of roll-tilt perceptions) to a physical characteristic of the motion profile: either 1) the roll tilt angle, 2) roll tilt velocity, or 3) an equal combination of both (jointly coupled). In addition, a sham condition (No GVS), yields 7 total coupling schemes (Fig 1B). Each of these was assessed with 3 different physical motion profiles comprised of dynamic (sum of sinusoids ranging from 0.07 to 0.36 Hz), head-centered whole-body roll tilt (Fig 1B).

Our experimental results first revealed differences in perceptual reports that were dependent on both the tilt profile and GVS waveforms, confirming our first experimental hypothesis that perceptions of roll tilt during whole-body physical roll tilts depend on the specific physical motion and the GVS waveform sensed by the vestibular organs. Two scalar metrics were utilized to quantify how our independent variables affected perceptions of roll tilt as captured by a subjective haptic horizontal (SHH) task: Mean Absolute Tilt Perception (which captures the amplitude of tilt perception, agnostic to physical tilt) and the slope of perceived tilt versus actual tilt (Perceived/Actual Tilt Slope, which compares tilt perception to the physical tilt at that moment). These metrics provide complimentary means of characterizing roll tilt perception amplification/attenuation across experimental conditions, agnostic to underlying central processes. For both of the metrics, a 3-factor repeated measures ANOVA across coupling scheme (7 conditions), physical motion profile (3 conditions), and initial motion direction (mirrored tilts; 2 conditions) revealed significant differences for coupling schemes (F (6,18) > 6.35; p< 0.001) for both metrics and significant differences between motion profiles (F(2,6) = 6.36; p = 0.033) for Mean Absolute Tilt Perception. There were no differences for right or left starting directions and no interaction effects (p>0.22), revealing that left/right mirrored repetitions of motions did not affect perceptions, as expected.

Amplification and attenuation of roll tilt perception is achieved through selective directional current coupling

Next, we assessed the directional dependency of GVS on over and under-estimation of tilt. Qualitatively, the effect of GVS in each of the three unique motion profiles and seven unique coupling schemes revealed consistently amplified perceptions of physical tilt during positive directional couplings and attenuated perceptions during negative directional couplings (Fig 1B). Conversely, perceptions during the No GVS condition paralleled the temporal dynamics of actual tilt. To quantitatively evaluate differences in directional GVS couplings across physical couplings, single-factor repeated measures ANOVAs were subsequently run for all metrics, computed by pooling data for a given coupling scheme across motion profiles and initial motion directions. Confirming our second experimental hypothesis, we found that binaural bipolar GVS amplifies and attenuates perceptions of physical roll tilt, dependent on the positive and negative GVS couplings respectively. Moreover, we find that the extent of amplification and attenuation is dependent on the specific GVS waveform coupling. To compute effect sizes, Glass’s Δ was used for comparisons to the control (i.e., No GVS condition), and Hedge’s g was used in alternative comparisons.

For the Mean Absolute Tilt Perception metric, the single factor repeated measures ANOVA indicated a difference between the seven coupling schemes (F(6,60) = 13.07; p<0.001). On average, the Mean Absolute Tilt Perception metric yielded larger values for positive GVS coupling schemes (velocity = 1.65 ± 0.28 (mean±SD in deg); joint = 1.98 ± 0.43; angle = 1.89 ± 0.34) and smaller values for negative coupling schemes (velocity = 1.54 ± 0.38; joint = 1.37 ± 0.21; angle = 1.37 ± 0.34). Compared to the No GVS condition (1.52 ± 0.13), the Mean Absolute Tilt Perception metric reveals amplifying and attenuating effects respectively (Fig 1C). Post hoc tests with Bonferroni corrections comparing each coupling scheme with the No GVS condition showed significance for only the positive joint (t(10) = 2.5184; p = 0.032; Δ = 2.5) coupling scheme. Post hoc tests between the positive and negative versions of each coupling scheme showed significance between joint couplings (t(10)>4.587; p<0.001; Hedges’ g = 1.79) and angle couplings (t(10) = 3.413; p = 0.008; g = 1.48), but not pure velocity couplings. Subsequent ANOVAs between just the three positive and negative coupling schemes showed significance between the positive and approached significance between the negative coupling schemes (F(2,20) = 6.644; p = 0.006 and F(2,20) = 2.794; p = 0.085 respectively). These results support the earlier finding that perceptions depend on the GVS waveform and additionally reveal that the specific GVS waveform impacts the magnitude of amplification and attenuation. Comparing coupling schemes, including roll tilt as part of the coupling scheme produced stronger amplification/attenuation than the roll velocity couplings.

Reinforcing the finding that GVS amplifies and attenuates perceptions of physical roll tilt, Perceived/Actual Tilt Slope yielded steeper slopes for positive (amplifying) couplings (velocity = 1.02 ± 0.20; joint = 1.27 ± 0.29; angle = 1.22 ± 0.28; No GVS = 0.90 ±0.14) and shallower slopes for negative (attenuating) couplings (velocity = 0.70 ± 0.27; joint = 0.53 ± 0.48; angle = 0.49 ± 0.37) (Fig 1D). Repeated measures ANOVA indicated a difference between coupling schemes (F(6,60) = 19.7; p<0.001). Post hoc tests with Bonferroni corrections comparing each coupling scheme to the No GVS condition approached significance for the negative angle (t(10) = 2.215; p = 0.0516; Δ = -1.17) coupling scheme. Post hoc tests between the positive and negative versions of each coupling scheme showed significance between joint couplings (t(10)>4.587; p<0.001; g = 1.86 and angle couplings (t(10)>4.587; p<0.001; g = 2.23). Subsequent ANOVAs between just the three positive and negative coupling schemes showed significance between the positive and approached significance between the negative coupling schemes (F(2,20) = 10.9; p< 0.001 and F(2,20) = 2.69; p = 0.092, respectively).

GVS-evoked canal afferent dynamics explain altered roll-tilt perceptions following central processing

A computational model of GVS’s influence on self-motion perception offers characterizing and predicting the effect of GVS on roll tilt and other motion percepts due to any arbitrary GVS or motion waveform. To realize this model, we first provide new model relationships describing the influence of GVS on the signals transduced by the semicircular canals (Fig 2A). Currently, there have been no direct recordings of human vestibular afferents, so we adopt the rhesus macaque vestibular afferent unit recordings as a proxy (convolved into a firing rate), provided by the recent works of Kwan et al. [29] and Forbes et al. [28]

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Fig 2. Providing an extension of the vestibular afferent transfer functions evoked by GVS to frequencies beneath 0.1 Hz via the essential works of Kwan et al. [29] and Forbes et al. [28].

a, Depiction of binaural bipolar GVS’s depolarizing and hyperpolarizing effect. The cathode side (negative terminal) increases irregular and regular firing rates (i.e., depolarization). Conversely, the anode side (positive terminal) decreases firing rates (i.e., hyperpolarization). b, Resultant firing rates following a 1 mA step current input and subsequent termination of signal (solid lines). The empirical population firing rates originating from Forbes et al. [28] (located in Fig 3A) are overlayed with corresponding colors. The lower portion of the transfer function was fit to match the step response in the 0-40s range. Note that the step response afferent firing rate data stems from a different population of afferents than those used to generate the empirical data in panel b, likely contributing to some overshoot of the transfer functions during the simulated step response. c, The gain and phase responses of the extended transfer functions, which more closely match the phase data from Kwan et al. [29] near 0.1Hz for both regular and irregular afferents. For comparisons to the phase data, which was not segregated for anodal and cathodal stimulation types, averages of the anodal and cathodal transfer function phases were taken. Cathodal and Anodal phase responses are shown in the background with consistent colors to the gain response curves. d, The four irregular/regular cathodal/anodal transfer functions, which now span a greater frequency range thus enabling modeling of both DC and dynamic (up to 25 Hz) GVS evoked firing rates.

https://doi.org/10.1371/journal.pcbi.1012601.g002

First, we extend these existing transfer function approaches [28, 29] to capture the impact of GVS current on semicircular canal afferent firing rates, both for DC (Fig 2B) and sinusoidal currents (Fig 2C). Our transfer functions (Fig 2D) leverage the sub-0.1Hz frequency content inherent to the step response dynamics to characterize linear transfer functions more broadly at lower frequencies for both depolarizing/hyperpolarizing stimulation and regular/irregular afferents. Leveraging these extended transfer functions, we mechanistically model the influence of GVS on the human percept of tilt through peripheral modulation of the signals transduced by the semicircular canals across frequencies (roughly spanning 0.01-25Hz and critically, during DC stimulation).

To model how the CNS processes peripheral signals into percepts of self-orientation and self-motion, we utilize the commonly adopted observer framework to model central processing and sensory integration of semicircular canal and otolith pathways (Fig 3A and 3B). The observer model of spatial orientation perception first simulates how passive physical head movements result in vestibular afference. Following this, perceptions of angular velocity, linear acceleration, and tilt are produced through weighted comparisons of vestibular afference to expectations of vestibular afference (i.e., sensory conflict). These expectations are computed from internal models of sensory dynamics and kinematic relationships.

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Fig 3. Peripheral modulation of the canal afferents is coupled with an observer model of human motion perception.

a, Both physical motion-evoked and GVS-evoked afferent responses are combined for input into central nervous system estimation. b, Sequential model computations using the optimal point at K_Reg = 0 and K_GVS = 0.0245. c, GVS stimulates the anterior (blue), posterior (purple), and horizontal (green) canals, and their net signal is realized in the observer orthonormal reference frame as the linear combination of these individual vectors. d, Model training optimal fronts are displayed using both our dynamic experimental paradigm’s training dataset (solid white line) and Niehof et al.’s [22] static DC GVS paradigm (dashed white line), overlain on the mean squared error cost computed using the dynamic training dataset (green-purple contour) and separately on the mean squared error cost computed using the average effect observed by Niehof et al. [22] (see the Discussion for potential non-linearities as higher GVS current amplitudes are applied). Considering each paradigm alone, an optimal front exists where no single solution best explains the empirical dataset for a single paradigm. However, congruency between both paradigms is best achieved when K_Reg = 0. Conversely, when K_Reg = 1, the best fit of the dynamic training dataset incurs a large cost in the static dataset (while the inverse is not as extreme). e, To demonstrate this finding, three model simulations are conducted using three points on the dynamic best front corresponding to K_Reg = 0 (irregular only dynamics) in red, K_Reg = 0.75 (mixed 3:1 regular:irregular dynamics) in purple, and K_Reg = 1 (regular only dynamics) in blue. These simulations are compared to the mean Niehof et al. [22] effect of DC current (green star), which was used to compute the static front.

https://doi.org/10.1371/journal.pcbi.1012601.g003

We next hypothesize that the effect of GVS on vestibular afferents is additive to changes evoked by physical motion and additionally hypothesize that the same central mechanisms that process physical vestibular afferents are used with GVS-modulated afferents. Further, while GVS is known to impact individual otolith afferents [28, 29], the net influence of GVS on gravito-inertial cues transduced by the system of otolith afferents has been hypothesized and estimated to be near zero given the mirrored orientation of hair cells innervating the otolithic macula across the striola [30]. We adopt this third hypothesis for our modeling, leaving only the influence of GVS on the signals transduced by the canals, with relative depolarization and hyperpolarization components in the primary axes/planes of each of the three left and right canals (individual and net canal signal directions evoked by GVS for positive current are depicted in Fig 3C). Notably, while we model the effect of GVS as linear and additive on canal sensory transduction, we do not assume linear effects of GVS on resultant tilt perceptions, which are influenced by central processing. With this framework, our modeling approach of GVS’s influence on the canal afferents alone is capable of explaining tilt amplification and attenuation in the presence of physical motion. This is achieved by modeling how the CNS compares peripheral signals, altered by GVS, to the CNS’s expectation of those signals obtained via internal models of vestibular sensor dynamics and kinematic relationships. Subsequently, our model reveals how errors in expectation (sensory conflict) are altered by GVS, leading to amplified/attenuated percepts of gravity’s direction and thus tilt (Fig 3B).

Irregular afferent dynamics alone best explain observed self-orientation perceptions

Because GVS-evoked regular and irregular afferent dynamics differ from those evoked by physical motion, we investigated the roles of each afferent channel in human orientation perception by assessing if model fit depends on afferent regularity. Two free parameters are introduced in our model: K_GVS and K_Reg (where K_Irreg = 1−K_Reg). The former (i.e., GVS gain) relates scaling differences (e.g., differences in anatomies, electrode configurations, model unit conversions, etc.) between different experiments in rhesus macaque and human afferent dynamics evoked by GVS, and the latter (i.e., regular afferent channel gain) describes the canal regular afferent channel contribution to perception (vs. irregular afferents). Training the model considering four of the six GVS coupling schemes (tilt-coupled GVS and velocity-coupled GVS, both positive and negative, were used for training the model), there are non-unique best fits, revealing an optimal front (Fig 3D). To resolve these underdetermined optimal solutions into a unique set, we introduce a second paradigm: DC GVS during no physical motion (i.e., static GVS) from Niehof et al. [22]. A second optimal front was computed by simulating this experimental paradigm and comparing the model tilt gain to the average impact of GVS current on roll tilt perception found by their participant population (~1.5 deg/mA). A best fit considering both paradigms occurs when K_Reg = 0 with the optimal fronts diverging from one another when K_Reg increases beyond 0. Hence, the irregular canal afferent channel alone best predicts perceptions of tilt in the presence of GVS when considering DC GVS and dynamic GVS waveforms (comprised of 0.07–0.36Hz frequencies; Fig 3D and 3E).

Model predictions are more predictive than physical tilt and are equally predictive compared to unseen test data

With the model trained, we sought to evaluate its predictive capability. Model predictions were evaluated both against the training (Fig 4A and 4B) and test (Fig 4C) datasets (i.e., the joint coupled GVS scheme couplings, both positive and negative, were not used in the training of the model’s free parameters). We quantitatively assessed model predictions as against a null hypothesis that our model cannot better predict perceptions than physical tilts alone. For this, MSE was computed between the mean empirical perceptual reports and our model predictions (Experiment–Model), as well as between the mean perceptual reports and the provided physical tilt (Experiment–Actual Tilt (null)). This was conducted for each amplifying, attenuating, and No GVS condition for the training dataset (24 combinations of GVS and motion) and for the test dataset (12 combinations of GVS and motion), provided in Fig 4D. We found the model to have significantly lower MSE than actual tilt, evaluated on both the training dataset (t(23) = -3.93; p<0.001) and the test dataset (t(11) = -3.92; p<0.001). For our computational model, there was no difference between the training and test fits using MSE (t(34) = -0.93; p = 0.36), suggesting generalizability.

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Fig 4. a-c, Model predictions (solid lines) are shown for amplifying (red) attenuating (blue) and no-GVS (grey) conditions, averaged across all participants and repeat trials of mirrored motions using the optimal point at K_Reg = 0 and K_GVS = 0.0245 Shaded regions correspond to the SEM bounds of our empirical data (N = 11).

a, Model predictions using tilt angle coupled GVS. b, Model predictions using tilt velocity coupled GVS. c, Model predictions using joint coupled GVS (the test dataset). d, Comparisons of model performance (inversely related to the evaluation metric, MSE, computed against the empirical data) compared to a null hypothesis (that angle tilt angle explains the empirical data). The model performed significantly better than the null in both the training (***p<0.001) and test (**p<0.001) datasets. No significant differences in model performance were found between the training and test datasets.

https://doi.org/10.1371/journal.pcbi.1012601.g004

An assortment of elicited perceptions are predicted, dependent on gravity and individual differences

Next, we asked how perceptions of roll-tilt evoked by GVS may be modulated from various physical stimuli, and we sought to characterize how differences in susceptibility to GVS in our sample population might be realized in these scenarios. To first capture individual differences to GVS, both the training and test datasets were used to compute participant-specific GVS gains, the model gain producing the lowest MSE between model predictions and the entirety of a participant’s empirical perceptual reports during the GVS trials. We report the distribution of participants’ individualized gains on a scale that is normalized by the best-fit K_GVS during training (0.0245) while setting K_Reg = 0. This metric serves as a robust means to capture the dynamic effects of GVS on perception (i.e., K_GVS = 0 indicates no effect) across all GVS waveforms and physical motion profiles using a scalar metric. Our population’s distribution was found to be normally distributed (Shapiro-Wilks test of normality: p = 0.37) with μ = 1.03 and σ = 0.41 (with individual values provided in Table A in S3 Text). This distribution is significantly non-zero when analyzed by a one-sample two-tailed t-test (t(10) = 8.33; p<0.0001) and all of our participants were found to have positive GVS gains, meaning that GVS produced a significant effect and altered roll tilt perceptions for all participants in a directionally consistent manner. This statistical outcome reinforces our empirical findings using simple model agnostic metrics (Mean Absolute Tilt Perception and Perceived/Actual Tilt Slope).

Characterizing individual susceptibility to GVS additionally allows us to generate uncertainty bounds on our mean model predictions by directly sampling from our population distribution via Monte Carlo simulations. We compare our model predictions with resultant σ bounds to the SEM bounds reported in Niehof et al. [22] (Fig 5). To demonstrate new utility afforded by this model using our findings, we extend our predictions with resultant population distributions to paradigms without empirical data for the case of direct current stimulation up to 4mA (Fig 6A) and direct current stimulation at 4mA with varying pitch tilt profiles (Fig 6B). In doing so, we find that the population coefficient of variation is predicted to be constant across GVS applications, equal to the coefficient of variation of , CV = 0.40, with an individual’s underlying GVS susceptibility determining the magnitude of their predicted tilt perception. This predicts larger inter-individual variations in tilt perception produced by GVS when larger amplitude currents are applied.

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Fig 5. Mean model predictions (dashed lines) and σ bounds (grey shaded regions) generated by simulating the DC paradigm in Niehof et al. [22] are compared to their empirical data, unbiased by an average reporting bias of -0.43deg and time delay of 0.6s.

Corresponding model inputs (current without physical motion) are shown above the perceptions and model predictions. The model mean predictions largely lay within the SEM bounds of the 16-participant mean perceptions during an upright (i.e., no physical roll tilt) DC GVS stimulation paradigm. While DC GVS creates near-instantaneous changes in afferent firing rates (Fig 2), resultant perceptions of tilt for the onset of DC GVS stimulation contain delayed transient dynamics which eventually approach a steady state. Following the termination of DC GVS stimulation, perceptions of tilt demonstrate exponential decay with two dominant time constants. Our model predictions capture the time course of these temporal dynamics.

https://doi.org/10.1371/journal.pcbi.1012601.g005

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Fig 6. Mean and population distribution roll tilt perception predictions for new, testable paradigms without empirical data.

Population perception distributions are formed through 1,000 Monte Carlo simulations, sampling from the population GVS susceptibility distribution. a, 1, 2, 3, and 4mA DC GVS applied in the absence of physical motion while upright. At a peak mean perception occurring at t = 25s, population distributions for the four DC GVS cases are shown, all with equal CVs. When upright without physical motion, a mean effect of -1.6deg/mA is predicted at 25 seconds of DC stimulation. b, 4mA DC GVS applied in conjunction with quasistatic pitch tilts. At a peak mean perception occurring near t = 42s, population distributions for the three DC GVS cases are shown, all with equal CVs. Pitching back to 90 degrees allows for delivering greater roll tilt perceptions than when upright (shown in a) or at intermittent pitch angles. The effect is nonlinear, demonstrated by the three pitch tilts shown here.

https://doi.org/10.1371/journal.pcbi.1012601.g006

Ethics statement

This study was approved by the Institutional Review Board of the University of Colorado, Boulder (Protocol 22–0171). Fourteen participants signed the written informed consent documents, but only 11 (age: 24.75 (SD = 1.83), 4 female) produced usable data sets. One was excluded due to an early onset of motion sickness. The others were excluded due to failure to perform the SHH tasks. Participants reported no known vestibular dysfunction and refrained from consuming alcohol within 6 hours prior to the study. Participants were between the heights of 5’2” and 6’3” and weighed less than 225 lbs as required by the TTS motion device used in the study.

Dynamic tilt experiment protocol

Participants were first outfitted with a 2x2” square sponge electrode on each mastoid which were held in place with a headband for all conditions (including the No GVS sham condition). Impedance was checked and found to be below 12kΩ for all participants. Participants received sample GVS profiles both with head restrained and unrestrained to ensure all equipment was working before proceeding with the experiment. For the experiment, participants sat upright in the Tilt Translation Sled (TTS), a motion device capable of providing combinations of tilt and translation, with their heads restrained by firm foam blocks on each side which were adjusted to fit the participant’s head. The lights were off to remove visual cues and white noise was provided to mask auditory cues from the device’s motors. During trials, participants were tilted about a head-centered roll tilt axis along a 30s pseudorandom sum of sines profile (±8°) with or without GVS stimulation, during which they continuously reported their sense of tilt with a subjective haptic horizontal (SHH) task. A SHH task was utilized, rather than a subjective visual vertical task to avoid potential effects of ocular torsion responses produced by GVS that might confound a subjective visual vertical task [53]. Two-way audio communication and one-way video allowed operators to make sure participants were ready at the start of each trial and to monitor participant motion sickness. Participants reported their level of motion sickness on a scale of “none”, “slight”, “moderate”, or “severe” after every other trial for reports of “none” and every trial following an affirmative report of motion sickness. Two consecutive reports of “moderate” resulted in an early termination of the study for one participant.

Data acquisition of dynamic tilt perception in humans

A subjective haptic horizontal task was used to measure tilt perception continuously throughout the trial [54]. This was implemented via a bar mounted to a potentiometer, which rotated with participants’ whole-body tilt. Participants held the bar between their fingers and were instructed to adjust its orientation to keep it aligned with their perception of the horizontal. For perfectly accurate perception, the participant would move the bar such that it is continuously aligned with the true horizontal. Participants completed at least three training trials without GVS to familiarize themselves with the reporting task and were reminded on how to properly complete the task after every other trial.

Experimental paradigms

Participants experienced six different motion profiles and seven different GVS coupling schemes. Motion profiles were based on three pseudorandom sums of sines with equal power frequency contents of: 0.07,0.18, and 0.31Hz; 0.07,0.25, and 0.33Hz; and 0.07,0.19, and 0.36Hz without phase shifts. Two full cycles of the 0.07Hz waveform were completed with the first and last half cycles including a sigmoidal ramp up/down. Each profile was then mirrored on the left/right (negative and positive roll tilt respectively) axis, creating 6 motion profiles. GVS coupling conditions included a No GVS sham condition, and GVS was either coupled to tilt angle, tilt velocity, or an average of the two normalized signals (joint coupled). To test the second hypothesis that the current direction dictates amplification and attenuation of roll tilt perceptions during physical motion, GVS was additionally coupled to run either positively (unlike sign) or negatively (like sign) with the physical coupling. Because we use a head-centric x-axis out the nose of the participant (i.e., positive roll corresponds to right ear down), positive coupling corresponds to a left anode right cathode GVS signal (negative current) when the physical motion characteristic is positive (hence GVS has unlike sign of the physical characteristic). The sign notation of GVS, where positive current corresponds to left cathode right anode current direction, was chosen to maintain consistency with existing literature [28–30].

The GVS waveforms were scaled so that the maximum current was +/-4mA. The GVS device was connected to the TTS such that initiating TTS motion also initiated the synchronized GVS waveform. Participants completed the No GVS case twice for a total of 48 trials. These trials were broken up into two blocks of 24 where each block contained a No GVS trial for all 6 motion profiles and one trial for each of the coupling schemes paired with only one of the left/right versions of the 3 base motion profiles. Combinations not contained in the first block were tested in the second block.

While the experimental paradigm only measured roll-tilt perception in the presence of physical tilts and GVS, one participant reported a lateral translation perception. Reports of GVS sensations of motion when upright are usually of tilt, however, stimulation typically occurs in circumstances where translation is unlikely. Here, the motion device we used to tilt participants in the experiment is also capable of translation. Although no translation occurred, this possibility and the lack of other sensory cues may have allowed the CNS to interpret GVS and physical stimuli as involving some translation, further supporting the need to consider central processing of GVS and physical motion rather than just peripheral vestibular modulation alone.

Data processing and analyses

The raw SHH report was processed to account for differences in participant left/right biases, reporting delays, and deflection magnitude. To do this a single tilt angle correction bias (known to occur during similar perceptual tasks [55]), time delay correction (due to reaction times during the SHH task), and a gain-scaling factor (representing a participant’s tendency to overestimate/underestimate their perceived tilt using the SHH task) was computed for each participant based on their No GVS trials. After sequentially computing a participant’s reporting bias, delay, and gain, these adjustments were applied to the entirety of a participant’s data. Bias was computed as the bias that minimized the MSE of a participant’s raw reports and the actual tilt. Time delay was computed as the delay that minimized the MSE of a participant’s bias-adjusted reports and the actual tilt, and gain was computed as a gain on the bias and time-adjusted reports that minimized the average absolute difference in reports and actual tilt (so as to not penalize the rare opposite deflections of the bar during the SHH task and small tilts) when actual tilt was greater than 2 degrees (to minimize the influence of reporting during small tilts). Each participant’s correction parameters are provided in Table A in S1 Text.

Our two primary outcome metrics were derived from the adjusted SHH data: Mean Absolute Tilt Perception and Perceived/Actual Tilt Slope. Quantifying the magnitude of participants’ average perceived tilt during each condition, the Mean Absolute Tilt Perception is a simple measure of the variation of responses agnostic to the physical tilt, which we expect to increase with amplification and decrease with attenuation. Quantifying perceived tilt as a linear function across physical tilt angles, the slope of the actual and perceived tilt was computed (i.e., Perceived/Actual Tilt Slope) using least-squares regression. The Perceived/Actual Tilt Slope describes the magnitude of tilt over/underestimation. Both metrics were first checked for normality using a Shapiro-Wilks normality test. With only slight deviations in normality, we proceeded with ANOVA analyses due to their robustness against normality deviations.

Statistical analyses

A repeated measures ANOVA was performed for each of the GVS effect metrics across each of the coupling schemes. This was followed by two-tailed paired t-tests between the No GVS condition and each of the other coupling schemes and two-tailed paired t-tests between each positive/negative coupling scheme pair. Effect sizes were computed for significant differences found via the follow-up t-tests. Glass’s Δ and Hedge’s G were used as appropriate for determining effect size in the case of comparisons to the control and comparisons between alternatives respectively [56]. Additionally, two subsequent, reduced ANOVAs were computed to compare just the amplifying and attenuating coupling schemes respectively. Bonferroni corrections for the maximum possible number of comparisons were used.

Extending the afferent firing rate model dynamics of rhesus macaques

We build our transfer functions relating GVS current and canal afferent firing rates, based on those existing in the literature for rhesus macaques monkeys (Kwan et al. [29] and Forbes et al. [28]). The original canal transfer functions fit by Kwan et al. [29] provide population-level irregular and regular afferent responses (i.e., rate-coded firing rate, FR(t)) for afferents stimulated by sinusoidal currents at 1mA. While these transfer functions do well in the 0.1-25Hz frequency range, the phase response begins to diverge at lower frequencies (around 0.1Hz) and they lack the exponential decay dynamics later provided by Forbes et al. [28] during cathodal (depolarizing) and anodal (hyperpolarizing) step current (direct current of 1mA) stimulation. Because of this gap, the Kwan transfer functions cannot be used to explain perceptual differences when DC current is applied and when sinusoidal (or sum-of-sines) current is applied below 0.1Hz. Forbes et al. [28] refit the gain data provided by Kwan et al. [29] separately for the portions of sinusoidal current corresponding to depolarizing and hyperpolarizing stimulations, but they do not provide these new transfer functions. Thus, we refit the separate depolarizing/hyperpolarizing transfer functions for the semicircular canals.

In doing so, we expand the functional range of frequencies that can be utilized by developing new population average transfer functions, building on these two prominent works of Kwan et al. [29] and Forbes et al. [28]. To not disturb the frequency characteristics of the transfer functions fit to the gain-phase data provided by Forbes et al. [28] in the 0.1-25Hz range, we selectively fit a transfer function with a gain upper limit (as s→∞ where s = σ+jω, the complex frequency variable) of unity, realized near 0.1Hz. Additionally required to represent the diminished steady-state afferent response noted by Forbes et al. [28], a lower limit (as s→0) must be a constant less than unity. Together, the lower frequency response dynamics (H_L(s)) is of the following form: (2)

A full derivation of the form above is contained in S2 Text. The new transfer functions we contribute are the combined response of the fitted transfer function of the step response capturing the lower frequency response, H_L(s), and the upper-frequency response, H_U(s), found by fitting the sinusoidal depolarizing (cathodal) and hyperpolarizing (anodal) gain data, provided by Forbes et al. [28], with the average phase data, provided by Kwan et al. [29]: (3)

The resultant step responses and gain-phase characteristics of H_SCC(s) for regular and irregular afferents are depicted in Fig 2.

Interpreting canal firing rates evoked by GVS

These transfer functions describe the dynamics of how externally applied current results in a change in afferent firing rate from a resting discharge rate (producing units of Δspk/s). In order to better understand the effect of current on the information transduced by the peripheral canal afferent pathways, we must convert changes in firing rate to units of angular velocity (as the semicircular canal afferents transduce angular velocity, which is processed by the central nervous system to produce perceptions). For GVS-evoked changes in afferent firing rates up to ± 50 Δspk/s, canal afferent neurons respond linearly to changes in physical angular velocity [57]. Thus, we use gain-interpreters for the regular and irregular pathways, corresponding to the inverse gain of the passband region of canal activation from physical motion (in the frequency range of 0.2-2Hz) where canals afferents are thought to accurately transduce physical motion (and this range corresponds to the most experienced frequencies during natural human motion [58]). In this region, the behavior of canal afferents transitions from high pass-filtering to high-pass tuning [59]. Using physical motion to canal afferent firing rate transfer functions for the rhesus macaque (provided in [57]), which behave similarly to those of the squirrel monkey [59], the gain interpreters are 1.85 and 2.29 deg/s-per-Δspk/s for the irregular and regular afferents respectively. However, the tuning parameter K_GVS (defined below) accounts for differing values of the gain interpreters when considering human anatomy.

Resolving the GVS-evoked afferent responses into an orthonormal basis

Similar to theoretical estimations first made by Fitzpatrick and Day [30], we calculate the virtual sensation of rotation in a head-centered orthonormal basis, denoted as the x-y-z coordinate system (subscript xyz). Here, the x-axis is aligned with the naso-occipital axis, the y-axis is aligned with the interaural axis, and z is perpendicular to these axes. We use the underpinning that the binaural bipolar GVS montage non-preferentially and equally stimulates the anterior, posterior, and horizontal canals (subscript APH) on a given side. The scalar magnitude of anterior-posterior-horizontal activation, ΔFR(t)_GVS, is determined by current signal and the transfer function H_SCC(s), which is dependent on if the local current is hyperpolarizing (anodal) or depolarizing (cathodal) and if the channel is regular or irregular (Fig 2A–2C). The following relationship is used to achieve this transformation: (4) In the above equation, is a basis comprised of unit normal vectors perpendicular to the planes of the average human anterior, posterior, and horizontal canals for either the right or left set of canals [60], and contains the 3D rotation rate information evoked by GVS current in units of Δspk/s. The additional rotation matrix, R_y, is a 7-degree rotation about the y-axis to align the x-axis of the GVS-evoked signal of virtual rotation from Reid’s Baseline down to the average naso-occipital axis. Excepting this final rotation, the approach dictated by the above equation is likely similar to other recent attempts to realize GVS-evoked signals in an orthonormal basis [24, 28] while not previously outlined.

Finally, we linearly combine the left and right afferent signals evoked by GVS through the following relationship: (5) We assume that the right and left vestibular contributions, K_R and K_L (and K_L = 1−K_R) respectively, contribute equally (both are 0.5). This operation can be taken before or after combining with physical motion (next section/step) and is mathematically equivalent.

Modeling the joint influence of physical and GVS stimuli

We represent the joint influence as a linear combination (depicted as the f(∙) block in Fig 3A): (6) In the above equation, is the net 3D rotation rate information due to both GVS and physical motion (subscript physical). Given our participants reporting of no history of vestibular dysfunction, we assume that the physical afferent transductions of the left and right sets of canals (for both and ) are equal, thus we utilize models of physical canal afferent transduction previously utilized within the observer model [25–27]. In the case of modeling unilateral vestibular loss with GVS for example, the physical canal signals would need to be altered and expanded such that: (7)

The GVS-effect gain, K_GVS, serves as a means of tuning the model via training to account for linear differences in human and rhesus macaque anatomy and electrode configurations (that may amplify or attenuate the effect of GVS on changes in canal firing rates). Further, anatomical differences may also result in different passband gains (used as our angular velocity gain-interpreter). Finally, while efforts were made to suppress non-vestibular cues of verticality, this gain also includes other factors that impact tilt perception inherent to the empirical data. When fitting K_GVS to individuals, this gain captures differences in the parameters of an individual’s particular observer model/CNS neural circuitry for spatial orientation perception.

The relative contribution of the regular afferent pathway to perception is denoted by the gain K_Reg∈[0, 1]. Complimentarily, the relative contribution of the irregular pathway is 1-K_Reg. The set of free parameters for model training is comprised of K_GVS and K_Reg.

Modeling self-orientation perception with an observer CNS representation

The modulation of vestibular afferents alone is insufficient to describe human perceptions, which are dependent on central expectations of sensory afference, generated through internal models of sensory dynamics and of the physical laws governing head motion [25–27, 33, 61, 62]. Such is an ‘observer’ model of self-motion and self-orientation. Here we utilized the observer framework with model parameters outlined in Clark et al. [25], consistent with other recent models of human perception [49, 63–65] and informed by a host of passive motion paradigms [27, 36, 66–68]. As depicted in Fig 3A, the observer model was augmented such that canal sensory afferents were modulated by binaural bipolar GVS, and because GVS is transient, the internal models of end-organ dynamics were unmodified (i.e., the internal models are assumed to remain maladapted to GVS).

Model training and validation procedure

We organized our empirical data into a training dataset, comprised of the angle-coupled and velocity-coupled perceptual responses, and a test dataset, comprised of the joint coupled perceptual responses for model validation. Our cost function was chosen to be the mean squared error computed between the model predictions and the mean perceptions in order to estimate the mean roll-tilt perceptions of the sample population over time (J_MSE contours in Fig 3D). Because the best fit found using dynamic data alone yielded an underdetermined set of optimal parameters (solid white line in Fig 3D), we paired our solution with the best fit of a DC GVS paradigm with no motion from Niehof et al. [22]. The best cost of the Niehof et al. [22] dataset alone (computed as the mean squared error of the average effect found at the end of GVS stimulation with our model’s prediction) also yielded an underdetermined set of optimal parameters. However, when paired together, a single set of optimal parameters was found that fit both datasets at K_Reg = 0, insensitive to the relative weighting between the two optimal fronts.

Following model training, we compared the performance of our model on the training dataset to that of our model on the test dataset, computing a mean squared error for all experimental conditions. Additionally, we compared the model performance to a null hypothesis that the perception could be explained by actual physical tilt alone. Two-tailed t-tests were conducted for both analyses. Statistical analyses were performed using log-transformations of the MSEs, which were found to be normally distributed (the un-transformed data was significantly non-normal using the Shapiro-Wilks test of normality).

Quantifying individual differences

In finding no differences between our model’s predictions on the training and test dataset, we fit an individual GVS susceptibility factor metric, , using each participant’s entire perceptual dataset during GVS (i.e., all positive and negative GVS trials during angle, velocity, and joint coupling schemes). A mean squared error cost function was chosen to estimate the mean of each participant’s GVS susceptibility as expressed within the confines of our experiment. We used a Shapiro-Wilks test of normality to confirm that the GVS susceptibility metric was normally distributed, and then we fit a normal distribution to our participants’ susceptibility metrics. One participant was revealed as an outlier with a normalized GVS susceptibility metric of 2.7, more than 1.5 times the interquartile range above the 3^rd quartile, making the distribution non-normally distributed. Upon visualization of this participant’s trials (participant 8), we noticed they often stopped adjusting their subjective haptic report for small tilts. Analogous to the reporting gain metric, refitting their data while ignoring portions when the actual tilt was under two degrees yielded a normalized GVS susceptibility metric of 1.7, which is within the normal distribution of the other participants.