Fig 1.
a, During dynamic GVS and applied whole-body roll, continuous perceptions of roll tilt were collected in human participants (N = 11) using a subjective haptic horizontal task.
b, Across trials, physical tilt was provided to participants with three GVS directional couplings: positively coupled (red), negatively coupled (blue), and No GVS (gray). Positive current corresponds to left cathode right anode current direction to maintain consistency with existing literature. Shaded regions correspond to SEM bounds around the mean for the sample population. Perceptual results are shown for a single motion and single direction, and more comprehensive results are shown in Fig 4C and 4D, Metric computations and resultant distributions are provided for the two scalar metrics. Box plots report medians and quartiles. Individual participant identifiers (markers) are consistent throughout. c, Results for the Mean Absolute Tilt Perception. d, Results for the Perceived/Actual Tilt Slope.
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.
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 KReg = 0 and KGVS = 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 KReg = 0. Conversely, when KReg = 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 KReg = 0 (irregular only dynamics) in red, KReg = 0.75 (mixed 3:1 regular:irregular dynamics) in purple, and KReg = 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.
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 KReg = 0 and KGVS = 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.
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.
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.