Introduction

The oculogyral illusion (OGI) is experienced when subjects viewing a head-fixed visual target are exposed to angular acceleration in a dark environment. The target will appear to move through both space and displace relative to the subject’s body in the direction of acceleration (Graybiel and Hupp 1946). The illusion involves a paradoxical dissociation of position and velocity with displacement relative to the body reaching a peak, while the target still seems to be moving relative to the subject (Brown et al. 1949). With high acceleration rates and long dwell times at constant velocity, reversals of direction of the illusion may occur during the constant velocity period as well as after deceleration to rest (Graybiel et al. 1946). The threshold for experiencing the OGI is below that for detecting self-rotation (Graybiel et al. 1948).

Explanations of the OGI initially focused on oculomotor control. Angular acceleration activates the semicircular canals inducing a reflexive eye response, the vestibuloocular reflex (VOR), driving the eyes in the direction opposite acceleration. The VOR is very important for stabilizing vision when the head is voluntary moved. It occurs as well, albeit with reduced gain, during passive body acceleration in complete darkness producing a nystagmus with slow phase opposite the direction of body rotation. If a subject views a head-fixed target in an otherwise dark test chamber, the nystagmus will be attenuated. In this situation, the central nervous system issues a predictive eye pursuit command that serves to cancel the VOR (Barnes 1988; Barnes and Eason 1988). The VOR drive signals presumably are still being generated by the semicircular canals but are being counteracted by the smooth eye pursuit system.

Whiteside et al. (1965) proposed that the OGI arises because the pursuit signal to override the VOR is centrally interpreted as a displacement of the eyes. They assumed that stable fixation is maintained, and consequently, a visual target would be perceived as displacing in the same direction and by the same magnitude as the change in registered eye position. This hypothesis accounts for why the OGI is in the direction of acceleration and presumes that the CNS mechanisms determining visual direction do not monitor or take into account the reflexive VOR drive on the eye muscles that is being countered.

An alternative hypothesis is that there is incomplete suppression of the VOR during the OGI. In this case, the target would be displaced off the foveae during the slow phase of nystagmus. Assuming the reflexive drive on the eyes is not centrally monitored, this would lead to an apparent displacement of the target in the direction of acceleration. Like the suppression hypothesis, the eye drift hypothesis assumes that the involuntary reflexive drive is not taken into account in computing visual direction. During angular acceleration in the dark, the beating field of the nystagmus elicited (the Schlagfeld) may deviate in the direction opposite acceleration. Thus, the average position of the eyes could be displaced in the head relative to the straight ahead. If the smooth eye pursuit command to override the nystagmus when a target is present effectively overcomes this average position shift, then the magnitude of the displacement component of the OGI should be of comparable magnitude but opposite sign.

A third hypothesis concerning the OGI relates to the fact that sound localization is also affected by angular acceleration. If an auditory rather than visual target is presented in a subject’s midline during acceleration, it will be heard to displace in the direction opposite acceleration, a phenomenon known as the audiogyral illusion (Clark and Graybiel 1949). A shift in the apparent midline of the head is one possible explanation of the audiogyral illusion (Lester and Morant 1969). Changes in apparent head position have also been associated with errors in localizing visual targets (Lackner and Levine 1979; Prieur et al. 2005; Ceyte et al. 2007) and might also explain the OGI. Recently, a strong correlation has been found between the errors in visual, auditory, and tactile localizations that are elicited during exposure to linear acceleration (Lackner and DiZio 2010).

Our goal in the present experiments was to determine the extent to which the OGI is related to (1) suppression of nystagmus, (2) retinal slip resulting from inadequate nystagmus suppression, and (3) change in the apparent midline of the head.

Materials and methods

Subjects

Eight male subjects (aged 26, 26, 28, 29, 31, 32, 39 and 55 years) participated. They completed a health questionnaire and signed informed consent forms approved by the Human Subjects Research Committee of Brandeis University. All were in good physical health, and none had a history of visual, auditory, balance, or vestibular disorders. The VOR gains and time constants for all subjects were within the normal ranges and were symmetric across rotation directions.

Apparatus

Labyrinthine stimulation was provided by means of a rotating chair that permitted a precise alignment of the physical Z-axis of the subject’s head with the axis of chair rotation, see Fig. 1. The subject’s head was ventriflexed approximately 25° and stabilized by an individually molded dental bite plate. This head position placed the horizontal semicircular canals approximately in the plane of rotation. Two crossed shoulder belts and a lap belt stabilized the torso. The chair was powered by a Neurokinetics servo motor. The velocity profile and rotation direction of the chair were controlled using custom-designed software. A red light–emitting diode that served as a fixation target was mounted in front of the subject, in alignment with the physical head midline, at an approximate distance of 30 cm from the bridge of the nose. The subject used a hand-held pointer to indicate the position of the target (see Fig. 1). Pilot studies indicated that the ability to maintain the pointer in a desired location was not affected by angular acceleration. The angular position of the pointer was indicated by a potentiometer signal sent to the data collection computer, which also collected eye position and chair velocity signals. These continuous signals were sampled at a rate of 60 Hz. These data were then transformed and filtered using MATLAB-based programs.

Fig. 1
figure 1

Servo-controlled rotating chair used to stimulate the semicircular canals and to present a visual target

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Eye movement recordings

Eye position was recorded using an ISCAN eye camera (model EC-501) mounted on the bill of a baseball cap to track the position of the left eye. The cap was secured to the head and was stable throughout all trials. Eye position was recorded in both the horizontal and vertical planes, but only the horizontal movements of the eyes were analyzed because our experimental manipulations only affect that plane. Eye movement calibration was achieved by having the subject fixate in turn each of three light-emitting diodes: one in the head midline and the others 20° to the left and right on the same azimuthal plane. This procedure was done before each experimental session and periodically repeated. The calibrations indicated that measurement drift was below 1°.

Experimental conditions and procedure

Each subject participated in three conditions involving a total of 24 trials. A trial included 10 s of baseline data collection, 5 s during acceleration, 30 s during constant velocity rotation, followed by 5 s of deceleration to rest. The three conditions included (1) OGI: the target light was present and subjects tried to fixate it and point continuously to it, (2) HM: the target light was present, subjects tried to fixate it and to point continuously to their apparent head midline, and (3) Dark: the target light was present during the 10-s pre-rotation period and subjects fixated it; the target light was turned off at the onset of rotation, and subjects tried to fixate its remembered straight ahead position. The trials were completed in two sessions conducted at least 2 days apart. The three conditions were presented in balanced order with the second condition for each subject divided between the two sessions. Acceleration rates of 2, 10, 20, and 30°/s² were run in alternating clockwise and counterclockwise directions. The same order of accelerations was used across conditions for each subject, but the orders were counterbalanced across subjects.

Data analysis

OGI condition

The time course of the OGI was determined from the pointer displacement by subtracting its position during the first 5 s of the baseline period from its position during the entire test period up to the onset of deceleration. The extent of retinal slip was determined by measuring the slow phase velocity and deviation of the eyes during the rotation periods and computing a cumulative slow phase displacement (SPD) based on the signed sum of all slow phase eye displacements.

Head midline condition

The time course of the HM was determined by the pointer displacements during rotation in relation to baseline as done for the OGI condition.

Dark condition

The slow phase velocity of the eyes and the cumulative slow phase displacement were calculated for the rotation period relative to baseline. The Schlagfeld deviation of the eyes from the straight ahead position during baseline was computed.

Assessing eye movement suppression in the OGI conditions

To estimate the magnitude of the nystagmus suppression, we compared the time course of the cumulative SPD of the eyes in the OGI and dark conditions for the different acceleration rates. The resulting differences were used in statistical comparisons. Cross-correlations were also performed on the OGI time course and other variables including OGI velocity, unsuppressed eye velocity, and cumulative SPD in the OGI condition. To compare the OGI time course with other variables, a least-squares piecewise linear fit was calculated (1) for the acceleration period, (2) from the end of acceleration to the peak of the variable, and (3) from the variable’s peak value to the end of the per-rotation period.

To relate the slow phase displacement of the eyes in the OGI and dark conditions with the OGI time course, we estimated the coefficients of the equation

$$ {\text{OGI}}_{{({\text{t}})}} = {\text{gain}} \times {\text{SPD}}_{{({\text{t}})}} $$

where OGI is the pointer displacement in the OGI condition, and SPD is slow phase eye displacement. This equation is generally found in the form X = bias + gain × Y. We considered the bias equal to zero because without acceleration the eyes were stably fixating. To compare the model’s ability to estimate the pointer displacement, the variance-accounted-for was computed: {VAF = 1 − [var (mod − OGI)/var (OGI)]} (Cullen et al. 1996). Mod represents the modeled pointer displacement, and OGI represents the actual pointer displacements in the OGI condition.

For each acceleration rate, we averaged the individual gains obtained during the previous fitting procedure. Then, we predicted the pointer displacement for the temporally averaged SPD (across subjects) and compared it with the actual average pointer displacement (across subjects). We also repeated the same procedures using a common gain across acceleration rates. The VAF shows how well the actual OGI displacement is predicted by the individualized or common gains in the model. Prediction of physiologic data by a linear model is typically considered good when the VAF is greater than 0.5.

Results

OGI condition

OGI magnitude

For each acceleration rate and direction, every subject reported body-relative target displacement in the direction of acceleration. Data averaged across direction of rotation are presented in Fig. 2a. A 2 × 4 ANOVA with repeated measures was used to determine the effects of rotation direction (clockwise vs. counterclockwise) and acceleration rate (2, 10, 20, 30°/s²) on the peak magnitude of the OGI. Acceleration rate but not direction had a significant effect [F(3,21) = 5.93; P = 0.04], and there was no interaction. A post hoc Newman–Keuls analysis indicated that the illusion was least at 2°/s² (~2°) and not different in magnitude (~10°) at the other acceleration rates. For the 10, 20 and 30°/s² accelerations, the OGI maximum deviation was reached at different times during the constant velocity periods. The maxima were reached approximately 10 s (8.7 s ± 13.4) after the beginning of constant velocity for 10°/s², and 20 s afterward for 20 and 30°/s² (18.6 s ± 5.8, 17.6 s ± 6.2, respectively). These differences were also reflected in the slopes of the least-squares piecewise linear fits. The slope during 10°/s² acceleration was steeper than at 20 and 30°/s² (0.16 vs. 0.07 vs. 0.08, respectively). In contrast, the slopes for these three acceleration rates did not statistically differ between the end of acceleration and the peak of the OGI and between the peak of the OGI and the end of the constant velocity period. Finally, the variability was greater at 2 and 10°/s² than at 20 and 30°/s².

Fig. 2
figure 2

a Mean time course and standard error of the OGI determined by pointer position (in degrees) for the four acceleration rates (2, 10, 20, and 30°/s²). The chair velocity is presented on the right ordinate (in °/s); 5 s of pre-rotation, 5 s of acceleration, and 30 s of constant velocity are presented. b Mean time course and standard error of the OGI velocity for the four acceleration rates. c Slow phase velocity mean time course and standard error for the four acceleration rates. d OGI magnitude (gray line) and model predictions made with a particular gain for each acceleration rate (green line) or with a common gain across the acceleration rates (blue line). The shading represents the standard error

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OGI velocity

These results are presented in Fig. 2b. Acceleration affected velocity [F(3,21) = 3.01, P = 0.053]. A post hoc Newman–Keuls analysis indicated that OGI velocity was least at 2°/s² (~3°/s), highest (~6.5°/s) at 10 and 20°/s², and not different at 30°/s² from 2, 10, and 20°/s² (~5°/s). Peak OGI velocity tended to be concomitant with the end of the acceleration period; consequently, the least-squares piecewise linear fit slopes were calculated from the onset of acceleration to the peak of the variables and from this peak to the end of the constant velocity period. The slopes were not significantly different during the accelerations, but the velocity decreased faster at 10°/s2 than at the other three acceleration rates, which did not differ.

Slow phase eye velocity

To determine whether retinal slip could be responsible for the OGI, we analyzed the eye movements present despite the presence of the fixation target (Fig. 2c). VOR suppression was not complete during acceleration except at 2°/s2. The peak slow phase velocity of eye movements was compensatory for body rotation and was approximately 5°/s at 10°/s² and 10°/s at 20°/s² and 30°/s² accelerations. Peak slow phase eye velocity did not differ from the OGI peak velocity at 10°/s² but was less than half of it at the 20 and 30°/s² acceleration rates. The slopes of the least-squares piecewise linear fits did not differ during the window beginning with the onset of acceleration to the peak of the variable, but did differ at 20 and 30°/s² during the window from the peak of the variable to the end of the constant velocity period. The coefficients of the cross-correlation maxima were non-significant (−0.26, −0.18, and −0.38 for 10, 20, and 30°/s², respectively). Thus, the velocity of unsuppressed eye movements and the velocity of the OGI were not related one-to-one.

Slow phase eye displacement

The peak of the cumulative SPD of the eyes in the OGI condition increased with the acceleration rates (−41.3°, −69.5°, and −90.6 for 10, 20, and 30°/s², respectively, P = 0.003). As described in the "Data analysis" section, we estimated the coefficients of the following equation to relate the OGI time course to the SPD of the eyes:

$$ {\text{OGI}}_{{({\text{t}})}} = {\text{gain}} \times {\text{SPD}}_{{({\text{t}})}}. $$

The averaged gains and VAFs are presented in Table 1 for each acceleration rate. Based on these gains, we predicted the pointer displacement for the averaged SPD values (across subjects) and compared it with the actual average pointer displacement (across subjects). In this context, the VAF represents the model’s ability to predict the OGI magnitude. The results are presented in Fig. 2d. The VAF was 0.56, 0.83, and 0.86 for 10, 20, and 30°/s², respectively with a different gain for each acceleration rate and 0.57, 0.76, and 0.58 using a common gain for each acceleration rate. Whether the gain used in the model was common or specific to each acceleration rate, the OGI magnitude is increased by the eye drift resulting from the slow phase velocity present despite the target light.

Table 1 Averaged gain and variance-accounted-for (VAF) for acceleration rates 10, 20, and 30°/s² for the comparison between the pointer displacement and the slow phase eye displacement during the OGI condition
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Schlagfeld deviation

Although retinal slip did occur in the OGI conditions, except at the 2°/s² acceleration rate, the average position of the eyes was not significantly displaced from the target light for any of the acceleration rates [F(3,21) = 1.17; P = 0.37].

Dark condition

The eye movements recorded in total darkness compared with those recorded in the OGI condition allowed us to determine the amount of suppression in the OGI condition.

Slow phase eye velocity

Slow phase velocity was significantly affected by acceleration [F(3,21) = 37.28; P = 0.002] (see Fig. 3a). It was lowest at 2°/s² (−5.5°/s) and highest at 30°/s² (−35.5°/s) and intermediate at 10°/s² (−17.7°/s) and 20°/s² (−22°/s). The lowest and highest acceleration rates were significantly different (P ≤ 0.007) from the middle two that were not different from each other, by Newman–Keuls tests (P = 0.13). The velocity of the OGI was not predictable from the slow phase velocity of the eyes in the dark condition because the coefficients of cross-correlation maxima were low (−0.16 ± 0.32, −0.52 ± 0.11, −0.47 ± 0.14, and −0.45 ± 0.16 for 2, 10, 20, and 30°/s², respectively).

Fig. 3
figure 3

a Mean time course and standard error of the slow phase velocity recorded in complete darkness for the four acceleration rates. b OGI magnitude (gray line) from the OGI condition and model predictions made with a particular gain for each acceleration rate (green line) or with a common gain across the acceleration rates (blue line). The shading represents the standard error. c Mean time course and standard error of the slow phase velocity suppression for the four acceleration rates. Slow phase velocity suppression is obtained by subtracting the slow phase velocity recorded during the OGI condition from the slow phase velocity recorded in complete darkness

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Slow phase eye displacement

The cumulative slow phase displacement of the eyes was least at 2°/s² (−77°), highest at 30°/s² (−414.5°), and intermediate at 10 and 20°/s² acceleration rates (−226.6°, −228.4°, respectively). We also estimated the gain and calculated the VAF for the relationship between OGI magnitude and cumulative SPD. The results are presented in Table 2, and each VAF value was significantly different from 0, t test, P ≤ 0.004. Fig. 3b shows the OGI magnitude and the best gain per acceleration rate (VAF: 0.67, 0.43, 0.53, and 0.79 for 2, 10, 20, and 30°/s²) and prediction with a common gain across the acceleration rates (VAF = 0.65, 0.49, 0.79, and 0.24). The cumulative slow phase displacement clearly parallels the OGI.

Table 2 Averaged gain and variance-accounted-for (VAF) for each acceleration rate for the comparison between the OGI magnitude and the slow phase eye displacement occurring during the dark condition
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Schlagfeld deviation

A one-way ANOVA of Schlagfeld deviation as a function of acceleration rate failed to show a significant difference. However, the general shape was slightly biased in the direction opposite to acceleration.

Head midline condition

Only small, non-significant changes in head midline settings were present regardless of acceleration rate or direction (see Table 3). The inter-individual variability did not relate to the patterns seen in the OGI condition. The head-midline remapping hypothesis can be ruled out of as an explanation of the OGI.

Table 3 Mean head midline displacement, standard errors, and P values
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Comparison of eye movements in the OGI and dark condition

The extent of suppression of slow phase velocity in the OGI condition was estimated by subtracting the eye movements in the OGI conditions from those in the dark conditions (Fig. 3c). For the lowest acceleration rate, 2°/s², suppression was complete in the OGI condition, with virtually no residual eye movements. The slow phase velocity suppression was 19.4°/s at 30°/s² and 12.5 and 9°/s at 10 and 20°/s², respectively. These last values do not differ. The velocity of the OGI and the magnitude of suppression of slow phase velocity differ at all acceleration rates [F(1, 7) = 31.05, P = 0.003] and the acceleration rates affected these variables differently [F(3,21) = 8.16, P = 0.01]. The coefficients of cross-correlation maximum were relatively low (−0.27, −0.3, −0.37, and −0.33 for 2, 10, 20, and 30°/s², respectively). Thus, suppression of slow phase velocity per se cannot explain the OGI except at the 2°/s² acceleration rate.

The relative suppression of SPD in the OGI conditions was determined through comparison with the corresponding SPD in the dark condition. We then estimated the gain and calculated the VAF for SPD versus OGI time course for the different acceleration levels. Table 4 presents the results for the estimation analysis, and Fig. 3b presents the results of the model predictions. VAF values ranged from 0.32 to 0.77 using individual gains for each acceleration rate and were 0.67, 0.52, 0.69, and 0.66 using a common gain for the four acceleration rates. These results show that the magnitude of the suppressed SPD of the eyes in the OGI condition correlates very well with illusory visual displacement magnitude.

Table 4 Averaged gain and variance-accounted-for (VAF) for each acceleration rate for the comparison between the OGI magnitude and the suppression of the slow phase eye displacement
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Together with the results on retinal slip present in the OGI condition, these findings show that both retinal slip and suppression are accounting for the OGI magnitude but their particular contribution is varying with acceleration rate (minimal retinal slip at 2°/s², primarily suppression). Figure 4 shows that the retinal slip contribution increases with increasing acceleration rate, while the contribution of the suppression parallels its magnitude through the acceleration rates (Fig. 4, common gain, dashed line).

Fig. 4
figure 4

Variance-accounted-for (VAF) between the actual pointer displacement and the predicted slow phase displacement during the OGI condition (a), in the dark condition (b) and the suppression of the slow phase displacement (c). The solid line represents the predictions based on a particular gain per acceleration rate, and the dashed line represents the prediction based on a common gain. No residual eye velocity was found at 2º/s² in OGI condition

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Discussion

The OGI represents one of the fundamental illusions encountered in aviation and aerospace when pilots are exposed to angular acceleration. The oculogravic illusion, the visual mislocalization associated with exposure to linear acceleration is another. Such illusions are contingent on unusual patterns of vestibular stimulation, patterns that are not experienced under normal conditions of voluntary self-motion. They are generally associated with apparent self-motion or changes in apparent orientation. An interesting feature of the OGI is that its threshold is very low, an order of magnitude below that of generating the percept of self-rotation, <0.1°/s vs. ~1°/s.

Our experimental results allowed us to evaluate the three primary explanations of the OGI that have been proposed a change in apparent head midline, nystagmus suppression, and retinal slip. A remapping of the apparent midline of the head—as reported in studies of other illusions, (e.g., Taylor and McCloskey 1991; Karnath et al. 2002; Lackner and DiZio 2010; Schindler et al. 2002)—cannot account for the OGI magnitudes in our study because the apparent head midline did not vary significantly from baseline at any of the acceleration rates.

The efference monitoring hypothesis of Whiteside et al. (1965) relates OGI to the suppression of a covert nystagmus, with the illusion being dependent on the magnitude of the smooth eye pursuit commands necessary to stabilize the eyes. There was significant suppression of slow phase velocity by the presence of fixation target in the OGI conditions, and it was complete at 2°/s². However, residual eye movements in the direction opposite to the rotation were present at the 10, 20, and 30°/s2 acceleration rates.

The best explanation of the OGI at the different acceleration rates can be obtained by relating the retinal slip present and the magnitude of suppression of involuntary eye movements. These results, taken additively, predict the magnitudes and the time courses of the OGI at the different acceleration rates. Our linear model with a common gain for all the acceleration rates predicts the OGI as corresponding to ~10% of slow phase eye displacement in the OGI condition and ~3% of the suppressed slow phase displacement in the OGI condition (the retinal slip minus the slow phase displacement in the OGI condition). Our results seem parallel to the data of Lackner and Levine (1979) and Seizova-Cajic and colleagues (Seizova-Cajic et al. 2006; Seizova-Cajic and Sachtler 2007) concerning the propriogyral illusion induced by neck muscle vibration, where no single factor can explain the illusory target displacement.

Clark and Stewart (1969) showed that the angular sensitivity threshold to detect the OGI was lower than that to detect self-motion, on average 0.11°/s2 vs 1.1°/s2 and that variability was much less for perception of the OGI. In other studies, Fluur et al. (1966), Guedry (1965) and Seemungal et al. (2004) have also found the threshold for eliciting nystagmus higher than for the OGI and for the perception of self-rotation. The present study has consequences for experiments that use a head-fixed target to cancel the VOR in humans (for example, Bloomberg et al. 1988, 1991; Israël et al. 1993; Blouin et al. 1997; Quarck et al. 2009) and non-human primates (Chowdhury et al. 2009; Takahashi et al. 2007). Spatial constancy has often been studied using the following paradigm: “(1) the subject fixates a central head-fixed target, (2) a peripheral space-fixed target is briefly flashed, (3) after the peripheral target is extinguished, the subject is either rotated or translated to a new position (while maintaining fixation on the head-fixed target that moves along with them), and (4) once the motion ends, the subject makes a saccade to the remembered location of the space-fixed target. Updating ability is then measured by examining the accuracy of the remembered saccade” (Angelaki et al. 2009). Typically, subjects rotated in yaw are unable to accurately update the target position (Baker et al. 2003; Blouin et al. 1995a, b). By contrast, performance is better for roll rotation that involves both canal and otolith stimulation (Angelaki et al. 2009). Our findings give a possible explanation. In passive yaw, there may be an illusory displacement of the central head-fixed target in the direction of body rotation. Thus, the distance of the fixated target relative to the goal target would be misjudged and lead to a “look-back” saccade of inappropriate magnitude.

In conclusion, our results show that at very low acceleration rates, the OGI is closely related to the suppression of nystagmus and to incomplete suppression coupled with retinal slip at higher acceleration rates (≥~5°/s²). After constant velocity is achieved, the OGI remains at considerable amplitude even when eye movements are no longer present or need to be suppressed to maintain target fixation (e.g., Figs. 2, 4). This pattern suggests that velocity storage signals also contribute and have different time constants for affecting visual perception of target location and for driving eye movements.