INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

The angular vestibuloocular reflex (VOR) adapts its behavior in response to image motion across the retina associated with head movements. The combination of signals required for such adaptation occurs naturally in instances such as changes in the peripheral vestibular system associated with aging or illness, as well as with optically induced changes in vision. Continuously worn spectacles that either magnify or minimize the visual world can also induce changes in VOR gain (Miles and Eighmy 1980). While the compensatory changes to these manipulations of the visual inputs are in the direction required to enhance image stabilization, the adapted gain typically does not reach the value required for complete image stabilization. When rhesus monkeys were tested in darkness with sinusoidal rotations of 0.5-2.0 Hz (±20-50°/s), the VOR gain increased to 1.5-1.8 following adaptation to ×2 spectacles and decreased to 0.2-0.3 following adaptation to ×0 spectacles (Lisberger 1984; Lisberger et al. 1983). Thus the adapted gain typically does not reach the value required for complete image stabilization.

Previous studies have identified different components to the dynamics of the VOR following spectacle-induced adaptation. Responses to transient changes in head velocity were studied in rhesus monkeys before and after adaptation to spectacles that produced an increase (×2.2) or decrease (×0.25 or ×0) in image motion relative to the head. The horizontal VOR was measured in darkness after an adaptation period of several days in which the animals made free head movements. The stimulus was a passive change in head velocity (of 30°/s) with an acceleration of 600°/s² for 50 ms to a peak velocity of ±15°/s, followed by a velocity plateau of 250 ms. The initial trajectory of the eye velocity in response to this stimulus was identical regardless of the adapted state of the monkey (normal, magnified gain, or minimized gain) (Lisberger 1984). The ratio of the peak eye velocity, reached during the acceleration, to the steady-state eye velocity, measured during the velocity plateau, changed depending on whether the VOR gain had been increased or decreased. This ratio was increased with adaptation to the minimizing spectacles and decreased following adaptation to the magnifying spectacles (Lisberger and Pavelko 1986). These findings were interpreted as indicating that the initial 4 to 9 ms of the VOR evoked by this stimulus was not modifiable, whereas the VOR measured during the remainder of the stimulus showed an increase or decrease in gain in relation to the spectacles. In the latter study, single-unit recordings from vestibular-nerve afferents revealed a correspondence between the responses of irregularly discharging afferents and the initial VOR during the acceleration portion of the stimulus. Lisberger and Pavelko hypothesized that irregularly discharging afferents provide inputs to the nonmodifiable VOR pathway, whereas regularly discharging afferents provide inputs to the modifiable pathway.

Adaptation of the VOR with other paradigms and testing with other stimuli following spectacle-induced adaptation has led to different conclusions about the dynamics of the adapted VOR. Khater et al. (1993) paired horizontal sinusoidal vestibular stimulation with phase-synchronized vertical optokinetic stimulation in cats. The VOR evoked by 4,000°/s² accelerations given in darkness after a 2-h adaptation period had horizontal and vertical components from the onset of the head rotation (i.e., there was no discernible latency between modified and nonmodified components). In another study using spectacle-induced adaptation, rhesus monkeys had eye movements evoked by brief current pulses delivered through an electrode implanted in the labyrinth (Broussard et al. 1992). These evoked responses differed in amplitude according to whether the VOR had been adapted with magnifying or minimizing spectacles. In this paradigm, there was no latency to the onset of the adapted responses, as the modified responses began at the onset of the evoked eye movements.

Frequency selectivity has also been demonstrated in the processes that mediate adaptation of the VOR. When monkeys were rotated at a single frequency of 0.2 or 2 Hz while wearing magnifying or minimizing spectacles and then tested over a range of frequencies (0.1-4 Hz), the change in VOR gain is the greatest at the adapting frequency (Lisberger et al. 1983). The phase and gain data suggested that the adaptation process was controlled by a series of parallel, frequency-specific channels each consisting of a low-pass filter with a corner frequency at the frequency of adaptation. When adapting frequencies of 5-10 Hz (peak-to-peak velocity of 20°/s) were used, the adapted changes in VOR gain and frequency specificity were less than those noted at lower frequencies (Raymond and Lisberger 1996). Directional selectivity of the adaptation process has been demonstrated in monkeys (Bello et al. 1991; Yakushin et al. 2000). When adapted with magnifying or minimizing spectacles to yaw, pitch, or roll rotations for six hours, changes in gain were observed when the monkey was tested with rotations that were in the same plane as the adapting rotations. There was no transfer of the adaptation response to orthogonal rotations.

We have recently described a nonlinearity in the horizontal VOR evoked by high-acceleration, high-frequency head rotations in the squirrel monkey; the gain of the reflex rises with velocity at higher rotational frequencies (Minor et al. 1999). The contribution of this nonlinear component to the dynamics of the VOR is clearly evident for frequencies and accelerations that are within the range of naturally occurring head movements in primates. We have further shown that this nonlinear component of the response augments the response to an excitatory stimulus but is driven into cutoff at stimulus velocities of ~30°/s for high-frequency, high-acceleration stimuli that are inhibitory. Based on the frequency dynamics of the linear and nonlinear components of the response and the velocity-dependent gain enhancement, we have modeled the VOR as being comprised of linear and nonlinear pathways that combine centrally to generate the observed responses. Preferential modification of the gain of the nonlinear pathway induced by retinal slip following unilateral plugging of the three semicircular canals (Lasker et al. 1999) or unilateral labyrinthectomy (Lasker et al. 2000) accounts for the rapid return of the gain of the VOR for contralesional rotations to values that are close to the prelesion values.

The purpose of this study was to investigate the contributions of the linear and nonlinear pathways inherent in the dynamics of the VOR to the responses following spectacle-induced adaptation of VOR gain. We show that the nonlinear pathway is highly modifiable and that the gain after adaptation to magnifying spectacles to stimuli that evoke a contribution from the nonlinear pathway is greater than that observed to stimuli that do not have a contribution from this pathway. A model in which the VOR receives inputs from linear and nonlinear pathways and the process of adaptation is driven by a signal related to a low-pass filtered representation of head velocity accounts for these data. The findings from earlier studies of spectacle-induced adaptation of the VOR are also predicted from this model.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Surgical procedures and eye movement recording

Surgery was done under sterile conditions in six adult squirrel monkeys anesthetized with inhalation of halothane/nitrous oxide/oxygen. The experimental procedures used for recording eye movements were identical to those that have previously been described for this laboratory (Minor et al. 1999). All surgical and other animal care procedures used in this study were done in accordance with a protocol approved by the Animal Care and Use Committee of the Johns Hopkins University School of Medicine. Each animal was seated in a plastic chair with its head restrained by securing the implanted bolt to a chair-mounted clamp. The chair was connected to a superstructure that was mounted to the top surface of a servo-controlled rotation table capable of generating a peak torque of 125 N-m (Acutronic, Pittsburgh, PA). The horizontal VOR was tested with the animal seated in the upright position in the superstructure and aligned such that the horizontal canals were in the earth-horizontal plane of rotation.

Two pairs of field coils, each with a side length of 45 cm, were rigidly attached to the superstructure and moved with the animal. A detection circuit (Remmel Labs) that extracted signals proportional to horizontal and vertical eye position monitored voltages induced in the scleral search coils. The peak-to-peak noise at the output of the circuit was equivalent to an eye movement of 0.02°. All signals transducing motion of the head or the eye were passed through eight-pole Butterworth anti-aliasing filters with a corner frequency of 100 Hz. These signals then were digitized with a sampling rate of 1,000 Hz for acceleration steps and sinusoidal rotations at frequencies 2 Hz and above. A sampling rate of 200 Hz was used for sinusoidal rotations <2 Hz.

The eye-coil system was calibrated in two ways. A search coil identical to the one implanted about each eye was placed in a gimbal located where the animal's head was positioned in the field coil. This search coil then was moved to angles of 5, 10, and 15° right-left and up down with respect to center, and calibration factors relating volts to degrees were determined. The second method involved sinusoidal rotation of the animal, before spectacle-induced adaptation, in light at 0.5 Hz, ± 60°/s, a stimulus in which the gain of the visual-VOR reflex has been shown to be 1.0 (Minor and Goldberg 1990; Paige 1983). Calibration factors obtained from these methods typically agreed to within 5% and varied by <5% between testing sessions.

Rotational testing

Responses to steps of acceleration were recorded with the animals in darkness. The stimuli consisted of 3,000, 1,000, 500, and 100°/s² accelerations to a peak velocity of 150°/s followed by a plateau of head velocity lasting 0.9-1.1 s and then deceleration at 3,000, 1,000, 500, or 100°/s² to rest, or 3,000°/s² acceleration to a peak velocity of 60°/s followed by a plateau of head velocity lasting 0.9-1.1 s and then deceleration at 3,000°/s² to rest. The acceleration direction, duration, and interstimulus interval were varied randomly from one trial to the next. Sinusoidal head rotations (0.5-15 Hz, peak velocity 20-150°/s) were given with animals in darkness. Each stimulus frequency was given for 60 s. The order in which different frequencies and velocities were tested was varied.

Adaptation paradigms

To induce adaptation, monkeys were fit with magnifying (×2.2) or minimizing (×0.45) spectacles that were attached to the acrylic skullcap. The monkeys wore the magnifying lenses for 5-7 days, 24 h a day, were housed in their normal environment, and were allowed to move about freely. Twice a day the monkeys were brought to the lab, and the spectacles were cleaned while the monkeys were kept in the dark. To ensure adequate exposure to a range of rotational stimuli, twice a day the monkeys were rotated for 2 h using a sum-of-sines stimulus (0.5, 1.1, 2.3, and 3.7 Hz, peak velocity of 20°/s).

Data analysis

The data were analyzed off-line using software that we wrote in the Matlab (The Math Works) programming environment. The methods of analysis are similar to those that we have described previously (Lasker et al. 1999; Minor et al. 1999).

ACCELERATION STEPS. The eye-position data first were passed through a 50-point, finite-impulse-response filter with a corner frequency of 100 Hz (to calculate latency) or 40 Hz (to assess dynamics of the response). Eye velocity was obtained from a seven-point central difference algorithm. The data from 10-30 trials in each direction were averaged to obtain a representation of the response.

SINUSOIDAL ROTATIONS. Eye-position data were differentiated with a four-point central difference algorithm to obtain eye velocity. Saccades were removed from responses at frequencies <4 Hz, and an average cycle was obtained based on the data representing slow-phase eye velocity at each point in time. Responses at frequencies 4 Hz and greater were not desaccaded, and only cycles without saccades were included in the analysis. Successive cycles (5-10 at 0.5 Hz, 10-35 at 2-6 Hz, and 25-75 at 8-15 Hz) were averaged. The amplitude and phase of the response fundamental were obtained from a Fourier analysis as were the corresponding values for the head-velocity signal. Gains and phases for eye with respect to head velocity were expressed with the convention that a unity gain and zero phase imply a perfectly compensatory VOR. A negative phase indicates that eye movements lag head movements.

Modeling of the VOR

Mathematical models of the VOR were formulated in Simulink (The Math Works). The Dormand-Prince method with a fixed step size of 0.0001 s was used for simulation of the ordinary differential equations. Fourier analysis was used to calculate gain and phase of the simulated responses to sinusoidal inputs.

Statistical analysis

Results were described as means ± SD. Repeated measures ANOVA were used to compare the data from more than two groups. Post hoc t-tests or one-way ANOVA tests were performed when the ANOVA demonstrated significant main effects or interactions, and the post hoc analyses are reported in the results section. Data from two groups were compared with unpaired t-tests. Paired t-tests were used when preadaptation and postadaptation data in one animal were analyzed.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Adaptation of the horizontal VOR was studied in six squirrel monkeys (M1-M6). The adapted responses were evoked by steps of head acceleration and by sinusoidal rotations in the dark. The adaptation conditions used in each of the monkeys were as follows: normal responses and responses following adaptation to both magnifying and minimizing spectacles (M1 and M2); normal responses and responses following adaptation with magnifying spectacles (M3 and M4); and normal responses and responses following adaptation with minimizing spectacles (M5 and M6).

Responses to steps of acceleration

The VOR evoked by steps of acceleration following adaptation with magnifying spectacles demonstrated increased gain during both the acceleration and constant velocity components of the stimulus. Similarly, the VOR gain during both components of the stimulus was reduced following adaptation to the minimizing spectacles. Examples of responses preadaptation, after adaptation to the magnifying spectacles, and after adaptation to the minimizing spectacles are shown in Fig. 1. For the four monkeys that were adapted with the magnifying spectacles, the mean G_A during 3,000°/s² to 150°/s acceleration steps was 1.05 ± 0.08 (mean ± SD) preadaptation and 1.96 ± 0.16 postadaptation (Table 1). For the same animals, the mean G_V prior to adaptation was 0.93 ± 0.04, and postadaptation the mean G_V was 1.36 ± 0.08. These increases in G_A and G_V postadaptation with the magnifying spectacles were significant. In addition, while both G_A and G_V increased with adaptation, there was a significant difference in the relative increases of the two components of the response [F_(1,15) = 61.41, P < 0.01]. The acceleration gain increased by a factor of 1.92, while the velocity gain only increased by a factor of 1.46. Similar increases in gain were observed for acceleration steps of 3,000°/s² to a peak velocity of 60°/s and 500°/s² to a peak velocity of 150°/s (Table 2). In the 3,000°/s² to 60°/s steps of acceleration, there was no difference between the increase in G_A and G_V. This is most likely due to the lower peak velocity of the stimulus and the shorter duration of the acceleration component.

View larger version (19K): [in this window] [in a new window]   Fig. 1. Averaged responses to 3,000°/s2 accelerations to a peak velocity of 150°/s prior to spectacle-induced adaptation (A), following adaptation to ×2.2 spectacles (B), and following adaptation to ×0.45 spectacles (C). Fast phases were removed prior to averaging the responses. In this and all subsequent figures, head velocity has been inverted to facilitate comparison with eye velocity. Negative values of eye and head velocity represent leftward and rightward motion, respectively. Dashed line, head velocity; average eye velocity, white line, shaded areas represent ±1 SD. Respective values for the acceleration gain (GA) and velocity gain (GV) are shown in each panel. An asterisk indicates a significant difference between GA and GV (P < 0.01).

Due to the presence of fast phases, which generally occurred either during (500°/s² to 150°/s steps) or at the peak (3,000°/s² to 150°/s) of the acceleration portion of the steps, we were only able to measure the DI during the 3,000°/s² to 60°/s acceleration steps. DI is the ratio of peak eye velocity during the acceleration phase of the stimulus divided by the eye velocity during the constant velocity phase of the stimulus (see METHODS). Following adaptation to the magnifying spectacles, we observed no change in the DI as compared with the preadaptation condition. Average responses for one animal are presented in Fig. 2. For the two monkeys that were adapted to the magnifying spectacles, the mean postadaptation DI was 1.12 ± 0.10, and the mean preadaptation index was 1.17 ± 0.09. This difference was not statistically significant [t₍₄₎ = 0.562, P > 0.1].

View larger version (16K): [in this window] [in a new window]   Fig. 2. Averaged responses to 3,000°/s2 accelerations to a peak velocity of 60°/s prior to spectacle-induced adaptation (A), following adaptation to ×2.2 spectacles (B), and following adaptation to ×0.45 spectacles (C). Respective values for the dynamic index (DI) are shown in each panel.

For the four monkeys that were adapted to the minimizing spectacles, the gain during the acceleration component of the 3,000°/s² to 150°/s acceleration steps decreased from 1.04 ± 0.05 to 0.61 ± 0.08 postadaptation. For the same animals, G_V prior to adaptation was 0.94 ± 0.03, and the postadaptation G_V was 0.59 ± 0.09. Paired t-tests of preadaptation and postadaptation measures of G_A and G_V showed that the decreases in gain during both components of the response were statistically significant. However, there was no difference between G_A and G_V following adaptation to the minimizing spectacles. Unlike the asymmetric increases in G_A and G_V following adaptation with the magnifying spectacles, the monkeys displayed essentially identical decreases in both G_A and G_V (61 and 65%, respectively). Similar symmetrical decreases in G_A and G_V were seen for acceleration steps of 3,000°/s² to 60°/s and 500°/s² to 150°/s (Table 2). There was no change in the DI measured in the responses to the 3,000°/s² to 60°/s acceleration steps following adaptation to the minimizing spectacles (Fig. 2). For the four monkeys that were adapted to the minimizing spectacles, the postadaptation DI was 1.16 ± 0.14, and the preadaptation index was 1.18 ± 0.08. This difference was not significant [t₍₈₎ = 0.321, P > 0.1].

Latency

The latency to the onset of the adapted response was measured for 3,000, 1,000, 500, and 100°/s² accelerations steps to peak velocities of 150°/s preadaptation and postadaptation with the magnifying spectacles. Responses to 10-30 steps of acceleration in each condition were averaged. The results from one animal, which were typical of findings in all the animals tested, are displayed in Fig. 3. For the purposes of this analysis, the latency to the onset of the adapted response was defined as the time required for the adapted response to rise above a reference line (1 SD above the mean response for the preadaptation acceleration steps). For this animal, the adapted response intersected the reference line 25 ms after the onset of the 3,000°/s² accelerations. For the 1,000 and 500°/s² accelerations, the adapted response intersected the reference line 29 and 32 ms, respectively, after the onset of the stimulus. The responses to the 100°/s² accelerations are not shown for this animal; however, the adapted response intersected the reference line 69 ms after the onset of the stimulus. For all the animals tested, the latencies of the adapted response were 19 ± 5 ms, 29 ± 8 ms, 30 ± 4 ms, and 81 ± 72 ms for the 3,000, 1,000, 500, and 100°/s² accelerations, respectively. These differences were statistically significant (t-tests, P < 0.01). For the 3,000°/s² accelerations, the adapted response intersected the reference line at an average velocity of 45.9 ± 18.76°/s. Similarly, the adapted response crossed the reference line at average velocities of 31.8 ± 12.61°/s, 20.2 ± 3.39°/s, and 23.5 ± 16.47°/s for the 1,000, 500, and 100°/s² accelerations, respectively. Thus there was no apparent velocity threshold for the onset of the adapted response.

View larger version (25K): [in this window] [in a new window]   Fig. 3. Averaged responses to 3,000, 1,000, and 500°/s2 accelerations to 150°/s (top to bottom traces). The shaded regions represent the mean ±1 SD of the responses prior to spectacle-induced adaptation. The solid lines show the averaged responses postadaptation to the magnifying spectacles. The circles mark the time that the postadaptation response intersected the line representing 1 SD above the mean preadaptation response. The dashed lines show the stimuli.

Response dynamics

The initial VOR during the step of acceleration was evaluated with linear and polynomial fits relating eye to head velocity (Fig. 4). The coefficients for the first- through third-order fits to the data records formed by concatenating responses to leftward and rightward rotations, the mean square error for each fit, and the Baysean information criterion (see description in METHODS) for each polynomial are presented in Table 3. As seen in earlier work describing responses to these stimuli (Minor et al. 1999), there was a significant cubic component to the responses under normal conditions and essentially no difference between the linear and a second-order polynomial fits to the data. In all six monkeys, there was a significant reduction in the BIC value when comparing the third-order to the linear fit. Also, there was no significant decrease in the BIC values when comparing fifth-order to third-order fits to the responses.

View larger version (21K): [in this window] [in a new window]   Fig. 4. Eye velocity (average of 30 trials) plotted against head velocity for 3,000°/s2 to 150°/s acceleration steps prior to adaptation (A), postadaptation to magnifying spectacles (B), and postadaptation to minimizing spectacles (C). Actual data are displayed by the plus signs, linear fit to the data by the solid line, and cubic fit to the data by the dashed line. For A and C the fits to the data are offset vertically by 6°/s for clarity. For B the fits are offset by 10°/s. Insets in each panel show the error for 1-ms sampling times between the data and the predicted values based on the linear and cubic fits to the data. Note the change in y-axis scale for both the main graph and insets in B. For both the preadaptation and postmagnification conditions, there was a marked decrease in the error between the data and the predicted values with the cubic fit.

There was an increase in the cubic component to the responses following adaptation to the ×2.2 magnifying spectacles. In the four monkeys that underwent adaptation to the ×2.2 spectacles (M1-M4), there was little change in the BIC values between the linear and second-order fits to the responses. There was, however, a significant reduction in the BIC value between the linear and third-order fits. The coefficient to the linear term in the third-order polynomial fit to the data increased by <40% following adaptation to the magnifying spectacles, while the coefficients to the cubic term increased by at least 200% (3.42 to 16.81).

The relationship between eye velocity and head velocity can be described by a third-order polynomial of the following general form

(1)

where E_V is the eye velocity, H_V is head velocity, A₃, B₃, and C₃ are the coefficients for the third-order, second-order, and first-order terms, respectively, and D₃ is the intercept of the third-order fit on the eye-velocity axis. The coefficients from the third-order polynomial fits in each of the four monkeys (M1-M4) that subsequently underwent adaptation with magnifying spectacles were pooled to calculate the mean coefficients, which are listed in Table 4. When the Eq. 1 is evaluated with H_V set to 100°/s for the preadaptation values, the linear component of the equation accounts for 91% of the response, the second-order term detracts from the response by 2%, and the third-order term accentuates the response by 12%. If Eq. 1 is evaluated with the same value for H_V using the postmagnification coefficients, then the linear term contributes 64% of the response, the second-order term contributes 3%, and the third-order term accentuates the response by 33%. The increases in both the linear and cubic terms between the normal and adapted conditions were significant. While the values of both the linear and cubic coefficients increased significantly, the change in the coefficient for the third-order term was significantly greater than that for the linear term coefficient [F_(1,12) = 13.14; P < 0.01], which suggests that there was greater enhancement of the third-order, or nonlinear, component of the response with adaptation to magnifying spectacles.

In the four monkeys that were adapted with the ×0.45 minimizing spectacles, there was still a slight reduction in the BIC values between the linear fit and third-order fit to the response. This reduction in BIC value was smaller following adaptation with the minimizing spectacles than in the normal condition. There was a 26-43% reduction in the value of the linear coefficient of the third-order equation and a 75-90% reduction in the value of the cubic term coefficient following adaptation to the minimizing spectacles.

When the coefficients for the third-order polynomials for the four monkeys that subsequently underwent adaptation with the minimizing spectacles (M1, M2, M5, and M6) were pooled (Table 4), we observed decreases in the values of the coefficients with an apparent greater modification of the nonlinear component of the response. While there were slight differences between the preadaptation coefficients and those for the four monkeys that were used in the VOR magnification portion of the study, the coefficients were quite similar. When Eq. 1 is evaluated with H_V equal to 100°/s and the coefficients for the postminimization response, the linear term contributes 107% of the response, the second-order term diminishes the response by 4%, and the third-order term diminishes the response by 1%. The decreases in both the linear and cubic terms between the normal and adapted conditions were significant. While the values of both the linear and cubic coefficients decreased significantly, the change in the coefficient for the third-order term was significantly greater than that for the linear term coefficient [F_(1,12) = 71.83, P < 0.01]. The pooled coefficient of the linear term was reduced by 34% after minimization, and the pooled coefficient of the cubic term was reduced by 94%. These results suggest that with adaptation to minimizing spectacles there is a significant modification of both the linear and nonlinear pathways, with the gain of the nonlinear pathway being reduced essentially to zero. The greater changes seen in the coefficients for the third-order term following adaptation to either magnifying or minimizing spectacles suggest that there is greater, or preferential, modification of the nonlinear component of the response with adaptation.

Responses to deceleration steps

The gains during both the acceleration (G_A) and deceleration (G_D) components of the stimulus were recorded in four monkeys preadaptation and postadaptation to the magnifying spectacles. The dynamics of the acceleration and deceleration stimuli were identical (3,000°/s²) except that the acceleration ramp started at 0°/s and rose to 150°/s while the deceleration ramp, which followed the 0.9-1.1 s velocity plateau, started at 150°/s and declined to 0°/s. The time period for the calculation of values of G_A and G_D was adjusted so that the range of stimulus velocities and time periods would be identical. The gain was measured over a 20-ms interval starting 15 ms after the onset of the ramp. The corresponding stimulus velocities were 45 to 105°/s for the acceleration ramp and 105 to 45°/s for the deceleration ramp. The G_A, G_D, and G_V values are presented in Table 5. Preadaptation there was no difference in the gain values between the acceleration and deceleration ramps. However, after adaptation to the magnifying spectacles, there was a significant asymmetry to the response with the acceleration response being greater than the deceleration response (Fig. 5). In contrast to the difference between G_A and G_D postadaptation, there was no difference between G_D and G_V postadaptation. This finding is consistent with the nonlinear component of the response being present only during the acceleration portion of a rotation.

View larger version (11K): [in this window] [in a new window]   Fig. 5. Averaged responses to 3,000°/s2 to 150°/s acceleration (A) and deceleration (B) steps following adaptation to ×2.2 spectacles. The deceleration step followed a 0.9-1.1 s constant velocity rotation.

Responses to sinusoidal rotations

The gain and phase plots of responses to sinusoidal rotations (0.5-15 Hz, ±20°/s) preadaptation, postmagnification, and postminimization are displayed in Fig. 6. There was no frequency-dependent change in gain under the preadaptation condition; however, a frequency-dependent change in gain was noted following adaptation with magnifying spectacles. Greater gains were observed at the lower testing frequencies [F_(7,16) = 13.54, P < 0.01]. Post hoc analyses with Fisher's pair-wise comparisons showed that for the testing frequencies from 0.5-6 Hz there were significant differences between the testing frequency and all remaining frequencies, except for the immediately adjacent frequency. For example, there was no difference between 0.5 and 2.0 Hz, but there were differences between 0.5 Hz and all testing frequencies from 4 to 15 Hz (P < 0.05). There was no significant difference for the gains at 8 Hz and higher frequencies. After adaptation with the minimizing spectacles, there was again a frequency-dependent change in gain, with the greatest decrease in gain evident at the lower testing frequencies [F_(7,19) = 2.87, P < 0.05]. Post hoc analyses (Fisher's pair-wise comparisons) showed differences only between the postadaptation gains at 15 Hz and testing frequencies of 2-8 Hz (P < 0.05).

View larger version (18K): [in this window] [in a new window]   Fig. 6. Gain and phase plots of responses to 0.5- to 15-Hz rotations in the dark (peak velocity 20°/s) prior to adaptation (), following adaptation to magnifying spectacles (), and following adaptation to minimizing spectacles (). The data points represent the average gain or phase values for the monkeys used in this experiment; the error bars show ±1 SD.

Following adaptation with the magnifying spectacles, there were significant increases in gain at all testing frequencies as compared with the normal condition. The gain increases varied across frequencies, with the greatest increases occurring at the lower frequencies. At 0.5 and 2 Hz, the gain postmagnification increased by 70%, while at 12 and 15 Hz, the gain increased by 30%. Paired t-tests showed a significant difference between pre- and postmagnification gains at all frequencies. After adaptation with the minimizing spectacles, there were decreases in gain at all testing frequencies. As seen in the postmagnification condition, the greatest changes were present at the lower testing frequencies. At 0.5 and 2 Hz, the gain decreased by 40%; at 12 and 15 Hz the gain decreased by 23%. Paired t-tests showed a significant difference between pre- and postminimization gains at all frequencies.

The phase of the adapted responses varied with frequency in an adaptation-specific manner (Fig. 6B). Following adaptation with magnifying spectacles, there was a frequency-dependent phase change, with progressively greater phase lags at the higher testing frequencies [F_(7,16) = 4.35, P < 0.01]. After adaptation with the minimizing spectacles, there was again a frequency-dependent change in phase, with progressive phase leads at the higher frequencies of stimulation [F_(7,19) = 13.42, P < 0.01].

Following adaptation with the magnifying spectacles, there were significant increases in phase lag at the higher testing frequencies as compared with the normal condition. There was a 1.5° phase lead at 0.5 Hz and a 10.4° greater phase lag at 15 Hz postmagnification. Paired t-tests showed a significant difference in phase between the preadaptation and postmagnification values at frequencies of 4 Hz and greater. There was no difference between the preadaptation and postmagnification phases at 0.5-2 Hz. After adaptation with the minimizing spectacles, there were marked increases in phase lead at the higher testing frequencies. There was a 0.5° phase lag preadaptation and a 16.3° phase lead postminimization at 15 Hz. As with the postmagnification results, post hoc paired t-tests showed a difference (P < 0.05) in phase at frequencies 4 Hz and greater. Again there were no significant differences in phase at testing frequencies between 0.5 and 2 Hz.

The frequency- and velocity-dependent nonlinearity in the response to sinusoidal rotations noted in normal monkeys (Minor et al. 1999) was observed in the monkeys following adaptation to magnifying spectacles. When tested at 4 Hz preadaptation, there was an increase in the gain of the response with increasing stimulus velocity. Following adaptation to magnifying spectacles, this gain increase with rising stimulus velocity was enhanced as compared with the normal condition (Fig. 7), consistent with a greater enhancement of the nonlinear pathway. After adaptation to the minimizing spectacles, there was little difference in the gain of the response with increasing velocity of stimulation. If the nonlinear portion of the response were used to lower the gain after adaptation to minimizing spectacles, then one would expect a progressive gain decrease with increasing velocity of rotation. The absence of a difference in gain with increasing velocity of rotation after adaptation with the minimizing spectacles argues that the nonlinear component is not used to actively lower the gain after adaptation. These results are consistent with the findings observed in the responses to steps of acceleration, in that the nonlinearity contributes to the enhanced response after adaptation with magnifying spectacles but does not contribute to or actively lower the response after adaptation with the minimizing spectacles.

View larger version (14K): [in this window] [in a new window]   Fig. 7. Gains for monkey M2 tested at 4 Hz with peak velocities of 20, 50, and 100°/s preadaptation and postadaptation to minimizing and magnifying spectacles. Error bars represent ±1 SD.

Polynomial fits were made to the data from the 4-Hz rotations at 100°/s preadaptation and postadaptation to both the magnifying and minimizing spectacles (2 animals magnifying spectacles and 4 animals minimizing spectacles). As reported previously in the preadaptation condition (Minor et al. 1999), there was little difference between the second-order and first-order fits to the data. The greatest improvement in the fit to the data was noted between the first-order and third-order polynomial fits (Table 6). On the basis of the response to acceleration and deceleration steps, it appears that the nonlinear portion of the VOR is evident only during ipsilateral acceleration. Consequently, we compared the first- and third-order coefficients during the acceleration and deceleration portions of the sinusoidal rotations separately. We did this by measuring the two quarter cycles during which the absolute value of the stimulus velocity was increasing or decreasing. Since we were using discontinuous portions of the stimulus and response, and concatenation of these two segments could alter the fits due to phase shifts, we analyzed each set of quarter cycles independently. The quarter cycles in one direction were inverted and then concatenated with the original signals at the origin. The best fit to the data was an odd-order polynomial without contribution from the even-order terms, because the method of forming the signal ensured the responses were symmetric about the origin (Lasker et al. 1999). The relationship between eye velocity and head velocity can be described by a third-order polynomial of the following general form:

(2)

where E_V is the eye velocity, H_V is head velocity, and A₃ and C₃ are the coefficients for the third-order and first-order terms, respectively. The linear and cubic term coefficients for the acceleration and deceleration responses preadaptation, postmagnification, and postminimization are listed in Table 7. When Eq. 2 is evaluated with H_V equal to 100°/s and the premagnification coefficients for the acceleration quarter cycles, the linear component of the equation accounts for 92.2% of the response, and the third-order term contributes 7.8% to the response. When the equation is evaluated using the acceleration quarter cycle, postmagnification coefficients, the linear term contributes 82.9% of the response, and the third-order term accounts for 17.1% of the response. Thus the greater enhancement of the nonlinear component of the response, which was seen during the steps of acceleration, was also observed during the sinusoidal rotations. If Eq. 2 is evaluated using the acceleration quarter-cycle, postminimization coefficients, the linear term contributes 98.9% of the response, and the third-order term accounts for 1.1% of the response. Thus there is a decrease in the relative contribution from the nonlinear component of the overall response following adaptation with the minimizing spectacles.

The linear and cubic term coefficients were analyzed separately to determine whether there was a differential effect on these terms depending on the nature of the stimulus (acceleration or deceleration). The linear term coefficients showed a significant increase following adaptation to the magnifying spectacles [F_(1,7) = 102.70, P < 0.01], and a significant decrease following adaptation to the minimizing spectacles [F_(1,15) = 55.71, P < 0.01]. In both cases there was no difference in this term between the postadaptation acceleration and deceleration quarter cycles. These findings indicate that the linear component of the response is not dependent on whether the stimulus is accelerating or decelerating.

Analysis of the coefficients for the cubic term following adaptation to the magnifying spectacles showed a significant increase from the preadaptation values for the acceleration quarter cycles [F_(1,7) = 12.16, P < 0.05] and no difference in the preadaptation and postmagnification deceleration quarter cycles. This pattern of change is consistent with the observed behavior during the steps of acceleration and deceleration postadaptation to the magnifying spectacles. Following adaptation to the minimizing spectacles, there was a significant decrease in the cubic term coefficients [F_(1,15) = 7.12, P < 0.05] for the acceleration quarter cycles as compared with the preadaptation levels. There was no difference in the cubic term coefficients for the deceleration quarter cycles pre- and postadaptation to the minimizing spectacles. In addition, there was no difference between the postminimization acceleration and deceleration cubic term coefficients. This lack of difference between the acceleration and deceleration cubic term coefficients can be interpreted as a loss of the excitatory input from the nonlinear pathway postadaptation to the minimizing spectacles.

To determine whether there were differential effects on the linear and cubic terms with adaptation, the linear and cubic terms were analyzed with two-factor ANOVA. Since there was such a large difference between the actual values of the coefficients for the linear and cubic terms, which would obscure any interaction between the terms, we standardized the terms by multiplying the coefficients of the cubic term by 10⁵. There was a significant increase in the values of the linear and cubic term coefficients postadaptation with the magnifying spectacles [linear: F_(1,4) = 34.24, P < 0.01; cubic: F_(1,4) = 9.52, P < 0.05]. In addition, there was a significant interaction between the linear and cubic term coefficients and the adaptive state. This interaction indicates that the increase in the coefficient for the cubic term was greater than that for the linear term, consistent with the preferential enhancement of the nonlinear component of the response. Following adaptation to the minimizing spectacles, there were significant decreases in both the linear and cubic terms [linear: F_(1,6) = 26.28, P < 0.01; cubic: F_(1,6) = 9.62, P < 0.05]. While there was no significant interaction between term and condition with the adaptation to the minimizing spectacles, there was a 10-fold decrease in the value of the cubic term. In contrast, the linear term decreased by less than half. The lack of significant interaction may be due to the variability in the coefficients of the cubic term.

The responses during the deceleration quarter cycles were analyzed in a similar fashion. Following adaptation to the magnifying spectacles, there was a significant increase in the linear term coefficients [linear: F_(1,4) = 78.33, P < 0.01], but no change in the cubic term coefficients. A similar result was seen following adaptation to the minimizing spectacles; there was a decrease in the linear term coefficient postadaptation [F_(1,6) = 29.44, P < 0.01] but no change in the cubic term coefficients. The lack of change in the cubic term coefficients during the deceleration portion of the stimulus is further support for the hypothesis that the nonlinear pathway on one side only enhances the response during the acceleration portion of an ipsilateral rotation.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

The previous three papers in this series have described the linear and nonlinear components of the VOR in response to high-acceleration rotations, and the modifications that occur in these responses following canal plugging and unilateral labyrinthectomy (Lasker et al. 1999, 2000; Minor et al. 1999). There are several lines of evidence that have led us to model this behavior as separate linear and nonlinear pathways that converge centrally. First, there are different frequency dynamics for the linear and nonlinear components. Second, the linear component fits well with the transfer function for regularly discharging canal afferents, and the frequency dependence of the nonlinear component fits with the dynamics of the irregularly discharging afferents. Third, the asymmetry between ipsilesional and contralesional rotations following unilateral canal plugging and labyrinthectomy fits the cutoff characteristics of the irregularly discharging afferents. Fourth, the observed differences between acceleration and deceleration responses are predicted from the behavior of the two classes of afferents. These results could be explained simply by the differences in the response properties of the afferents that are converging at the level of the secondary vestibular neuron. However, there is further evidence that suggests the linear and nonlinear pathways combine beyond the level of the secondary vestibular neuron. First, the dynamics of the irregularly discharging afferents do not predict the rise in gain with velocity for higher frequency rotations, so this aspect of the nonlinearity must arise centrally. Since the velocity-dependent gain enhancement is not observed at low frequencies, the enhancement must occur separately from the linear pathway. Second, to model the data following spectacle-induced adaptation, we need to change the gains of the linear and nonlinear components independently. The gains of the two components do not change in parallel. Thus the linear and nonlinear pathways are hypotheses suggested by the behavioral data, but the neural elements mediating these pathways will need to be defined through further studies and single-unit recordings. We proceed to discuss the findings of this study in light of these hypotheses and in comparison to previous studies on adaptation.

As expected, the gain of the VOR increased following adaptation with ×2.2 magnifying spectacles and decreased following adaptation with ×0.45 minimizing spectacles. Our findings extend the understanding of the adaptive processes of the VOR to high-frequency, high-acceleration rotations, stimuli for which the VOR is of critical importance for image stabilization (Grossman et al. 1988, 1989; Minor et al. 1999). The results indicate that both the linear and nonlinear components of the VOR, as described in earlier studies, are modified during the adaptation process. The first major finding of the study is that there does not appear to be a fixed latency to the onset of the adapted response, as the latency changes with the intensity of the stimulus. The second finding is that, following adaptation to magnifying spectacles, the response during the acceleration component of a high-acceleration, high-velocity rotational stimulus is nearly equal to the magnifying power of the spectacles and is considerably greater than the gain during the constant velocity component of the stimulus. In addition, there is a greater nonlinearity in the acceleration response following adaptation to the magnifying spectacles as compared with the preadaptation condition. A reduction in both acceleration and velocity gains is seen after adaptation to the minimizing spectacles. These responses fit with our understanding of the nonlinear and linear components of the VOR. We can model these responses by simply eliciting changes in the central gain elements for the linear and nonlinear pathways, and we suggest that there is a greater, or preferential, modification of the nonlinear component, or pathway, with adaptation. During the high-acceleration, high-velocity steps, we also observed that, although the metrics of the accelerations were equal, the response during the deceleration component (or off-ramp) differed from the acceleration (or on-ramp) response. In addition, the gain during the off-ramp did not differ from the gain during the constant velocity component of the stimulus. The greater enhancement of the nonlinear pathway is also seen in the responses to sinusoidal stimuli, although the differences in the response dynamics are subtle compared with those seen in the acceleration steps. All of the observed behaviors can be modeled with slight changes to our previously published model (Lasker et al. 1999, 2000; Minor et al. 1999).

Latency of the adapted response

The present results indicate that there is not a temporally fixed latency to the onset of the adapted response. Rather, the dynamics of both the stimulus and the central adaptation mechanisms determine the latency to the onset of the adapted response. There is a progressive decrease in the latency of the adapted response as the acceleration steps increase from 100 to 3,000°/s². These findings are in contrast with earlier reports of a temporally fixed latency, which was thought to be a consequence of modifiable and nonmodifiable pathways for the VOR (Lisberger 1984). This hypothesis of modifiable and nonmodifiable pathways for the VOR came from the observation that there was a fixed latency between the onset of the normal VOR and the beginning of the adapted response to both magnifying and minimizing spectacles. In these earlier studies, the monkeys were rotated with only one set of stimulus parameters (600°/s² accelerations to velocities of ±15°/s, a 30°/s change in velocity); thus a latency that varies with the dynamics of the stimulus would not be evident. In the present study we rotated the monkeys at four different accelerations, which enabled us to show that the onset of the adapted response was linked to the dynamics of the stimulus and not fixed in terms of time or velocity.

Responses to steps of acceleration

Following adaptation with the magnifying and minimizing spectacles, we observed changes in the gain of the VOR during the constant velocity component of the rotation (G_V) that were similar to previously reported values (Lisberger 1984; Lisberger et al. 1983). The gain changes seen with adaptation during the acceleration component of the stimuli have not been previously reported. After adaptation to the magnifying spectacles, there was a consistent increase in the value of the acceleration gain (G_A), which was significantly greater than the corresponding G_V values and approached the magnifying power of the spectacles. Thus there was a greater VOR response to the acceleration component of the stimulus in comparison to the constant velocity component. After adaptation to the minimizing spectacles, we did not see differences between G_A and G_V.

Previous studies have identified a nonlinear component to the VOR in addition to the recognized linear behavior (Minor et al. 1999). This nonlinear component is seen as an enhancement of the gain of the VOR to increasing velocities of stimulation at frequencies above 2 Hz. It is also observed in the trajectory of the eye responses to steps of acceleration (3,000°/s² to a peak velocity of 150°/s), which are better described by a third-order polynomial than linear fit. Under the present adaptive conditions, asking for essentially either a doubling or halving of the VOR gain, we see comparable changes in the gain of the linear pathway (28% increase postmagnification and 33% decrease postminimization). We also see substantially greater gain changes in the nonlinear pathway (420% increase postmagnification and 100% decrease postminimization). We hypothesize that the greater change in G_A as compared with G_V following adaptation to the magnifying or minimizing spectacles can be explained by a greater, or preferential, adaptation of the nonlinear pathway. The findings indicate that the nonlinear pathway can be used to enhance the gain of the VOR, but it cannot be used to actively lower the gain of the VOR.

The gain during the acceleration (on-ramp) portion of the stimulus was markedly greater than that during the deceleration (off-ramp) portion (G_D) of the stimulus following adaptation to the magnifying spectacles. This asymmetric response to acceleration and deceleration steps with identical stimulus profiles can also be explained by a greater enhancement of the nonlinear pathway. We have modeled the nonlinear pathway as a frequency- and velocity-dependent excitatory pathway that can boost the gain of the response during rotation in the excitatory direction. From this model, we predict that the inputs to the nonlinear pathway for a leftward step of acceleration arise from the left labyrinth, and the inputs for the deceleration response should arise from the right labyrinth. If this is the case, why then is there an asymmetry in the response? Since regularly discharging afferents innervating the semicircular canal display linear behavior with respect to frequency, acceleration, and velocity (Hullar and Minor 1999), these afferents could not cause the acceleration-deceleration asymmetry. The irregularly discharging afferents then would be a possible source of the nonlinear response. Simulation of irregularly discharging afferents using the Goldberg and Fernandez transfer functions (Fernandez and Goldberg 1971; Goldberg and Fernandez 1971) shows that the acceleration and deceleration responses will differ. Preliminary evidence also suggests that the irregular afferents respond differently to identical accelerations starting from rest and starting from a constant velocity rotation to the contralateral side (Hullar et al. 2001). For example, an irregular afferent on the left side will respond with a brisk increase in firing rate with an acceleration step to the left from rest. However, if the animal is rotating at 150°/s to the right, the irregularly discharging afferent is silent. If the animal is then decelerated with the same stimulus profile, the irregularly discharging afferent on the left will not start firing until the animal has decelerated to approximately 3°/s. As such, the VOR during the deceleration phase is due almost entirely to the input from regularly discharging afferents. This asymmetry in irregular afferent discharge could account for the differences in the acceleration gain values between the on-ramp and off-ramp responses. This would also explain why, following adaptation to the magnifying spectacles, the gain during the off-ramp response was no different from the gain during the constant velocity portion of the stimulus.

Responses to sinusoidal rotations

Following adaptation to the magnifying and minimizing spectacles, we observed changes in gain and phase that were similar to those reported earlier (Lisberger et al. 1983; Melvill Jones and Gonshor 1982; Paige and Sargent 1991). As in these earlier studies, the changes in VOR gain, particularly following adaptation to magnifying spectacles, were greatest at the lower testing frequencies. The decrease in amount of adaptation at the higher testing frequencies is consistent with previously published results (Raymond and Lisberger 1996). In that study, monkeys were adapted to ×2 or ×0 viewing conditions at either 0.5, 2, 5, 8, or 10 Hz and showed frequency-dependent gain changes, following adaptation at the lower frequencies. When adapted at the higher frequencies, the monkeys demonstrated less robust changes, and there was no frequency dependence. There were also similar frequency-dependent changes in gain reported in monkeys following compensation for a unilateral labyrinthectomy (Lasker et al. 2000). For stimuli that do not invoke the nonlinear pathway, the process that leads to adaptation in situations that require an increase in the gain of the VOR behaves as a low-pass filter. Conversely, the process that leads to adaptation in situations that require a decrease in the gain of the VOR behaves as a high-pass filter. In both situations the behavior of the system is consistent with a low-pass filtered adaptation response being added to (postadaptation to magnifying spectacles) or subtracted from (postadaptation to minimizing spectacles) the VOR. The nature of retinal slip, the presumed error signal, may provide an explanation for these findings. Retinal slip is dependent on visual following mechanisms, which have been shown to degrade at higher frequencies (Martins et al. 1985).

The frequency-dependent changes in gain seen in the sinusoidal responses would not be predicted from the asymmetrical gain changes (G_A > G_V) observed in the response to steps of acceleration. In the case of the sinusoidal responses, the greatest changes in gain were observed at the lower frequencies, whereas the greatest change in gain during the steps of acceleration was seen during the acceleration component (or higher frequency portion) of the step. This apparent difference in the adaptation response may be due to the inherent difference between the unpredictable acceleration steps and the predictable sinusoidal stimuli. Another possible explanation for this discrepancy is that the responses to sinusoidal stimulation were measured at peak velocities of 20°/s, which is below the threshold for activation of the nonlinear pathway (Minor et al. 1999), while the steps of acceleration were of sufficient intensity to recruit the nonlinear component of the response. Thus the greater adaptation of the nonlinear pathway may account for the difference between responses to sinusoidal rotations and steps of acceleration.

While the preferential adaptation of the nonlinear pathway was not seen when tested with sinusoidal stimuli with peak velocities of 20°/s, the adaptation of this pathway was found in the response to sinusoidal stimuli at stimulus intensities of sufficient frequency and velocity to recruit the nonlinearity. When the responses to 4-Hz stimuli of increasing velocity were analyzed, there were proportionally greater increases in gain with increasing velocity of stimulation following spectacle-induced magnification of the VOR (see Fig. 7). Thus this aspect of the sinusoidal responses following spectacle-induced adaptation would be predicted from the responses to steps of acceleration. However, the postmagnification gain of the VOR during the 4 Hz, 100°/s sinusoidal stimuli was still less than the G_A measured during the 3,000°/s² acceleration steps. There are two other factors that could contribute to this difference. First, the gains that were measured during the response to sinusoidal stimulation were derived from the full cycle (both acceleration and deceleration portions of the stimulus), and we have shown that there was a significant difference between the acceleration and deceleration gains postmagnification. Second, there are substantial differences in the relationship between acceleration and velocity for sinusoidal stimuli and steps of acceleration. For the steps of acceleration, we measured G_A over an interval of constant acceleration where the stimulus velocity was increasing from 60 to 120°/s. For the sinusoidal stimuli, however, the peak acceleration occurs at 0°/s head velocity and decreases to 0°/s² as the stimulus reaches peak velocity. Thus during comparable segments of increasing stimulus velocity, the acceleration is constant during the steps of acceleration and decreasing during the sinusoidal stimuli. The nonlinear pathway would be contributing to the VOR during this period of increasing velocity during the step of acceleration (see the discussion of the model in the APPENDIX and Fig. 12). However, during the period of increasing velocity for the sinusoidal stimulus, the contribution of the nonlinear pathway would be decreasing. Due to these differences in the stimulus parameters, the responses to sinusoidal rotations and steps of acceleration are qualitatively similar, but differ quantitatively.

The responses to the acceleration and deceleration portions of the sinusoidal stimuli were consistent with the responses observed during the steps of acceleration and deceleration. For both preadaptation and postadaptation conditions, there were no differences between the linear term coefficients for the acceleration and deceleration quarter c