Horizontal Vestibuloocular Reflex Evoked by High-Acceleration Rotations in the Squirrel Monkey. III. Responses After Labyrinthectomy

David M. Lasker,1 Timothy E. Hullar,1 and Lloyd B. Minor1,2,3

 1Department of Otolaryngology---Head and Neck Surgery,  2Department of Biomedical Engineering, and  3Department of Neuroscience, The Johns Hopkins University, Baltimore, Maryland 21287-0910


    ABSTRACT
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Lasker, David M., Timothy E. Hullar, and Lloyd B. Minor. Horizontal Vestibuloocular Reflex Evoked by High-Acceleration Rotations in the Squirrel Monkey. III. Responses After Labyrinthectomy. J. Neurophysiol. 83: 2482-2496, 2000. The horizontal angular vestibuloocular reflex (VOR) evoked by high-frequency, high-acceleration rotations was studied in four squirrel monkeys after unilateral labyrinthectomy. Spontaneous nystagmus was measured at the beginning and end of each testing session. During the period that animals were kept in darkness (4 days), the nystagmus at each of these times measured ~20°/s. Within 18-24 h after return to the light, the nystagmus (measured in darkness) decreased to 2.8 ± 1.5°/s (mean ± SD) when recorded at the beginning but was 20.3 ± 3.9°/s at the end of the testing session. The latency of the VOR measured from responses to steps of acceleration (3,000°/s2 reaching a velocity of 150°/s) was 8.4 ± 0.3 ms for responses to ipsilesional rotations and 7.7 ± 0.4 ms for contralesional rotations. During the period that animals were kept in darkness after the labyrinthectomy, the gain of the VOR measured during the steps of acceleration was 0.67 ± 0.12 for contralesional rotations and 0.39 ± 0.04 for ipsilesional rotations. Within 18-24 h after return to light, the VOR gain for contralesional rotations increased to 0.87 ± 0.08, whereas there was only a slight increase for ipsilesional rotations to 0.41 ± 0.06. A symmetrical increase in the gain measured at the plateau of head velocity was noted after the animals were returned to light. The VOR evoked by sinusoidal rotations of 2-15 Hz, ±20°/s, showed a better recovery of gain at lower (2-4 Hz) than at higher (6-15 Hz) frequencies. At 0.5 Hz, gain decreased symmetrically when the peak amplitude was increased from 20 to 100°/s. At 10 Hz, gain was decreased for ipsilesional half-cycles and increased for contralesional half-cycles when velocity was raised from 20 to 50°/s. A model incorporating linear and nonlinear pathways was used to simulate the data. Selective increases in the gain for the linear pathway accounted for the recovery in VOR gain for responses at the velocity plateau of the steps of acceleration and for the sinusoidal rotations at lower peak velocities. The increase in gain for contralesional responses to steps of acceleration and sinusoidal rotations at higher frequencies and velocities was due to an increase in the contribution of the nonlinear pathway. This pathway was driven into cutoff and therefore did not affect responses for rotations toward the lesioned side.


    INTRODUCTION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Unilateral labyrinthectomy results in an ablation of vestibular inputs from one labyrinth and leads to static and dynamic signs of hypofunction in the angular vestibuloocular reflex (VOR) (Baarsma and Collewijn 1975; Fetter and Zee 1988; Maioli et al. 1983; Vibert et al. 1993). Spontaneous nystagmus is the static sign attributable to semicircular canal dysfunction. The slow phase components of this nystagmus in the horizontal plane are directed toward the lesioned labyrinth. The dynamic signs differ according to the stimuli being used to assess the function of the VOR. When lower frequency sinusoidal stimuli are used, the performance of the VOR often recovers over time and asymmetries (gain lower for rotations toward the lesioned side) are only noted at higher rotational velocities (Fetter and Zee 1988; Jenkins 1985; Paige 1989). In contrast to the rather subtle changes in the VOR noted with less dynamic stimuli, the responses to higher frequency and acceleration rotations show an enduring response asymmetry. Rotations in the yaw plane toward the lesioned side evoke a VOR with substantially lower gain than those toward the intact side. These effects have been most extensively documented in humans (Aw et al. 1996; Crane and Demer 1998; Halmagyi et al. 1990; Tabak et al. 1997) but parallel findings have been noted in guinea pigs after ablative vestibular lesions (Gilchrist et al. 1998).

Most previous studies have explored these asymmetries for responses to rotations that have high peak velocity but relatively low frequency and acceleration. Fetter and Zee (1988) identified asymmetries in the gain of the horizontal VOR evoked by steps of head velocity after unilateral labyrinthectomy in rhesus monkeys. When tested in darkness within 1 day after the lesion, gain was decreased by ~50% in comparison to preoperative values. As the peak velocity of the stimulus was increased from 30 to 300°/s, the gain of the VOR for ipsilesional rotations decreased progressively with increasing head velocity. Similar findings also have been observed in cats (Maioli et al. 1983) and in humans (Paige 1989; Tusa et al. 1989) for responses to higher velocity rotations. Asymmetries to analogous stimuli were noted in squirrel monkeys after unilateral plugging of the horizontal canal (Paige 1983b). In each case, the findings have been interpreted as a manifestation of Ewald's second law: lower gains to ipsilesional rotations are thought to be due to inhibitory cutoff in vestibular-nerve afferents and/or central vestibular neurons on the contralateral side (Ewald 1892).

The VOR in response to steps of acceleration (2,000-4,000°/s2 for 40-70 ms) becomes profoundly asymmetric after unilateral vestibular lesions. These findings are evident at stimulus velocities that are lower than those required to produce asymmetries to rotations of lower frequency and acceleration. In a recent study of the horizontal VOR evoked by high-frequency, high-acceleration rotations in squirrel monkeys, Minor et al. (1999) showed that the reflex has inputs from linear and nonlinear pathways. The nonlinear pathway is responsible for a rise in the gain of the VOR with increasing frequencies and velocities of rotation. This pathway is rectified such that there is inhibitory cutoff in its responses to stimuli >30°/s for rotational frequencies >= 4 Hz. The gain of the nonlinear pathway is selectively modifiable and accounts for the return of the contralesional responses to normal levels after unilateral plugging of the three semicircular canals (Lasker et al. 1999). Recovery of gain for ipsilesional responses does not occur because the nonlinear pathway on the intact side is driven into inhibitory cutoff for these more dynamic stimuli.

The goal of this study was to define the dynamics of the horizontal VOR evoked by high-acceleration, high-frequency rotations in the yaw plane after unilateral labyrinthectomy. Our findings demonstrate asymmetries in the reflex similar to those we have reported after unilateral plugging of the three semicircular canals. In contrast to canal plugging, a large spontaneous nystagmus was noted after labyrinthectomy. This spontaneous nystagmus led to an offset in the eye-velocity responses and a bias velocity noted during the stimuli.


    METHODS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Surgical preparation

Surgery was done under sterile conditions in four adult squirrel monkeys anesthetized with inhalation of halothane/nitrous oxide/oxygen. The techniques for implantation of the head restraining bolt and eye coils have been described (Minor et al. 1999).

Labyrinthectomy was performed by making a postauricular incision and removing the mastoid bone with an otologic drill and curettes to expose the horizontal and posterior semicircular canals. The petrous bone was removed further anteriorly and superiorly to visualize the superior canal near its union with the common crus. Each of the semicircular canals then was obliterated with removal of the ampulla. The vestibule was entered, and the utriculus and sacculus were removed. The internal auditory canal was opened next, and the distal ends of the ampullary nerve branches were removed. The space created by the labyrinthectomy was packed with muscle and fascia and the postauricular incision was closed.

Eye-movement recordings

The experimental procedures used for recording eye movements were identical to those that have previously been described for this laboratory (Minor et al. 1999). 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. Voltages induced in the scleral search coils were monitored by a detection circuit (Remmel Labs) that extracted signals proportional to horizontal and vertical eye position. 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. 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 in light at 0.5 Hz, ±60°/s, a stimulus in which the gain of the visual-vestibuloocular reflex has been shown to be 1.0 (Minor and Goldberg 1990; Paige 1983a). Calibration factors obtained from these methods typically agreed to within 5%. The center of the oculomotor range that corresponded to straight-ahead horizontal eye position was determined from the midposition of the responses to the sinusoidal rotations in light. These calibrations initially were made in the animals before labyrinthectomy and were shown to be constant from one experimental session to the next.

Measurement of spontaneous nystagmus

The animals were kept in darkness for 4 days after labyrinthectomy. There were no restrictions on their movement at any time after the procedure. The spontaneous nystagmus was measured in five testing sessions after the labyrinthectomy: 8-18 h and 3 days (while animals were still in darkness), 1 day after animals had been returned to normal light-dark cycles, and days 10 and 21 after the procedure. Spontaneous nystagmus was evaluated at two points during each recording session. The first measurement was before delivery of any motion stimuli after the animals had been seated in a primate chair with their heads stationary for 15-20 min. The second measurement was at the end of the recording session after a 30-min period of motion stimuli consisting of sinusoidal rotations and steps of acceleration. The assessment of the spontaneous nystagmus at the end of the recording session was >= 1 min after the delivery of the previous rotational stimulus. The room lights had been off for >= 15 s before the recording of the spontaneous nystagmus in darkness.

Rotational testing

Responses to steps of acceleration (3,000°/s2 acceleration to a peak velocity of 150°/s followed by a plateau of head velocity lasting 0.9-1.1 s and then deceleration to rest) were recorded with animals in darkness. The acceleration magnitude, 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.

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 to 30 trials in each direction were averaged to obtain a representation of the response. All data were taken before the first fast phase of the eye-velocity response.

Response latency was measured by a method that determined the onset of head and eye movements as the points at which the velocity signals deviated from the mean value measured before the onset of the stimulus for head and eye velocity, respectively, by >3 SD. The difference in these two onset points measured for each trial was defined as response latency (Minor et al. 1999).

Measurements of the gain of the VOR were made during the step of acceleration and after the plateau of head velocity had been reached. The acceleration gain of the VOR, GA, was measured for each trial as the ratio of the slope of a line through the eye velocity points to the slope of a line through the head velocity points during the period of 20-40 ms after the onset of the stimulus when head velocity was increasing from 60 to 120°/s. The velocity gain of the VOR, GV, was measured from the ratio of the mean eye and head velocity evaluated at 100-300 ms after the plateau head velocity had been reached for each trial. For display of the data, fast phases were removed from each trace, and an average response was calculated at each point based on the traces without a fast phase at that point. This method avoided any distortion of the data due to interpolation or smoothing at the time of the fast phases.

As noted after unilateral plugging of the three semicircular canals (Lasker et al. 1999), distinctly different responses (requiring different analytic fits) were evident for contra- and ipsilesional steps of acceleration after labyrinthectomy. We analyzed the ipsilesional and contralesional responses separately. To compare these responses with the data obtained from animals with normal vestibular function, we inverted the eye- and head-velocity signals for the averaged response to rotations in each direction and concatenated this signal with the corresponding noninverted trace. Polynomial fits were made for the contralesional responses, and the ipsilesional responses were fit with a hyperbolic tangent function (see Lasker et al. 1999).

An average response to the steps of acceleration was obtained from 10 to 30 trials in each direction. For the contralesional responses, first- through fifth-order polynomial fits then were made to head and eye velocity data extending from 10 to 40 ms after the onset of the stimulus. The order of the polynomial necessary and sufficient to account for the trajectory of the response was specified by the Bayesian information criterion (BIC) (Cullen et al. 1996; Galiana et al. 1995). This analytic method takes into account the decrease in the difference between the fit and the data that will occur simply from the addition of high-order parameters to the model and weighs this decrease against the order of the model (Schwarz 1978). A reduction in BIC value justifies the use of a more complex (higher order) model, whereas an unchanged or increased value of BIC indicates that no additional information is obtained from an increase in the complexity of the model.

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 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 regard 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. Data from two groups were compared with an unpaired t-test. ANOVA was used to compare data from more than two groups.


    RESULTS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

The horizontal VOR evoked by steps of head acceleration and by sinusoidal rotations was examined in four squirrel monkeys after unilateral labyrinthectomy. The labyrinthectomy was performed on the right in two animals (M798 and M1308) and on the left in the other two animals (M243 and C86). The animals were kept in darkness for 4 days after the labyrinthectomy and were tested 8-18 h after the procedure and again on day 3. They then were brought into the light and tested on day 1 after being in the light as well as days 10 and 21 after the labyrinthectomy. Unless otherwise noted, all responses were measured in darkness.

Spontaneous nystagmus

A spontaneous nystagmus with slow phase components directed toward the side of the lesion was noted in each of the animals after labyrinthectomy. When evaluated 8-18 h after the labyrinthectomy (day 1 dark), the velocity of the horizontal spontaneous nystagmus (measured as the average velocity during the slow phases) was 17.3 ± 7.8°/s at the beginning of the testing session and 17.6 ± 8.6°/s (P > 0.90) at the end. The nystagmus at the beginning and end of the testing session at day 3 after labyrinthectomy (day 3 dark) was 16.7 ± 11.0 and 23.2 ± 17.4°/s, respectively (P > 0.64). After animals were returned to light, the amplitude of the spontaneous nystagmus at the beginning of the recording session was decreased substantially. On the first day after return to light (day 1 light), the spontaneous nystagmus at the beginning of the recording session was 2.8 ± 1.5°/s (P < 0.01 with respect to measurements made when animals had been kept in darkness). In contrast, the spontaneous nystagmus at the end of this recording session was 20.3 ± 3.9°/s, significantly larger than that measured at the beginning of the session (P < 0.01) and not different from that recorded before the animal was returned to light (P > 0.80). This difference in the slow-phase velocity of the nystagmus measured at the beginning and end of the recording session also was present at day 10 after the labyrinthectomy (4.7 ± 2.2°/s beginning, 17.2 ± 7.6°/s end, P < 0.02).

In three of the four animals (M798, M1308, and M243) the slow-phase components of the spontaneous nystagmus evaluated 8-18 h after labyrinthectomy showed an increase in eye velocity during the course of each slow-phase component (Fig. 1, A and B). The acceleration of the eye during the slow phase in these three animals measured 294.9 ± 168.1°/s2 when evaluated 8-18 h after labyrinthectomy. Eye velocity did not vary during the course of the slow-phase components in C86. Although there was considerable variability in the trajectory of the slow phases of the spontaneous nystagmus after the first testing session, the trend was for acceleration component of the slow phases to decrease with time. When data from the three animals were pooled across all days after the first testing session, the acceleration of the eye during the spontaneous nystagmus measured 109.9 ± 86.8°/s2 (P < 0.02, with respect to values obtained 8-18 h after labyrinthectomy).



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Fig. 1. Horizontal eye position (A and C) and velocity (B and D) of the spontaneous nystagmus on day 1 after left labyrinthectomy in M243 (A and B) and on day 10 after right labyrinthectomy in M1308 (C and D). To facilitate direct comparison between the eye-movement traces in these 2 animals, we inverted the eye-position and -velocity traces in C and D. Velocity of the slow-phase components of the nystagmus rose during the course of each slow phase in M243 (A and B). In contrast, the slow-phase eye velocity was relatively constant in M1308. For A and B, rightward eye movements are represented by positive values of eye position and velocity, whereas leftward eye movements are negative values. For C and D, leftward eye movements are represented by positive values of eye position and velocity whereas rightward eye movements are negative values.

Steps of acceleration

The gain of the VOR measured during the period of the acceleration and at the velocity plateau of the stimulus was decreased after labyrinthectomy. Responses measured during the period of the acceleration had a lower gain for ipsilesional in comparison to contralesional rotations (Fig. 2).



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Fig. 2. Eye-velocity responses for ispi- and contralesional rotations on day 1 (while the animal was still in darkness) and day 10 after left labyrinthectomy in M243. Superposition of 4 traces for ipsi- and contralesional rotations, respectively, are shown in A and B with corresponding means and SD for 10 trials in C and D. Individual trials at day 10 are shown in E for ipsilesional and F for contralesional rotations with means and SD for 10 trials in G and H. Fast phases were removed from the records during the analysis and only the portion of the response that was not associated with a fast phase was used in the averages. In this and all other figures, head velocity was inverted to facilitate direct comparison with eye velocity. Dashed line, head velocity; solid line, eye velocity. Averages of these responses are represented by the white curve with 1 SD indicated by shading. Rightward eye movements and leftward head movements are represented by positive values on the position and velocity traces.

GA for ipsilesional rotations (GA-ipsi) when measured 3 days after labyrinthectomy, while animals were still being kept in darkness, was 0.39 ± 0.04. GA for contralesional rotations (GA-contra) measured at the same time was 0.67 ± 0.12 (P < 0.02). In contrast, GV measured at the velocity plateau of these same stimuli was symmetric for ipsilesional (GV-ipsi) and contralesional (GV-contra) rotations: 0.38 ± 0.02 and 0.44 ± 0.08, respectively (P > 0.3).

The asymmetry in values of GA became larger when tested 18-24 h after return to light (day 1 light): GA-ipsi = 0.41 ± 0.06 and GA-contra = 0.87 ± 0.08 (P < 0.0001). This asymmetry continued to grow with time after labyrinthectomy due primarily to an increase in GA-contra. On day 10 after labyrinthectomy, GA-contra = 1.04 ± 0.07 and GA-ipsi = 0.44 ± 0.08 (P < 0.001). The values of GA-contra were larger on day 10 than on day 3 after labyrinthectomy (P < 0.01). In contrast, the values of GA-ipsi were unchanged on day 10 in comparison to day 3 after labyrinthectomy (P > 0.4). The asymmetry in GA-contra and GA-ipsi was still present at day 21 after labyrinthectomy: 1.01 ± 0.22 and 0.52 ± 0.03, respectively (P < 0.02). One animal, M243, was tested on day 66 after labyrinthectomy. In this testing session, GA-contra = 0.89 ± 0.20 and GA-ipsi = 0.48 ± 0.08 (P < 0.0001).

The values of GV increased acutely after animals were brought into light but remained relatively constant thereafter. There was no asymmetry in values of GV during any of the testing sessions after labyrinthectomy. When tested 8-18 h after the lesion, while animals were still in darkness, GV-contra = 0.44 ± 0.08 and GV-ipsi = 0.38 ± 0.03 (P > 0.25). On day 1 after animals had been returned to light, GV-contra = 0.53 ± 0.03 and GV-ipsi = 0.52 ± 0.11 (P > 0.85). At day 21, GV-contra = 0.57 ± 0.03, GV-ipsi = 0.59 ± 0.05 (P > 0.6).

There was an increase in values of GV when animals were returned to light after labyrinthectomy. To evaluate changes in GV over time after the lesion, we pooled data for GV-ipsi and GV-contra obtained at the same testing session. GV for day 1 dark and day 1 light was 0.41 ± 0.06 and 0.53 ± 0.07, respectively (P < 0.02). At day 21, GV was 0.58 ± 0.04 (P = 0.17 when compared with day 1 light). Thus most of the recovery in GV occurred within the first day after animals were brought into light. The data for GA and GV at intervals <= 21 days after labyrinthectomy are shown in Fig. 3.



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Fig. 3. Values for acceleration gain of the vestibuloocular reflex (VOR; GA) and velocity gain of the VOR (GV) in the 4 animals at specific times after unilateral labyrinthectomy. Stimulus in each case was an acceleration step of 3,000°/s2 with a duration of 50 ms (peak velocity = 150°/s). GA was measured during the acceleration and GV at the plateau of head velocity as described in METHODS. Earliest point represents data at 8-18 h after labyrinthectomy (while the animals were still in darkness). Next point is for data obtained at 18-24 h after animals were returned to light. Successive points are at days 10 and 21 after labyrinthectomy. In this and all other figures for gain and phase, error bars show 1 SD.

Latency

Figure 4 shows the initial responses evoked by ipsilesional and contralesional rotations at day 10 after labyrinthectomy. Table 1 presents the values of VOR latency calculated from the steps of acceleration at various times after labyrinthectomy in the four animals. There were no differences between the measures at specific times after labyrinthectomy for contralesional (P > 0.5) or for ipsilesional (P > 0.9) rotations. The data for all of the measurement times in the animals were pooled to compare the responses in each direction. The contralesional latency measured 7.7 ± 0.4 ms, and the ipsilesional latency measured 8.4 ± 0.3 ms (P < 0.05).



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Fig. 4. Latency of the VOR as evaluated by 3-SD method. Average of 50 stimulus repetitions for data pooled in the 4 animals at day 10 are presented as mean with shading for ±1 SD for ipsilesional and contralesional rotations. - - -, head velocity. Onset of head movement for each direction is indicated (up-arrow ). Noise in the eye-velocity trace before the stimulus was measured from 30 to 10 ms before the onset of the head movement. Points at which each single trial deviated by >3 SD from this noise were averaged to obtain a measure of the response onset as indicated by × on the ipsilesional and contralesional records.


                              
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Table 1. Latency of the VOR measured from responses to 3,000°/s2 steps of acceleration after canal plugging

Fits to steps of acceleration

CONTRALESIONAL. The gain of the VOR was noted to increase with head velocity after the labyrinthectomy. Responses to contralesional rotations were analyzed with linear and cubic fits as described in METHODS. Table 2 gives the values for the coefficients of the terms for each of these fits. Figure 5 shows a plot of these responses at day 10 in M1308.


                              
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Table 2. Polynomial fits to contralesional responses for steps of acceleration at specific times after labyrinthectomy



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Fig. 5. Contralesional responses displayed as eye vs. head velocity for steps of acceleration (3,000°/s2, peak velocity = 150°/s) on day 10 after unilateral labyrinthectomy in M1308. Linear and cubic fits to the data are shown along with insets depicting the error for each of these fits in relation to the data.

When animals were evaluated 8-18 h after the labyrinthectomy (while still kept in darkness), there was essentially no difference between the parameters determined based on the linear and cubic fit methods. The coefficient calculated by the linear fits was 0.508 ± 0.22. The coefficient for the first-order term calculated by the cubic fits measured 0.481 ± 0.24 (P > 0.9). There was an increase to the contribution of the third-order term to the responses after the animals were brought in the light. The value of the third-order term calculated from the cubic fit increased from (0.447 ± 0.33) × 10-5 when evaluated 8-18 h after the labyrinthectomy (while still in darkness) to (1.40 ± 0.61) × 10-5 when evaluated 24 h after the return to light. A further increase was observed at day 10 after the labyrinthectomy to (2.94 ± 0.11) × 10-5 (P < 0.01). There was no significant difference between days 10 and 21 (P > 0.3). Pooling the values of the third-order term for these 2 days gave a mean value of (2.51 ± 0.98) × 10-5 in comparison with the value of (1.02 ± 1.07) × 10-5 obtained from five animals without a unilateral labyrinthectomy (Minor et al. 1999).

IPSILESIONAL. The responses to ipsilesional, in contrast to contralesional, rotations showed no increase in gain with velocity. In fact, for all of the testing sessions (day 1 in the dark; days 1, 10, and 21 in the light), there was a decrease in the gain with increasing stimulus velocity. To quantify these responses, we fit the ipsilesional data obtained from these 4 days with a hyperbolic tangent optimized to fit the trajectory of the relationship between eye and head velocity (Fig. 6). The coefficients of this equation varied in accord with the day on which the data were obtained (Table 3). These findings indicate that the ipsilesional response becomes more linear with time after labyrinthectomy.



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Fig. 6. Fit to data from ipsilesional rotations in the 4 animals expressed as eye vs head velocity at 8-12 h after labyrinthectomy while animals were still in the dark as well as day 1 and day 10 after return to light.


                              
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Table 3. Fits to ipsilesional responses for steps of acceleration with a hyperbolic tangent function at specific times after labyrinthectomy

Responses to sinusoidal rotations

Figure 7 displays the gain and phase plots of responses to sinusoidal rotations (0.5-15 Hz, ±20°/s) measured while animals were in darkness 8-18 h after unilateral labyrinthectomy, day 1 after the return to light, and days 10 and 21 after the lesion.



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Fig. 7. Gain and phase of responses to sinusoidal rotations at 0.5-15 Hz, ±20°/s measured 8-18 h after labyrinthectomy while animals were still in darkness (dark 1), 18-24 h after return to light (light 1), day 10, and day 21 after labyrinthectomy. - - -, fit of a transfer function with a single pole to the data pooled from days 10 and 21.

A bias velocity was noted in the responses to sinusoidal rotations. It was manifested as a DC shift in the eye-velocity record in the direction of the slow-phase components of the spontaneous nystagmus. There appeared to be an interaction between the bias component and the sinusoidal response for 2-Hz rotations. This interaction was most pronounced during the testing session performed 8-18 h after the labyrinthectomy, while animals were still in darkness (Fig. 8, A and B). Note that the fast phases in the eye-velocity record occur at a fixed location in the stimulus. Removal of these fast phases gave a record that was incomplete and distorted. For this reason, data from responses to the 2-Hz stimulus at 8-18 h after labyrinthectomy were not included in Fig. 7. Although the profile of the response was less distorted after the animals were returned to light, there appeared to be an interaction between the bias velocity and the gain of the response (Fig. 8, C and D). To test this hypothesis, we summed the spontaneous nystagmus (with slow- and fast-phase components) measured on the same day and in the same animal with a sinusoidal waveform (2 Hz, ±20°/s; Fig. 8, E and F). In this summed response, the gain for ipsilesional half cycles was 1.20 ± 0.25, whereas that for contralesional half cycles was 1.29 ± 0.29. Had there been no interaction between the spontaneous nystagmus and the stimulus, a sinusoidal response with a gain of 1.0 would have been expected from the addition of these signals. This was the only frequency where such interactions were noted.



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Fig. 8. Analysis of responses to 2 Hz ±20°/s after labyrinthectomy in M243. Eye and head velocity for several cycles of the stimulus are shown in A, C, and E with average responses in B, D, and F, respectively. In A and B, head and eye velocity are shown for responses on day 1 after left labyrinthectomy. In C and D, head and eye velocity are shown for responses 10 days after the labyrinthectomy. In E and F, spontaneous nystagmus from day 10 was added to the sinusoidal head-velocity stimulus to obtain a measure of the effect of bias velocity on the dynamics of the response. Note that the eye velocity in F is larger than the head velocity. Head velocity is indicated by dashed curve and eye velocity by solid curve in A, C, and E. Head velocity is indicated by dashed curve and eye velocity by white curve with surrounding shading depicting 1-SD for B, D, and F.

The bias velocity for the stimuli used in this study did not vary in relation to the stimulus frequency (P > 0.6), amplitude (P > 0.3) or to the time after labyrinthectomy (P > 0.14). When responses to different stimuli and velocities were pooled, the bias velocity measured 19.4 ± 11.0 (day 1 dark), 14.2 ± 13.7 (day 1 light), 18.0 ± 7.8 (day 10), and 12.8 ± 5.8°/s (day 21). The average bias velocity over these 4 days of testing was 16.1 ± 3.1°/s. The spontaneous nystagmus recorded at the end of the testing sessions on these dates measured 19.4 ± 1.2°/s, which was not different from the bias velocity (P > 0.10). The bias velocity showed changes similar to those observed for the spontaneous nystagmus during the course of the testing sessions after animals were returned to light. It was larger for stimuli delivered near the end in contrast to the beginning of the testing session for day 1 in the light and for days 10 and 21 after labyrinthectomy (P < 0.005).

The gain of the VOR increased over time after the labyrinthectomy. While animals were still in darkness 8-18 h after the lesion, the gain was 0.47 ± 0.03 for frequencies ranging from 4 to 15 Hz. These gains did not change with respect to individual frequency (P > 0.7). The reduction in gain compared with prelesion values was 44 ± 4%. Gain increases were noted after the animals were returned to light. A larger gain was measured at 2 and 4 Hz in comparison with higher frequencies for responses evaluated on days 10 and 21 after labyrinthectomy. We pooled the data from days 10 and 21 to evaluate the effect of frequency of stimulation on gain. The gain values for responses to 2 and 4 Hz rotations were 0.73 ± 0.09 and 0.75 ± 0.06, respectively (P > 0.7). The gain of the response decreased as frequency was increased: 0.67 ± 0.09 at 6 Hz and 0.59 ± 0.05 at 15 Hz (P < 0.05 with respect to gains at 2 and 4 Hz). There was no difference in gain over the range of 6-15 Hz (P > 0.55).

The phase of the VOR when animals were still in darkness showed a lag that increased with frequency to reach -9.3 ± 3.6° at 15 Hz (Fig. 7). This lag at higher frequencies increased after animals were returned to light. At day 21 after the lesion, the phase at 15 Hz measured -20.2 ± 6.0°. There were no differences at any frequency between the phase data at days 10 and 21 (P > 0.4). The data from these 2 days were pooled to develop a comparison with data obtained in darkness. An increase in lag was noted at frequencies of 6-15 Hz when the pooled data from days 10 and 21 were compared with the data obtained in darkness (P < 0.03).

The following first-order transfer function was derived from a least-squares fit to the data pooled for days 10 and 21 
<IT>E</IT><SUB><IT>v</IT></SUB><IT>=</IT><FR><NU>(<IT>0.68</IT>)</NU><DE>(<IT>0.0042</IT><IT>s</IT><IT>+1</IT>)</DE></FR><IT>·</IT><IT>H</IT><SUB><IT>v</IT></SUB> (1)
where Hv and Ev are head and eye velocity, respectively. Figure 7, A and B, shows the responses and fits for the gain and phase data.

Differences in gains for ipsi- and contralesional half-cycles were compared for each frequency and day after the lesion (Fig. 9). The differences reached significance at individual frequencies and testing sessions only for 12 Hz at day 1 after return to light (P < 0.009) and at 15 Hz at day 10 (P < 0.03). The asymmetry, defined as the difference between ipsi- and contralesional gains divided by the sum of these gains, did not change with time after labyrinthectomy at any frequency (P > 0.4). We compared the asymmetry at different frequencies and testing sessions after the data for different days had been pooled. Half-cycle asymmetry measured 0.08 ± 0.02 and did differ with respect to frequency for responses at 2-15 Hz (P > 0.12). In contrast, the half-cycle asymmetry measured 0.01 ± 0.01 at 0.5 Hz, which was lower than that measured over the range of 2-15 Hz (P < 0.03). These findings indicate that, even for the responses to 20°/s rotations, there is a small half-cycle asymmetry at higher frequencies that is not observed at lower ones.



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Fig. 9. Half-cycle gains for responses to sinusoidal rotations at 0.5-15 Hz, ±20°/s measured 8-18 h after labyrinthectomy while animals were still in the dark (A); day 1 (18-24 h) after return to light (B); day 10 (C), and day 21 (D) after labyrinthectomy.

Half-cycle asymmetries were dependent on stimulus frequency and velocity (Fig. 10). These comparisons were made on data pooled from days 10 and 21. Larger half-cycle asymmetries were noted for responses to higher frequency and velocity stimuli. At 4 Hz, ±100°/s, contralesional gain was 0.69 ± 0.14 and ipsilesional gain was 0.53 ± 0.06 (P < 0.05). This half-cycle asymmetry was not significant at 4 Hz, ±20°/s. At this lower stimulus velocity, the gain of the contra- and ipsilesional half-cycles was 0.74 ± 0.07 and 0.69 ± 0.05 (P > 0.55), respectively. A similar pattern was noted for the responses to 10-Hz rotations. At 10 Hz, ±20°/s, contralesional half-cycle gain was 0.58 ± 0.11, whereas ipsilesional half-cycle gain was 0.55 ± 0.07 (P > 0.7). The half-cycle asymmetry rose with increasing stimulus amplitude at 10 Hz. At 10 Hz, ±50°/s, contra- and ipsilesional half-cycle gains were 0.76 ± 0.03 and 0.55 ± 0.07, respectively (P < 0.04).



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Fig. 10. Normalized half-cycle gain of responses to sinusoidal rotations at 0.5-15 Hz; ±20, 50, and 100°/s averaged for data pooled in all 4 animals at days 10 and 21 after labyrinthectomy.

In contrast to these findings at higher frequencies, at 0.5 Hz there was a decline in both contra- and ipsilesional gain as stimulus velocity increased from 20 to 100°/s. At 0.5 Hz, ±20°/s, contralesional gain was 0.59 ± 0.07 and ipsilesional gain was 0.59 ± 0.10 (P > 0.9). At 0.5 Hz, ±100°/s, contralesional gain was 0.44 ± 0.02 and ipsilesional gain was 0.46 ± 0.04 (P > 0.3). The data for contra- and ipsilesional half-cycle gains for 20 and for 100°/s were pooled. Contralesional and ipsilesional gains were lower at 100°/s than at 20°/s (P < 0.001).


    DISCUSSION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Asymmetries after unilateral labyrinthectomy

There are many similarities in the changes we observed after unilateral labyrinthectomy and those that we have reported after unilateral canal plugging (Lasker et al. 1999). The asymmetry in values of GA for ipsilesional in comparison with contralesional steps of acceleration is similar, as is the slightly longer latency for ipsilesional responses. There was no asymmetry in GV measured at the plateau of the stimulus for either lesion. Responses to sinusoidal rotations at 2-15 Hz, ±20°/s showed a comparable reduction in gain, but only a slight asymmetry, after each lesion.

Important differences in the effects of labyrinthectomy and canal plugging on the horizontal VOR also were noted. Spontaneous nystagmus was much greater after labyrinthectomy and resulted in a bias velocity noted in the responses to sinusoidal rotations after this lesion. The bias velocity altered dynamics of the response at 2 Hz after labyrinthectomy. The time course of recovery for responses to steps of acceleration toward the intact side was longer after labyrinthectomy than after canal plugging. The ipsilesional responses had a trajectory that was fit by a hyperbolic tangent function for <= 21 days after the labyrinthectomy whereas this trajectory was only noted after return to light in one of the four animals that underwent unilateral canal plugging (Lasker et al. 1999). Sinusoidal responses to higher velocity rotations also differed for the two lesions. A larger reduction in gain at higher velocities was noted after labyrinthectomy in comparison to canal plugging.

These asymmetries for responses to steps of acceleration are similar to those that have been observed in humans (Aw et al. 1996; Halmagyi et al. 1990) and in guinea pigs (Gilchrist et al. 1998) after ablative vestibular lesions. The mechanism responsible for the asymmetry appears to be fundamentally different from the inhibitory cutoff in responses of vestibular-nerve afferents and/or central VOR interneurons (Ewald's second law) that has been assumed to be the cause of the asymmetries at lower frequencies and higher velocities (Fetter and Zee 1988; Paige 1983b, 1989). For the responses in our study, GA was significantly larger for contralesional than for ipsilesional rotations yet there was no asymmetry in GV measured once the stimulus had reached a plateau of head velocity. If the asymmetry was solely dependent on stimulus velocity, then GV should have been more asymmetric than GA because head velocity was higher at the velocity plateau than during the period of acceleration.

Similar asymmetries for ipsi- and contralesional responses after unilateral labyrinthectomy or plugging of the horizontal canal in cats recently have been reported by Broussard et al. (1999a,b). Their studies utilized steps of acceleration that were lower in amplitude (50-750°/s2 reaching a velocity plateau of 15-50°/s) than those we have used. Ipsi- and contralesional half-cycle gains also were measured for sinusoidal rotations <= 8 Hz with a peak velocity of 10°/s. The asymmetry between contra- and ipsilesional responses to steps of acceleration was larger than that observed at the plateau of head velocity. For responses to sinusoidal rotations, the half-cycle asymmetry (due to a rise in contralesional half-cycle gain) was noted to increase with frequency while stimulus velocity was maintained constant. These findings in the cat provide further support for the notion that a nonlinear component of the reflex dynamics, present for excitation and absent for inhibition, is responsible for the rise in contralesional gain after labyrinthectomy or canal plugging.

Spontaneous nystagmus

A spontaneous nystagmus with slow-phase components directed toward the side of the lesion was noted immediately after labyrinthectomy and persisted throughout the time the animals were followed afterward. The velocity of this nystagmus was somewhat lower than that observed in the rhesus monkey after unilateral labyrinthectomy (44°/s) (Fetter and Zee 1988). In the case of both species, it is clear that a strong process that balances inputs from the two sides centrally must be present from a very early time after the lesion. The following considerations support this concept. Regularly discharging afferents are known to provide the principal inputs to the VOR for stimuli of low to mid frequencies and velocities (Minor and Goldberg 1991). If the spontaneous nystagmus is due mainly to an imbalance in activity from regular afferents between the two sides, then the predicted velocity should be given by EV = FR/RS, in which the average rotational sensitivity (RS) of regular afferents is ~0.3 spikes · s-1/deg · s-1 and the mean firing rate (FR) is ~90 spikes/s (Goldberg and Fernández 1971; Lysakowski et al. 1995). Thus the predicted slow phase eye velocity (EV) would be ~300°/s, considerably greater than that observed in any species after such a lesion.

The trajectory of the slow phases of the nystagmus recorded while animals were still in darkness after the lesion showed a rising velocity profile. There are at least two possible explanations for this finding. First, the static imbalance in vestibular activity brought about by the labyrinthectomy may have resulted in an unstable velocity-to-position integrator (Cannon and Robinson 1987; Kramer et al. 1995). Second, the slow phase trajectories may have been influenced by the dynamics of the inhibitory process that reduces the asymmetry in the resting rates of central vestibular neurons immediately after the lesion.

The spontaneous nystagmus, tested in darkness, after animals were returned to light was greater when measured at the end in comparison to the beginning of each testing session. This effect indicates that the asymmetry in resting rates between central vestibular neurons on the contra- and ipsilateral sides after labyrinthectomy is enhanced after rotational stimulation. Such a finding could occur because rotations cause a reduction in the inhibition that is responsible for minimizing the spontaneous nystagmus after the lesion (McCabe and Ryu 1969; Newlands and Perachio 1990). The increase in spontaneous nystagmus after head rotations is reminiscent of the head-shaking induced nystagmus that has been reported in patients with unilateral vestibular hypofunction (Hain et al. 1987).

Changes in the dynamics of the horizontal VOR after unilateral labyrinthectomy

LATENCY. Our findings after unilateral labyrinthectomy are similar to those reported after unilateral plugging of the three semicircular canals (Lasker et al. 1999). The striking observation is that the VOR latency, which measures 7.3 ± 1.5 ms for animals with intact vestibular function, changes little after unilateral labyrinthectomy. Thus loss of half of the total population of inputs to this push-pull system has little effect on the initiation of the reflex. The VOR latency was slightly longer for ipsi- than for contralesional rotations. This difference could be related to the lower gain of the VOR for rotations toward the lesioned side. The overall similarity in the VOR latency before and after unilateral labyrinthectomy means that the initiation of the reflex is sensitive to inhibitory as well as excitatory modulation. Unlike the VOR gain and phase, the latency did not change with time after the lesion. This finding suggests that vestibular compensation occurs independently from signals conveying the onset of head rotation.

RESPONSES TO STEPS OF ACCELERATION. Many aspects of the responses after unilateral labyrinthectomy were similar to those observed after unilateral canal plugging. The overall decrease in GA and GV immediately after each lesion was ~50%. A similar asymmetry for both lesions in the values of acceleration gain (GA-contra was 30-40% > GA-ipsi) was noted after animals were returned to light. Polynomial fits to the data showed that the gain enhancement of GA-contra after return to light was caused by a nonlinear increase in gain with head velocity. There was no evidence for this nonlinear increase in gain in GA-ipsi after either lesion. GA-ipsi showed a profile of saturation for head velocities >30°/s for day 1 in the dark. This saturation decreased over the course of time after animals were returned to light. There was effectively no asymmetry between values of GV-contra and GV-ipsi at any day tested after either canal plugging or labyrinthectomy.

The most striking difference between unilateral labyrinthectomy and unilateral canal plugging for responses to steps of acceleration was the time course for recovery of gain. The first term for the cubic fit to GA-contra after labyrinthectomy was smaller [(1.40 ± 0.61) × 10-5] in comparison with the value obtained on day 10 [(2.94 ± 0.11) × 10-5]. This is in contrast to the data obtained after canal plugging, which showed no difference between the first day the animals were brought into the light and days 10 and 21. Recovery was also slower for GA-ipsi after the unilateral labyrinthectomy in comparison with canal plugging. This effect was seen in the rate at which the hyperbolic tangent fits to GA-ipsi converged to a straight line. In all of the animals there was still evidence of some saturation occurring at day 21 after the unilateral labyrinthectomy. Only one animal after canal plugging showed any saturation at day 10 or greater. The largest increase in values of GV for contra- and ipsilesional rotations after each lesion occurred when animals initially were brought into light after each lesion. A larger increase in GV with time for both directions of rotation was noted after canal plugging in comparison with after labyrinthectomy. Interestingly, the recovery in gain with time for responses to 0.5 Hz, ±20°/s rotations was relatively the same for both lesions. Differences in the peak velocity of the sinusoidal rotations (20°/s) and steps of acceleration (150°/s) may be responsible for these findings. All of the observed differences between canal plugging and labyrinthectomy can be accounted for based on an increased inhibitory influence, particularly evident in responses to higher velocity stimuli, on the latter in comparison with the former.

RESPONSES TO SINUSOIDAL ROTATIONS. A bias velocity, manifested during the stimulus as a DC shift in the eye-velocity record in the direction of the slow-phase components of the spontaneous nystagmus, was noted in the responses after labyrinthectomy. This bias velocity could vary considerably in amplitude between trials but did not differ from the spontaneous nystagmus measured near the end of each testing session. Unlike the spontaneous nystagmus, bias velocity did not change during the course of a testing session. For rotations at 2 Hz on day 1 in the dark, the bias velocity with associated slow- and fast-phase components appeared to distort the response to the rotation in that there were fast phases of nystagmus that were phase locked to the frequency of the stimulus. There appeared to be an interaction between the gain of responses to 2-Hz rotations and the bias velocity at this frequency when examined on other testing sessions. This interaction increased the apparent overall gain of the response at that frequency and was evident when a comparison was made between responses that were simulated (by the addition of a spontaneous nystagmus with slow- and fast-phase components to a sinusoidal input) and those that were recorded at 2 Hz (see Fig. 8). The factors that may have influenced this interaction include the temporal sequencing of the fast phases relative to the stimulus and the influence of fast phases on the dynamics of slow phases (Galiana 1991).

The gain from rotations at 0.5-15 Hz, ±20°/s before animals were brought in the light after the unilateral labyrinthectomy did not differ across frequencies (Fig. 7). However, once the animals were returned to light, the lower frequencies recovered better than higher frequencies with a gain of 0.78 ± 0.07 occurring at 4 Hz compared with a gain of 0.63 ± 0.06 at 15 Hz. In addition, the phase lag at the higher frequencies increased to a peak of 20.2° at 15 Hz on day 21 after the labyrinthectomy. We derived a transfer function to describe the low-pass filter characteristics of this recovery (Eq. 1). There are two possible explanations for this type of recovery. First, as previously described, the bias velocity appears to contribute to the gain at 2 Hz. Although we do not see evidence of this interaction at other frequencies, it is possible that the gain at 4 Hz is higher than at 15 Hz because of this effect. Second, there is evidence that the lower frequencies (0.5-4 Hz) adapt better than higher frequencies (6-15 Hz) during spectacle-induced adaptation (Minor et al. 1998). This difference likely is related to the error signal, retinal slip, which relies on visual following mechanisms that degrade at frequencies >2-4 Hz (Minor et al. 1999). It seems likely that compensation of the VOR after labyrinthectomy also would rely on these same mechanisms.

There is a small half-cycle gain asymmetry for sinusoidal rotations at 2-15 Hz, ±20°/s (Fig. 9) that is not seen at 0.5 Hz. It is important to recognize that there are more fast phases in the responses at 0.5 Hz in comparison with those at other frequencies. The fast phases could help linearize the reflex, thereby making the response more symmetric (Galiana 1991).

As the peak velocity increases from 20 to 100°/s at 0.5 Hz, the contra- and ipsilesional gains remain symmetric but decrease by ~15%. This symmetric reduction in gain is not seen at higher frequencies. At 4 Hz, ±100°/s, the contralesional gain is not different from that measured at 20°/s, but the ipsilesional gain decreases from 0.69 ± 0.05 to 0.53 ± 0.06. At 10 Hz, the contralesional gain increases from 0.58 ± 0.11 to 0.76 ± 0.03 as the peak velocity rises from 20 to 50°/s. We suggest that inputs from a nonlinear pathway prevent the contralesional gain from decreasing at 4 Hz and increase the gain for contralesional rotations at 10 Hz.

RELATIONSHIP TO STUDIES OF SINGLE-UNIT PHYSIOLOGY. Recordings of single-unit activity in the vestibular nuclei after unilateral labyrinthectomy provide some useful insights into the changes in neuronal activity that may underlie these effects on the VOR. The resting rate of Type I, horizontal canal-related central vestibular neurons decreases from ~40 spikes/s before the lesion to <10 spikes/s immediately afterwards in gerbils (Newlands and Perachio 1990) and in guinea pigs (Ris et al. 1995). There is a reciprocal rise in resting rate of Type I neurons contralateral to the side of the lesion (Ris and Godaux 1998). Resting rates in the ipsilateral and contralateral vestibular nuclei return to control values within 1 wk after the lesion. In contrast, the sensitivity to head velocity of Type I neurons in the ipsi- and contralateral vestibular nuclei decreases after unilateral labyrinthectomy with a gradual, although incomplete, recovery over 1 wk (Ris and Godaux 1998; Ris et al. 1995). These changes parallel the resolution of the spontaneous nystagmus and the gradual recovery in responses mediated by the linear pathway. Sinusoidal rotational stimuli of relatively low frequency and velocity (0.1-1.3 Hz, peak velocity = 20-50°/s) were used in these previous studies. Effects of the nonlinear pathway were not observed---probably because the stimuli were not of sufficient frequency, acceleration, and velocity.

Modeling of asymmetries in the VOR after labyrinthectomy

Figure 11 shows a bilateral model of the VOR that we used to simulate the asymmetries in ipsi- and contralesional responses after labyrinthectomy. This model is similar to the one we described in our previous study of asymmetries after unilateral plugging of the three semicircular canals (Lasker et al. 1999). We propose that inputs to the reflex come from linear and nonlinear pathways. The linear pathway confers the dynamics of the reflex responses to sinusoidal rotations over the frequency range of 0.5-15 Hz at 20°/s peak stimulus velocity. This pathway is also responsible for the linear component of the polynomial fit to the responses for steps of acceleration. The nonlinear pathway confers the frequency- and velocity-dependent increase in gain noted in the sinusoidal responses and manifested in the coefficients for the higher-order polynomial fits.



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Fig. 11. Schematic diagram of the bilateral model used in the simulations. Model has linear and nonlinear pathways each of which receive an angular head velocity signal. Linear pathway has a sensitivity to head velocity, pl, that is 0.4 spikes/s. Time constants in the transfer function representing afferent inputs to the linear pathway are Tc = 5.7 s, Tg = 0.00625 s. There is also a transfer function with 2 poles and 1 zero in the central processing mechanisms for the linear pathway: Tz = 0.19 s, Tp1 = 0.139 s, Tp2 = 0.0044 s. There is a central gain element, kl, that is set to 1.0 but the value of which varies, as described in the simulations, during the process of compensation. A saturation-cutoff block, modeled by the input-output function described in the text, also is included in the linear pathway. Nonlinear pathway has a sensitivity to head velocity, pn1, that is 3.0 spikes/s. Time constants in the transfer function representing afferent inputs to the nonlinear pathway are Tc = 5.7 s, Th = 0.11 s. Central gain elements in the nonlinear pathway are pn2 = 0.33 spikes · s-1/deg · s-1 and kn = 1.0 × 10-5. There is also a cubic dependence of this pathway on head velocity represented by u3. The resting rate of units in both the linear and nonlinear pathways is 90 spikes/s. Units in the nonlinear pathway have an excitatory saturation at 500 spikes/s. Signals from both sides are passed through the neural integrator and 4th-order model of the oculomotor plant (Minor et al. 1999).

The larger asymmetry between ipsi- and contralateral values of GA in comparison with GV can be understood in terms of the contributions of the linear and nonlinear pathways to the responses. The higher values of GA-contra in comparison with GA-ipsi are due to inhibitory cutoff of the nonlinear pathway on the intact side in response to rotations toward the lesioned side. The nonlinear pathway is inherent in the dynamics of the horizontal VOR for responses to high-frequency, high-acceleration rotations (such as during the 3,000°/s2 acceleration). The nonlinear pathway makes up ~20-30% of the response during this step of acceleration. Values of GA-contra are higher than those for GA-ipsi because the nonlinear pathway on the intact side is responding in an excitatory direction for rotations toward the intact side. The nonlinear pathway makes little contribution to the response at the velocity plateau of the stimulus. Values of GV are almost exclusively determined by dynamics of the linear pathway. Responses of the linear pathway from the intact side are relatively symmetric for excitation and inhibition. Thus GV-ipsi and GV-contra show little asymmetry.

There are two main differences in the model of the linear pathway after labyrinthectomy in comparison with that used to describe the data after canal plugging. First, a transfer function was fit (Fig. 11) to the sinusoidal data at 20°/s and placed in the linear pathway to model the changes noted with time and frequency of rotation after animals were returned to light (i.e., frequencies at 2-4 Hz recover better than 6-15 Hz). Second, a least-squares fit analysis was used to fit a sigmoidal function to the data at 0.5 Hz, ±20 and ±100°/s. This function provides a representation of the saturation noted for rotations at higher velocities. This equation was of the following form:
<IT>E</IT><SUB><IT>v</IT></SUB><IT>=</IT><FR><NU><IT>180</IT></NU><DE>(<IT>1+</IT><IT>e</IT><SUP><IT>−0.026</IT>(<IT>H</IT><SUB><IT>v</IT></SUB><IT>+2.34</IT>)</SUP>)</DE></FR> (2)
where Hv is head velocity and Ev is eye velocity.

Because we were concerned mainly in modeling asymmetries that persist after a unilateral vestibular lesion, we used data from >= 10 days after labyrinthectomy to determine the coefficients of this equation. To simulate the effects of the lesion, we removed the inputs from one side and decreased the spontaneous rate of central vestibular neurons on the lesioned side from 90 to 80 spikes/s. This asymmetry in spontaneous rate between the ipsi- and contralesional vestibular nuclei will lead to a spontaneous nystagmus that is close to the value we measured (20°/s). We could account for the increases observed in responses over time after labyrinthectomy by adjusting the central gain elements in the linear and nonlinear pathways (kl and kn).

Because there was no manifestation of the nonlinear pathway for ipsilesional rotations after labyrinthectomy, we propose that this pathway was driven into inhibitory cutoff for velocities of ~30°/s. This cutoff point is predicted based on the sensitivity of units in the nonlinear pathway (pn1 = 3.0 spikes · s-1/deg · s-1). On the basis of this premise of inhibitory cutoff for the nonlinear pathway, the gains for the ipsilesional responses were used to specify kl, the central gain element for the linear pathway. The data support the conclusion that the gain of the linear pathway (kl) is symmetric for rotations in each direction. The gain of the nonlinear pathway (kn) then was calculated from the third-order coefficient of the fits to the contralesional responses.

The gain and phase plot of the simulated responses at day 10 after labyrinthectomy is shown in Fig. 12A. The increase in gain for contralesional responses was accounted for by an increase in kn from 1.0 × 10-5 before to 2.5 × 10-5 after labyrinthectomy. The value of kl was raised from 1.0 before to 1.20 after labyrinthectomy. The increase in kl occurred more gradually and was responsible for the increase in gain at lower frequencies and velocities that occurred with time after the lesion.



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Fig. 12. A: gain from simulation of responses to sinusoidal rotations with bilateral model shown in Fig. 11 after removal of inputs from one side. For the simulation, kl was increased by a factor of 1.2 and kn was increased by a factor of 2.5. B: comparison of the response at 4 Hz, ±100°/s rotations at day 10 after unilateral plugging of the 3 semicircular canals in M51 to the simulation (data and simulation obtained from Lasker et al. 1999). C: comparison of the response at 4 Hz, ±100°/s rotations in M243 at day 10 after unilateral labyrinthectomy to the simulation described in Fig. 11.

Figure 12, B and C, shows a comparison of the data and simulations at 4 Hz, ±100°/s plotted as eye versus head velocity at day 10 after unilateral canal plugging and labyrinthectomy, respectively. After canal plugging, there was an increase of gain with rising head velocity in the contralesional direction that was not as apparent after labyrinthectomy. We propose that, at least at 4 Hz, this rise in gain with stimulus velocity for contralesional half-cycles after canal plugging is effectively canceled by saturation of the linear pathway.

The response of the model to steps of acceleration at 3,000°/s with the same coefficients developed from the sinusoidal data are shown in Fig. 13. Although the contralesional gain (0.78) is higher than the ipsilesional gain (0.45), it is not as high as predicted by the data (0.9-1.0). This finding suggests that the nonlinearity is more sensitive to transient than steady-state motion. There are two possible ways that this behavior could be manifested. First, the saturation that is seen during the sinusoidal rotations might not be as prominent during the responses to steps of acceleration. Second, the steps of acceleration may be more effective for eliciting the nonlinearity than are the sinusoidal rotations.



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Fig. 13. Ipsilesional response and simulation (A) and contralesional response and simulation (B) for steps of acceleration in M243 at day 10 after labyrinthectomy. For the simulation, kl was increased by a factor of 1.2 and kn by a factor of 2.5. Mean (center curve in white) and ±1 SD interval (shaded area) are shown for both ipsilesional and contralesional responses. Head velocity is indicated by heavy dashed curve and simulation by light dashed curve.

Properties of the stimuli or the nonlinearities in the neuronal responses to the stimuli we have used may be responsible for these differences in responses to steps of acceleration and sinusoidal rotations. The frequencies encompassed by the steps of acceleration include 8-12 Hz with peak velocities in the range of 100-150°/s (Minor et al. 1999). These peak velocities are higher than those that our rotation system is capable of delivering at these high frequencies. Vestibular-nerve afferents and/or central vestibular neurons may be more sensitive to steps of acceleration than to sinusoidal rotations. More information is needed about the response dynamics of these neurons to the stimuli that we have shown to be important in eliciting the asymmetries.


    ACKNOWLEDGMENTS

We thank P. D. Cremer for helpful comments on an earlier version of the manuscript.

This work was supported by National Institute on Deafness and Other Communication Disorders Grants R01 DC-02390 and T32 DC-00027, National Aeronautics and Space Administration Cooperative Agreement NCC 9-58 with the National Space Biomedical Research Institute, and the Research Fund of the American Otological Society.


    FOOTNOTES

Address for reprint requests: L. B. Minor, Dept. of Otolaryngology---Head and Neck Surgery, Johns Hopkins University School of Medicine, 601 N. Caroline St., Rm. 6253, Baltimore, MD 21287-0910.

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

Received 18 October 1999; accepted in final form 27 December 1999.


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