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Multiplicative Computation in the Vestibulo-Ocular Reflex (VOR)

¹Departments of Otolaryngology and Communicative Sciences, ²Neurology, and ³Anatomy, University of Mississippi Medical Center, Jackson, Mississippi; and ⁴Department of Neurobiology and Anatomy, University of Texas Health Science Center at Houston, Houston, Texas

Submitted 4 August 2006; accepted in final form 19 January 2007

	ABSTRACT

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION GRANTS NOTE ADDED IN PROOF ACKNOWLEDGMENTS REFERENCES

 
Multiplicative computation is a basic operation that is crucial for neural information processing, but examples of multiplication by neural pathways that perform well-defined sensorimotor transformations are scarce. Here in behaving monkeys, we identified a multiplication of vestibular and eye position signals in the vestibulo-ocular reflex (VOR). Monkeys were trained to maintain fixation on visual targets at different horizontal locations and received brief unilateral acoustic clicks (1 ms, rarefaction, 85110 db NHL) that were delivered into one of their external ear canals. We found that both the click-evoked horizontal eye movement responses and the click-evoked neuronal responses of the abducens neurons exhibited linear dependencies on horizontal conjugate eye position, indicating that the interaction of vestibular and horizontal conjugate eye position was multiplicative. Latency analysis further indicated that the site of the multiplication was within the direct VOR pathways. Based on these results, we propose a novel neural mechanism that implements the VOR gain modulation by fixation distance and gaze eccentricity. In this mechanism, the vestibular signal from a single labyrinth interacts multiplicatively with the position signals of each eye (Principle of Multiplication). These effects, however, interact additively with the other labyrinth (Principle of Addition). Our analysis suggests that the new mechanism can implement the VOR gain modulation by fixation distance and gaze eccentricity within the direct VOR pathways.

	INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION GRANTS NOTE ADDED IN PROOF ACKNOWLEDGMENTS REFERENCES

 
The vestibulo-ocular reflex (VOR) produces short-latency eye movement that compensates for rotational and translational head motion. It has been well documented, however, that the VOR does not generate the same eye movement in response to a given head motion. Rather, the VOR gain is modulated by behavioral contexts. One example of this is that the VOR gain depends on the distance a target is from the eyes. Previous behavioral and single unit recording studies suggest that the VOR gain modulation by fixation distance is implemented by a multiplicative interaction of the vestibular signal and the vergence eye position signal (i.e., the difference between the left and right eye positions) (Angelaki 2004; Chen-Huang and McCrea 1998, 1999a,b; Crane and Demer 1998; Crane et al. 2003; Hine and Thorn 1987; King et al. 2003; Lasker et al. 2002; Meng and Angelaki 2006; Meng et al. 2005; Paige and Tomko 1991; Ramat and Zee 2003; Schwarz et al. 1989; Snyder and King 1992; Viirre et al. 1986; Zhou et al. 2003). However, where and how the multiplication is implemented remains unknown.

To identify the neural substrates that mediate the VOR gain modulation by fixation distance, several studies used sinusoidal rotational and/or translational head motion to examine the effects of vergence on the vestibular-evoked responses in the VOR interneurons [burst-tonic (BT) neurons; eye-head (EH) neurons, and position-pause-vestibular (PVP) neurons] in the vestibular nuclei (Chen-Huang and McCrea 1998, 1999a,b; King et al. 2003; McConville et al. 1996; Meng and Angelaki 2006; Meng et al. 2005). These studies found that all of these VOR interneurons modulated their vestibular-evoked responses as a function of fixation distance. Given the extensive interconnections between the VOR premotor neurons, however, the analysis of steady-state responses cannot address whether the VOR interneurons are the sites that perform the fixation-distance related computation or the sites that transmit the outputs of the computation performed elsewhere, such as a bilateral network (Angelaki 2004; Green and Angelaki 2004) or the flocculus/ventral paraflocculus (Lisberger and Pavelko 1988; Lisberger et al. 1994; Partsalis et al. 1995a,b; Zhang et al. 1995a,b). To elucidate the neural substrates that perform the fixation-distance related multiplicative computation, we used unilateral short-duration acoustic clicks to evoke impulse responses in the abducens neurons while monkeys were trained to fixate on visual targets at different horizontal locations. We found that the interaction of vestibular and eye position signals was multiplicative in the abducens neurons. Based on the latency of the eye position effect, we further determined that the multiplication was implemented within the direct VOR pathways. Based on these results, we propose a novel neural mechanism that modulates the VOR gain with fixation distance within the direct VOR pathways.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION GRANTS NOTE ADDED IN PROOF ACKNOWLEDGMENTS REFERENCES

 
Four male rhesus monkeys were used in the experiments. The surgical and experimental procedures had been approved by the University of Mississippi Medical Center's Institutional Animal Care and Use Committee.

Eye movement recording, acoustic stimulation and behavioral paradigms

The procedures for the surgery and the initial behavioral training were the same as those described previously (Zhou and King 1998; Zhou et al. 2003, 2004). Under general anesthesia and using sterile procedures, a search coil was implanted in each eye to monitor binocular eye position signals. In this study, acoustic clicks were used as a vestibular stimulus. Acoustic activation of the vestibular system has been well documented in humans and animals (Colebatch et al. 1994; in humans; Young et al. 1977; in squirrel monkeys; McCue and Guinan 1994; in cats; Murofushi et al. 1995; in guinea pig; Zhou et al. 2004 2005, in behaving monkeys; Carey et al. 2004; in chinchillas) and their potential value in the diagnosis of vestibular disorders has been widely recognized (for review, see Halmagyi et al. 2005). Acoustic clicks (1 ms, rarefaction, 85110 db NHL) generated by a MA3 microphone amplifier (Tucker-Davis Technologies, Alachua, FL) were triggered by our behavioral control program. Unilateral acoustic clicks were delivered to a monkey's external ear canal through an insert earphone (ER-3A), which reduced the bone conductance–induced stimulation of the contralateral labyrinth by >75 db. Because the highest intensity used in our study was 110 db, the stimulation of the contralateral labyrinth (<35 db) was lower than the threshold of 80 db at which clicks can evoke any observable behavioral and neuronal responses. Thus acoustic clicks offered the advantage of unilateral vestibular stimulation, which allowed us to study the eye position influences on the vestibular inputs from a single labyrinth (Carey et al. 2004).

During these experiments, the monkey was comfortably seated in a custom-designed chair, with its head upright and stabilized with respect to the electromagnetic field of the eye coil system by attaching a stainless steel rod to the monkey's head holder. Each eye coil was calibrated at the start of each experimental day by requiring the monkey to fixate on horizontal or vertical target positions (±20°, every 5°). Monkeys were trained to fixate on visual targets for apple juice rewards. Visual targets were projected by lasers onto a far screen located 275 cm from monkeys’ eyes. Acoustic clicks were delivered in individual trials that lasted 2–4 s. Each trial started with the appearance of a visual target of randomly chosen ocular eccentricity (–20, –10, 0, 10, 20°). The monkey was trained to fixate on the target with both eyes, i.e., maintaining eye position within a small window (1–4° in size) centered on the target's position. After a successful fixation interval varying from 300 to 900 ms, six clicks, 400 ms apart, were delivered to one of the monkey's ears. The monkey was trained to maintain fixation through the trial. At the end of each successful trial, the monkey was rewarded with two drops of juice. To study the effect of eccentricity on the click-evoked neuronal responses, trials with different eccentricities were combined randomly and delivered in one single block. Each condition consisted of 300 stimulations.

Single unit recording

Standard procedures were used to record single unit activity (for more details, see Zhou and King 1998; Zhou et al. 2001). Briefly, a stainless steel cylinder was implanted stereotaxically and a tungsten microelectrode was advanced through a 21-gauge guide cannula by a motorized microdrive. The abducens nucleus was identified by the characteristic tonal quality of the background activity as heard on the audio monitor (Fuchs et al. 1988; Robinson 1970). We included in our sample only neurons that were recorded concurrently with the characteristic background activity of the abducens nucleus. For each abducens neuron, we first recorded the neuron's responses during pursuit of a sinusoidal target motion at 0.3 Hz and ±10° and fixation of the target in 5° steps from –20 to 20°. We recorded the abducens neuron's responses to acoustic clicks (1 ms, rarefaction, 110 db NHL) delivered to each ear.

Data acquisition and data analysis

A PC running specialized software controlled the experiments, and a CED Power 1401 system (Cambridge Electronics Devices, Cambridge, UK) was used for data acquisition. Single unit responses were amplified and filtered (100–10,000 Hz) and a two-stage, time-amplitude window discriminator was used to discriminate single spikes (Bak Electronics, Mount Airy, MD). Signals of binocular horizontal and vertical eye position, target position, and the acceptance pulse for action potential (0.01-ms temporal resolution) were sampled at 2 kHz with 16-bit resolution and stored with the amplified extracellular voltage trace (sampled at 20 kHz) on a hard disk for off-line analyses.

Eye movement responses were analyzed using Spike2 (Cambridge Electronics Devices). Raw eye position data were filtered and differentiated with a band-pass of DC to 100 Hz to obtain eye velocity data. Trials in which monkeys made a saccade within 50 ms of the onset of the sound stimuli were rejected (approximately one-third trials rejected). Trials in the data stream were sorted, aligned on the onset of the sound stimulation, and averaged (200 trials per condition) to obtain low-noise estimates of eye velocity as a function of time.

Single unit responses to acoustic clicks were analyzed using Spike2 and SigmaPlot. The amplitude of the click-evoked response was measured as the peak firing rate in the binned histogram with a bin size of 0.5 ms. We measured a neuron's responses at three or four horizontal eccentricities and computed the slope and the intercept of the firing rate-eye position regression line in control (i.e., without clicks) and stimulation (i.e., with clicks) conditions (K_evoked, K_control, INTERCEPT_evoked, and INTERCEPT_control). To quantitatively assess the interaction of vestibular and eye position signals, we computed a multiplication index that was defined as the ratio of the slopes in stimulation and control conditions, i.e., K_evoked/K_control. A multiplication index different from 1 indicates a multiplicative interaction of the two signals. We also computed an addition index that was defined as the ratio of the intercepts in stimulation and control conditions, i.e., INTERCEPT_evoked/INTERCEPT_control. An addition index different from 1 indicates an additive interaction of the two signals. The interactions of vestibular and eye position signals were assessed for individual neurons and the population.

To assess the effect of eye position on click-evoked behavioral responses, we computed a scaling factor for an eye position E, which was defined as the percentage changes of click-evoked eye movement at the eye position E (A_E) with respect to that at the center gaze (A₀), i.e., (A_E – A₀)/A₀. Because A_E = A₀ + K x E, the scaling factor is K x E/A₀. Compared with the multiplicative index, the scaling factor is a better way to measure the amplitude of eye position effect on click-evoked responses because it takes the magnitude of the response at the center gaze into consideration. However, because the multiplicative index is the ratio of eye position sensitivities (K) in control and stimulation conditions, it is good to evaluate the nature of the interaction of vestibular and eye position signal in an abducens neuron. Thus in this study, we used the multiplicative index to assess the click-evoked neuronal responses in abducens neurons and used the scaling factor to assess the effect of eye position on click-evoked eye movements.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION GRANTS NOTE ADDED IN PROOF ACKNOWLEDGMENTS REFERENCES

 
Effects of eye position on vestibular-evoked responses in the abducens neurons

Figure 1, A and B, shows an example of the eye movement responses and an abducens neuron's responses to acoustic clicks. Figure 1A shows the responses while the monkey was at the center gaze, and Fig. 1B shows the responses while the monkey fixated 20° right from the center. In this example, acoustic clicks were delivered to the left ear canal. They evoked contralateral eye movements (Fig. 1, A and B, top 2 traces) and increased the firing rates of the abducens neuron on the contralateral side (Fig. 1, A and B, middle and bottom traces). Note that the calibration bar is 1,000 spikes/s for histograms and 12°/s for eye velocity traces. The amplitudes of the click-evoked eye movements depended on eye position. In this example, the click-evoked eye movements had a peak eye velocity of 5.2 ± 0.3°/s at 20° to the right (Fig. 1B). This was more than twice of that at the center gaze (2.4 ± 0.2°/s; Fig. 1A). The amplitudes of the click-evoked neuronal responses also depended on eye position. In this example, the click-evoked response of the abducens neuron was 1,000 spikes/s at 20° to the right (Fig. 1B). Again, this was more than twice of that at the center gaze (440 spikes/s; Fig. 1A).

View larger version (23K): [in this window] [in a new window]   FIG. 1. Click-evoked responses of an abducens neuron. A and B: click-evoked horizontal eye movements (top traces, black trace for eye ipsilateral to stimulated ear and gray trace for eye contralateral to stimulated ear) and click-evoked neuronal responses (middle rasters and lower histograms with a bin size of 0.5 ms) at the center gaze and 20° to the right, respectively. Calibration bar is 1,000 spikes/s for histograms and 12°/s for eye velocity traces. C: firing rates of abducens neuron are plotted as functions of eye position for control (dotted regression line) and stimulation (solid regression line) conditions. D: average firing rates of population of abducens neurons are plotted as functions of eye position for control (dotted regression line) and stimulation conditions (solid regression line). SE bars are within symbols.

In Fig. 2A, we plotted abducens neurons’ slopes to eye position in the stimulation condition (K_evoked) against that in the control condition (K_control). The correlation between the two slopes were weak (Fig. 2A; R² = 0.02), indicating that abducens neurons’ slopes to eye position at the stimulation condition cannot be accounted for by their slopes in the control condition. Figure 2B shows the distribution of the multiplication indexes for the population of abducens neurons when the contralateral ear was stimulated. On average, the population had a multiplication index larger than 1 (4.49 ± 0.4, P < 0.001) and an addition index close to 1 (1.03 ± 0.05, P > 0.1), indicating a pure multiplicative interaction of vestibular and eye position signals in the VOR pathways.

View larger version (21K): [in this window] [in a new window]   FIG. 2. Distributions of multiplication and addition indexes of abducens neurons. A: scatter plot of abducens neurons’ eye position slopes in stimulation condition (Kevoked) vs. that in control condition (Kcontrol). Each symbol is 1 neuron. Gray line is unitary line. B: distribution of multiplication indexes of population (n = 124). C: scatter plot of abducens neurons’ eye position intercepts in stimulation condition (INTERCEPTevoked) vs. that in control condition (INTERCEPTcontrol). Each symbol is 1 neuron. Gray line is unitary line. D: distribution of addition indexes of the same population.

Latency of the click-evoked peak responses in the abducens neurons

As shown in Fig. 1, the click-evoked peak responses of the abducens neurons exhibited linear dependencies on eye position. Thus the latencies of the peak responses were used to locate the sites of the multiplicative computation. Figure 3 shows the summary response of the population at the center gaze (Fig. 3A) and the distribution of the peak response latencies (Fig. 3B). We found that 87% of the abducens neurons exhibited their peak responses at the latency of 2.8 ms (Fig. 3B). The mean latency of the population was 2.78 ± 0.3 ms. Because the latency of the vestibular afferents to click stimulation was 0.82 ± 0.22 ms (Murofushi and Curthoys 1997), we estimated that the latency from the vestibular afferents to the abducens neurons was 1.96 ms, i.e., di-synaptic, suggesting that the multiplicative computation takes place within the direct VOR pathways.

View larger version (14K): [in this window] [in a new window]   FIG. 3. Latencies of abducens neurons’ peak responses to click stimulation of the contralateral ear. A: composite histogram showing summed responses of population. B: distribution of latencies of peak responses shows that 87% of abducens neurons were activated by contralateral clicks at a latency of 2.8 ms.

To examine whether there is a scaling effect of eye position signal on the vestibular-evoked eye movements, we measured the click-evoked eye movements at five horizontal eccentricities (–20, –10, 0, 10, 20) using clicks of six intensities (80–105 db NHL). Figure 4A compares the stimulus-response curves at different eccentricities. In Fig. 4B, for each eccentricity, the click-evoked peak eye velocities were compared with that at the center gaze for all click intensities. Figure 4B shows that the data points from the same eccentricity fall on a single straight line, indicating a scaling effect of eye position on the click-evoked VOR responses. The scaling factor for an eye position was measured by the slope of the corresponding regression line in Fig. 4B, which was dependent on horizontal eccentricity but was independent of click intensity. Compared with the center gaze, the click-evoked VOR responses increased at eye positions that were more contralateral to the stimulated ear and decreased at eye positions that were more ipsilateral to the stimulated ear. Figure 4C summarizes the eye position-dependent scaling factors of the four monkeys. Within 20° from the center gaze, scaling factors exhibited approximately linear dependencies on eye position (ipsilateral eye: 2.05 ± 0.13%/°; contralateral eye: 1.65 ± 0.47%/°). While only peak responses are plotted in Fig. 4, regression analysis was performed on the whole response profile including rising, peaking, and falling phases, revealing that the same scaling effect of eye position signal were present through the frequency spectrum of the vestibular-evoked VOR responses. Because natural head movements reciprocally activate the two labyrinths with much lower frequency contents than the clicks, the interaction of vestibular and eye position signals during natural head movements may exhibit different characteristics and will be determined in future studies.

View larger version (21K): [in this window] [in a new window]   FIG. 4. Amplitudes of click-evoked eye movements are modulated by gaze eccentricity in a multiplicative fashion. A: click-evoked eye movements in eye ipsilateral to stimulated ear as a function of click intensity. Each line was obtained at 1 eccentricity as indicated by different symbols. B: click-evoked eye movements at several gaze eccentricities are plotted against that at center gaze, revealing a scaling effect of eye position signal on click-evoked vestibulo-ocular reflex (VOR) responses. C: scaling factors for eye ipsilateral (solid lines) and contralateral (dotted lines) to stimulated ear are plotted as functions of gaze eccentricity for 4 monkeys as indicated by different symbols.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION GRANTS NOTE ADDED IN PROOF ACKNOWLEDGMENTS REFERENCES

Interaction of vestibular and eye position signals in putative abducens motoneurons and internuclear neurons

In this study, we examined the interaction of vestibular and horizontal conjugate eye position signals in the abducens nucleus. It has been well established that the abducens nucleus has both motoneurons that innervate the ipsilateral rectus muscle and internuclear neurons that project to the contralateral medial rectus motoneurons and the flocculus of the cerebellum (Langer et al. 1985; Steiger and Buttner-Ennever 1978). Our population of abducens neurons was likely comprised of both motoneurons and internuclear neurons. We did not directly identify whether abducens neurons were motoneurons or internuclear neurons. However, we tried to identify indirectly whether abducens neurons were putative motoneurons or internuclear neurons using the criteria of Fuchs et al. (1988). In the earlier study, Fuchs et al. (1988) showed that the firing rates of both motoneurons and internuclear neurons were linearly associated with eye position and eye velocity. The firing rates associated with eye position can be described by the eye position sensitivity (K) and the eye position threshold (T). The firing rates associated with eye velocity can be described by the eye velocity sensitivity (R). Fuchs et al. (1988) showed that R increased with T for motoneurons but not for internuclear neurons. Based on this criteria, Broussard et al. (1995) categorized abducens neurons into putative motoneurons and internuclear neurons. We adopted the same approach in this study. For each abducens neuron, we computed its K, R, and T using the same methods of Fuchs et al. (1988). In Fig. 5B, R is plotted as a function of T, and the solid line is the regression line for identified motoneurons obtained by Fuchs et al. (1988) (R = 0.02 x T + 1.23). The dashed line in Fig. 5B divides motoneurons from internuclear neurons in the sample of Fuchs et al. (1988) (R = 0.044 x T + 2.2). Using the approach of Broussard et al. (1995), we identified abducens neurons that are plotted to the left and right of the dashed line in Fig. 5B as putative internuclear neurons and motoneurons, respectively. The two populations exhibited similar characteristics as that described in Fuchs et al. (1988). The addition index and the latency to click are found to be similar between the two groups (P > 0.5). However, the putative internuclear neurons had larger multiplication index than the putative motoneurons (motoneuron: 6.92 ± 1.9, n = 11; internuclear neuron: 4.11 ± 0.5, n = 54; P < 0.05). This analysis indicates that the interaction of vestibular and eye position signals may be different in the two groups of abducens neurons. Nevertheless, because there is overlap between the two populations that cannot be separated using a single straight line, we suggest that more information should be obtained by analyzing identified motoneurons. This will be examined in future studies by directly recording from the abducens nerve fibers (motoneurons of the lateral rectus muscle) and the oculomotor nerve fibers (motoneurons of the medial rectus muscle).

View larger version (18K): [in this window] [in a new window]   FIG. 5. Identification of abducens neurons into putative motoneurons and putative internuclear neurons using the criteria of Fuchs et al. (1988) and Broussard et al. (1995). Sensitivities to eye position (K) and velocity (R) are plotted as functions of eye position threshold (T) in A and B, respectively. Solid line (R = 0.02 x T + 1.23) and dashed line (R = 0.044 x T + 2.2) in B are adopted from Broussard et al. (1995) to separate the abducens neurons into putative motoneurons () and putative internuclear neurons ().

To account for the VOR gain modulation by viewing distance, the current theory suggests that the vestibular signal interacts multiplicatively with the vergence eye position signal (Angelaki 2004; Chen-Huang and McCrea 1999a,b; Crane and Demer 1998; Crane et al. 2003; King et al. 2003; Lasker et al. 2002; Meng and Angelaki 2006; Meng et al. 2005; Paige and Tomko 1991; Ramat and Zee 2003; Schwarz et al. 1989; Snyder and King 1992; Viirre et al. 1986; Zhou et al. 2003). According to this theory, the vestibular-evoked responses should not be modulated by horizontal eye position signal in our paradigm because there was no change in vergence angle. To our surprise, however, we found that the vestibular-evoked responses were linearly related to eye position signal even in the absence of any change in vergence angle. These results indicate that multiplication is not limited to the interaction of the vestibular signal and the vergence eye position signal. It is also present in the interaction of the vestibular signal and the conjugate eye position signal. Thus we suggest that it is the position signals of the two eyes that modulate the VOR gain of each eye. These results are consistent with the hypothesis that the brain stem vestibular/oculomotor circuits encode monocular eye position signals (i.e., using a left/right eye coordinate frame) (King et al. 1994; McConville et al. 1994; Sylvestre and Cullen 2002; Sylvestre et al. 2003; Zhou and King 1998).

The multiplication of vestibular and eye position signals may take place in the VOR interneurons in the vestibular nuclei, in the motoneurons in the abducens nuclei, or in both sites because these neurons receive separate vestibular signals (from vestibular afferents) and eye position signals (from neural integrators). Figure 6 shows a hypothetical convergence of vestibular and eye position signals in a VOR motoneuron or interneuron. Vestibular synapses are labeled as "contralateral (+)" or "ipsilateral (–)" to reflect that the VOR neuron receives monosynaptic (VOR interneurons: BT, EH, and PVP) or di-synaptic (VOR motoneurons) vestibular signals from the two labyrinths in a reciprocal fashion (Chubb et al. 1984; Fuchs and Kimm 1975; Keller and Daniels 1975; Keller and Kamath 1975; King et al. 1976; McFarland and Fuchs 1992; Miles 1974; Scudder and Fuchs 1992; Tomlinson and Robinson 1984). Eye position synapses are labeled as "left eye" or "right eye" to reflect that the VOR circuits encode monocular eye position signals (King et al. 1994; McConville et al. 1994; Sylvestre and Cullen 2002; Sylvestre et al. 2003; Zhou and King 1998). During fixation before click stimulation, the VOR neuron fires at a rate determined by eye position signals. After click stimulation, the click-evoked vestibular signals are first transmitted to the VOR interneurons (monosynaptic) and to the VOR motoneurons (di-synaptic).

View larger version (15K): [in this window] [in a new window]   FIG. 6. Hypothetical convergence of contralateral (excitatory, +) and ipsilateral (inhibitory, –) vestibular signals and the left and right eye position signals in a VOR neuron.

Novel neural mechanism that implements the VOR gain modulation by fixation distance

The dependence of the translational VOR (TVOR) on target distance and gaze eccentricity has been well documented (Angelaki 2004; Crane and Demer 1998; Crane et al. 2003; Paige and Tomko 1991; Ramat and Zee 2003; Schwarz et al. 1989; Snyder and King 1992; Zhou and King 2003). It is generally accepted that central signals proportional to fixation distance and eccentricity must exist to modulate otolith signals. The dependence of the angular VOR (AVOR) on target distance has been reported, but there has been controversy on whether semicircular canal signals are also modulated by fixation distance. Earlier studies (Snyder and King 1992; Viirre et al. 1986) documented the vergence effect on the gain of the AVOR, but the effect was attributed to the interaction of canal and otolith signals. These authors suggested that the canal-ocular reflex was not modulated by viewing-distance. Using head rotations with much higher frequency and acceleration, later studies (Chen-Huang and McCrea 1998, 1999a,b; Crane et al. 2003; Paige et al. 1998), however, found that the canal-mediated ocular reflexes were modulated by viewing distance. It is now believed that both canal and otolith signals are modulated by central signals proportional to fixation distance and eccentricity. Furthermore, the viewing distance effect was observed at the onset of both the TVOR and the AVOR, indicating that the VOR gain modulations are implemented not only by the indirect VOR pathways through the flocculus, but also by the direct VOR pathways in the brain stem (Angelaki 2004; Crane and Demer 1998; Crane et al. 2003; Lasker et al. 2002; Meng and Angelaki 2006; Meng et al. 2005; Paige and Tomko 1991; Ramat and Zee 2003; Schwarz et al. 1989; Snyder and King 1992; Zhou et al. 2003).

This study extends previous findings and further shows a multiplicative interaction of vestibular and horizontal conjugate eye position signals in the abducens neurons with di-synaptic latency. Based on these results, we propose a novel neural mechanism that implements the VOR gain modulation by fixation distance and gaze eccentricity. The new mechanism consists of two principles that are derived from experimental data. The first principle is the Principle of Multiplication, which states that the effects of stimulating a single labyrinth interact multiplicatively with the position signals of each eye. The second principle is the Principle of Addition, which states that the effects of stimulating the two labyrinths interact additively. In the next section, we will show that the VOR gain modulation by fixation distance and gaze eccentricity can be implemented based on the two principles (Fig. 7).

View larger version (23K): [in this window] [in a new window]   FIG. 7. Schematic illustration of proposed mechanism that implements VOR gain modulation by fixation distance and eccentricity based on Principles of Multiplication and Addition. A: unilateral vestibular stimulation. Top: schematic illustration of multiplicative interaction of vestibular and eye position signals, i.e., GLabyrinthL = GcLeye + KLeye x ELeye + GcReye + KReye x EReye. Bottom: eye movement evoked by activating left labyrinth is rightward (contralateral). Contributions to VOR gain by left (ipsilateral eye) and right eyes (contralateral eye) are represented by blue and red lines, respectively. Sum of left and right eye lines represents VOR gain as a function of eye position for a far target (black solid line) and a near target (black dotted line). Vergence angle of 10° shifts the left eye line leftward (blue dashed line) and further shifts sum of left and right lines upward (black dotted line), indicating a vergence enhancement effect. B: bilateral vestibular stimulation. Top: schematic illustration of additive interaction of 2 unilateral VOR pathways, i.e., GLabyrinthB = GLabyrinthL + GLabyrinthR. Bottom: leftward head rotation or translation results in differential activation of 2 labyrinths. Excitation of left labyrinth results in a rightward eye movement that is linearly related to eye position (blue solid line, L+). Inhibition of right labyrinth also results in a rightward eye movement that is linearly related to eye position (red solid line, R–). Summed effects of 2 labyrinths are independent of eye position (black solid line, L+ + R–). Forward nasal-occipital translation activates 2 labyrinths in the same way, but generated eye movements are in opposite directions (blue solid line, L+ and red dotted line, R+). Summed effects of 2 labyrinths are modulated by gaze eccentricity (dotted black line, L+ + R+).

(1.1)

where G_LabyrinthL is the VOR gain of the right eye when the left labyrinth is stimulated, G_cLeye and G_cReye are the VOR gains when the left and right eyes are at the center gaze, respectively, E_Leye and E_Reye are the left and right eye positions, respectively, and K_Leye and K_Reye are the sensitivities of the VOR gain to the left and right eye positions, respectively. In the bottom panel of Fig. 7A, the relationships of the VOR gain with the position signal of the right eye are represented by a straight line with a slope and an intercept that are corresponding to the K and G_c of that eye (e.g., K_Reye and G_cReye), respectively. When a subject fixates on a far target, the positions of the two eyes are equal (E_Leye = E_Reye). When the subject fixates on a near target that requires a 10° vergence angle, the left eye needs to rotate 10° more to the right than the right eye (E_Leye = E_Reye + 10). The right eye at the center gaze is now accompanied by the left eye at the right 10°, i.e., the left eye line is shifted leftward by 10° and Eq. 1.1 becomes the following equation

(1.2)

Equation 1.2 indicates that, compared with a far target, the VOR gain-eye position line for a near target has the same slope but a larger intercept (G_cLeye + G_cReye + K_Leye x 10), i.e., an upward shift of the black dotted line in the bottom panel of Fig. 7A. The new mechanism indicates that the VOR gain modulation by fixation distance can take place when only a single labyrinth is activated. This prediction is supported by data obtained in subjects with unilateral labyrinthectomy (Angelaki et al. 2000; Aw et al. 2003). However, there will be a potential problem if the Principle of Multiplication works alone. As indicated by the black lines in the bottom panel of Fig. 7A, the AVOR gain is dependent on gaze eccentricity, which is not appropriate because the AVOR gain should be independent of gaze eccentricity. We propose that the proper relationship of the VOR gain and gaze eccentricity can be achieved when the Principles of Multiplication and Addition work together.

Figure 7B shows how the VOR gain modulation by fixation distance and gaze eccentricity can be implemented by appropriate activations of the two labyrinths. The top panel of Fig. 7B schematically shows the Principle of Addition, i.e., the effects of the vestibular signals from the two labyrinths are linearly summed to drive the movements of one eye. According to the Principle of Addition, the VOR gain of one eye (e.g., the right eye) of a bilateral stimulation is the linear summation of the VOR gains of the two unilateral vestibular stimulations, which both are linearly dependent on eye position signals. These relationships can be described by the following equations

(2.1)

(2.1a)

(2.1b)

where G_LabyrinthB is the VOR gain of the bilateral stimulation, G_LabyrinthL and G_LabyrinthR are the VOR gains of the left or the right labyrinth stimulation, respectively, G_cLabyrinthL and G_cLabyrinthR are the VOR gains of the left and right labyrinth stimulation, respectively, at the center gaze, and K_LabyrinthL and K_LabyrinthR are the sensitivities of the VOR gain to eye position when the left or the right labyrinth is stimulated, respectively. During a leftward head rotation or a leftward interaural head translation, the left labyrinth is excited (Fig. 7B, bottom, blue line labeled L+) and the right labyrinth is inhibited (Fig. 7B, bottom, red line labeled R–). When the two labyrinths are reciprocally stimulated, eye movements generated by the two labyrinths are in the same direction, but the slopes of the VOR gains to eye position have opposite signs (K_LabyrinthL = –K_LabyrinthR). Thus Eq. 2.1 is simplified as

(2.2)

The solid black line in the bottom panel of Fig. 7B has slope 0, indicating that the VOR gain during the reciprocal activation of the two labyrinths is independent of eye position, as required by the geometrical constraints.

The new model can also account for the VOR gain modulation by gaze eccentricity during a nasal-occipital translation, which similarly activates the two labyrinths (Fig. 7B, bottom, solid blue line, L⁺ and dotted red line, R⁺). In this situation, eye movements generated by the two labyrinths are in opposite directions, and the lines of the TVOR gain to eye position signal have the same slope but opposite intercepts (K_LabyrinthL = K_LabyrinthR; G_cLabyrinthL = –G_cLabyrinthR). Thus Eq. 2.1 is simplified as

(2.3)

The dotted black line (L⁺ + R⁺) in the bottom panel of Fig. 7B shows that the nasal-occipital TVOR gain is proportionally dependent on gaze eccentricity as required by the geometric constraints (McHenry and Angelaki 2000; Paige and Tomko 1991). For example, as the head moves forward, the eyes must rotate rightward at a right gaze, leftward at a left gaze, and remain stationary at the center gaze.

For abducens motoneurons, this gaze eccentricity effect on the nasal-occipital translation VOR indicates that the neuronal responses caused by otolith activation should increase for a more lateral gaze. Because clicks activate the ipsilateral otolith-abducens pathways, the ipsilateral click-evoked abducens neurons’ responses should increase for either a more contralateral gaze or a more ipsilateral gaze. When the ipsilateral click-evoked responses increase for a more contralateral gaze, abducens neurons exhibit positive multiplicative indexes. When click-evoked responses increase for a more ipsilateral gaze, abducens neurons exhibit negative multiplicative indexes. Thus some abducens neurons mediating the nasal-occipital translational VOR are expected to exhibit negative multiplicative indexes. Indeed, when tested with ipsilateral clicks that activated the translational VOR pathways, a subgroup of abducens neurons (8 of the 34 neurons) had negative multiplication indexes. When tested with contralateral clicks that activated the angular VOR pathways, however, abducens neurons had positive multiplicative indexes. These results suggest that the interaction of vestibular and eye position signals in the AVOR pathways and the TVOR pathways may be implemented at different sites with different neural mechanisms.

Although the direct VOR pathways have the computational capacity to modulate the VOR gain by fixation distance, indirect VOR pathways have also be shown to contribute to the VOR gain modulation. For example, Snyder and King (1996) found that, during sudden off-axis head rotation, the responses of the gaze-velocity Purkije cells in the cerebellar flocculus and ventral paraflocculus of rhesus monkeys was modulated by fixation distance. These indirect pathways may play an important role to account for the large differences in viewing distance effect for the TVOR and the AVOR. As shown in Fig. 8, the viewing distance effect is much larger for the TVOR than for the AVOR (Viirre et al. 1986). For example, when viewing distance is changed from 0.1 to 2 m, the AVOR gain is changed by a factor of 1.47, but the TVOR gain is changed by a factor of 20. Furthermore, earlier studies have shown TVOR gain changes in advance of (or even in the absence of) a change in eye position (Paige 1989; Schwarz and Miles 1991; Shelhamer et al. 1995; Skipper and Barnes 1989; Snyder et al. 1992), indicating that VOR gain changes could also be caused by other inputs to the direct or indirect pathways. We suggest that the appropriate parameters in the preceding equations for the direct and indirect TVOR and AVOR pathways need to be acquired through mechanisms of motor learning and neural plasticity.

View larger version (13K): [in this window] [in a new window]   FIG. 8. Comparison of the VOR gain modulation by viewing distance for translational VOR (TVOR, black line) and angular VOR (AVOR, gray line). VOR gains at different viewing distances are normalized with respect to VOR gain at viewing distance of 0.5 m or 2 vergence MA (Viirre et al. 1986). Gain modulation by viewing distance is much larger for TVOR than that for AVOR. For viewing distances from 0.1 to 2 m, AVOR gain is changed by a factor of 1.47 but TVOR gain is changed by a factor of 20.

	GRANTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION GRANTS NOTE ADDED IN PROOF ACKNOWLEDGMENTS REFERENCES

 
This study was supported by National Institute of Deafness and Communication Disorders Grant DC-05785 to W. Zhou.

	NOTE ADDED IN PROOF

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION GRANTS NOTE ADDED IN PROOF ACKNOWLEDGMENTS REFERENCES

 
A similar multiplicative and additive mechanism was proposed by Zee et al. (1988) to account for the Ewalds Second Law.

	ACKNOWLEDGMENTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION GRANTS NOTE ADDED IN PROOF ACKNOWLEDGMENTS REFERENCES

 
We thank J. Cai for writing the data acquisition program and J. Allison for technical assistance.

	FOOTNOTES

 
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.

Address for reprint requests and other correspondence: W. Zhou, Dept. of Otolaryngology and Communicative Sciences, Univ. of Mississippi Medical Center, 2500 North State St., Jackson, MS 39216 (E-mail: wzhou{at}ent.umsmed.edu)

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