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Research Article  |   July 2008
Relationships between versional and vergent quick phases of the involuntary version–vergence nystagmus
Author Affiliations
  • Mingxia Zhu
    The Laboratory of Visual and Ocular Motor Physiology, The Children's Hospital of Pittsburgh and The UPMC Eye Center, Department of Ophthalmology, The University of Pittsburgh, Pittsburgh, PA, USAjjj@cns.nyu.edu
  • Richard W. Hertle
    The Laboratory of Visual and Ocular Motor Physiology, The Children's Hospital of Pittsburgh and The UPMC Eye Center, Department of Ophthalmology, The University of Pittsburgh, Pittsburgh, PA, USAhttp://ophthalmology.medicine.pitt.edu/personnel.asp?id=127&ptype=2jjj@cns.nyu.edu
  • Dongsheng Yang
    The Laboratory of Visual and Ocular Motor Physiology, The Children's Hospital of Pittsburgh and The UPMC Eye Center, Department of Ophthalmology, The University of Pittsburgh, Pittsburgh, PA, USAhttp://www.cns.nyu.edu/corefaculty/jones.html
Journal of Vision July 2008, Vol.8, 11. doi:10.1167/8.9.11
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      Mingxia Zhu, Richard W. Hertle, Dongsheng Yang; Relationships between versional and vergent quick phases of the involuntary version–vergence nystagmus. Journal of Vision 2008;8(9):11. doi: 10.1167/8.9.11.

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Abstract

We used ground-plane motion stimuli displayed on a computer monitor positioned below eye level to induce involuntary version–vergence nystagmus (VVN). The VVN was recorded with a search coil system. It was shown that the VVN had both vertical versional and horizontal vergence components. The VVN induced by backward motion (toward subjects) had upward versional and divergence quick phases, whereas those induced by forward motion (away from subjects) had downward and biphasic divergence–convergence quick phases. The versional and vergence components of the VVN quick phases were analyzed. A temporal dissociation of about 20 ms between version velocity peak and convergence velocity peak was revealed, which supported a modified saccade-related vergence burst neuron (SVBN) model. We suggest that the temporal dissociation may be partly because of a lower-level OKN control mechanism. Vergence peak time was dependent on version peak time. Linear relationships between vergence peak velocity and versional saccadic peak velocity were demonstrated, which was in line with the new multiplicative model. Our data support the hypothesis that the vergence system and the saccadic system can act separately but interact with each other whenever their movements occur simultaneously.

Introduction
Saccades are rapid eye movements during which the eyes move in the same direction. In contrast, pure vergence eye movements are slower movements in which both eyes move in opposite directions. Saccades and vergence eye movements are commonly considered to be two separate subsystems with distinct characteristics in anatomy and neurophysiology. Pure vergence eye movements can only be induced in laboratories after extremely careful alignment of eyes and a visual target. Under natural conditions, in order to achieve binocular single vision, combined version–vergence movements are frequently generated to shift gaze between objects at different distances and directions. 
When combined saccade–vergence movements occur, conjugate saccades and disjunctive vergence interact with each other. Reports on the saccade–vergence interactions have shown that vergence movements increase in velocity, while horizontal and vertical saccades slow down (Collewijn, Erkelens, & Steinman, 1995; Enright, 1984, 1992; Ono, Nakamizo, & Steinbach, 1978; Sylvestre, Galiana, & Cullen, 2002; van Leeuwen, Collewijn, & Erkelens, 1998; Zee, Fitzgibbon, & Optican, 1992). It has been suggested that activities of saccadic burst neurons and vergence neurons might be gated by the same group of neurons (omnipause neurons, OPN). During saccades, inhibition from OPN is lifted not only for saccades but also for vergence. Thus, vergence would be enhanced. This is known as the saccade-related vergence burst neuron (SVBN) model (Zee et al., 1992). The SVBN model has obtained support from many studies (Collewijn et al., 1995; Mays, 1984; Sylvestre et al., 2002), but more recent data do not support the SVBN hypothesis. For example, vergence enhancement increased with saccadic peak velocity in monkeys (Busetinni & Mays, 2005a) and a temporal dissociation between conjugate saccades and disjunctive vergence was observed by Kumar (Kumar, Han, Dell'osso, Durand, & Leigh, 2005; Kumar et al., 2006). To explain the new findings, a new model (Busetinni & Mays, 2005b) and modified SVBN model have recently been suggested (Kumar et al., 2006; Leigh & Zee, 2006). 
Most previous studies used small visual targets to induce combined voluntary version–vergence eye movements. In the present study, we used large motion stimuli to induce involuntary version–vergence nystagmus (VVN). We term this VVN because it has vertical version and horizontal vergence components. We previously reported VVN with our analysis focusing on the slow-phases (Yang, Zhu, Kim, & Hertle, 2007). In the present study, we have focused on relationships between the versional and vergence components and have sought to extend our knowledge of saccade–vergence interaction by studying the small, involuntary VVN under lower level control. 
Materials and methods
Subjects
Five subjects participated in this study, including two authors and three naive volunteers, aged 25–44 years, with normal ophthalmic and ocular motor evaluations as well as normal binocular vision. Their best corrected visual acuity was 20/20 in each eye. The protocol and testing was approved by the Institutional Review Board of the University of Pittsburgh. All procedures observed the Declaration of Helsinki and informed consent was obtained on all subjects. 
Stimuli
Motion in the frontal plane
For the purpose of comparison with experiments in the ground plane, a horizontal square-wave-grating pattern was displayed on a computer monitor (View Sonic, G220fb) set in the frontal plane. The monitor has a resolution of 2048 × 1024 pixels and refresh rate of 70 Hz. The size of the pattern was 30° × 40° at a viewing distance of 47 cm. The width of an individual bar of gratings was 1°. The luminance was 85 cd/cm2 for the white bar and 0.5 cd/cm2 for the black bar. The grating stimulus was the only pattern visible in the dark room since the frame of the monitor was covered in black. The grating pattern moved up or down at various velocities of 10°/sec, 20°/sec, 30°/sec, 40°/sec, or 50°/sec. All parameters were preprogrammed with VEX-REX software (from The Laboratory of Sensorimotor Research, NEI, NIH). 
Motion in the ground plane
The same stimulus pattern used for the frontal plane experiment was positioned face up and 9 cm below eye level. The direction of the motion was thus forward or backward, simulating optic flow in the ground plane. The viewing distance to the center of the stimuli was 25 cm. Subjects tilted their head down by 5° and rotated their eyes down by 15° when they looked at the center of the screen. See Figure 1 for a detailed setting. Surface motion velocities were 4, 8, 12, 16, and 20 cm/sec (approx. 10°, 20°, 30°, 40°, and 50°/sec to the eyes). 
Figure 1
 
Schematic draw for the setting of the monitor, head position, and fixation direction. The head tilts down by 5 degrees and the eye looks down by 15 degrees.
Figure 1
 
Schematic draw for the setting of the monitor, head position, and fixation direction. The head tilts down by 5 degrees and the eye looks down by 15 degrees.
Experimental paradigms
Subjects were seated with their heads stabilized on a chin and forehead rest and performed calibration tasks by fixating on a 0.5° dot displayed at 5 different locations with a separate right-eye and left-eye viewing before each session. After the calibration, the subject was instructed to look at the center of the stationary pattern and press a button to trigger the pattern motion, which lasted for 5 seconds in each trial. During the motion, subjects were instructed to obtain a clear image and not to track any single bar. Ten trials (five different velocities in two directions) composed one block. Eye-movement recording for monocular and binocular viewing conditions was usually performed in one session and sometimes in different sessions on different days. Approximately 30 minutes were required to record 20 blocks. At least 10 blocks for binocular viewing and 10 blocks for monocular viewing (right eye patched) were obtained. 
Eye-movement recording
Horizontal and vertical eye movements of both eyes were recorded with an electromagnetic technique (Remmel Labs) using scleral search coils embedded in a silastin ring. Coils were placed in each eye following application of 1–2 drops of anesthetic (Proparacaine HCl). Coil wearing time for each session was approximately 30 minutes. The AC voltages induced in the scleral search coils were connected to a phase-locked amplifier that provided separate DC voltage outputs proportional to the horizontal and vertical positions of the two eyes with corner frequencies (−3 dB) at 1 kHz. Interocular distance was measured to the nearest millimeter. Peak-to-peak voltage noise levels were equivalent to an eye movement of 1–2 min of arc. A photocell was positioned on the upper-left corner of the monitor to detect the physical start of motion and to mark the onset of motion with a code in eye-movement data. 
Data analysis
The horizontal and vertical eye-position data obtained during the calibration procedure were each fitted with a third-order polynomial that was then used to linearize the horizontal and vertical eye-position data recorded during the experiment proper. The experimental data were then smoothed with a cubic spline function of weight 107 to reduce high frequency noise. The polarity of the rightward and upward eye movements were defined as positive and vergence position was computed by subtracting the position of the right eye from the position of the left eye. This meant that horizontal convergence was positive when the left eye moved rightward with respect to the right eye, or the right eye moved leftward with respect to the left eye. Version position was the average of the right and left eye positions. 
Estimates of the amplitude of the version and vergence responses were obtained by measuring the change in version position from maximum point to minimum point using programs written in MatLab. Velocities were obtained by two-point backward differentiation of the position data. A criterion of 3°/sec was used to decide the beginning of the version and vergence responses to determine the response peak time. 
Results
General properties of the version–vergence nystagmus
Figure 2 shows nystagmus induced by motion in the ground plane. The nystagmus had ocular tracking slow phases and corrective quick phases that contained vertical version and horizontal vergence components—version–vergence nystagmus (VVN). The VVN induced by backward motion (motion toward subjects) is shown in the top panel of Figure 2, where upward quick phases are shown in the first row and horizontal divergent quick phases are shown in the second row. The VVN induced by forward motion (motion away from subjects) is shown in the bottom panel of Figure 2, where downward quick phases are shown in the first row and convergent quick phases are in the second row. Asymmetrical horizontal components from each eye were displayed in third and fourth row. These horizontal movements were small compared to vertical components. It is possible that they were induced due to the stimulus condition where there was no fixation target in the center of the screen and subjects' fixation might stay off the center. 
Figure 2
 
Representative samples of version–vergence nystagmus. Top panel: VVN induced by backward motion. Bottom panel: VVN induced by forward motion. VVs: Vertical version. HVg: Horizontal vergence. REH: Right eye horizontal movement. LEH: Left eye horizontal movement. S1–S4: Subject #1–subject #4.
Figure 2
 
Representative samples of version–vergence nystagmus. Top panel: VVN induced by backward motion. Bottom panel: VVN induced by forward motion. VVs: Vertical version. HVg: Horizontal vergence. REH: Right eye horizontal movement. LEH: Left eye horizontal movement. S1–S4: Subject #1–subject #4.
Amplitudes of the vertical versional saccades were about 5° on average. The amplitudes of saccadic horizontal vergences were from 0.3° to 0.45°. They are similar to the slow-phase amplitudes. Peak velocities of horizontal vergence quick phases reached about 10–15°/sec, and peak velocities of vertical versional quick phases reached up to 100°/sec (Yang et al., 2007). 
Characteristics of horizontal vergent and vertical saccades
Figure 3 shows plots for peak velocities and duration of convergences and downward saccades from S1. Scatter plots are displayed in Figures 3A and 3B. The horizontal convergence represented with dark crosses shows a different pattern from vertical saccades (gray diamonds). For a statistical comparison, logarithmic plots are displayed in Figures 3C and 3D. Linear patterns are demonstrated in both velocity–amplitude and duration–amplitude plots (p < 0.0001) using one-way analysis of variance (ANOVA). Regressions for horizontal convergence quick phases are significantly different from regressions for vertical version quick phases (p < 0.02). The velocity–amplitude relationships of vertical quick phases are similar to a previous study (Garbutt et al., 2003). 
Figure 3
 
Plots of saccadic characteristics for vergence and vertical saccades. (A) Scatter plot for peak velocities of convergences versus their amplitudes (dark crosses) and peak velocities of downward saccades versus their amplitudes (gray diamonds). (B) Scatter plot for durations of convergences versus their amplitudes and for durations of downward version versus their amplitudes. (C) The data are the same as in A except that they are shown in a logarithmic plot. (D) The data are the same as in B except that they are shown in a logarithmic plot.
Figure 3
 
Plots of saccadic characteristics for vergence and vertical saccades. (A) Scatter plot for peak velocities of convergences versus their amplitudes (dark crosses) and peak velocities of downward saccades versus their amplitudes (gray diamonds). (B) Scatter plot for durations of convergences versus their amplitudes and for durations of downward version versus their amplitudes. (C) The data are the same as in A except that they are shown in a logarithmic plot. (D) The data are the same as in B except that they are shown in a logarithmic plot.
Velocity–amplitude relationships for horizontal vergence and vertical version for all subjects were analyzed. Parameters of the relationship (regression coefficients (R2), intercept (I), and slopes of the regression lines (S)) are shown in Table 1
Table 1
 
The velocity–amplitude relationships for horizontal vergence and vertical version for all subjects. The correlations were analyzed under logarithmic plots. All relationships are linearly positive (**p < 0.0001). The bino-vg: Vergence from binocular condition; bino-vs: Version from binocular condition; mono-vg: Vergence from monocular condition; mono-vs: Version from monocular condition; divg: Divergence; convg: Convergence; vs: Version.
Table 1
 
The velocity–amplitude relationships for horizontal vergence and vertical version for all subjects. The correlations were analyzed under logarithmic plots. All relationships are linearly positive (**p < 0.0001). The bino-vg: Vergence from binocular condition; bino-vs: Version from binocular condition; mono-vg: Vergence from monocular condition; mono-vs: Version from monocular condition; divg: Divergence; convg: Convergence; vs: Version.
Backward motion: Divg and up vs Forward motion: Divg and down vs Forward motion: Convg and down vs
Slope Intercept R 2 Slope Intercept R 2 Slope Intercept R 2
Bino-vg 4.01 28.7 0.82** 3.83 32.6 0.82** 2.89 23.0 0.70**
Bino-vs 4.85 42.4 0.86** 5.12 43.0 0.89** 5.12 43.0 0.89**
Mono-vg 4.84 35.1 0.84** 4.44 34.4 0.83** 2.95 22.9 0.66**
Mono-vs 5.19 42.5 0.89** 5.39 39.2 0.88** 5.39 39.2 0.88**
Duration–amplitudes relationship for horizontal vergence and vertical version for all subjects were analyzed, and parameters of the relationship are presented in Table 2
Table 2
 
Duration–amplitudes relationships for horizontal vergence and vertical saccades for all subjects. The correlations were analyzed under logarithmic plots. All relationships are linear (p < 0.0001). The bino-vg: Vergence from binocular condition; bino-vs: Version from binocular condition; mono-vg: Vergence from monocular condition; mono-vs: Version from monocular condition; divg: Divergence; convg: Convergence; vs: Version.
Table 2
 
Duration–amplitudes relationships for horizontal vergence and vertical saccades for all subjects. The correlations were analyzed under logarithmic plots. All relationships are linear (p < 0.0001). The bino-vg: Vergence from binocular condition; bino-vs: Version from binocular condition; mono-vg: Vergence from monocular condition; mono-vs: Version from monocular condition; divg: Divergence; convg: Convergence; vs: Version.
Backward motion divg and up vs Forward motion divg and down vs Forward motion convg and down vs
Slope Intercept R 2 Slope Intercept R 2 Slope Intercept R 2
Bino-vg 3.13 62.0 0.71** 3.17 50.5 0.72** 4.34 93.0 0.81**
Bino-vs 2.60 42.5 0.53** 2.63 40.2 0.69** 2.63 40.2 0.69**
Mono-vg 2.79 52.8 0.61** 3.01 52.7 0.72** 4.59 92.8 0.76**
Mono-vs 2.01 45.5 0.43** 2.38 47.9 0.55** 2.38 47.9 0.55**
Dynamic properties of the version–vergence nystagmus
To demonstrate the detailed dynamic properties of the version and vergence components, samples of velocity and position profiles of vertical quick phases and vergence quick phases are displayed in Figure 4. A divergent quick phase and an upward quick phase induced by backward motion stimuli are displayed in Figure 4A, and a biphasic divergence–convergence quick phase and a downward quick phase induced by forward motion stimuli are displayed in Figure 4B. The divergent component of the biphasic vergence responses is small but consistent and robust in all subjects under all conditions tested. Temporal dissociation between the horizontal vergence and vertical version are labeled and analyzed separately. Position traces are represented with dotted lines, and solid lines are for velocity traces. Notice the left y-axis is labeled in degrees for position traces, and the right y-axis is in deg/sec for velocity traces. 
Figure 4
 
Representative velocity and position profiles of vertical saccades and horizontal vergent quick phases. Dotted lines: Position traces; solid line: Velocity traces. Time intervals for initiations and peaks of response velocity are indicated. Negative values on the axes represent downward eye movements and divergence. Positive values represent upward eye movements and convergence.
Figure 4
 
Representative velocity and position profiles of vertical saccades and horizontal vergent quick phases. Dotted lines: Position traces; solid line: Velocity traces. Time intervals for initiations and peaks of response velocity are indicated. Negative values on the axes represent downward eye movements and divergence. Positive values represent upward eye movements and convergence.
Temporal dissociation of vergence and version responses
Temporal dissociations (TD) between version velocity peaks of quick phases and vergence velocity peaks of quick phases were analyzed. As shown in the Figure 4A, the velocity peak of the divergence occurs a few milliseconds ahead of the velocity peak of the upward saccade. This temporal dissociation is defined as TD 1. In Figure 4B, the velocity peak of the divergence component of the biphasic vergence is followed by velocity peak of downward saccades by about 7 ms, and the temporal dissociation is defined as TD 2. The velocity peak of the convergence follows the velocity peak of downward saccades by about 26 ms, and this temporal dissociation is TD 3. TD 3 is much longer than what was reported by Kumar et al. (2005) in their Far-Up Near-Down condition, although the eye movements made in their study were much larger. Summarized TD 1, TD 2, and TD 3 are displayed in Figure 5. T-tests showed that TD 2 is not significantly longer than TD 1 at most speeds (p < 0.05 for speed 4 and 8 cm/sec, p > 0.05 for speed 12, 16, and 20 cm/sec), whereas TD 3 is significantly longer than TD 2 (p < 0.005) and TD 1 (p ≤ 0.0007) for all speeds. TD 3 seems to show an increasing trend with stimulus velocities. However, one-way analysis of variance (ANOVA) did not show any significant difference among different velocities (p = 0.16). 
Figure 5
 
Temporal dissociations between vergence and versional saccades. See text for the definition of TDs. TD 2 is longer than TD 1, but not significantly at most speeds. TD 3 is significantly longer than TD 2 for each speed (p < 0.005) and TD 1 (p ≤ 0.0007). Negative values mean vergence peaks occurred before version peaks. Positive values mean vergence peaks occurred after version peaks.
Figure 5
 
Temporal dissociations between vergence and versional saccades. See text for the definition of TDs. TD 2 is longer than TD 1, but not significantly at most speeds. TD 3 is significantly longer than TD 2 for each speed (p < 0.005) and TD 1 (p ≤ 0.0007). Negative values mean vergence peaks occurred before version peaks. Positive values mean vergence peaks occurred after version peaks.
Timing of vergent and versional velocity peaks
We examined the timing of the horizontal vergence quick phases and vertical versional quick phases. The time of velocity peak is defined as the time from the point the response reached 3°/sec to the velocity peak. 
Under the backward motion condition, the relationships between the time of divergence velocity peak and time of upward saccadic peak are positive. For the purpose of clarity, only one subject's data are shown in Figure 6A. Correlation coefficients, intercept (I), and slopes of the regression lines for other subjects are displayed in Table 3. Positive linear relationships are demonstrated for all subjects (p < 0.05). 
Figure 6
 
Timing of vergent and versional velocity peaks. Representative data from S1. (A) Divergence from backward motion. (B) Divergence from forward motion. (C) Convergence from forward motion.
Figure 6
 
Timing of vergent and versional velocity peaks. Representative data from S1. (A) Divergence from backward motion. (B) Divergence from forward motion. (C) Convergence from forward motion.
Table 3
 
Relationships between the time of vergence velocity peaks and time of saccade velocity peaks for all subjects. R2: Correlation coefficients; S: Slopes of the regression lines. All relationships of the subjects are linearly positive (**p < 0.0001).
Table 3
 
Relationships between the time of vergence velocity peaks and time of saccade velocity peaks for all subjects. R2: Correlation coefficients; S: Slopes of the regression lines. All relationships of the subjects are linearly positive (**p < 0.0001).
Backward motion divergence Forward motion divergence Forward motion convergence
Slope Intercept R 2 Slope Intercept R 2 Slope Intercept R 2
CK 0.74 0.006 0.52** 0.67 0.003 0.77** 1.43 0.01 0.69**
DY 1.14 0.001 0.76** 0.76 −0.0007 0.84** 1.59 0.004 0.72**
KG 0.80 0.003 0.69** 0.97 −0.005 0.95** 1.37 0.01 0.79**
LR 0.08 0.03 0.10** 0.67 0.004 0.64** 1.07 0.02 0.54**
MZ 0.61 0.001 0.28** 0.44 0.008 0.14** 0.90 0.01 0.22**
Under the forward motion condition, relationships between the time of velocity peaks of biphasic divergence–convergence responses and the time of downward saccadic velocity peak for the same subject are shown in Figures 6B and 6C, respectively. 
Relationships between peak velocities of horizontal vergence and vertical saccades
Under the backward motion condition, divergence and upward saccades were induced. The relationships between the peak velocity of divergence and peak velocity of upward saccades were analyzed. Regression lines for S1 are displayed in Figure 7A. Data for other subjects are listed in Table 4
Figure 7
 
Representative relationships between vergence peak velocity and version peak velocity for S1. (A) Divergence from backward motion; (B) divergence from forward motion; (C) convergence from forward motion.
Figure 7
 
Representative relationships between vergence peak velocity and version peak velocity for S1. (A) Divergence from backward motion; (B) divergence from forward motion; (C) convergence from forward motion.
Table 4
 
Parameters for relationships between peak velocity of horizontal vergence and peak velocity of vertical saccades for binocular viewing conditions. R2: Correlation coefficients; I: Intercepts; S: Slopes of the regression lines. Positive relationships of the subjects are indicated with stars (*p < 0.05; **p < 0.0001).
Table 4
 
Parameters for relationships between peak velocity of horizontal vergence and peak velocity of vertical saccades for binocular viewing conditions. R2: Correlation coefficients; I: Intercepts; S: Slopes of the regression lines. Positive relationships of the subjects are indicated with stars (*p < 0.05; **p < 0.0001).
Backward motion divergence Forward motion divergence Forward motion convergence
Slope Intercept R 2 Slope Intercept R 2 Slope Intercept R 2
CK 0.05 16.5 0.13** 0.05 18.2 0.08* 0.08 12.1 0.21**
DY 0.10 3.4 0.43** 0.03 11.2 0.10* 0.09 7.9 0.19**
KG 0.23 6.0 0.59** 0.10 2.07 0.56** 0.08 2.9 0.44**
LR 0.10 3.9 0.58** −0.04 18.9 0.02 0.10 2.6 0.38**
MZ 0.11 8.9 0.32** −0.01 7.8 0.004 0.05 5.4 0.10**
Under the forward motion condition, biphasic divergence–convergence responses are associated with downward saccades. Regression lines for peak velocities of the divergent components of the biphasic vergence responses and peak velocity of downward saccades for S1 are shown in Figure 7B. Three of the five subjects showed similar positive correlations (Table 4, middle group). Pooled data from all subjects showed R2 = 0.07 and p < 0.0001, indicating a positive correlation in general. Relationships between peak velocities of the convergent components of the biphasic vergence responses and peak velocity of downward saccades for S1 are shown in Figure 7C. It can be seen from Table 4 that weak but consistently positive correlations were demonstrated for each of the subjects. Pooled data for all 5 subjects also showed a dependence of convergent peak velocity on peak velocity of downward saccades (R2 = 0.26, p < 0.0001). 
Monocular viewing experiments
Version and vergence nystagmus induced under monocular viewing conditions was almost the same as binocular viewing conditions. Amplitude and peak velocity of vertical version and horizontal vergence for all subjects were similar to those under binocular viewing conditions. 
Velocity–amplitude relationships and duration–amplitudes relationships of the horizontal vergence are shown in Tables 1 and 2. Slopes, intercepts, and R2 are similar to binocular conditions. 
Time dissociations are similar to those under binocular viewing conditions. The means of TD 1, TD 2, and TD 3 are −3.26 ms, −8 ms, and 23.98 ms, respectively. 
Relationships between the timing of the velocity peak of horizontal vergence and vertical saccades are the same as with binocular viewing condition. Under the backward motion condition, relationships between the time of the divergence velocity peak and time of the upward saccade peak from pooled data showed that R2 was 0.22 and p < 0.0001. With forward motion, pooled data showed that the time of the divergence peak of biphasic divergence–convergence was dependent on the time of the downward saccade peak (R2 = 0.64, p < 0.0001), and the time of the convergence peak of biphasic divergence–convergence was dependent on the time of the downward saccade peak (R2 = 0.56, p < 0.0001). 
Relationships between peak velocity of horizontal vergence and vertical saccades under monocular conditions are presented in Table 5. Compared to binocular conditions, there was either very weak or no dependence of vergence peak velocity on peak velocity of vertical saccades under monocular conditions. 
Table 5
 
Relationships between peak velocity of horizontal vergence and peak velocity of vertical saccades for monocular viewing conditions. R2: Correlation coefficients. I: Intercepts. S: Slopes of the regression lines. Positive relationships of the subjects are indicated with * and ** (*p < 0.05; **p < 0.0001).
Table 5
 
Relationships between peak velocity of horizontal vergence and peak velocity of vertical saccades for monocular viewing conditions. R2: Correlation coefficients. I: Intercepts. S: Slopes of the regression lines. Positive relationships of the subjects are indicated with * and ** (*p < 0.05; **p < 0.0001).
Backward motion divergence Forward motion divergence Forward motion convergence
Slope Intercept R 2 Slope Intercept R 2 Slope Intercept R 2
CK −0.02 19.5 0.01 0.12 19.7 0.19** 0.06 13.0 0.04*
DY 0.03 13.2 0.04* −0.03 17.5 0.06* −0.02 17.6 0.005
KG 0.15 15.9 0.16** 0.02 13.5 0.02* 0.06 7.9 0.16**
LR 0.07 8.2 0.16** 0.05 7.13 0.15** 0.09 5.7 0.18**
MZ 0.03 28.4 0.003 −0.07 20.7 0.03* −0.01 15.9 0.004
Control experiments: Motion stimulus in the frontal plane
There was no measurable horizontal vergence nystagmus recorded during downward motion in the frontal plane (Figure 8). However, sometimes tiny convergence was evoked during upward motion when the starting eye position was below the center of the screen. 
Figure 8
 
Representative samples of nystagmus induced with vertical motion. Left panel: Nystagmus induced by backward motion. Right panel: Nystagmus induced by forward motion. VVs: Vertical version. HVg: Horizontal vergence. REH: Right eye horizontal movement. LEH: Left eye horizontal movement. S3 and S4: Subject #3 and subject #4.
Figure 8
 
Representative samples of nystagmus induced with vertical motion. Left panel: Nystagmus induced by backward motion. Right panel: Nystagmus induced by forward motion. VVs: Vertical version. HVg: Horizontal vergence. REH: Right eye horizontal movement. LEH: Left eye horizontal movement. S3 and S4: Subject #3 and subject #4.
Discussion
We have presented version–vergence nystagmus (VVN) induced by optic flow motion in the ground plane. Compared with version–vergence eye movements from studies of saccade–vergence interactions (Collewijn et al., 1995; Collewijn, Erkelens, & Steinman, 1997; Kumar et al., 2005; Sylvestre et al., 2002; Zee et al., 1992), the VVN are relatively small (Figures 2 and 3). Although small, unique properties of the VVN have been observed in our study. Our discussion will focus on the detailed properties of the VVN, temporal dissociations between the horizontal vergence and vertical version components of the VVN, timing of the horizontal vergent and vertical saccadic quick phases, and relationships between horizontal vergent and vertical saccadic velocity peaks. 
The details of horizontal vergent and vertical saccadic components are presented in Figure 4. Under the backward motion condition (Figure 4A), the divergent components consistently occurred earlier than the upward saccadic components in most situations, although the differences were as small as 3 ms on average (Figures 4 and 5). Since these quick phases are in line with a requirement to reset eye positions to a distant target in order to keep binocular single vision, we think a central neural process is responsible for the response. The small temporal separations of the divergent and upward saccadic velocity peaks may be an indication of independent neural activities for vergent and vertical saccades. Under the forward motion condition, we expected to see convergent quick phases and downward saccades. However, a transient divergence occurred prior to convergence—a “biphasic vergence response” (Figure 4B). A similar transient divergent component was reported to occur with both horizontal and vertical saccades (Collewijn et al., 1995, 1997; Hung, 1998; Maxwell & King, 1992; Sylvestre et al., 2002; van Leeuwen et al., 1998; Zee et al., 1992). In a recent report, the divergence occurred in association with upward saccades (Kumar et al., 2005). It appears to us that the divergent component was unrelated to the directions of accompanying saccades (upward, downward, and horizontal). In the present study, the divergent component of the biphasic responses that occurred with downward saccades was in a direction opposite to that required for binocular single vision. Thus, our data support Enright's suggestion that the divergent component may be generated by a peripheral mechanism in the ocular motor plant (Enright, 1989) although Collewijn et al. (1997) and van Leeuwen et al. (1998) believed that the divergent component was centrally controlled. Regarding the convergent components of the biphasic vergence responses, they are in line with a central mechanism since they are required eye movements for binocular single vision. 
Regarding the temporal dissociation (TD), it was reported that the peak velocities of saccadic and vergence components occurred at almost the same time for most saccade–vergence movements (Zee et al., 1992). However, in the present study, the temporal dissociation (Figure 5, TD 3) between the convergent and downward saccades is quite large given the facts that the vergent and versional components were so small compared to other studies (Kumar et al., 2005, 2006). It was observed that TD was longer under an instrument-space environment than a free-space environment (Hung, 1998). We believe that in this study the larger TD 3 may be related to the large stimulus and the nature of the involuntary nystagmus controlled mainly by low level nuclei, such as nucleus of the optic tract (NOT) in the pretectum and dorsal terminal nucleus (DTN) of the accessory optic system (Schiff, Cohen, Büttner-Ennever, & Matsuo, 1990; Schmidt, Zhang, & Hoffmann, 1993). In contrast, when a small visual target was used, desired change in conjugate position and desired change in vergence drove voluntary version–vergence eye movements. The inputs with intentional effort might synchronize the horizontal vergent and vertical saccades. Thus, the temporal dissociation might be reduced in the eye movements with intentional effort. For simultaneous vergent and versional saccades, the version–vergence interaction can be explained by the SVBN model proposed by Zee et al, (Zee et al., 1992), in which omnipause neurons synchronously remove inhibition from both saccadic and vergence burst neurons. However, this model could not account for dissociated vergent and versional saccades. Using a unique setting, Kumar et al. (2006) observed a large temporal dissociation between vergent and versional saccades. Kumar et al. suggested a modified SVBN model in which both saccadic burst and omnipause-neuron inhibition influence the generation of the vergence. The large temporal dissociation observed in the present study is in agreement with the observation made by Kumar et al and support their suggestion. 
In seeking to better understand the temporal relationships between vergence and version, we also examined the timing of the horizontal vergent and vertical saccadic quick phases (Figure 6, Table 3). The positive linear relationships for all subjects showed that the timing for vergence and version is linearly correlated. In other words, when the time for the version to reach its peak was longer, the time for vergence to reach its peak also became longer, indicating a close dependent relationship between vergence and vertical version. 
The relationships between vertical versional and vergence peak velocities show that there is a dependence of vergence peak velocity on vertical version peak velocity (Figure 7). It is consistent with reports by Maxwell and King (1992) and Sylvestre et al. (2002). However, this feature is not consistent with findings that vergence movements increase in velocity while versional saccades slow down during combined version–vergence movements. In other words, this is not in agreement with the SVBN model (Collewijn et al., 1995; Enright, 1984, 1992; Ono et al., 1978; Sylvestre, Choi, & Cullen, 2003; van Leeuwen et al., 1998; Zee et al., 1992). A recent electrophysiological study has obtained evidence to support a new model called the multiplicative model (Busettini & Mays, 2005a, 2005b). In the model, it has been suggested that the vergence enhancement could be a multiplication of a short latency vergence motor error by a saccadic burst signal. In other words, the saccadic burst might enhance the discharge of the vergence burst neurons. Based on our results that vergence velocity increases with vertical saccade velocity, the version–vergence interaction from VVN is in agreement with the Multiplicative Model. 
There are other hypotheses to explain the vergence enhancement, such as the suggestion of independent neurobiological substrates for conjugate saccades and disjunctive vergence (King & Zhou, 2002; Zhou & King, 1998). However, we think a mechanism of non-selective enhancements of saccades on other associated eye movements may be involved in the enhancement of vergence during version–vergence eye movements since it is well known that saccades enhance many other associated eye movements, including disparity and optic flow vergence (Busettini, Masson, & Miles, 1997; Yang, Fitzgibbon, & Miles, 1999, 2003), ocular following (Busettini, Fitzgibbon, & Miles, 2001; Kawano & Miles, 1986; Yang & Miles, 2003), smooth pursuits (Lisberger, 1998), accommodation (Schor, Lott, Pope, & Graham, 1999), and vestibular ocular responses (Das, Dell'Osso, & Leigh, 1999). 
We attribute the VVN to optic-flow inputs for the following reasons: (1) monocular VVN was almost the same as the binocular VVN; (2) accommodation and proximal vergence cues may play a minor role in generating the vergence in a natural world (Hung, Ciuffreda, & Rosenfield, 1996); and (3) the stimuli did not have any horizontal disparity. Optic flow has been used to induce vergence eye movements (Busettini et al., 1997; Miles, Busettini, Masson, & Yang, 2004; Yang et al., 1999) and version eye movements (Lappe, Pekel, & Hoffmann, 1998; Niemann, Lappe, Büscher, & Hoffmann, 1999) depending on optic-flow settings. The VVN from the ground plane has been proven to be a useful approach in the study of saccade–vergence interaction using human subjects. Since the VVN are under low-level control, this method would need little training in studies using animals. It could be a better approach for electrophysiological studies of saccade–vergence interaction using animals. 
In summary, the time dissociation between version velocity peak and convergence velocity peak and the linear relationships between vergence peak velocity and versional saccadic peak velocity have been demonstrated in small, involuntary VVN. These findings are in line with reports from Kumar et al. (2005, 2006) and Busettini and Mays (2005a, 2005b) in large, voluntary version–vergence eye movements. Our data support the hypothesis that the vergence system and the saccadic system can act separately but interact with each other whenever they act simultaneously. 
Acknowledgments
This project is partly supported by NEI EY015797 Grant and The Research to Prevent Blindness. 
Commercial relationships: none. 
Corresponding author: Dongsheng Yang. 
Email: yangd@upmc.edu. 
Address: The Laboratory of Visual and Ocular Motor Physiology, The Children's Hospital of Pittsburgh, and The UPMC Eye Center, Department of Ophthalmology, The University of Pittsburgh, Pittsburgh, PA 15260, USA. 
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Figure 1
 
Schematic draw for the setting of the monitor, head position, and fixation direction. The head tilts down by 5 degrees and the eye looks down by 15 degrees.
Figure 1
 
Schematic draw for the setting of the monitor, head position, and fixation direction. The head tilts down by 5 degrees and the eye looks down by 15 degrees.
Figure 2
 
Representative samples of version–vergence nystagmus. Top panel: VVN induced by backward motion. Bottom panel: VVN induced by forward motion. VVs: Vertical version. HVg: Horizontal vergence. REH: Right eye horizontal movement. LEH: Left eye horizontal movement. S1–S4: Subject #1–subject #4.
Figure 2
 
Representative samples of version–vergence nystagmus. Top panel: VVN induced by backward motion. Bottom panel: VVN induced by forward motion. VVs: Vertical version. HVg: Horizontal vergence. REH: Right eye horizontal movement. LEH: Left eye horizontal movement. S1–S4: Subject #1–subject #4.
Figure 3
 
Plots of saccadic characteristics for vergence and vertical saccades. (A) Scatter plot for peak velocities of convergences versus their amplitudes (dark crosses) and peak velocities of downward saccades versus their amplitudes (gray diamonds). (B) Scatter plot for durations of convergences versus their amplitudes and for durations of downward version versus their amplitudes. (C) The data are the same as in A except that they are shown in a logarithmic plot. (D) The data are the same as in B except that they are shown in a logarithmic plot.
Figure 3
 
Plots of saccadic characteristics for vergence and vertical saccades. (A) Scatter plot for peak velocities of convergences versus their amplitudes (dark crosses) and peak velocities of downward saccades versus their amplitudes (gray diamonds). (B) Scatter plot for durations of convergences versus their amplitudes and for durations of downward version versus their amplitudes. (C) The data are the same as in A except that they are shown in a logarithmic plot. (D) The data are the same as in B except that they are shown in a logarithmic plot.
Figure 4
 
Representative velocity and position profiles of vertical saccades and horizontal vergent quick phases. Dotted lines: Position traces; solid line: Velocity traces. Time intervals for initiations and peaks of response velocity are indicated. Negative values on the axes represent downward eye movements and divergence. Positive values represent upward eye movements and convergence.
Figure 4
 
Representative velocity and position profiles of vertical saccades and horizontal vergent quick phases. Dotted lines: Position traces; solid line: Velocity traces. Time intervals for initiations and peaks of response velocity are indicated. Negative values on the axes represent downward eye movements and divergence. Positive values represent upward eye movements and convergence.
Figure 5
 
Temporal dissociations between vergence and versional saccades. See text for the definition of TDs. TD 2 is longer than TD 1, but not significantly at most speeds. TD 3 is significantly longer than TD 2 for each speed (p < 0.005) and TD 1 (p ≤ 0.0007). Negative values mean vergence peaks occurred before version peaks. Positive values mean vergence peaks occurred after version peaks.
Figure 5
 
Temporal dissociations between vergence and versional saccades. See text for the definition of TDs. TD 2 is longer than TD 1, but not significantly at most speeds. TD 3 is significantly longer than TD 2 for each speed (p < 0.005) and TD 1 (p ≤ 0.0007). Negative values mean vergence peaks occurred before version peaks. Positive values mean vergence peaks occurred after version peaks.
Figure 6
 
Timing of vergent and versional velocity peaks. Representative data from S1. (A) Divergence from backward motion. (B) Divergence from forward motion. (C) Convergence from forward motion.
Figure 6
 
Timing of vergent and versional velocity peaks. Representative data from S1. (A) Divergence from backward motion. (B) Divergence from forward motion. (C) Convergence from forward motion.
Figure 7
 
Representative relationships between vergence peak velocity and version peak velocity for S1. (A) Divergence from backward motion; (B) divergence from forward motion; (C) convergence from forward motion.
Figure 7
 
Representative relationships between vergence peak velocity and version peak velocity for S1. (A) Divergence from backward motion; (B) divergence from forward motion; (C) convergence from forward motion.
Figure 8
 
Representative samples of nystagmus induced with vertical motion. Left panel: Nystagmus induced by backward motion. Right panel: Nystagmus induced by forward motion. VVs: Vertical version. HVg: Horizontal vergence. REH: Right eye horizontal movement. LEH: Left eye horizontal movement. S3 and S4: Subject #3 and subject #4.
Figure 8
 
Representative samples of nystagmus induced with vertical motion. Left panel: Nystagmus induced by backward motion. Right panel: Nystagmus induced by forward motion. VVs: Vertical version. HVg: Horizontal vergence. REH: Right eye horizontal movement. LEH: Left eye horizontal movement. S3 and S4: Subject #3 and subject #4.
Table 1
 
The velocity–amplitude relationships for horizontal vergence and vertical version for all subjects. The correlations were analyzed under logarithmic plots. All relationships are linearly positive (**p < 0.0001). The bino-vg: Vergence from binocular condition; bino-vs: Version from binocular condition; mono-vg: Vergence from monocular condition; mono-vs: Version from monocular condition; divg: Divergence; convg: Convergence; vs: Version.
Table 1
 
The velocity–amplitude relationships for horizontal vergence and vertical version for all subjects. The correlations were analyzed under logarithmic plots. All relationships are linearly positive (**p < 0.0001). The bino-vg: Vergence from binocular condition; bino-vs: Version from binocular condition; mono-vg: Vergence from monocular condition; mono-vs: Version from monocular condition; divg: Divergence; convg: Convergence; vs: Version.
Backward motion: Divg and up vs Forward motion: Divg and down vs Forward motion: Convg and down vs
Slope Intercept R 2 Slope Intercept R 2 Slope Intercept R 2
Bino-vg 4.01 28.7 0.82** 3.83 32.6 0.82** 2.89 23.0 0.70**
Bino-vs 4.85 42.4 0.86** 5.12 43.0 0.89** 5.12 43.0 0.89**
Mono-vg 4.84 35.1 0.84** 4.44 34.4 0.83** 2.95 22.9 0.66**
Mono-vs 5.19 42.5 0.89** 5.39 39.2 0.88** 5.39 39.2 0.88**
Table 2
 
Duration–amplitudes relationships for horizontal vergence and vertical saccades for all subjects. The correlations were analyzed under logarithmic plots. All relationships are linear (p < 0.0001). The bino-vg: Vergence from binocular condition; bino-vs: Version from binocular condition; mono-vg: Vergence from monocular condition; mono-vs: Version from monocular condition; divg: Divergence; convg: Convergence; vs: Version.
Table 2
 
Duration–amplitudes relationships for horizontal vergence and vertical saccades for all subjects. The correlations were analyzed under logarithmic plots. All relationships are linear (p < 0.0001). The bino-vg: Vergence from binocular condition; bino-vs: Version from binocular condition; mono-vg: Vergence from monocular condition; mono-vs: Version from monocular condition; divg: Divergence; convg: Convergence; vs: Version.
Backward motion divg and up vs Forward motion divg and down vs Forward motion convg and down vs
Slope Intercept R 2 Slope Intercept R 2 Slope Intercept R 2
Bino-vg 3.13 62.0 0.71** 3.17 50.5 0.72** 4.34 93.0 0.81**
Bino-vs 2.60 42.5 0.53** 2.63 40.2 0.69** 2.63 40.2 0.69**
Mono-vg 2.79 52.8 0.61** 3.01 52.7 0.72** 4.59 92.8 0.76**
Mono-vs 2.01 45.5 0.43** 2.38 47.9 0.55** 2.38 47.9 0.55**
Table 3
 
Relationships between the time of vergence velocity peaks and time of saccade velocity peaks for all subjects. R2: Correlation coefficients; S: Slopes of the regression lines. All relationships of the subjects are linearly positive (**p < 0.0001).
Table 3
 
Relationships between the time of vergence velocity peaks and time of saccade velocity peaks for all subjects. R2: Correlation coefficients; S: Slopes of the regression lines. All relationships of the subjects are linearly positive (**p < 0.0001).
Backward motion divergence Forward motion divergence Forward motion convergence
Slope Intercept R 2 Slope Intercept R 2 Slope Intercept R 2
CK 0.74 0.006 0.52** 0.67 0.003 0.77** 1.43 0.01 0.69**
DY 1.14 0.001 0.76** 0.76 −0.0007 0.84** 1.59 0.004 0.72**
KG 0.80 0.003 0.69** 0.97 −0.005 0.95** 1.37 0.01 0.79**
LR 0.08 0.03 0.10** 0.67 0.004 0.64** 1.07 0.02 0.54**
MZ 0.61 0.001 0.28** 0.44 0.008 0.14** 0.90 0.01 0.22**
Table 4
 
Parameters for relationships between peak velocity of horizontal vergence and peak velocity of vertical saccades for binocular viewing conditions. R2: Correlation coefficients; I: Intercepts; S: Slopes of the regression lines. Positive relationships of the subjects are indicated with stars (*p < 0.05; **p < 0.0001).
Table 4
 
Parameters for relationships between peak velocity of horizontal vergence and peak velocity of vertical saccades for binocular viewing conditions. R2: Correlation coefficients; I: Intercepts; S: Slopes of the regression lines. Positive relationships of the subjects are indicated with stars (*p < 0.05; **p < 0.0001).
Backward motion divergence Forward motion divergence Forward motion convergence
Slope Intercept R 2 Slope Intercept R 2 Slope Intercept R 2
CK 0.05 16.5 0.13** 0.05 18.2 0.08* 0.08 12.1 0.21**
DY 0.10 3.4 0.43** 0.03 11.2 0.10* 0.09 7.9 0.19**
KG 0.23 6.0 0.59** 0.10 2.07 0.56** 0.08 2.9 0.44**
LR 0.10 3.9 0.58** −0.04 18.9 0.02 0.10 2.6 0.38**
MZ 0.11 8.9 0.32** −0.01 7.8 0.004 0.05 5.4 0.10**
Table 5
 
Relationships between peak velocity of horizontal vergence and peak velocity of vertical saccades for monocular viewing conditions. R2: Correlation coefficients. I: Intercepts. S: Slopes of the regression lines. Positive relationships of the subjects are indicated with * and ** (*p < 0.05; **p < 0.0001).
Table 5
 
Relationships between peak velocity of horizontal vergence and peak velocity of vertical saccades for monocular viewing conditions. R2: Correlation coefficients. I: Intercepts. S: Slopes of the regression lines. Positive relationships of the subjects are indicated with * and ** (*p < 0.05; **p < 0.0001).
Backward motion divergence Forward motion divergence Forward motion convergence
Slope Intercept R 2 Slope Intercept R 2 Slope Intercept R 2
CK −0.02 19.5 0.01 0.12 19.7 0.19** 0.06 13.0 0.04*
DY 0.03 13.2 0.04* −0.03 17.5 0.06* −0.02 17.6 0.005
KG 0.15 15.9 0.16** 0.02 13.5 0.02* 0.06 7.9 0.16**
LR 0.07 8.2 0.16** 0.05 7.13 0.15** 0.09 5.7 0.18**
MZ 0.03 28.4 0.003 −0.07 20.7 0.03* −0.01 15.9 0.004
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