To maintain binocular fixation on near targets during fore-aft translational disturbances, largely disjunctive eye movements are elicited the amplitude and direction of which should be tuned to the horizontal and vertical eccentricities of the target. The eye movements generated during this task have been investigated here as trained rhesus monkeys fixated isovergence targets at different horizontal and vertical eccentricities during 10 Hz fore-aft oscillations. The elicited eye movements complied with the geometric requirements for binocular fixation, although not ideally. First, the corresponding vergence angle for which the movement of each eye would be compensatory was consistently less than that dictated by the actual fixation parameters. Second, the eye position with zero sensitivity to translation was not straight ahead, as geometrically required, but rather exhibited a systematic dependence on viewing distance and vergence angle. Third, responses were asymmetric, with gains being larger for abducting and downward compared with adducting and upward gaze directions, respectively. As frequency was varied between 4 and 12 Hz, responses exhibited high-pass filter properties with significant differences between abduction and adduction responses. As a result of these differences, vergence sensitivity increased as a function of frequency with a steeper slope than that of version. Despite largely undercompensatory version responses, vergence sensitivity was closer to ideal. Moreover, the observed dependence of vergence sensitivity on vergence angle, which was varied between 2.5 and 10 MA, was largely linear rather than quadratic (as geometrically predicted). We conclude that the spatial tuning of eye velocity sensitivity as a function of gaze and viewing distance follows the general geometric dependencies required for the maintenance of foveal visual acuity. However, systematic deviations from ideal behavior exist that might reflect asymmetric processing of abduction/adduction responses perhaps because of different functional dependencies of version and vergence eye movement components during translation.
Translatory motion and head perturbations occur most commonly in fore-aft directions in everyday physical activities, like walking, running, and driving. Contrary to lateral motion where gaze directions usually are centered on axes roughly perpendicular to the head displacement, the kinematic dependencies of the vestibuloocular reflex patterns during fore-aft motion (fore-aft trVORs) are bound to be complex because gaze directions are nearly parallel to the direction of motion. Moreover because the two eyes have nonparallel, converging gaze directions during near target fixation, compensatory trVOR responses must include both a version and a vergence component. Indeed vergence responses have been reported during fore-aft motions (Paige and Tomko 1991; Smith 1985).
The only studies so far examining the geometric consequences of translatory movements that are nearly parallel to gaze direction have concentrated either on a general description of the eye movement organization and the combined effects of vision (Paige and Tomko 1991) or on the plasticity of the reflex following adaptation through wedge prisms (Seidman et al. 1999). In these studies, it has been nicely shown that the combination of horizontal and vertical eye movements that are generated during fore-aft translations exhibit a systematic dependence on both gaze direction and vergence angle (Paige and Tomko 1991). However, the conclusions of this earlier work were rather qualitative where emphasis was given on the fact that “responses were properly directed and temporally synchronized relative to the translation” rather than a detailed investigation of the quantitative features of these responses. For example, the accuracy with which these eye movements comply with the geometric requirements and the precision of tuning versus gaze direction remains unknown.
The goal of the present study was threefold. The first goal was to quantitatively examine the geometric dependence of the fore-aft trVORs on target eccentricity and vergence angle. Specifically, we sought to investigate how precisely the complex eye movement pattern during fore-aft motion is governed by the expected geometric requirements for maintaining foveal acuity during binocular fixation. Second, we wanted to investigate the high-frequency dynamics of the reflex. Third, we were interested in examining the evoked eye movements not only in terms of right/left eye responses but also in terms of version/vergence components. We think that the latter comparison is important for two reasons. First, a decomposition of eye movements into version and vergence will reveal more easily potential differences in adduction and abduction responses. Accordingly, abduction/adduction asymmetries in both latency and initial eye acceleration were present during transient motion stimuli (Angelaki and McHenry 1999). Second, recent work has suggested that different visual mechanisms are responsible for version and vergence responses to planar and radial optic flow stimuli (for a review, see Miles 1998). Because visual and vestibular signals most likely work in close synergy during translation, it is possible that vestibuloocular reflex properties are quantitatively different for version and vergence components. Preliminary results of this work have been presented in abstract form (McHenry and Angelaki 1998).
Animal preparation and training
Nine juvenile rhesus monkeys provided the data presented here. For details of general methods, see Angelaki (1998) andAngelaki et al. (2000). Each animal was chronically implanted with a lightweight delrin head ring anchored to the skull with stainless steel screws and dental acrylic. Dual scleral eye coils were implanted in both eyes beneath the conjunctiva and sutured to the globe anterior to all muscular insertions (Hess 1990). All surgical procedures were performed aseptically in accordance with National Institutes of Health guidelines. After adequate recovery time, animals were trained with juice rewards to fixate randomly presented red light-emitting diode (LED) targets for variable periods (300–1000 ms) and to maintain fixation, after the target was extinguished and an auditory cue remained, for ≤2 s. Adequate fixation was determined on-line by comparing binocular horizontal and vertical eye positions with ideal target position windows of less than ±1° for central targets (<20°) and less than ±2° for more eccentric targets. Animals were usually trained 5 days/wk with free access to water on the weekend.
Experimental setup and protocols
During vestibular testing, animals were secured rigidly to the inner axis of a three-dimensional rotator mounted on a linear sled (Acutronics), such that the animal's nasooccipital axis was parallel to the direction of motion of the sled. In all experiments, the head was statically pitched 18° nose-down from the horizontal stereotaxic plane. Animals were secured with lap and shoulder belts to a primate chair, and their limbs were loosely bound. Special care was taken to rigidly couple the animal's head to the fiberglass inner gimbal of the motion delivery system (Angelaki 1998; Angelaki et al. 2000). As explained in the preceding paper (Angelaki et al. 2000), control experiments were performed to obtain an estimate of error in our measurements (estimated to be <10%). In addition, all data reported here were corrected for head movement (as explained in Angelaki et al. 2000).
The linear acceleration stimuli consisted of randomly selected sinusoidal oscillations (peak acceleration 0.3–0.4 g, frequencies 4, 5, 6, 8 10, and 12 Hz) (see Table 1 of Angelaki et al. 2000 for stimulus parameters). Onset of motion was contingent on adequate fixation (300–1,000 ms) of a randomly selected LED target (see following text). Binocular eye positions were computed on-line to monitor fixation based on geometric target position windows computed as described in the preceding paper (Angelaki et al. 2000).
Several target arrays were fabricated to present visual targets at a variety of distances and eccentricities. In a first set of experiments (6 animals, tested at 4–12 Hz), a flat surface with 31 LEDs mounted at different horizontal and vertical positions (±6 and ±12 cm eccentricities, measured relative to the right eye) was positioned at 20 cm. In a second, more recent set of experiments (6 animals, tested at 10 Hz), nine isovergence target arrays were constructed to present LED targets at 2.5 or 5° intervals to ±35° along five horizontal horopters at distances of 10, 15, 20, 30, and 40 cm and four vertical horopters at distances of 10, 15, 20, and 40 cm (Fig. FA1, Aand B, respectively). At an interocular distance ofd ioc = 3 cm, for example, the isovergence arrays at these distances would correspond to vergence angles of 15.9, 10.7, 8.4, 5.3, and 4.2° (horizontal) and 14.6, 11.1, 8.4, and 4.3° (vertical), respectively. Because all targets on an isovergence surface subtend the same vergence angle (ε), the isovergence arrays permitted quantitative analysis of the effects of eccentricity on the trVOR while holding vergence angle constant. In addition, the dependence of fore-aft trVORs on vergence angle (ε ≈ 4–18°) also was investigated by comparing data collected during fixation at the nine different isovergence arrays. In most experiments, targets remained head-fixed, although two animals also were tested with space-fixed targets (see following text).
Demodulated eye coil signals (4 for each eye) and the outputs of a three-axis accelerometer (rigidly attached to the fiberglass members to which the magnetic field coil assembly and the animal's head were attached firmly) were antialias filtered (200 Hz, 6-pole low-pass Bessel). The signals were digitized at 833.3 Hz (Cambridge Electronics Design, model 1401 plus, 12- or 16-bit resolution) and stored for off-line analysis.
Eye movements were calibrated using a combination of preimplantation and daily calibration procedures, as previously described (Angelaki 1998; Angelaki et al. 2000). Binocular, three-dimensional (3-D) eye position was computed as rotation vectors, E (Haustein 1989) with straight ahead as the reference position. The signals were smoothed and digitally filtered as described in the preceding paper (Angelaki et al. 2000). Eye angular velocity (Ω) was computed and used for the remaining of analyses. Torsional, vertical, and horizontal eye movements were defined as the components along the x (fore-aft),y (interaural), and z (vertical) head axes (positive directions are forward, leftward, and upward, respectively).
Average response cycles from a manually selected saccade-free steady-state portion (i.e., starting a minimum of 3 cycles after motion onset) from each experimental trial were computed for the three components of eye velocity of each eye, the horizontal vergence velocity (Ωh,R − Ωh,L), the horizontal version velocity [½(Ωh,R + Ωh,L)], as well as the stimuli (output of a 3-D linear accelerometer mounted close to the animal's head; see preceding text). A sinusoidal function including first and second harmonics and a DC offset was fit to each average cycle with a nonlinear least-squares optimization algorithm based on the Levenberg-Marquardt method (MATLAB, Mathworks). For each eye velocity component, as well as vergence and version, sensitivity then was computed as the ratio of the respective peak sinusoidal amplitude to peak linear head velocity (in °/s per cm/s, which is equivalent to °/cm). Peak linear head velocity was computed from the respective (i.e., fore-aft component of) linear acceleration fits. Response phase was expressed as the difference between each eye (or vergence and version) velocity relative to backward linear head velocity. Based on the sign conventions used here (positive eye movement is to the left and down; positive head movement is backward), compensatory phase is 0° when looking to the right or up and −180° when looking to the left or down. The sensitivity and phase estimates, as well as mean eye position over the first stimulus cycle, were stored for each experimental run. The second harmonic component fit was generally at least an order of magnitude less than the fundamental component and was not considered further in the analyses.
The derivation of the ideal kinematics to maintain fixation during fore-aft motion has been provided in the (Eqs. A1–A5), whereas simulations of the geometric dependencies of the horizontal, vertical, and vergence sensitivities as a function of eye position have been illustrated in Fig. 1. Given the ideal kinematic requirements dictating binocular fixation for fore-aft motion, the sensitivity should increase as eye position increases from a zero-sensitivity point (ideally straight-ahead, i.e., 0°; Fig.1, A and C). In addition, the steepness of this dependence on horizontal and vertical eccentricity should increase as a function of the prestimulus (static) vergence angle, ε. To quantify the steepness of this increase and the accuracy of the reversal point, the absolute value of the functions described by Eq. A1 (horizontal arrays) or A5(vertical arrays) was fitted to the data from each animal and isovergence target array (limited to eye positions of ±20°). Functions (1) and (5) were optimized by allowing two parameters to vary, vergence angle, ε (computed trVOR vergence) and either a horizontal or vertical offset to the reversal point (that allowed a shift of the curves to the left or to the right). The computed trVOR vergence reflected the corresponding fixation distance for which the movement of each eye would be compensatory in magnitude. Ideally, of course, the computed trVOR vergence and the prestimulus (static) vergence should be identical.
The accuracy of fore-aft response tuning to target (and eye) eccentricity was determined not only by the horizontal/vertical offset of zero sensitivity but also by the corresponding change in phase. To quantify the transition of phase from 0 to ±180°, a three-segment piecewise linear function was fit to the phase dependence on horizontal/vertical eccentricity (e.g., Figs. 6 A and 8). The three-segment function consisted of two outer segments of constant phase (with variable amplitude) that were joined by a variable-slope middle segment. The fitted width of this segment served as a measure of the abruptness of the phase transition.
These analyses were applied to data from all animals (head-fixed targets), as well as to data collected in two of the animals during fixation at earth-fixed targets. Because there were no detectable differences between the space- and head-fixed data, the following presentation only focuses on the head-fixed results that were available in all animals.
Fore-aft translations elicited eye movements the amplitude and direction of which depended on target distance and eccentricity. Typical exemplary responses during sinusoidal fore-aft translation at 10 Hz are shown in Fig. 2 for fixations of three targets with different horizontal eccentricities, all lying on a horizontal isovergence array with ε ∼ 9.5° (5 MA). While looking to the left or to the right, horizontal eye velocity modulated sinusoidally, albeit the amplitude of modulation was generally less than that required for binocular fixation at the target (Fig. 2, compare Ωhor with Ideal responses). In line with the kinematic requirements of the reflex, the movement of the two eyes was disjunctive, with the eye in adduction (i.e., contralateral to the target) moving faster than the abducting eye. Nevertheless, despite largely undercompensatory responses for each eye, the difference between the velocities of the two eyes (i.e., vergence velocity) was qualitatively similar in actual and ideal responses. During fixation at a target located in between the two eyes, horizontal eye velocity was small and the modulation appeared more variable (Fig. 2,middle). Despite the small amplitude of the eye velocity, responses were clearly disjunctive, consisting mainly of vergence and little version components.
The systematic dependence of fore-aft trVOR on target (and eye) position is illustrated further in Fig.3, where vertical and horizontal right and left eye velocity during 4-Hz oscillations are compared for nine different targets located at different horizontal/vertical eccentricities on a flat screen at a distance of 20 cm from the eyes (see methods). The organization of the plot reflects the positions of the fixation targets (relative to the animal), with center, up/down, left/right in the plot corresponding to the respective location of the targets on the screen. While fixating a target centered between the eyes (center group of plots), both the vertical and horizontal responses were small. In addition, the out-of-phase horizontal components of the two eyes further illustrate the predominance of vergence over version eye movements during center target (midsagittal) fixation. Horizontal version eye movements were elicited during fixation at left and right targets (Fig. 3,left and right columns). During fixation to the left, for example, peak positive horizontal eye velocity was leading positive (backward) linear acceleration by ∼90°, i.e., it was approximately in phase with forward linear velocity. According to the coordinate system used here where leftward eye movements and backward head movements were defined as positive, this phase relationship corresponded to a leftward eye movement during forward motion and a rightward eye movement during backward motion. During fixation to the right, the opposite phase relationship was observed, reflecting the fact that a rightward eye movement was now elicited during forward motion. A similar phase reversal was observed for vertical eye velocity, as the fixation target shifted from up, center and down (Fig. 3, top, middle, and bottom groups, respectively). Forward motion elicited upward (downward) eye movements for up (down) targets, respectively.
In the following, the dynamics and geometric dependencies of these horizontal and vertical eye movement components on target distance and eccentricity are described in detail. In a first set of experiments, targets on a flat screen at a distance of 20 cm were used to investigate the trVOR dynamics (4–12 Hz) at different target eccentricities. In a second set of experiments, isovergence arrays were constructed (see methods). The horizontal and vertical isovergence arrays have been used to quantitatively examine the geometric dependencies of 10-Hz responses on target distance and eccentricity.
Frequency response characteristics
Data from 4,078 experimental presentations of sinusoidal fore-aft translation (4–12 Hz) while fixating targets on the flat target array were included in the following analyses. Both horizontal and vertical response components were characterized by high-pass filter properties. The frequency response of the fore-aft trVOR depended on eye (i.e., target) position. This property is better illustrated in Fig.4, where average (±SD) sensitivity and phase have been plotted separately for the right and left eyes (● vs. ○, respectively). Even though the horizontal sensitivity of both eyes exhibited high-pass filter properties, quantitative differences emerged. The adducting eye (i.e., right eye during left target fixation and the left eye during right target fixation) was characterized by both greater sensitivities (as expected from Eq. A1, e.g., Figs. 2 and 3) and more high-pass filter properties compared to the abducting eye. In addition, high-frequency phase lags were smaller for the adducting compared with the abducting eye.
Vergence and version components: dynamics
For a reflex that elicits largely disjunctive eye movements such as the fore-aft VOR, an alternative decomposition of the movement of the two eyes is through version and vergence (as compared with left and right eye sensitivities). Average version and vergence sensitivity data for three of the targets in the horizontal meridian have been plotted in Fig. 5. Vergence sensitivity exhibited a steeper dependence on frequency (i.e., stronger high-pass filter characteristics) compared with version [F(5,262) = 23.8, P < 0.01].
Scaling of left and right eye sensitivity with target eccentricity and vergence angle
The kinematic analysis shows that fore-aft trVORs depend on both vergence angle, ε, and eye position (Eqs. A1–A5). Whereas targets on a flat screen differ in both parameters, targets on an isovergence screen differ only in eccentricity. Because target fixation on an isovergence surface always requires the same vergence angle, isovergence surfaces offer a unique advantage to quantitatively and independently examine the geometric dependence of the trVORs on target (and eye) eccentricity. A total of 3,676 experimental trials of 10-Hz fore-aft translations during fixation at targets on several different horizontal and vertical isovergence arrays have been included in this analysis. Examples of the geometric dependence of the horizontal component of fore-aft trVOR are illustrated in Fig.6 for two different isovergence arrays, ε = 15.9° and ε = 5.3°. For targets on the horizontal isovergence arrays, horizontal trVOR sensitivity increased with eccentricity (i.e., prestimulus eye position of the respective eye) and exhibited a V-shape curve, as predicted by the ideal relationships (Eq. A1, a and b). However, despite qualitatively appropriate tuning as a function of prestimulus fixation, sensitivities were consistently undercompensatory for maintaining fixation on the respective target (Fig. 6 A, compare solid and open circles with thin solid and dashed lines, respectively).
Assuming that the observed horizontal sensitivities would be compensatory to some fixation distance along the gaze direction of the respective eye, we computed a “trVOR vergence angle,” ε = εtrVOR, by fitting Eq. A1, a andb, separately for the right and left horizontal sensitivities (Fig. 6 A, thick solid and dashed lines, respectively). This trVOR vergence was computed separately for each of five horizontal isovergence screens and plotted for each animal as a function of the actual prestimulus vergence in Fig.7 A. Despite some variability among animals, the computed trVOR vergence (which would correspond to the virtual fixation distance at which the motion of each eye would be compensatory) was consistently less than the actual vergence angle. A linear regression through the data from all five animals yielded a slope of ∼0.5 (Fig. 7 A, compare — with the ideal, unity slope line plotted as · · · ). Similar values were also obtained in the two animals the responses of which also were tested with space-fixed targets.
Fitting Eq. A1, a and b, to the whole data set for each isovergence array would assume that there are no asymmetries in the accuracy with which the trVOR sensitivity tuning follows the geometric dependence for abducting and adducting eye positions. To investigate the accuracy of this assumption, a modified version ofEq. A1 that allowed the fitted vergence parameter to be different for positive and negative fixations also was fitted to the data. The computed εtrVOR values were significantly larger for the abducting compared with the adducting eye [F(1,72) = 49.2, P ≪ 0.01]. For the left eye, for example, the computed vergence was closer to the prestimulus values during fixation to the left compared with fixations to the right. The opposite was true for the right eye. Linear regressions similar to those of Fig. 7 A drawn separately for adducting and abducting responses yielded slopes of 0.5 and 0.68, respectively. This asymmetry in the εtrVOR values for the adducting and abducting eyes was independent of vergence angle and viewing distance [F(4,72) = 6.5, P > 0.05].
Similarly undercompensatory responses were observed for the vertical trVOR component during fixation at targets on the vertical isovergence arrays. Examples of the geometric dependence of the vertical component of fore-aft trVOR for two vertical isovergence arrays, ε = 13.3° and ε = 4.9°, are illustrated in Fig.8. For targets on the vertical isovergence arrays, vertical sensitivity also increased with vertical eye position and exhibited a V-shape curve. Small differences between the vertical sensitivities of the two eyes were seen (e.g., Fig. 8 for upward gaze directions), but they were inconsistent among animals. To quantitatively describe the dependence of vertical sensitivity on gaze direction, and in parallel with the analyses of the horizontal sensitivity data, we computed a trVOR vergence, ε = εtrVOR, by fitting Eq. EA5 separately to the right and left vertical eye sensitivities (Fig. 8, thick solid and dashed lines, respectively). The computed trVOR vergence values have been plotted as a function of prestimulus vergence angle in Fig.7 B. Similarly as with the horizontal trVOR components, vertical sensitivities were consistently undercompensatory, with a linear regression slope of ∼0.5. When the fitted vergence angle inEq. EA5 was allowed to be different for positive and negative vertical eye positions, the εtrVOR values were significantly larger for positive (downward) compared with negative (upward) fixations [F(1,43) = 33.6, P ≪ 0.01, regression slopes of 0.45 and 0.29, respectively]. In contrast to the horizontal sensitivities, there was no difference in the εtrVOR values computed from the vertical sensitivities of the two eyes [F(1,43) = 1.0,P > 0.05].
Zero sensitivity and phase reversal
For an ideal reflex performance, the eye positions for which the trVOR sensitivities of the left and right eyes approach zero should be straight ahead for the respective eye (i.e., θ = 0°). This requirement was not followed accurately and there seemed to be systematic deviations from such an ideal performance (Table1). For example, the eye eccentricity at which the horizontal sensitivity approached zero was similar for the two eyes during fixation at the nearest targets but shifted opposite for the two eyes as viewing distance increased [F(1,26) = 11.9, P < 0.01]. Specifically, the zero-sensitivity eye position shifted further to the left for the left eye and to the right for the right eye (Table1 A). The eye eccentricity at which vertical trVOR sensitivity approached zero also depended on viewing distance [F(3,8) = 21.8, P < 0.01], albeit similarly for the two eyes [Table 1 B; F(3,8) = 0.9,P > 0.05]. Specifically, the zero-sensitivity position of both eyes was shifted slightly upward at the nearest target. As viewing distance was increased, the zero-sensitivity eye position crossed ∼0° (straight ahead) and was shifted downward (∼5–12° for the smallest vergence angles).
A departure from ideal performance was also observed regarding the dependence of response phase on eye position. Ideally, a sharp transition of the response phase from 0 to 180° should occur at θ = 0°. In contrast, the actual phase transitions occurred over several degrees (e.g., Figs. 6 A and 8). For the horizontal isovergence arrays, the further away the target, the more gradual the phase transition (Table 1 A). For the vertical isovergence arrays, no such dependence on viewing distance was observed, albeit phase reversal for the most distant vertical isovergence array was characterized by much larger variability (Table1 B).
Vergence sensitivity: dependence on target distance and eccentricity
The ideal kinematic requirements of the trVOR dictate that not only left and right eye sensitivities but also their difference (vergence sensitivity) should be a function of both target distance and horizontal eccentricity (Eq. EA2 ). Specifically, the dependence of vergence sensitivity on horizontal eye position should be quadratic (Fig. 1 B), as is also its ideal dependence on vergence angle. Examination of the vergence sensitivity for the horizontal isovergence target arrays indeed revealed a quadratic dependence on horizontal eye position (Fig. 6 B). Peak vergence sensitivity occurred for (center) targets in the midsagittal plane. As horizontal target eccentricity increased in a horizontal isovergence screen, vergence sensitivity decreased (Figs. 6 Band 1 B).
In contrast to right and left eye velocity sensitivities, which were consistently undercompensatory for all tested fixation distances, vergence sensitivity was generally undercompensatory for targets on the closest isovergence array but consistently overcompensatory for vergence angles <10° (Fig. 6 B, compared the solid lines with the open circles). To quantify this observation and to examine whether the vergence sensitivity follows the ideal quadratic dependence on vergence angle, ε, peak vergence sensitivity at 10 Hz was computed for each animal and plotted as a function of vergence angle in Fig.9 A. In all animals, the dependence of peak vergence sensitivity on vergence angle was largely linear, unlike the prediction of Eq. EA3 (Fig. 9, dotted line; linear regression parameters are included in Table2). Second-order regressions did not significantly improve the fits.
To examine if vergence sensitivity followed the expected, quadratic dependence on vergence angle for other than the midsagittal targets, in three of the animals an average vergence sensitivity was also computed for right eye positions spanning a range of ±5 ∼ −10° (solid symbols), 0° (open symbols), and +10° (gray symbols) and plotted versus vergence angle in Fig. 9 B. Regression fits through the data also revealed a linear dependence on vergence angle.
Maintenance of binocular fixation during linear disturbances of the head represents a major challenge for the primate oculomotor system. During fore-aft translations, the amplitude and direction of the motion of each eye should be shaped by unique three-dimensional geometric constraints that dictate disjunctive eye movements that are dependent on target distance and eccentricity (Paige and Tomko 1991). The accuracy with which the vestibuloocular system can comply with these geometric demands was investigated here by systematically varying target distance and eccentricity during high-frequency sinusoidal fore-aft translations.
Foveal stabilization hypothesis: compliance and departure from ideal behavior
Because the retinal optic flow during fore-aft motion is directed radially, only a small portion of the retinal image can be stabilized. This constraint is unique as the rotational VOR is associated with parallel retinal optic flow patterns permitting image stabilization over larger retinal areas. The horizontal sensitivities described byEq. A1 assume that the fore-aft trVOR is optimized to stabilize the retinal images on the fovea. The sensitivity data, while largely undercompensatory, followed the trend predicted by the ideal dependence on eye position. Both horizontal and vertical sensitivities exhibited a V-shape dependence, being zero at gaze orientations around straight ahead.
Despite this qualitative compliance with the geometric dependencies required by the foveal stabilization hypothesis, there were three quantitative differences. First, zero sensitivity was not always observed at zero eye position (straight ahead) but tended to depend on vergence angle. For both the horizontal and vertical target arrays, the best alignment was observed for the largest vergence angles (ε > 10°). As vergence angle decreased, however, inappropriate horizontal and vertical components were observed for fixations on midsagittal or zero vertical elevation targets, respectively. Specifically for the horizontal target arrays (but not the vertical), the zero sensitivity point was shifted opposite for the two eyes. For the left eye, it shifted more to the left, whereas for the right eye, it shifted to the right.
Similarly to this imperfect geometric dependence of the response amplitude on eye eccentricity, response phase also did not exhibit an abrupt 180° transition that should ideally occur around an eye position of 0°. In contrast, trVOR response phase exhibited a gradual phase transition (10–30°), which tended to become more gradual as viewing distance increased. The gradual phase transition and its dependence on viewing distance may be a consequence of the underlying neural computations which integrate oculomotor parameters (eccentricity, viewing distance) and vestibular signals to generate the trVORs.
Finally, there was a systematic and significant asymmetry for adducting/abducting as well as upward/downward eye movements (see alsoAngelaki and McHenry 1999). The difference in the horizontal movement of each eye could result from asymmetries in the underlying otolith-abducens and -medial rectus pathways. The adduction/abduction asymmetries and the directional misalignment of the horizontal response sensitivity might be related to a functional demand to improve the gain of the horizontal vergence sensitivity (see following text). Despite a systematic and consistent horizontal vergence response, no consistent vertical disconjugacy was observed. The latter observation was verified by the lack of any statistically significant difference between the two eyes for the two parameters fitted, i.e., the computed trVOR vergence and the “zero sensitivity offset.”
Translational VOR gain
Most of the analysis here has concentrated on response sensitivities rather than response gains (e.g., Angelaki et al. 2000). The reason for this is twofold. First, the small responses during fixation at targets with small horizontal and vertical eccentricities result in gains (ratio of actual over ideal eye velocity) that are quite variable, with individual values that can vary as much as 10-fold. Second, the nonlinear dependence of response sensitivity on eye eccentricity, as well as the departure of the zero-crossing point from ideal behavior, result in gains that depend on eye eccentricity.
To investigate the effectiveness of fore-aft trVOR in maintaining fixation, an overall “gain” for the fore-aft VOR was estimated for each isovergence array, as follows: on the basis of the assumption that the response sensitivities observed would be compensatory to some fixation distance along the gaze direction of the respective eye, a trVOR vergence was computed and compared with the actual prestimulus vergence angle (Fig. 7). These computed vergence angles for which the movement of each eye would be ideal were consistently less than the actual fixation vergence angle (linear regression line slopes of ∼0.5; for the abducting eye, slopes were larger, ∼0.68). The closer the target, the more undercompensatory the response. Extrapolating from these data, the virtual and actual fixation distance would only coincide at ∼70 cm.
Differences in the gain and dynamics of version/vergence and abduction/adduction components: different functional goals for version and vergence?
One of the most important results of the present study was the distinctly different properties of the vergence and version components of the responses during fore-aft motion. These differences can be summarized as follows: first, vergence and version components differed in gain. At a distance of 10 cm, vergence sensitivity was less than ideal. At viewing distances >20 cm, however, vergence sensitivities approached and exceeded ideal values (Fig. 6 B). Version eye movements, on the other hand, were consistently undercompensatory for all viewing distances tested. Similarly undercompensatory version responses also were observed during lateral motion (Angelaki et al. 2000; Schwarz and Miles 1991; Telford et al. 1997).
Second, vergence and version also differed in response dynamics. The frequency dependence of the version component during fore-aft motion was similar to that during lateral motion and center target fixation (Angelaki et al. 2000). In contrast, vergence was characterized by stronger high-pass filter properties than the version component (Fig. 5). A similar difference in response dynamics also was observed for lateral motion during eccentric fixation (Angelaki et al. 2000). Because vergence response components to lateral motion increase as a function of eye eccentricity, it is very likely that these observations are interrelated. The larger the ratio of vergence- to-version response components, the more high-pass filtered properties characterize trVOR sensitivities.
Because decomposition of the elicited eye movements into version and vergence is totally equivalent to the description in terms of right and left eye responses, it is important to point out that the observed differences between version and vergence are totally equivalent and a direct consequence of corresponding differences in abduction and adduction responses. For example, the differences in the dynamics of version and vergence sensitivity (Fig. 5) are a direct consequence of the different dynamic dependencies of the abducting and adducting responses of each eye (Fig. 4). Similarly, the nearly compensatory vergence sensitivity values are largely due to the two “problems” characterizing the tuning curves of the response sensitivity of each eye. First, the zero sensitivity positions shifted in opposite directions for the two eyes as a function of viewing distance. Such an opposite shift increases the difference between the right and left eye sensitivities for a given eccentricity and thus their difference, vergence sensitivity, also is increased. Second, the observed tuning curves were asymmetric, with the abducting eye increasing with a steeper slope than the adducting eye. This asymmetry further increases vergence sensitivity. Therefore it would appear that these two inaccuracies in the geometric tuning curves of the sensitivity of each eye are linked directly to the improved performance of vergence sensitivity. Without the adduction/abduction asymmetry and the opposite zero sensitivity shifts for the two eyes, it would be impossible for the largely undercompensatory movement of each eye to result in nearly (or over-) compensatory vergence response sensitivities.
The observed differences in the gain and dynamics of the adducting and abducting trVOR response sensitivities could arise from at least partly separate processing of otolith-abducens and -medial rectus pathways. According to these data and considering only agonist muscle actions, translational signals to the abducens nuclei would need to exhibit higher gains and less high-pass filter properties than the corresponding signals to the medial rectus motoneurons. Given the largely unknown neural processing elements and computations in the trVORs, the most interesting question at this point is not how but rather why these differences exist. We would like to propose that perhaps the reason behind these differences in the adduction/abduction components of the response is different functional demands for version and vergence. One way of interpreting this behavior is as sacrificing some accuracy in the version component of the fore-aft trVOR to improve the vergence response.
Interestingly and contrary to geometric predictions, the dependence of vergence sensitivity on vergence angle was linear for all tested animals (Fig. 9 and Table 2). A closer to ideal quadratic dependence has been reported previously in squirrel monkeys (Paige and Tomko 1991). The difference in the results is not obvious, particularly because mean data (without any measure of variability) from only a single animal were presented in the Paige and Tomko (1991) study. Furthermore the gaze directions for the response cycles used to obtain these values were not reported. As predicted by geometry (Fig. 2) and as is the case for actual responses (Fig.6 B), vergence sensitivity exhibits a quadratic dependence on eye position. Thus if values at different eye eccentricities are combined (as possibly done by Paige and Tomko), the comparison of vergence sensitivity as a function of vergence angle is inaccurate. Finally, differences in stimulus frequency (5 Hz in the Paige and Tomko study, compared with 10 Hz used here), as well as the range of vergence angles tested, also could contribute to the difference in the results. Nevertheless the only other report addressing the dependence of vergence sensitivity on vergence angle is in agreement with results from this study: A similar linear (and not quadratic) dependence on vergence angle also has been reported for the vergence responses elicited by radial optic flow steps (Yang et al. 1999).
Vestibular signals and ocular (gaze) following: functional and physiological overlap
There has been ample behavioral and neurophysiological evidence demonstrating that visual stabilization mechanisms and labyrinthine reflexes have evolved to operate in concert and complement each other in maintaining visual acuity. Miles (1993) recently has proposed that as foveal vision emerged, accompanied by vergence eye movements and stereopsis, novel visual and vestibular mechanisms also evolved to stabilize binocular gaze on the depth plane of interest. Ocular following and the translational VORs therefore have been proposed to operate together to provide rapid ocular compensation and binocular gaze stability (Miles 1993, 1998; Miles and Busettini 1992; Miles et al. 1991). Not only version but also short-latency vergence responses have been shown to be elicited in response to both radial optic flow and disparity steps (Busettini et al. 1996a,b, 1997; Masson et al. 1997).
The proposal of a common functional role for trVORs and ocular following/radial flow vergence responses has been supported by several behavioral experiments. It has been shown, for example, that both the trVOR during lateral motion and the ocular following responses exhibit a similar, linear dependence on vergence angle (Busettini et al. 1991, 1994; Schwarz and Miles 1991;Schwarz et al. 1989). Recent studies of radial optic flow in humans also have reported a linear dependence of the short-latency vergence eye movements on vergence angle (Busettini et al. 1997; Yang et al. 1999). Despite a geometrically appropriate quadratic dependence, our data in five animals suggest that the vestibularly driven vergence sensitivity also is characterized by a similar, linear dependence on vergence angle. Therefore ocular following, as well as radial flow and disparity vergence responses, are characterized by similar geometric dependencies as the lateral and fore-aft trVORs. Whether and to what extent the optic flow and trVOR systems share neuronal elements remains to be seen. Even though the neural substrates of ocular following have been shown to include the middle superior temporal area of the cortex (MST), the dorsolateral pontine nucleus and the ventral paraflocculus (Gomi et al. 1998;Kawano and Shidara 1993; Kawano et al. 1990; Kobayashi et al. 1998; Shidara and Kawano 1993), our knowledge of the trVOR circuitry is very limited. It is possible that the visual and vestibular signals converge onto cells in the ventral paraflocculus, for example, which then could represent the major site for a common optic flow/translational vestibular signal processing. Vestibular responses to head translation, however, have been reported to exist as far upstream as the MST (Duffy 1998), albeit the functional role of such signals is at present unknown.
The authors are grateful to Dr. Bernhard Hess for valuable comments on the manuscript.
This work was supported by grants from the National Eye Institute (EY-12814 and EY-10851) and by Grant F-49620 from the Air Force Office of Scientific Research.
Present address and address for reprint requests: D. Angelaki, Dept. of Anatomy and Neurobiology, Washington University School of Medicine, Box 8108, 660 S. Euclid Ave., St. Louis, MO 63110.
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.
- Copyright © 2000 The American Physiological Society
Isovergence kinematics during sinusoidal fore-aft translation
Let θ R, θL, and ϕR, ϕL be the horizontal and vertical Fick angles of the right and left eye, respectively (Fig. FA1). Let alsod ioc be the interocular distance (2.8–3.2 cm; measured for each animal). Let's assume a fixation point at distance D, a horizontal eccentricity H(leftward is positive) and a vertical eccentricity V(downward is positive). After a forward displacement throughr x, the new eye position required to maintain fixation is Under the assumption that r x≪ D, it easily is computed that the idealsensitivity (defined as eye velocity/linear velocity) is In addition where ε is the prestimulus (static) vergence angle defined as ε = θR − θL. On the basis of simple substitutions, the right and left ideal horizontal sensitivities (°/s per cm/s or °/cm), while fixating targets along horizontal isovergence arrays, are as follows: Equation A1a Equation A1bThe sensitivity amplitude described by Eq. A1 has been simulated for the left and right eyes in Fig. 1 A(- - - and —, respectively). It should be added that Eq. A1 gives horizontal trVOR sensitivity also for tertiary targets. Because these equations are expressed as rate of change of Fick angles, horizontal sensitivity is independent of vertical eye position.
Vergence sensitivity, defined as the difference between right and left velocity sensitivities, exhibits the following dependence on horizontal eye position and interocular distance Equation A2The dependence of ideal vergence sensitivity on horizontal eye position is quadratic, as shown in Fig. 1 B. Notice that peak vergence sensitivity ideally should occur for targets in the midsagittal plane (θR = −θL = ε/2) [because vergence sensitivity in Fig. 1 B has been plotted vs. right eye position, the quadratic waveforms peak at positive (leftward) right eye positions]. In this case of midsagittal targets, vergence sensitivity is Equation A3The simplified Eq. EA3 clearly shows that peak vergence sensitivity should increase proportionally to the square of vergence angle. A similar quadratic dependence on vergence angle should also exist for all eye positions (not just the midsagittal targets), albeit not directly obvious from Eq. EA2 .
The vertical sensitivity can be computed using similar geometric considerations. After a forward displacement throughr x, the new right eye position for a fixation point at a horizontal eccentricity H, a vertical eccentricity V and a perpendicular distance D is Under the assumption that r x≪ D, it is easily computed that the idealsensitivity (defined as eye velocity/linear velocity) is Equation A4Because these equations are expressed as rate of change of Fick angles, the vertical sensitivity is a function of both horizontal and vertical eye positions. Specifically for targets in the midsagittal plane (as those in the vertical isovergence arrays used here), the ideal vertical sensitivity simplifies to [because tan ε/2 = (d ioc/2)/D and θR = −θL = ε/2)] Equation A5Similar equations describe the sensitivity of the left eye. The sensitivity amplitude described by Eq. EA5 has been simulated in Fig. 1 C.
The dependence of both horizontal and vertical sensitivities on eye position is nonlinear. Therefore to quantify the geometric dependence on target eccentricity, the absolute magnitude of Eqs. A1 and EA5, rather than linearized versions, was fit to the data (see methods). The sensitivity functions derived here (and simulated and fitted to the data) were computed as the rate of change of Fick angles. However, the actual sensitivities reported here in the data have been expressed in head coordinates. For secondary positions of ±20° (range in which the two sensitivities were compared), the horizontal components coincide, whereas the vertical components differ by ≤6%.