INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Daily activities depend critically on excellent visual acuity upon a small but neurally over-represented part of the retina, the fovea. Because of its importance, fast reorienting saccadic and smooth-tracking eye movements have evolved to effectively place and maintain targets of interest on the fovea. Such a preferential treatment of the fovea would leave the third degree of freedom of the eye, rotation about the line of sight, potentially underdetermined if it wasn't for Listing's law. Even though its functional role remains speculative (Haslwanter 1995; Helmholtz 1867; Hepp 1990, 1995; Hering 1868; Schreiber et al. 2001), Listing's law specifies ocular torsion during pursuit and saccades as a unique function of the horizontal and vertical components of eye position such that the instantaneous rotation axis of the eye tilts half as much as gaze (known as the half-angle rule) (Haslwanter et al. 1991; Tweed and Vilis 1987, 1990; Tweed et al. 1992). This unique organization of the three-dimensional (3D) kinematics of ocular rotations was originally proposed to be neural in origin (Tweed and Vilis 1987, 1990). More recently, however, the histological discovery that the pulling directions of extraocular muscles do not remain fixed in the orbit but tilt through half the angle of gaze has motivated several theoretical and behavioral studies arguing for or against a potentially mechanical implementation of Listing's Law (Demer et al. 2000; Misslisch and Tweed 2001; Quaia and Optican 1998; Raphan 1998; Tweed 1997; Smith and Crawford 1998; Tweed et al. 1994).

When we move, the vestibuloocular reflexes (VOR) exist to provide a quick and efficient mechanism for keeping images stable on the retina. Phylogenetically the oldest VOR rotates the eye in the opposite direction to the head rotation (rotational VOR or RVOR). The RVOR is present in both foveate and afoveate animals and has a goal to stabilize images on the whole retina (Misslisch et al. 1994). Foveate animals also possess an additional vestibularly driven visual stabilization mechanism known as the translational VOR (TVOR), which functions during translational motions (Miles 1993, 1998). Because of differences in the geometry of gaze stabilization during rotations and translations that call for different functional goals for the RVOR and the TVOR (i.e., full-field vs. foveal image stability), only the TVOR exhibits an eye-position-dependent torsion similar to smooth pursuit (Angelaki et al. 2000, 2003). In contrast, the RVOR exhibits a very small eye-position-dependent torsion, consistent with the functional goal of keeping images stable on the entire retina (Crawford and Vilis 1991; Misslisch and Hess 2000; Misslisch et al. 1994).

Despite differences in the functional goals of the RVOR and the TVOR, natural activities rarely involve purely rotational or translational head movements. Instead, be it active head and body movements or passive displacements, the need for maintaining visual acuity requires activation of both the RVOR and TVOR stabilization mechanisms. Combined activation of the RVOR and the TVOR has been traditionally studied during rotations with subjects eccentric relative to the axis of rotation. The closer the target and the larger the radius of rotation, the higher the contribution of the TVOR relative to the RVOR. This stimulus has been commonly used to study horizontal eye movements (Anastasopoulos et al. 1996; Crane et al. 1997; Fuhry et al. 2000; Seidman et al. 2002; Snyder and King 1992; Telford et al. 1996, 1998), although the gaze-dependent torsional components have never been characterized.

Specifically, the fact that in contrast to the RVOR the TVOR exhibits an eye-position-dependent torsion consistent with Listing's law allows for two alternative expectations regarding the 3D kinematic properties of the combined VOR. First, it is possible that an eye-position-dependent torsion is computed downstream of a site for RVOR/TVOR convergence. If true, the velocity axis of the combined VOR would tilt through a gaze-dependent angle that is fixed and independent of the relative RVOR and TVOR contributions to the total eye movement. This "fixed-rule" hypothesis is motivated by the postulated mechanical constraints based on the location of the extraocular muscle pulleys and their ability to change the axis of eye rotation as a function of gaze, thus generating the half-angle rule (Demer et al. 2000; Quaia and Optican 1998; Raphan 1998). However, such a solution does not preserve the different functional goals of the RVOR and the TVOR. Alternatively, it is possible to preserve the functional goals of the RVOR and TVOR in terms of both foveal and peripheral image stability by computing the eye-position-dependent torsion separately for the RVOR and the TVOR components (image-stabilization hypothesis). This could be done if the respective 3D processing takes place upstream of a site for RVOR/TVOR convergence. As shown here, the image-stabilization hypothesis results in different predictions from those of the fixed-rule hypothesis. Thus the present study aimed to investigate how the two functionally and geometrically distinct VORs combine in generating an eye movement in 3D: is the elicited ocular response governed by the functional goal for foveal and/or full-field image stability or is there a compromise in function because of the mechanical constraints imposed by the anatomical location of extraocular muscle pulleys?

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Binocular eye movements were recorded in four rhesus monkeys during 4-Hz (±5-20°/s) yaw rotations. The animals were seated in a primate chair that was secured inside a rotator/sled motion system (Neurokinetics) that could rotate and translate in the horizontal plane. The animal was placed inside the rotator at a variable distance from the center of rotation such that the axis of rotation was either passing through a line connecting the two ear canals (r = 0 cm) or being displaced through a radius, r, in one of two ways. First, when the animal was facing away from the axis of rotation (face-out condition), the eye movement required to compensate for the animal's translation in space was in the same direction as that required for its rotational movement. For example, a rotation to the right would occur simultaneously with a translation to the right. Thus under these conditions, the RVOR and TVOR combined in a synergistic manner (both requiring a leftward eye rotation). We refer to this stimulus configuration with positive radii (r > 0). Second, when the animal was facing into the axis of rotation (face-in condition), the eye movement required for compensating for head translation was of opposite direction to compensate for head rotation. Thus the RVOR and TVOR were antagonistic, and we refer to this stimulus configuration with negative radii (r < 0). For comparison, data were also collected during lateral translation (4 Hz, ±0.25 G).

All animals were trained to fixate targets at distances of 12, 18, 32, or 100 cm in a softly illuminated room. Laser targets were back-projected onto one of four screens and were presented as single dots (<0.5° of visual angle) using a laser/mirror galvanometer system (General Scanning). Both eyes in two animals and one eye in the other two animals were implanted with a dual coil for 3D eye-movement recordings (Hess 1990). For the latter two animals, the second eye was implanted with a traditional two-dimensional coil. Signals from these 2D coils were only used for behavioral control but not analyzed quantitatively (because torsion was not recorded).

The eye-position dependence of the VOR velocity axis was tested by requiring the animals to fixate targets in the mid-sagittal plane at different vertical eccentricities (±25°). During motion, periods of target presentation were alternated with periods in total darkness. Trained animals were required to keep their eyes within binocular behavioral windows of <2°, even in darkness (typically with larger windows ~3°). Eye movements were calibrated by requiring the animals to monocularly fixate far targets at different horizontal and vertical eccentricities (Angelaki and Hess 2001; Angelaki et al. 2000). Stimulus presentation and data acquisition were controlled with custom-written scripts within the Spike2 software environment using the Cambridge Electronics Device (CED, model power 1401) data-acquisition system. Data were anti-alias filtered (200 Hz, 6-pole Bessel) and digitized by the CED at a rate of 833.33 Hz (16-bit resolution). Off-line, eye-movement data were converted into rotation vectors using straight ahead as the reference position. Fast phases were removed form the velocity records, and the angular velocity was computed (Hepp 1990). Positive directions were leftward, downward, and clockwise (as viewed from the animal) for the horizontal, vertical, and torsional components, respectively.

The amount of eye-velocity axis tilt in the animal's sagittal plane was evaluated in one of two ways: first, the elicited eye-velocity vector was plotted in head coordinates and a line was fitted in 3D. A VOR tilt angle was then computed from the direction cosines of the 3D lines as the angle between the line and the positive horizontal axis in the sagittal plane (Angelaki et al. 2003). In addition, sinusoidal functions were fitted to each of the horizontal, vertical, and torsional eye-velocity components. The ratio of peak torsional over peak horizontal eye velocity was defined as the "torsion/horizontal ratio," and its arctangent gave the VOR velocity tilt. The ratios and computed VOR tilt angles were considered positive if the horizontal and torsional response phase differed by less than ±30° and negative when between ±150° and ±210° (data were excluded otherwise). The equivalency between these two methods is summarized in Fig. 1 for the RVOR (at r = 0 cm) and the TVOR. To illustrate how the latter method was used to compute the VOR tilt angle, the peak horizontal and peak torsional eye-velocity components calculated from the sinusoidal fits to TVOR data from one of the animals have been plotted versus vertical eye position in Fig. 1A. Their ratio (scale for left ordinate) and the corresponding VOR tilt angle computed as the tangent of the ratio (scale for right ordinate) have been illustrated in Fig. 1B. Linear regressions for VOR velocity tilt angles versus vertical eye position quantitatively described this dependence. As shown in Fig. 1C, which summarizes RVOR and TVOR data from all animals at all viewing distances, the slopes computed from the 3D-line fit and from the torsional/horizontal ratio were similar. Although only the torsion/horizontal ratio results will be presented here, the 3D-line method gave equivalent results. Because the eye-position dependence of VOR tilt angle is independent of viewing conditions (Angelaki et al. 2003), the data were combined across cycles with the target on or in complete darkness.

View larger version (35K): [in this window] [in a new window]   Fig. 1. A and B: examples illustrating the analysis method. A: peak horizontal and torsional eye-velocity components calculated from the sinusoidal fits to translational vestibuloocular reflex (TVOR) data from animal (K) have been plotted vs. vertical eye position. As the animal looked at vertically eccentric targets placed at different viewing distances during lateral translation, both the horizontal and torsional components changed with target distance. B: the ratio of torsional vs. horizontal peak responses (and, thus, VOR tilt angle) was plotted as a function of vertical eye position, and the slope of linear regressions was used to quantify the dependence. VOR tilt angle was computed as the arctangent of the torsion/horizontal ratio. C: the equivalency of the 3-dimensional (3D) line fit (Angelaki et al. 2003) (see METHODS) and ratio analyses are illustrated by comparing the slopes computed from each method for rotational VOR (RVOR) and TVOR data from all animals at all viewing distances.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Theory and hypotheses

To interpret the data, two different hypotheses regarding the expected 3D kinematic behavior were developed (Fig. 2). The first can best be described as a mechanistic rule that could be implemented based on the hypothesized action of the pulleys. The second hypothesis is based on the functional goal of the VOR.

View larger version (37K): [in this window] [in a new window]   Fig. 2. Schematic outline (left) and simulations (right) of 2 different hypotheses for the eye-position dependence of the combined VOR, the "fixed-rule" (A) and the "image-stabilization" (B) hypotheses. In all simulations, the VOR tilt angle, (), has been plotted as a function of gaze angle  (Eqs. (1) and (2)). Simulations with R = 0.17 (black lines, Rvor) and T = 0.7 (dashed lines, Tvor),  = 1, D = 18 cm and different values of the radius of rotation (r = 5, 12, 25, and 50 cm; see color coding scheme in B; In A, simulations at all radii superimpose; red solid lines). Positive values (r > 0) represent synergistic combinations of RVOR/TVOR (corresponding to face-out motion) and negative values (r < 0) to antagonistic RVOR/TVOR combinations (corresponding to face-in motion). Dotted lines illustrate 0 and half-angle slope lines.

FIXED-RULE HYPOTHESIS (FIG. 2A). This hypothesis assumes that translational and rotational signals are first combined before an eye-position-dependent torsion is computed (Fig. 2A, left; 3D kinematics box). Thus during eccentric rotation, the eye-velocity axis tilt for the combined VOR would be equal to a fixed slope, C, times the gaze angle, , i.e.

(1)

where C is the fixed slope; e.g., C = C_T, or C = C_R, where C_T and C_R are the slopes of the eye-position dependence of the TVOR and RVOR velocity axes, respectively (Angelaki et al. 2003). Alternatively, the combined VOR slope could have an in-between value as shown in Fig. 2A where the combined VOR slope (red lines) is between C_T = 0.7 and C_R = 0.17; dashed Tvor and solid Rvor black lines, respectively. No matter what the exact value for the combined VOR slope is, this hypothesis predicts that the velocity axis will tilt by a constant amount that is independent of the radius of rotation and the viewing distance (both of which would change the amount of eye velocity that is generated by the TVOR).

IMAGE-STABILIZATION HYPOTHESIS (FIG. 2B). According to this hypothesis, an eye-position-dependent torsion is computed separately for the RVOR and TVOR prior to their site of convergence, and each of the torsional and horizontal components of the total eye movement is the sum of the respective contributions from the RVOR and TVOR¹ (Fig. 2B, left). Such a solution would be necessary, if the functional goals of the RVOR (full-field image stabilization) and TVOR (foveal image stabilization) must be fulfilled. Because of these differences, the combined VOR would achieve its image stabilization goal only if the TVOR component was allowed to behave as a foveal-stabilization system and the RVOR component was allowed to use its own 3D kinematics, more appropriate for a full-field image stabilization system. Thus if the 3D kinematics of the combined VOR are dictated by its functional role, the slope of the eye-position-dependent velocity axis tilts should be computed from the total torsional to the total horizontal eye-velocity ratio [referred to here as Rt() = tan ()], after each is calculated as the sum (for r > 0) or difference (for r < 0) of the respective RVOR and TVOR components (Fig. 2B).

(2)

(3)

Experimental observations

Binocular 3D eye movements were recorded in four rhesus monkeys during 4-Hz sinusoidal oscillations in the horizontal plane as the animals fixated targets at different distances and eccentricities. Examples of the horizontal, vertical, and torsional eye velocities for a target on a screen located at a distance D = 18 cm are illustrated in Fig. 3. The corresponding polar plots illustrating eye velocity in the head sagittal plane, where horizontal eye velocity has been plotted versus the instantaneous torsional component, have been plotted in Fig. 4. During rotation at a radius of r = 0 cm, tangential accelerations were negligible and the response reflected a horizontal RVOR with a gain that was slightly larger than one, as expected from the geometry of near targets (Table 1). During rotation at a radius r = 25 cm, the horizontal eye movement increased but remained out of phase with head velocity as expected because the eyes both rotated and translated through a larger arc in space (Fig. 3, left). In contrast, during rotation at a radius of r = 25 cm, the horizontal VOR was reduced because the eye movements required to compensate for head rotation and head translation were in opposite directions. When the animal was placed more eccentrically during rotation, the elicited horizontal VOR even reversed direction as shown for r = 50 cm, where the eye rotated in the same direction as the head (Fig. 3, right).

View larger version (35K): [in this window] [in a new window]   Fig. 3. Dependence of the combined VOR during eccentric rotation on vertical gaze. The torsional, vertical, and horizontal eye velocity () are illustrated for 20° up (top), center (middle), and 20° down (bottom) gaze during 4-Hz yaw rotations with D = 18 cm and radii of r = 25 cm (face-out motion), r = 0 cm (i.e., animal centered on the axis or rotation), r = 25 cm and r = 50 cm (face-in motion). Head, head velocity.

View larger version (37K): [in this window] [in a new window]   Fig. 4. Dependence of the combined VOR during eccentric rotation on vertical gaze. Same data as in Fig. 3 (from more response cycles) are plotted in head coordinates (i.e., the instantaneous horizontal eye velocity, hor, is plotted as a function of the instantaneous torsional eye velocity, tor). The animal was fixating 20° upward (A), straight ahead (B), and 20° downward (C) located targets. Data at r = 25 cm (face-out motion), r = 0 cm (i.e., animal centered on the axis of rotation), r = 25 cm, and r = 50 cm (face-in motion). Gray lines represent the 3D line fit (see METHODS).

As long as fixation was maintained close to primary position, torsional eye velocity was small (Fig. 3, middle), and eye velocity remained head-horizontal (Fig. 4, middle). When gaze was directed up or down, however, torsional eye velocity became a significant component of the VOR response. For simplicity, let's examine the torsional velocity during up gaze (Fig. 3, top). At a radius r = 0 cm, the torsional eye velocity was only a small fraction of the horizontal component. A small gaze-dependent torsion would be consistent with the fact that the RVOR did not follow Listing's law and RVOR velocity only exhibited a small dependence on gaze (Fig. 4, r = 0 cm; see Table 2) (see also Angelaki et al. 2003; Crawford and Vilis 1991; Misslisch and Hess 2000; Misslisch et al. 1994). During rotation at r = 25 cm, however, a large torsional eye velocity modulation was presented at eccentric gaze positions. This occurred when eye velocity consisted of combinations of both RVOR and TVOR because the TVOR exhibited a strong eye-position-dependent velocity axis tilt (Fig. 1 and Table 2) (see also Angelaki et al. 2003). When looking up during eccentric rotations with positive radii, the relative phase of torsional and horizontal eye velocity components were 180° out of phase. Thus a leftward (positive) horizontal eye movement was accompanied by a negative torsional component, resulting in a rotation of the VOR velocity axis in the same direction as gaze (upward; Fig. 4, top left).

The observations were different when rotations involved antagonistic interactions between the RVOR and the TVOR (for face-in eccentric rotations). For example, when comparing the relationship between the horizontal and torsional components for r = 25 cm and r = 25 cm, two important differences emerged. First, for antagonistic RVOR/TVOR interactions (r = 25 cm), peak positive torsional eye velocity occurred simultaneously with peak positive horizontal eye velocity, i.e., the relative phase of the torsional component was opposite from the one at r = 25 cm. Thus a leftward (positive) horizontal eye movement was accompanied by a positive torsional component, resulting in a rotation of the VOR velocity axis in a direction opposite to gaze (downward; Fig. 4, r = 25 cm; top). Second, with r = 25 cm, the torsional eye velocity was as large as that of the horizontal component. Thus VOR velocity would deviate away from a purely horizontal axis through an angle that was larger than the gaze angle (Fig. 4, r = 25 cm; top).

When the radius of rotation was increased to r = 50 cm, the relative phase of horizontal and torsional eye velocity became once again ~180° because the horizontal component was now in phase rather than out of phase with head rotation (as the contribution of the TVOR increased with increasing radius, r). However, the relative ratio of peak torsional versus peak horizontal eye velocity remained large, suggesting that when plotted in head coordinates, the VOR velocity axis would deviate in the same direction as gaze, although through an angle that would be larger than the gaze angle (Fig. 4, top right). Qualitatively similar results were obtained during rotation when gaze was directed downward (Figs. 3 and 4, bottom).

The peak gain and phase for each of the horizontal and torsional velocity components for targets on a screen at a distance of 18 cm have been plotted for different radii as a function of vertical gaze angle in Figs. 5 and 6. For face out rotations (r > 0), corresponding to synergistic TVOR/RVOR combinations, both the horizontal and torsional components increased at larger radii (Fig. 5). As a result, the ratio of torsional over horizontal eye velocity and, consequently, VOR tilt angle, was characterized with similar slopes, although there was a systematic increase as a function of the magnitude of the radius and increasing contribution of the TVOR (Fig. 7A).

View larger version (34K): [in this window] [in a new window]   Fig. 5. Horizontal and torsional eye-velocity gain and phase (re head velocity) plotted as a function of vertical eye position during synergistic RVOR/TVOR combinations. Different symbols and colors are used for data collected during rotations at different radii (r = 0, 12.5, 25, 37.5, and 50 cm). Target distance was 18 cm.

View larger version (38K): [in this window] [in a new window]   Fig. 6. Horizontal and torsional eye-velocity gain and phase plotted as a function of vertical eye position during antagonistic RVOR/TVOR combinations. Different symbols and colors are used for data collected during rotations at different negative radii (r = 0, 12.5, 25, 37.5, and 50 cm). Target distance was 18 cm.

View larger version (26K): [in this window] [in a new window]   Fig. 7. The ratio of horizontal vs. torsional eye velocity and the corresponding tilt angle of the VOR velocity vector plotted as a function of vertical eye position during synergistic (A) and antagonistic (B) RVOR/TVOR combinations. Different symbols and colors are used for data collected during rotations at different radii (r = 0, 12.5, 25, 37.5, and 50 cm). Target distance was 18 cm (same data as in Figs. 5 and 6).

The same radius of rotation, however, yielded different results for subtractive combinations of RVOR/TVOR (face-in motion; Figs. 6 and 7B). At small radii (r = 12.5 cm), horizontal VOR gain decreased in amplitude but maintained the same phase relationship with the VOR at r = 0 cm (compare blue with black symbols in Fig. 6, left). In contrast, the torsional response component at r = 12.5 cm was 180° out of phase compared to that at r = 0 cm (Fig. 6, right). As a result of the phase change of the torsional but not the horizontal component, both the torsional/horizontal eye-velocity ratio and the combined VOR tilt angle exhibited an eye-position dependence with negative slope (Fig. 7B, blue diamonds). At a radius of r = 25 cm, the horizontal response decreased further (Fig. 6, cyan triangles), resulting in an eye-position dependence of the combined VOR with a slope of 2.1 (Fig. 7B, cyan triangles). As the radius of rotation increased further to r = 37.5 cm, horizontal response phase reversed 180° (Fig. 6, green triangles). During rotation at r = 50 cm, horizontal VOR gain increased further, reaching a gain that was near unity, although of reversed polarity to that at r = 0 cm (Fig. 6, compare red with black symbols). For both of these conditions, the torsional/horizontal ratio and thus the eye-position dependence of the combined VOR velocity axis exhibited once again a positive slope, although slope values were much larger than those expected from the half-angle rule (Fig. 7B; green and red symbols with slopes of 2.3 and 1.9, respectively, vs. 0.5 of the half angle rule).

Thus the ratio of torsional to horizontal eye velocity and eye-velocity tilt angle exhibited a variety of dependencies on vertical gaze during the antagonistic combinations (face-in motions with r < 0) that were very different from those during synergistic RVOR/TVOR combinations (face-out motions with r > 0; Fig. 7). This occurred because the reversal in torsional and horizontal response modulation phase due to a larger TVOR contribution took place at different radii, resulting in an opposite eye-position dependence of the VOR (Fig. 7B, blue and cyan symbols). In addition, even for large radii when the TVOR dominated the eye velocity of the combined VOR, tilt angles continued to be large, much larger than those characterizing either the RVOR or the TVOR (Fig. 7B, green and red symbols). The results are consistent with the predictions of the image-stabilization and inconsistent with the fixed-rule hypothesis (Fig. 2).

The eye-position dependence of the combined VOR was quantified by fitting linear regressions as illustrated in Fig. 7. The slopes of these regression lines for all distances and radii tested in all four animals have been summarized and plotted versus the r/D ratio in Fig. 8. For synergistic RVOR/TVOR combinations, the slope of the eye-position-dependent torsional to horizontal ratio increased from a small value for the RVOR at r = 0 cm toward the TVOR slope. In contrast, for subtractive RVOR/TVOR combinations, the slope steeply decreased, reaching large negative values. At a r/D ratio of ~1-1.5, the VOR slope became positive (i.e., the VOR velocity tilted in the same direction as gaze), although slopes were 10 times larger than those predicted by the half-angle rule. As the ratio r/D increased further, the VOR slopes decreased, although they always remained larger than those of the RVOR and the TVOR. To quantitatively test that these experimental results are what would be predicted from the "image-stabilization" hypothesis, we have superimposed with the data of Fig. 8 simulations of Eq. 3 for two different values of the TVOR gain. The dashed lines assumed a TVOR gain of unity (i.e.,  = 1), whereas the solid lines assumed a TVOR gain of  = 0.67. These values mark the range of TVOR gain measured in these animals at the different viewing distances used for testing (12-100 cm; see Table 1).

View larger version (23K): [in this window] [in a new window]   Fig. 8. Summary of the computed slopes for the torsion/horizontal ratio, plotted as a function of the r/D ratio during synergistic (A) and antagonistic (B) RVOR/TVOR combinations. Values were taken from the linear regressions similar to those illustrated in Fig. 7. Dotted lines correspond to either no eye-position dependence or a torsion/horizontal ratio slope of 0.012 (eye velocity slope of 0.7), which was the mean slope for the TVOR (Table 2). The superimposed lines represent simulations of Eq. 3 for the image-stabilization hypothesis with 2 different values for TVOR gain (dashed lines:  = 1; solid lines:  = 0.67). The fixed-rule hypothesis would predict a straight line parallel to the abscissa, corresponding to a constant slope similar to the TVOR or with a value that is in between the 2 dotted lines. Data summarized results from all 4 animals tested at different viewing distances and rotation radii.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

In the present study, we have investigated the 3D kinematics of the combined VOR during yaw rotations with the animal eccentric relative to the axis of rotation. The experiments were motivated by and compared with the predictions of two distinct hypotheses about the principles governing 3D ocular kinematics. The first (fixed-rule) hypothesis predicted that the velocity axes for the combined VOR would exhibit a fixed eye-position dependence, following the pattern observed for either the TVOR alone, the RVOR alone or some combination of the two. The second (image-stabilization) hypothesis was based on the functional requirement that the 3D kinematics of the combined VOR should be governed by the need to keep images on the fovea with slip on the peripheral retina being dependent on the different functional goals of the two VORs. The data demonstrated a variable eye-position-dependent torsion for the combined VOR that was different for synergistic and antagonistic RVOR/TVOR combinations and that resulted in eye-velocity slopes that could be large and often in the opposite direction as gaze. These results are qualitatively and quantitatively consistent with the image-stabilization hypothesis. As will be discussed here, these results have three important implications. First, they suggest that the 3D kinematics of the combined VOR are dependent on functional rather than mechanical constraints. Second, they relate to recent theories regarding the relative roles of extraocular muscle pulleys versus neural signals in the active control of torsional eye movements. Finally, the data have implications for the premotor processing of RVOR and TVOR signals.

Two VORs

Among the different neural systems that generate eye movements perhaps the phylogenetically oldest is the RVOR. In contrast, a phylogenetically new VOR, the TVOR, has also evolved to provide fast binocular coordination and gaze stability and to facilitate stereopsis during head translations (Miles 1993, 1998). The proposal that, in contrast to the RVOR and its role in full-field visual stabilization, the function of the TVOR is tightly coupled with foveal vision and stereopsis has received strong experimental support. For example, the TVOR appears to be well-developed only in primates, whereas it is either absent or weak in lateral-eyed species (Baarsma and Collewijn 1975; Barmack and Pettorossi 1988; Dickman and Angelaki 1999; Hess and Dieringer 1990, 1991). In addition, the primate TVOR anticipates and accounts for the motion parallax associated with viewing targets at different depth planes during translation as it scales inversely proportional to viewing distance (Miles 1998; Paige and Tomko 1991; Schwarz and Miles 1991; Schwarz et al. 1989; Telford et al. 1997). Moreover, the horizontal and vertical components of the evoked eye movement depend on heading direction and eye position as expected according to the geometrical dependencies associated with keeping images stable on the fovea (Angelaki and Hess 2001; McHenry and Angelaki 2000; Tomko and Paige 1992). In contrast, the RVOR's goal is to stabilize images on the whole retina (Misslisch et al. 1994).

3D kinematics for different eye movements

In a reflex the goal of which is to stabilize images on the whole retina, like the RVOR, all degrees of freedom of the eyes are unambiguously specified. For a gaze (i.e., foveal)-stabilization eye-movement system, on the other hand, only the two degrees of freedom of the gaze direction suffice, whereas ocular torsion remains unspecified. It is now well established that the third degree of freedom of the eyes during smooth pursuit (and all visually guided eye movements whose goal is restricted to redirect or stabilize gaze) obeys Listing's law (Haslwanter et al. 1991; Tweed and Vilis 1987, 1990; Tweed et al. 1992). For an eye movement to follow Listing's law, the velocity axis of the eye must deviate toward the direction of gaze by approximately half as much (a property known as the "half-angle rule") (Tweed and Vilis 1987, 1990).

The differential preference in the image-stabilization goals of the two VORs has also been demonstrated by corresponding differences in their 3D kinematics. The TVOR, whose function is linked to foveal image-stabilization, exhibits 3D kinematics that are similar to those during other foveal-specific ocular responses, like pursuit (Angelaki et al. 2000, 2003). In contrast, the RVOR, whose goal is to stabilize images on the whole retina and whose sensory input can uniquely specify all three degrees of freedom of the eye, does not follow Listing's law (Crawford and Vilis 1991; Misslisch and Hess 2000; Misslisch et al. 1994).

Ocular mechanics

There is growing evidence that the peripheral ocular mechanics might be more complicated than once thought. Specifically, several studies have reported the existence of mobile, soft-tissue sheaths or "pulleys" in the orbit that influence the pulling direction of the extraocular muscles (Demer et al. 1995, 2000; Miller 1989; Miller et al. 1993). Based on theoretical arguments, it has been proposed that pulleys may simplify the brain's work in implementing Listing's law (Quaia and Optican 1998; Raphan 1998). Specifically, a theoretical study by Quaia and Optican (1998) has shown that appropriately placed pulleys can both generate physiologically realistic saccades and implement the half-angle rule without a need to use nonlinear neural computations (Tweed and Vilis 1987, 1990). More recently, magnetic resonance imaging of rectus muscle paths has demonstrated that the arrangement of the pulleys and their translation along the extraocular muscle path as a function of gaze angle are consistent with an oculomotor plant that implements the eye-position dependence of Listing's law (Demer et al. 2000; Kono et al. 2002).

Whereas the proposed pulley arrangement would work for implementing the half angle rule of Listings' law, their function during the RVOR has been more controversial. It was originally proposed that the pulleys might advance and retract along their muscle paths, adopting one arrangement for Listing's law and another for the RVOR (Demer et al. 2000; Thurtell et al. 1999, 2000). This theory, however, has been recently shown to be incorrect, as the required retraction to explain the RVOR would be so large as to be nonphysiological. Furthermore, the proposed retraction, no matter how large, would not in fact explain the full pattern of eye-velocity axis tilts seen in the RVOR (Misslisch and Tweed 2001). The present results would further argue against the active pulley hypothesis, at least in the form originally proposed by Demer et al. (2000). We observed eye-velocity tilts not only in the opposite direction to gaze but also having slopes as large as 10 times those expected from the half-angle rule, which is the "default" position of the pulleys (Demer et al. 2000; Kono et al. 2002). These large, systematic variations away from a Listing's law strategy would strongly argue for a large neural component to the 3D ocular kinematics.

More recently, the way that the active pulley hypothesis deals with the RVOR was revised. Demer (2002) has suggested that the violation of Listing's law during the RVOR is mediated by the oblique extraocular muscles whose velocity axes are actively maintained orthogonal to the Listing's velocity axes of the rectus muscles. This new proposal was based on experimental findings during ocular convergence, where rectus pulleys rotated in the orbit but remained fixed relative to the pulling direction of the obliques (Demer et al. 2002). According to this revised hypothesis, "appropriate" neural signals would activate the oblique muscles, causing not only the eye to rotate torsionally but also to simultaneously rotate the rectus pulleys such that the rectus muscles pulling directions would remain fixed relative to the obliques but change relative to head coordinates.

Although attractive, the newly revised active pulley hypothesis remains speculative at present. Further work is necessary to provide both experimental verification and development of mathematical models demonstrating if this formulation can indeed predict the eye-position dependence of the VOR velocity axes. Interestingly, avoiding neural circuits having to deal with the issues of noncommutativity of rotations has been proposed as one of the main functional advantages of the active pulley hypothesis (Demer et al. 2000; Quaia and Optican 1998; Raphan 1998; Thurtell et al. 2000). It remains unclear how this newly revised hypothesis proposes to neurally compute a torsional signal appropriate to activate the oblique muscles without considering the issues of noncommutativity of rotations.

Neural strategies versus mechanical constraints

The demonstration of the extraocular muscle pulleys and their functional role in changing the pulling direction of the muscles as a function of gaze has sometimes been taken to an extreme interpretation that the 3D ocular kinematics merely reflect the constraints of the peripheral mechanics. The fact that oculomotor systems with different functional goals are associated with different 3D strategies (e.g., the RVOR vs. the TVOR or pursuit) would argue against this idea. More importantly, the present results showing that there is no single eye-position-dependent rule that is used by the combined VOR provides further support for the proposal that the eye-position dependence of each eye-movement system represents a strategy that is closely linked to the goals of the system. For example, if the eye-position-dependent torsion of the VOR reflected a mechanical constraint, why not follow the fixed-rule predictions, which could be easily made consistent with the hypothesized action of the pulleys? However, this solution would not preserve the peripheral-image-stability solutions associated with each of the two VORs. Thus the combined VOR follows a mixed-up rule, as long as the kinematics and, thus, functional consequences for each of the TVOR and RVOR components were maintained and images were kept stable on the fovea. A profound functionally appropriate strategy has also been previously demonstrated for eye/head control (Ceylan et al. 2000).

Functional considerations for the neural circuitry of the VOR

The image-stabilization hypothesis that was followed by the combined VOR was based on the conjecture that the total eye movement response had a horizontal component that was qualitatively given as the sum of the RVOR and TVOR horizontal components and a torsional component that was equal to the sum of the eye-position-dependent RVOR and TVOR torsional components (Fig. 9). Such a result has important implications for the neural circuits that generate the VORs. Based on recent work, it has become increasingly clear that the short-latency connections to the horizontal eye muscles are different for the utricle and the horizontal canal systems (Schwindt et al. 1973; Uchino et al. 1994, 1997). In addition, the signal flow for the RVOR and the TVOR might involve different pathways (Angelaki et al. 2001; Green and Galiana 1998). Nevertheless, both reflexes have to share the same premotor neurons, projecting to horizontal motoneurons, e.g., the position-vestibular-pause, burst-tonic, and eye-head neurons (Angelaki et al. 2001; Chen-Huang and McCrea 1999). Based on the results of the present study, one could speculate that premotor neurons, which presumably receive RVOR/TVOR convergent signals have already had the influence of the respective 3D ocular kinematics. If true, this observation would strongly argue not only for a strong neural element in the 3D kinematics of the VOR but also point to a site of RVOR/TVOR convergence that lies downstream from the 3D kinematics site(s). At present, the answers to these questions remain unknown, although both concepts raise challenging issues for future study.

View larger version (16K): [in this window] [in a new window]   Fig. 9. Hypothesized rotational and translational signal convergence for the generation of the combined VOR during eccentric rotation. According to the image-stabilization hypothesis, an appropriate gaze-dependent torsion is computed prior to RVOR/TVOR convergence. This combined gaze-dependent torsion, as well as horizontal signals, are both sent to downstream oculomotor areas.