If the rotational vestibuloocular reflex (VOR) were to achieve optimal retinal image stabilization during head rotations in three-dimensional space, it must turn the eye around the same axis as the head, with equal velocity but in the opposite direction. This optimal VOR strategy implies that the position of the eye in the orbit must not affect the VOR. However, if the VOR were to follow Listing's law, then the slow-phase eye rotation axis should tilt as a function of current eye position. We trained animals to fixate visual targets placed straight ahead or 20° up, down, left or right while being oscillated in yaw, pitch, and roll at 0.5–4 Hz, either with or without a full-field visual background. Our main result was that the visually assisted VOR of normal monkeys invariantly rotated the eye around the same axis as the head during yaw, pitch, and roll (optimal VOR). In the absence of a visual background, eccentric eye positions evoked small axis tilts of slow phases in normal animals. Under the same visual condition, a prominent effect of eye position was found during roll but not during pitch or yaw in animals with low torsional and vertical gains following plugging of the vertical semicircular canals. This result was in accordance with a model incorporating a specific compromise between an optimal VOR and a VOR that perfectly obeys Listing's law. We conclude that the visually assisted VOR of the normal monkey optimally stabilizes foveal as well as peripheral retinal images. The finding of optimal VOR performance challenges a dominant role of plant mechanics and supports the notion of noncommutative operations in the oculomotor control system.
Stabilization of the entire retinal image requires that the three-dimensional (3D) rotational vestibuloocular reflex (VOR) spins the eye around the same axis as the head and in the opposite direction, independent of eye position (optimal VORstrategy). To determine whether the VOR actually follows this strategy, the effect of eye position on VOR slow phases has been studied in humans during active or passive rotations in yaw, pitch, and roll with various frequencies and illuminations (Misslisch 1995;Misslisch et al. 1994, 1996;Solomon et al. 1997; Thurtell et al. 1999; Tweed et al. 1994). The findings showed that the eye rotation axis tilted with the gaze line during yaw or pitch and opposite to the gaze line during roll. This pattern has been interpreted as a specific compromise between perfect retinal image stabilization and perfect compliance with Listing's law (partial Listing VOR strategy).
Listing's law is a kinematic constraint that holds during saccades and fixations (e.g., Ferman et al. 1987;Minken et al. 1993; Tweed and Vilis 1990), smooth pursuit (Haslwanter et al. 1991;Tweed et al. 1992), and, more generally, during VOR fast phases (Hess and Angelaki 1997). Listing's law implies a particular relation between eye position and eye velocity that is relevant for understanding its possible role in the VOR: when the eye is in a given position, then the eye velocity vector must lie in a head-fixed plane, the velocity plane associated with that position. The velocity planes for different eye positions differ by half the change in gaze direction (half-angle rule). The unique eye position for which the gaze line is orthogonal to its associated velocity plane is called primary position, its velocity plane Listing's plane (Tweed and Vilis 1990; Von Helmholtz 1863, 1867).
Figure 1 illustrates the theoretical predictions of optimal VOR and partial Listing VOR strategies during pitch (top panel) and roll (bottom panel) head rotation for a 20° left gaze direction. Velocity vectors are plotted in Listing's coordinates, i.e., Listing's plane (LP) aligns with they-axis and primary gaze direction (gaze line when the eye is in primary position) with the x-axis of the coordinate system. A VOR that perfectly follows Listing's law predicts eye velocity vectors to lie in the velocity plane (VP) which, according to the half-angle rule, is tilted by (20/2)° in the direction of gaze. The optimal VOR strategy requires an eye velocity that is equal and opposite to head velocity and independent of gaze direction, i.e., completely violates Listing's law (see Ωoptand Ωhead in Fig. 1). The parallel projection Listing VOR model yields a velocity vector that stabilizes the foveal image and is found by projecting the optimal VOR vector parallel to the gaze line onto VP. Any vector with its tip along the dotted lines (and its origin in the center of the coordinate system) represents such a VOR response, each with a particular degree of compliance with Listing's law as quantified by a Listing factor (LL): the unique velocity vector that lies in VP (LL = 1) corresponds to a Listing factor of one (full compliance). The optimal VOR velocity vector (LL = 0) corresponds to a Listing factor of zero (no compliance). All vectors in between (along the dotted line) represent Listing factors ranging from 1 to 0, depending on the distance of their tips from VP. For example, a half-Listing VOR (LL = 0.5) lies halfway in between the responses denoted by LL = 1 and LL = 0. Previous studies have shown that the human VOR follows this parallel projection half-Listing strategy (Misslisch 1995; Misslisch et al. 1996).
Another possible compromise between optimal VOR and Listing VOR is theorthogonal projection model, where the velocity vector is found by projecting the optimal vector on VP and orthogonal to it. Any vector with its tip along the dashed lines represents such a VOR response. Again, the degree of compliance with Listing's law (eye position–dependent tilt of the VOR response) can be characterized by a Listing factor. As will be shown in this study, the orthogonal projection model accounts for the direction of VOR responses in monkeys with low torsional gains (due to plugging of their vertical semicircular canals; see Figs. 4 and 6). Note that both Listing's law models predict VOR responses that tilt in the direction of gaze during pitch (and yaw, not shown) and opposite to gaze during roll head rotations. The functional significance of the two compromise strategies will be considered in the discussion(see also ).
The performance of the VOR and its possible dependence on eye position has implications for two general problems in oculomotor control. First, the recent discovery of soft rectus muscle pulleys that restrict the path of extraocular muscles (Demer et al. 1995, 1997; Miller and Demer 1997; Miller et al. 1993) has revived the long standing debate on whether or not Listing's law can be attributed to mechanical properties of the oculomotor plant rather than to neural control systems. As a recent example, Thurtell et al. (1999) studied high acceleration active and passive yaw head rotations in humans and found eye position–dependent VOR responses in directions predicted by Listing's law. The authors concluded that the eye position dependence is probably due to the effect of fibromuscular pulleys on the paths of the rectus muscles. This supports the earlier proposal of Raphan (1997), who claimed that a commutative VOR model, when implementing the action of extraocular muscle pulleys, can account for the half-Listing behavior described in humans (Misslisch et al. 1994).
Second, in a comprehensive modeling work, Smith and Crawford (1998) demonstrated the necessity of noncommutativeoperations in the brain circuits underlying the VOR. Their computer simulations demonstrated that any commutative VOR model predicts nonoptimal VOR responses with slow phase rotation axes that deviate from the axis of head rotation, a behavior that results in a severe degradation of vision. Moreover, this finding was independent of the mechanical properties of the oculomotor plant, i.e., whether the effect of fibromuscular pulleys was incorporated in the model or not. Smith and Crawford concluded that an internal multiplicative processing of eye position and head velocity signals was required to account for the noncommutative properties of 3D rotations and to produce optimal VOR responses that allow a stable image on the entire retina. Additional evidence for noncommutative operations in the brain was reported by Tweed et al. (1999), who found the predicted (noncommutative) VOR responses after two sequences of head rotations around the same axes but in reversed order.
A detailed quantitative study on the influence of eye position on the monkey rotational VOR has not been performed so far. Observations made in nontrained monkeys suggested no systematic effect (Crawford and Vilis 1991). The aim of this study was to characterize the monkey VOR in a condition where the animals were trained to fixate eccentric targets, with or without a visual background, while being oscillated at various frequencies in yaw, pitch, and roll. We found that when full-field vision was present, monkeys showed optimal VOR behavior in all three dimensions. When visual and/or vestibular inputs were reduced, eye position–dependent VOR responses in accordance with the orthogonal projection model were found during roll but not during pitch or yaw. Preliminary results have been published in abstract form (Misslisch and Hess 1998).
Five juvenile rhesus monkeys (Macaca mulatta;abbreviated JU, SU, RO, JE, and TW) were chronically prepared with skull bolts for head restraint. Dual search coils were implanted on one eye under the conjunctiva at about 4 mm from the limbus corneae (Hess 1990). In two animals (JE and TW), all anterior and posterior semicircular canals were plugged about 1 yr before participating in this study. All surgical procedures were performed under sterile conditions, with the monkeys in deep anesthesia. After surgery, animals were treated with antibiotics and analgesics. All procedures were in accordance with the National Institutes of Health Guide for the Care and Use of Laboratory Animals, and the Veterinary Office of the Canton of Zürich approved the protocol.
Recording, calibration, and representation of 3D eye position and velocity
3D eye positions were measured with the magnetic search coil technique (Robinson 1963) using an Eye Position Meter 3000 (Skalar, Delft, The Netherlands). A coil mounted on a cubic frame of 0.3-m side length generated a horizontal and vertical magnetic field (20 kHz, phase and space quadrature). The output of the dual search coil corresponded to the horizontal and vertical angular orientation of two sensitivity vectors, one pointing roughly in the direction of the visual axis and the other approximately perpendicular to that. The four coil voltages, as well as the head position and velocity signals and a signal from a photodiode indicating illumination inside the sphere, were digitized at a rate of 833 Hz (Cambridge Electronic Design, model 1401plus) and stored on the hard disk of a microcomputer for off-line analysis.
3D eye position was calibrated as described in detail elsewhere (Hess et al. 1992). In short, the magnitude of the two coil sensitivity vectors as well as the angle between them was computed in an in vitro procedure. On each experimental day, the monkeys repeatedly fixated three light-emitting diodes (LEDs) placed at straight ahead and 20° up or 20° down. The measured voltages were used in combination with the parameters determined in vitro to compute the 3D orientation of the search coil on the eye. As a control of the quality of eye position recording, monkeys were made to fixate visual targets in the laboratory for about 90 s before each experiment. Then, a Listing's plane was computed for the complete data set including saccadic and fixation intervals as described elsewhere (Hess et al. 1992).
Three-dimensional eye positions were expressed as rotation vectors, where the eye's orientation when looking straight ahead was chosen as reference position (Haustein 1989; Hess et al. 1992). The eye angular velocity vector Ω was computed as described in Hepp (1990). Eye position and eye velocity vectors were expressed using a head-fixed, right-handed coordinate system with the x-, y-, andz-axes pointing along the nasooccipital, interaural, and longitudinal head axis, respectively. Positive directions of the coordinate axes represented clockwise, downward and leftward components (as seen from the subject's point of view) of eye position and eye velocity.
Training, experimental setup, and protocols
The monkeys were seated in a primate chair and secured with shoulder and lap belts. The head was restrained in an upright position (lateral semicircular canals elevated by about 15° anteriorly). The primate chair was then secured inside the inner frame of a vestibular rotator with three motor-driven axes (Acutronic, Jona, Switzerland). The rotator was surrounded by a lightproof sphere of 0.8-m radius to guarantee experiments with or without a full-field visual background. The profile and onset of sinusoidal chair rotation (frequency, amplitude) was chosen and controlled via computer.
All animals were pretrained to fixate LEDs using water rewards. The quality of fixation was controlled with behavioral windows. Animals were usually trained 3 or 4 days per week with free water access during the other days.
The effect of eye position on the monkey VOR was tested for different frequencies of sinusoidal yaw, pitch, and roll chair rotation (0.5, 1, 2, and 4 Hz; amplitude ±18, 5, 1.5, and 0.5°; peak velocity: 56.6, 31.4, 18.9, and 12.6°/s). Due to technical constraints, animals with plugged vertical semicircular canals were tested only at 0.5 Hz (TW) and 1.0 Hz (TW and JE). The target LEDs were on during the whole 4-s test period. The illumination inside the sphere was either on (SU and JU) or not (all animals) so that the numerous, randomly placed and different-sized (between 2 and 17 cm diam at 0.9 m distance, corresponding to a visual angle covered by the disks between 1.3 and 10.8°) black disks against a white background were either visible or not. An experiment started with the selection of a type of chair rotation (yaw, pitch, or roll). A computer program then randomly picked the first target, located either straight ahead or 20° eccentric (for yaw: up, center, down; for pitch: left, center, right; for roll: up, down, center, left, right). The current combination (head rotation, target) was signaled to a second computer, which set and controlled the behavioral reward window on-line. After the main computer initiated data recording, the vestibular rotator started moving if the monkey had kept proper fixation for 500–800 ms. The monkey was required to keep its gaze on the earth-stationary target while being rotated for 4 s. The animals were rewarded with water after the rotator had come to a stop. Trials were aborted when the monkey's eye position exceeded the behavioral window. The computer program selected each combination of chair rotation and target location until 10 successful repetitions were obtained. For a given frequency and illumination condition, the total number of trials was 110 (3 times 10 during yaw, 3 times 10 during pitch, and 5 times 10 during roll).
Digitized 3D eye velocity and eye position data were desaccaded with a semi-automatic computer program using thresholds for the second derivative of 3D eye velocity (jerk). Falsely placed or missing markers were identified and corrected interactively. Data were then cut such that the first (last) sample corresponded to the onset (offset) of vestibular stimulation. A sinusoidal function was fitted (in the least-squares sense) to the chair velocity, yielding an estimate of frequency and amplitude of 3D head rotation. These head velocity data,Ω Head, were combined with the data representing 3D eye position, E, to model slow-phase eye velocity, Ω, following a multivariable function fitting approach as used in a previous study (Misslisch et al. 1994; Press et al. 1988). To quantify how eye position E influences the VOR responses for a given head velocity Ω Head, we assumed that angular eye velocity Ω was not only a linear function of head velocity but also depended linearly on eye position as follows Equation 1
where Ω s is ocular drift velocity, [G] is a 3 × 3 gain matrix, and [B] is a 3 × 3 × 3 array representing the influence of eye position for a given head velocity (for more details seeappendix of Misslisch et al. 1994). In practice, we rearranged the three input vectorsΩ s, Ω Head, and E in this linear equation by defining a 3 × 13generalized gain matrix [C], which is applied to the following 13 × 1 input vector Q (written in transposed form for convenience) Equation 2where, for example, Ω Head_V is the vertical component of head velocity andΩ Head_T E H is the product of the torsional component of head velocity and the horizontal component of eye position. Note that the first element inQ represents a possible velocity drift, whereas the other elements are given by the particular stimulus condition of each experiment. A fitting algorithm then computed the 3 by 13 generalized gain matrix [C] such that [C]Qyielded the best response in the sense of minimal least-squared errors to eye velocity Ω. To compare VOR responses for a given combination of head rotation and eye position, we used the computed matrix [C]. Given Ω Head andE, the torsional, vertical, and horizontal components of eye velocity Ω were determined by computing the vectorQ as a function of Ω Head andE (Eq. 2 ) and applying the matrix [C] to the vector Q (Eq. 1 ). This method allowed an accurate characterization of the data (see black lines in Figs. 2−4 for examples of best-fit VOR responses derived from the computed generalized gain matrices).
Concepts of optimal VOR and eye position dependence
Unfortunately, different notions of gaze dependence have been used in previous VOR studies due to the fact that researchers did not always carefully distinguish between angular velocity Ω and coordinate velocity v. Here, we define the VOR as optimal if it achieves a perfectly stable image of the visual world on the entire retina, with VOR angular velocity being equal in magnitude and opposite in direction to angular head velocity (independent of current eye position). The concept of angular velocity is a kinematic property describing rigid body motion independent of the particular coordinates used (Goldstein 1980). Accordingly, eye angular velocity represents the motion of the eye from one position to another where its axis coincides with the axis of rotation and its length represents the speed of rotation. Thus if one aims to examine the effect of eye position on VOR slow phases, one has to analyze angular eye velocity with the eye in various positions. This issue cannot be addressed by representing eye velocity as coordinate velocity, for example as time derivative of the Fick angles, since this time derivative will depend on eye position for elementary kinematic reasons leading to results whose physiological interpretation is dubious (for the mathematical concepts involved in 3D kinematics see, e.g., Haslwanter 1995; Tweed 1997;Tweed and Vilis 1987, 1990).
The main observations of this study can be summarized as follows. First, when testing normal animals under “natural” conditions, i.e., with the animal fixating a target against a structured background, the visually assisted VOR optimally compensated for the head rotation: the eyes were driven in the opposite direction as the head, at the same speed and around the same axis. The fact that the slow phase rotation axis was not affected by the current position of the eye was invariably found in both animals tested in this condition. Second, when normal monkeys were tested while fixating a target in an otherwise dark environment, small eye position–dependent tilts of the slow-phase axis were observed in directions predicted by Listing's law. Third, in monkeys with low vertical and torsional VOR gains after plugging of the vertical semicircular canals, prominent eye position–dependent tilts were observed during roll, but not during pitch and yaw head rotations.
Optimal VOR responses in the presence of full-field vision
Figure 2 illustrates that the visually assisted VOR in normal monkeys was not influenced by eye position. Representative eye angular velocity vectors (gray dots) are plotted during four cycles of sinusoidal whole-body rotations at 1 Hz (± 5°; peak velocity 31°/s) in yaw (Fig. 2 A), pitch (Fig. 2 B), and roll (Fig. 2, C and D). In these examples, the (normal) animal was fixating visual targets placed either at 20° up, center and 20° down (Fig. 2, A and C) or 20° left, center and 20° right (Fig. 2, B and D). A structured background was visible throughout the experiment. The tips of the eye velocity vectors are seen from the subject's right side so that horizontal velocity is plotted versus torsional velocity in magnetic field coordinates (Fig. 2, A and C), or from above the subject, i.e., vertical velocity is plotted versus torsional velocity (Fig. 2, B and D; see cartoon monkey heads). Slow-phase responses derived from the computed generalized gain matrices (heavy black lines, see methods) are plotted on top of the data (gray lines). Dashed arrows denote the direction of the gaze line, dashed planes indicate the velocity planes, i.e., the planes that would contain the slow-phase velocity vectors if the VOR would perfectly follow Listing's law.
When the monkey was rotated in yaw while fixating the center target (middle panel in Fig. 2 A), the slow-phase velocity vectors perfectly aligned with the axis of rotation (ordinate), i.e., the eye rotation axis was parallel to the head rotation axis (according to the right-hand rule, vectors lying along the positive/negative ordinate denote leftward/rightward eye rotation). Thus when looking straight ahead the orientation of the slow-phase axes was consistent with the optimal VOR strategy. More interestingly, the direction of yaw VOR responses remained optimal for eccentric gaze directions. For example, if gaze was 20° up (left panel in Fig. 2 A) or 20° down (right panel in Fig.2 A) VOR velocity vectors were still aligned with the head rotation axis. Recall that the half-angle rule (Listing's law) predicts that the axis of eye rotation must tilt by half the angle of gaze eccentricity, i.e., by 10° (dashed plane tilted backward/forward when gaze is 20° up/20° down), a prediction not matched by the data. Thus eye position does not influence the axis of eye rotation during yaw head rotation.
Analogous results were obtained when the animal was rotated in pitch and roll (Fig. 2, B–D). In all cases, the velocity vectors were aligned with the axis of head rotation (ordinate in Fig.2 B, abscissa in Fig. 2, C and D), i.e., the eye rotation axis was completely independent of eye position.
Minor deviations from optimal VOR responses in the absence of full-field vision
When peripheral vision was eliminated, the axis of slow phases showed minor eye position–dependent deviations from the optimal VOR responses. Figure 3 shows examples of VOR velocity vectors (gray dots) for the same animal, the same rotational stimuli (plotted in the same format) as in Fig. 2, but this time collected in a condition without a visible structured background. In the yaw case and when looking straight ahead, the axis of the best-fit VOR response (solid black line) tilted slightly back from perfect alignment with the head rotation axis (ordinate). When looking 20° up (dashed arrow in Fig. 3 A, left panel), the VOR's rotation axis tilted further back (by 1.6°) and when looking 20° down (Fig. 3 A, right panel) the axis tilted slightly forward (by 1.6°). Thus VOR responses tilted slightly in the directions predicted by Listing's law (dashed planes).
Minor eye position–dependent tilts of the slow-phase rotation axis were also observed during pitch head rotations (Fig. 3 B), but in this example the axis tilted slightly opposite to the direction of gaze (to the right by 2.1° when gaze is 20° left and to the left by 1.8° when gaze is 20° right). In other words, the VOR rotation axis tilted slightly in directions violating the predictions of Listing's law.
The tilt of the VOR rotation axis was generally larger during roll head rotations and in directions that were opposite to the change in gaze, in agreement with the predictions of Listing's law. In this example, when gaze changed in elevation (Fig. 3 C) the best-fit VOR rotation axis tilted by 4.3° down (gaze 20° up) and by 4.4° up (gaze 20° down). When gaze changed in azimuth the rotation axis tilted by 6.7° right (gaze 20° left) and 6.8° left (gaze 20° right).
Large deviations from optimal roll VOR responses in animals with low torsional gain
Animals whose vertical semicircular canals have been plugged showed low vertical and even lower torsional gains in combination with eye position–dependent tilts of the eye rotation axis during roll but not during pitch head rotations. Figure 4illustrates an example of prominent tilts of slow-phase axes during four cycles of sinusoidal roll (1 Hz, ± 5°, peak velocity 31°/s, no visual background). In Fig. 4 A, the animal was fixating targets located either at straight ahead (middle panels) or at 20° up (left panel) or 20° down (right panel). The cartoon heads indicate that slow-phase velocity vectors are viewed from the subject's right side (top panels) and from above the subject (bottom panels). Thus the top panels plot the horizontal component of eye angular velocity versus the torsional component. As in Figs. 2 and 3, VOR responses determined from the best-fit generalized gain matrices (black lines) are plotted on top of the velocity vectors (gray dots). When gaze was straight ahead, the velocity vectors were tilted slightly down (due to the fact that in this animal the Listing's plane was tilted slightly up with respect to the magnetic field coordinates). Relative to this orientation, the vectors tilt much further down when gaze was 20° up (left panel) and further up when gaze was 20° down (right panel). That is, VOR responses showed substantial tilts in directions predicted by Listing's law (dashed lines). Plotting the vertical component of slow-phase velocity against the torsional component revealed that the direction of VOR responses was limited to the plane of gaze changes and did not change in thex-y plane, i.e., did not tilt left- or rightward (bottom panels, Fig. 4 A).
Similar results were obtained when the monkey fixated targets at 20° left or 20° right (Fig. 4 B). Here, the angular velocity vector tilted prominently to the right (relative to its orientation at center gaze) when gaze was 20° left and to the left when gaze was 20° right (Fig. 4 B, top panels). In this case, the orientation of the eye rotation axis in the x-z plane was not affected by the change in gaze direction (Fig. 4 B,bottom panels).
Influence of frequency of head rotation and visual background
The effect of eye position on individual slow phases was quantified as described in methods, ultimately yielding the tilt angles of the VOR rotation axis, relative to their orientation during center gaze, for each stimulus combination (yaw with gaze 20° up/down, pitch with gaze 20° left/right, roll with gaze 20° up/down and roll with gaze 20° left/right). Each combination of vestibular stimulation and gaze direction was repeated 10 times. Because the eye velocity vectors for a given head rotation (e.g., yaw) showed symmetrical tilt angles for the two gaze directions (e.g., yaw: 20° up/down; see Figs. 2 and 3), the relative tilt angles of the 20 corresponding values were averaged.
Figure 5 summarizes the means ± SD of the tilt angles collected in normal animals during yaw (○), pitch (□), and roll (left- and rightward pointing triangle for 20° up/down and 20° left/right gaze directions) as a function of head rotational frequency. Figure 5, A and B, shows data obtained with (JU and SU) and without (JU, SU, and RO) a visual background, i.e., with or without full-field vision. Positive tilt angles were defined to indicate a tilt of the eye rotation axis in the direction predicted by a VOR, which qualitatively obeys Listing's law, i.e., inthe direction of gaze during yaw and pitch and opposite to the direction of gaze during roll (Fig. 1, Misslisch et al. 1994; Tweed et al. 1994).
The optimal VOR strategy predicts that eye angular velocity is always parallel to head angular velocity despite changes in gaze direction so that the computed tilt angles should be zero in all examined conditions. If the VOR would fully obey Listing's law, tilt angles of 10.0° would be expected during yaw or pitch and tilt angles of 80.0° during roll (20° eccentric gaze). Smaller angles would be predicted if Listing's law was onlypartially followed (see Figs. 1 and6−8). For example, if the monkey VOR would show the same eye position–dependent pattern of axis tilts as found in humans, i.e., half-follow Listing's law, one would expect tilt angles of about 5.0° during yaw or pitch and tilt angles of 9.4° (orthogonal projection model) and 17.9° (parallel projection model) during roll (Fig. 1).
Two main observations can be made from inspecting Fig. 5. First, when normal animals were tested against a full-field visual background (Fig.5 A), tilt angles were close to zero for all rotational frequencies. This indicates that the responses of the visually assisted VOR agree with the predictions of the optimal VOR strategy. Second, when normal animals were tested without visual background (Fig.5 B), a weak dependence of the direction of VOR responses on eye position was found. In this condition, slow phases were somewhat more influenced by eccentric gaze direction during roll as compared with yaw or pitch, especially at higher frequencies of head rotation. Note that the tilt angles obtained during roll were always positive, i.e., the eye rotation axis invariantly tilted in the direction predicted by Listing's law (opposite to gaze). During yaw and pitch, the small tilt angles were usually largest at the lowest frequency of 0.5 Hz and generally decreased to values close to zero at higher frequencies.
Thus VOR responses in normal monkeys were not influenced by the direction of gaze when tested in a relatively natural condition, i.e., during head rotations while viewing a target of interest against a structured visual background. When information from the retinal periphery was eliminated, VOR responses showed small deviations from perfect alignment with the head rotation axis. As shown in Fig. 4, even larger misalignments were seen in animals with plugged vertical semicircular canals during roll. In what follows, we shall describe that the tilt of slow-phase axes, and therefore the adherence to one of the competing predictions of the optimal VOR versus the partial Listing VOR strategies, was related to the strength of the VOR response (gain) during roll, but not during pitch or yaw head rotations.
Orientation of roll VOR axis as a function of torsional gain
Figure 6 shows the mean relative tilt angles of the slow phase rotation axis (±SD) during roll head rotation as a function of torsional gain. As mentioned before, tilt angles for 20° eccentric eye positions are computed relative to their orientation during center gaze. Each symbol denotes the average of 40 measurements obtained at one frequency of torsional head rotation, i.e., 10 repeated measurements of slow-phase tilt for each of the four eccentric gaze directions (20° up, down, right, left). Positive tilt angles denote that the slow-phase axis during roll head rotation tilts in the direction predicted by Listing's law, i.e., opposite to gaze. In this and the subsequent two figures, the following data are shown: for two normal animals (SU and JU), data were obtained at all frequencies and for both visual conditions: without visual background (filled symbols in Figs. 6-8) or with visual background (empty symbols in Figs. 6-8). In the remaining animals, data were collected without a visual background: in the third normal monkey (RO) at all frequencies and in the monkeys with plugged vertical semicircular canals (stars) at 1.0 Hz (JE) or at 0.5 and 1.0 Hz (TW), respectively.
For comparison, the predictions of different VOR strategies are plotted: optimal VOR (black solid line), parallel projection model (black dotted line), and orthogonal projection model (black dashed line). The ordinate on the right side represents the Listing factor associated with the computed tilt angles as predicted by the orthogonal projection model (the one that actually fits the roll data under conditions with reduced visual and vestibular inputs). This factor denotes which tilt angle had to be expected for a 20° eccentric gaze if the VOR would follow Listing's law by the degree shown on the scale. If the Listing factor is zero, the eye rotation axis during roll should tilt by zero degrees, corresponding to the optimal VOR strategy. This factor of Listing's law adherence is linked with torsional VOR gain by a nonlinear relation, i.e., it increases with decreasing torsional gain ( , Fig. FA1). Note that a torsional gain of unity (optimal VOR) goes along with a Listing factor of zero.
Figure 6 A compares VOR responses obtained in normal animals with or without a visible structured background. In the presence of full-field vision (empty symbols) the tilt angles of the eye rotation axis clustered around zero; i.e., under this condition the VOR rotates the eye around the same axis as the head (cf. Figs. 2 and5 A). The corresponding torsional gains were close to unity, indicating that the visually assisted roll VOR counterrotates the eye with about the same speed as the head. The combination of these two findings implies that the visually assisted VOR during roll head rotations optimally stabilizes the retinal image in normal animals. When tested without a visual background (filled symbols), normal animals (SU, JU, and RO) showed torsional gains between about 0.7 and 0.85 and tilt angles of a few degrees. Note, however, that on average the eye rotation axis invariantly tilted in the direction consistent with Listing's law (positive angles).
Figure 6 B illustrates that in animals with plugged semicircular canals (JE and TW) torsional gains were very low, ranging from 0.2 to 0.5, and the corresponding tilt angles were quite large, ranging between about 12 and 32° (note the different scales for abscissa and ordinates: gray shaded area in Fig.6 B corresponds to the range used in Fig. 6 A). Interestingly, the tilt angles from normal and plugged canal animals collected without visual background lay close to the curve predicted by the orthogonal projection model (black dashed curve). To quantify the relation between data and model prediction, we computed a Listing's law function that best fitted the entire data set, characterizing the tilt angle γ as a function of the torsional gain and the projection angle (for details see , Fig. FA1). Note that the fitted curve (solid gray line) lay very close to the orthogonal projection function (dashed black line) and clearly deviated from the parallel projection function (dotted black line). For example, if one sets the Listing's factor to 0.5, corresponding to a VOR that half follows Listing's law, then the following tilt angles γ are derived from the data and the two model predictions: data fit, 10.2°; orthogonal projection model, 9.4°; parallel projection model, 17.9°. Very similar results were obtained for the data fits when restricting the fit on separate data sets: all data for normal animals only equal 11.0°; data for plugged animals without visual background: γ = 10.1°; data for normal animals without visual background equal 11.0°. Thus the orthogonal projection model adequately described the eye position–dependent VOR axis tilts that emerged when torsional gain decreased due to a reduction of visual and/or vestibular inputs.
Orientation of pitch and yaw VOR axis as a function of vertical and horizontal gain
Figure 7 shows the average relative tilt angles of the VOR rotation axis (±SD) during pitch head rotations with eccentric gaze as a function of vertical gain. To illustrate the theoretical predictions, the same line style conventions were used as in Fig. 6: optimal VOR strategy (black solid line), orthogonal projection model (dashed line), and parallel projection model (dotted line). Again, the ordinate on the right side represents the Listing factor associated with the orthogonal projection model. A Listing factor of one indicates full compliance with Listing's law and predicts that when gaze was 20° left or right the eye rotation axis should tilt by 10° (half-angle rule), and in the direction of gaze.
As in the roll case, tilt angles determined for the condition where full-field vision was present were very close to zero (open symbols), and vertical gains were close to unity, indicating optimal performance of the visually assisted VOR during pitch head rotations.
When no structured background was present, the vertical gain of normal animals was still larger than 0.9, and the tilt angles (filled symbols) clustered around zero, with minor positive (in the direction of gaze) and negative (opposite to the direction of gaze) values. Animals with their vertical canals plugged (stars) showed even lower vertical gains, ranging from about 0.5 to 0.8 and tilt angles near zero. That is, despite the low response gains, slow-phase axes in these animals were well aligned with the pitch axis, in accordance with the optimal VOR strategy.
A regression analysis performed on the pooled data (normal animals for both visual conditions and plugged animals for the no-background condition; gray line in Fig. 7) verified that tilt angles and vertical gain were not correlated (r = 0.1023, n= 23, P = 0.05, 2-sided). No significant correlation between tilt of the eye rotation axis and vertical gain was found when applying the regression analysis on separate data sets (normal monkeys, pooled for both visual conditions; normal monkeys, one visual condition; plugged monkeys).
Figure 8 summarizes the relation between averaged relative tilt angles of the VOR rotation axis (±SD) during yaw head rotations with eccentric gaze as a function of horizontal gain. Data were denoted by the same symbols as in Figs. 6 and 7, and the same line style conventions were used to plot the predictions of the different VOR models. As in the pitch case, the optimal VOR predicts tilt angles of 0°, whereas a pure Listing VOR predicts relative tilt angles of 10° (gaze 20° up/down).
Horizontal head rotation evoked optimal VOR responses in the presence of full-field vision. That is, horizontal gain was close to unity, and the averaged tilt angles of the slow-phase eye rotation axis were near zero. As in the pitch case, when the VOR was tested by presenting a target without a visible background, slightly smaller gain values were observed, but the tilt angles were still close to zero. Animals with plugged vertical canals, tested without visual background, showed horizontal gains that did not differ from those obtained in the normal animals for the same condition. With one exception, mean tilt angles were very small and scattered around zero. The regression line fitted on the pooled data (gray solid line) as a function of horizontal gain showed no significant correlation between relative tilt angles and horizontal gain (r = 0.3279, n = 23,P = 0.05, 2-sided). Further, no correlation between axis tilts and horizontal gain was observed when applying the regression analysis on separate data sets.
It is important to note that the absence of eye rotation axis tilts during yaw and pitch head rotations while animals fixated an eccentric point target cannot be attributed to the contribution of the smooth pursuit system. On the contrary, because smooth pursuit obeys Listing's law, one would expect that the eye rotation axis tilts half as far as the gaze line, i.e., by 10°. In contrast, our data show tilt angles near zero, indicating that smooth pursuit did not contribute to the measured eye rotation.
The main result of this study is that the visually assisted VOR in the rhesus monkey invariantly rotates the eye around the same axis as the head (i.e., optimally stabilizes the entire retinal image), independent of the current position of the eye. Deviations from this optimal VOR behavior were found during roll head rotations when the visual and vestibular inputs were reduced, being most prominent for vestibular-deficient animals with low torsional gains. In the following we will consider the implications of these results for the role of vision in human and nonhuman primates, for oculomotor control models, and for the intrinsic coordinate system of the monkey VOR.
Role of vision on monkey and human VOR strategies
Crawford and Vilis (1991) reported that monkey slow-phase velocity axes did not consistently depend on eye position when tested during head rotations at 0.5 Hz in a lighted visual environment. We found that VOR eye rotation axes during yaw and pitch (at 0.5 Hz) and during roll (at all frequencies) without a visual background did show small but consistent tilts in directions predicted by Listing's law (Figs. 3 and 5 B). However, this effect became negligible when animals were tested with a structured visual background (Figs. 2 and 5 A, empty symbols in Figs. 6-8) corroborating Crawford and Vilis's (1991) observations. The finding that the visibility of a structured background cancels the weak influence of eye position on normal monkey VOR disagrees with findings in human studies (Misslisch 1995; Misslisch et al. 1994,1996; Solomon et al. 1997; Tweed et al. 1994). Regardless of whether humans imagined targets in complete darkness or fixated visible targets on a structured visual background, the eye position–dependent VOR rotation axis tilts were almost indistinguishable (Misslisch 1995). Why does full-field vision apparently alter the VOR strategy in monkeys but not in humans?
One possibility is that the different VOR strategies reflect a difference in the relative importance of central and peripheral vision in human and nonhuman primates. In fact, earlier studies found cortical magnification factor curves, which indicated that human visual areas have a greater emphasis on foveal vision than observed in macaques (Sereno et al. 1995; Tolhurst and Ling 1988). More recent studies, however, seem to challenge this notion (Horton and Hocking 1997; Sereno 1998). Yet, the functional differences between monkey and human VOR favor the earlier reports of differences in nonfoveal versus foveal vision. Namely, our monkey data showed that the stimulation of the retinal periphery reduced the small deviations from optimal VOR performance observed when there were no peripheral stimuli, indicating that stabilization of peripheral retinal images is an important task of the monkey VOR. In comparison, humans showed the parallel projection version of a half-Listing VOR (Fig. 1), which reduced the optical flow over the fovea at the expense of an increased image slip over more peripheral retinal parts (Misslisch 1995; Tweed et al. 1994) (see also below, Fig.FA2). Remarkably, this behavior was found even in darkness when there was no optical flow (Misslisch 1995; Misslisch et al. 1994). Because the observed VOR responses could not be explained by the effect of ocular plant mechanics (Misslisch et al. 1994), it has been suggested that the brain combines information on head rotation (vestibular organs) with eye position signals (efference copy and/or proprioception) to compute the direction of VOR responses that would reduce the optical flow over the fovea in a lighted environment (Tweed et al. 1994) (see also arguments on noncommutative operations below).
Optimal VOR strategy and current models of oculomotor control
The finding of optimal VOR performance in monkeys is significant for clarifying two controversial problems in 3D oculomotor control, i.e., the existence of noncommutative neural operations and the consequences of oculomotor plant mechanics.
To account for the fundamental noncommutative properties of 3D rotations in the saccadic system, Tweed and Vilis (1987)proposed a multiplicative interaction between 3D eye position and eye velocity signals upstream from the neural integrator. Recent work claimed that this noncommutative multiplicative step may not be needed in the brain stem circuits generating saccades and possibly VOR slow phases (Quaia and Optican 1998; Raphan 1997, 1998) if one assumes an oculomotor plant equipped with the recently discovered fibromuscular pulleys (Demer et al. 1995, 1997; Miller and Demer 1997; Miller et al. 1993). In contrast, Smith and Crawford (1998) concluded from their simulation studies that an optimal VOR strategy is incompatible with any commutative VOR models (Raphan 1997) and that this result was independent of the mechanical properties of the plant (i.e., whether the effects of fibromuscular pulleys were included in the simulation of the plant or not). The role of muscle pulleys has also been discussed in a recent investigation on the human yaw VOR, which confirmed that slow-phase axes tilt when varying vertical eye position (Thurtell et al. 1999).
Along with the results of the Smith and Crawford study (Smith and Crawford 1998), the simplest interpretation of our data are to assume neuronal control mechanisms rather than mechanical plant properties to account for the different VOR strategies that accomplish the different visual needs in humans and monkeys. One problem with the argument that the plant mechanics provide Listing's law during saccadic and smooth pursuit eye movements (Miller and Demer 1997) is that the deviations of VOR eye movements from the Listing's law behavior would have to be interpreted as an incomplete neural compensation of the mechanically set default behavior. This kind of reasoning, however, could not explain the differential effects of eye position on VOR responses during roll (large axis tilts) and pitch (minor axis tilts) when visual and vestibular inputs are impaired (cf. data of plugged animals denoted by stars in Figs. 6 and 7).
Listing's law and coordinate system of the VOR
The main finding of this study is that the visually assisted VOR in normal monkeys functions in head-fixed coordinates and is independent of the current gaze direction (optimal VOR strategy). Previous investigations have shown that the orientation of the semicircular canals in the head represents the sensory coordinate system for rotational vestibular information processing (Blanks et al. 1985; Reisine et al. 1988). Moreover, the pulling directions of the extraocular muscles as well as the on-directions of their motoneurons align approximately with those of the semicircular canals (Miller and Robins 1987;Suzuki et al. 1999). Neurons in the rostral interstitial nucleus of the medial longitudinal fasciculus showed directional coding in the head-fixed coordinates defined by Listing's law (Crawford and Vilis 1992; Hepp et al. 1994; Vilis et al. 1989). And finally, the vertical-torsional integrator in the interstitial nucleus of Cajal also seems to operate in Listing's coordinates (Crawford 1994). Taken together, this suggests that both sensory and motor brain structures in the monkey use head-fixed coordinate systems that may simplify sensorimotor transformations and facilitate accurate VOR eye movements at short latency.
When rotating normal monkeys during roll without a visual background, we found that torsional gain decreased and slow-phase axes tilted slightly in the directions predicted by the Listing models (Figs. 3 and5 B). Monkeys with reduced torsional and vertical gains following plugging of the vertical semicircular canals showed large eye position–dependent tilts of the axis of slow-phase velocity during roll but not during pitch head rotations (Figs. 4, 6, and 7). The relative importance of optimal VOR versus partial Listing's law strategies during roll appeared to depend on the torsional gain: if torsional gain decreased, a dependence of the VOR rotation axis on eye position emerged—in a manner that was remarkably consistent with the orthogonal projection model. The functional significance of this strategy could be to reduce deviations from visuomotor constraints imposed by Listing's law, i.e., to restrict torsional eye velocity. The fact that VOR in normal monkeys completely ignores Listing's law makes this explanation improbable, however. A more likely reason relates to the geometric fact that during roll head rotation the optical flow over the fovea strongly depends on the gaze direction (Tweed et al. 1994). For example, a counterclockwise head rotation with the subject looking straight ahead induces a clockwise optical flow, with a stable foveal center and increasing clockwise flow velocities in the eccentric retinal regions. If the subject looks 20° left (see bottom panel in Fig. 1), targets around the fovea have a predominantly upward motion component relative to the head (purely upward at the center of the fovea). Thus efficient tracking of targets in that condition demands that the eye rotates upward in addition to the compensatory counterclockwise rotation. In other words, the VOR rotation axis should move rightward, a requirement matched by the data (Fig. 4 B). Even though this strategy of tilting the eye rotation axis as predicted by the orthogonal projection model cannot perfectly stabilize the retinal image it improves foveal and perifoveal image stabilization. Perfect stabilization of the fovea, at the expense of the retinal periphery, is achieved by tilting the eye rotation axis according to the parallel projection strategy. This strategy was found in normal human subjects and requires much larger axis tilts than the orthogonal projection strategy (e.g., Misslisch 1995; Misslisch et al. 1994; Tweed et al. 1994). The moderate axis tilts found in plugged-canal monkeys were consistent with the orthogonal projection model. It can be shown that this strategy considerably reduces the optical flow over foveal and off-foveal regions, compared with a low-gain roll VOR with a nontilting rotation axis (for details see , Fig. FA2).
Under natural visual conditions, normal monkeys choose the unique VOR angular velocity vector that provides a stable image on the entire retina: opposite in direction (and of equal size) than head velocity. When visual and/or vestibular inputs are reduced, eye position–dependent responses in directions predicted by Listing's law appear during roll but not pitch or yaw head rotations. The finding of optimal yaw, pitch, and roll VOR behavior in normal monkeys may be related to the greater significance of peripheral relative to central vision in nonhuman as compared with human primates. The demonstration of optimal VOR behavior in the monkey also supports the notion of noncommutative operations in the oculomotor system and questions a dominant role of plant mechanics.
We thank B. Disler and A. Züger for excellent technical assistance.
This work was supported by Swiss National Science Foundation Grant 31-47 287.96.
Address for reprint requests: H. Misslisch, Dept. of Neurology, University of Zurich, Frauenklinikstr. 26, CH-8091 Zurich, Switzerland.
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
Tilt angles, Listing factor, and VOR models
To compare the experimentally determined tilt angles of VOR responses, we fitted an angle β to the data describing the tilt of eye velocity (angle γ) as a function of torsional gain (k,see Fig. FA1) Equation A1This equation is obtained by eliminating the unknownq in the two relations tan(γ) =q/k and tan(β) = q/1 −k. The orthogonal projection model is satisfied if β = α/2, whereas the parallel projection model is fulfilled if β = α.
To quantify the degree of compliance with the orthogonal projection model (Listing factor LL), we measured the length P of the vector difference between the normalized optimal VOR eye velocity vector (Ω opt) and the normalized measured eye velocity vector (Ω exp) as a function of the torsional gain (k; i.e., the projection of the vectorΩ exp onto the x-axis). In the orthogonal projection model (β = α/2), full compliance with Listing's law (half-angle rule) would yield a maximal, gaze-dependent torsional gain of k L = sin2(α/2) (Fig. FA1). Any further increase in torsional gain k would decrease the Listing's law factor (LL = p*) as follows
Equation A2where p max is the maximal orthogonal deviation of eye velocity from VP for a torsional VOR with unity gain [p max = cos(α/2); see Fig. FA1]. If the Listing factor p* = 0 the roll VOR implements the optimal VOR strategy (k = 1, γ = 0). If p* = 1 the roll VOR follows a perfect Listing's law strategy (k = k L, γ = π/2 − α/2). In the latter case, torsional gain decreases to zero as gaze approaches the x-axis (α = 0).
Retinal image stabilization and VOR models
The consequences of the partial Listing VOR models for gaze stabilization during roll head rotations can be quantified by thefoveal gain, G fovea, defined as the ratio of image velocity over the fovea (when gaze deviates from the head's roll axis) and VOR-induced velocity of the gaze line. The foveal gain depends on gaze eccentricity α as follows
Equation A3As in Eq. A1, the roll gain kis defined as k = (Ωexp/Ωopt) cos γ. Alternatively, k can be expressed as a function of axis tilt γ and projection angle β. That is, k = −sin(β) cos(γ)/sin(γ − β). The second expression on the right hand side of Eq. A3 is obtained by substituting the relation (Eq. A1) for tan (γ) in Eq. A2. In the parallel projection model (stars in Fig. FA2),G fovea is unity since the projection line is parallel to the gaze line, i.e., β = α [so that cot (α) tan (β) = 1]. As a consequence, foveal gain becomes independent of gaze direction and tilt angle γ. Note that the limiting value of the roll gain k for a decreasing axis tilt γ depends on how the axis tilt changes as a function of gaze eccentricity α.
Figure FA2 (left panel) shows that if the VOR follows the projection model (filled symbols) the foveal gain is considerably enhanced over a range of gaze eccentricities. For example, a tilt of the rotation axis of γ = 8.3°/17.2° would increase foveal gain from 0.38/0.38 (average torsional gain in 3 monkeys with plugged vertical semicircular canals for an axis tilt γ = 0, open symbols in Fig. FA2, cf. stars in Fig. 6) to 0.69/0.67 when gaze is 10°/20° eccentric. Thus a comparable foveal gaze enhancement requires increasingly larger axis tilts when gaze becomes more eccentric. Note that Ωexp/Ωopt = 0.38 is kept constant, reflecting the assumption that the vestibular signals are constant and independent of the gaze direction. Figure FA2(right panel) shows the result of using Eq.A2 to compute the change in meridional gain,G merid, defined as the gain at different eccentricities along a meridian through the fovea. In the simulation shown, gaze direction is 20° left. For the parallel projection model (stars), G merid is ideal at the fovea and increases or decreases in the retinal periphery, producing additional retinal image slip off the fovea. For the orthogonal projection model (filled symbols),G merid is ideal 10° right from the fovea and also shows an increase or decrease at other retinal eccentricities.