Neural Constraints on Eye Motion in Human Eye-Head Saccades

H. Misslisch1, D. Tweed1, 2, 3, and T. Vilis2

1 Department of Neurology, University of Tübingen, 72076 Tubingen, Germany; and 2 Department of Physiology and 3 Department of Applied Mathematics, University of Western Ontario, London, Ontario N6A 5C1, Canada

    ABSTRACT
Abstract
Introduction
Methods
Results
Discussion
References

Misslisch, H., D. Tweed, and T. Vilis. Neural constraints on eye motion in human eye-head saccades. J. Neurophysiol. 79: 859-869, 1998. We examined two ways in which the neural control system for eye-head saccades constrains the motion of the eye in the head. The first constraint involves Listing's law, which holds ocular torsion at zero during head-fixed saccades. During eye-head saccades, does this law govern the eye's motion in space or in the head? Our subjects, instructed to saccade between space-fixed targets with the head held still in different positions, systematically violated Listing's law of the eye in space in a way that approximately, but not perfectly, preserved Listing's law of the eye in head. This finding implies that the brain does not compute desired eye position based on the desired gaze direction alone but also considers head position. The second constraint we studied was saturation, the process where desired-eye-position commands in the brain are "clipped" to keep them within an effective oculomotor range (EOMR), which is smaller than the mechanical range of eye motion. We studied the adaptability of the EOMR by asking subjects to make head-only saccades. As predicted by current eye-head models, subjects failed to hold their eyes still in their orbits. Unexpectedly, though, the range of eye-in-head motion in the horizontal-vertical plane was on average 31% smaller in area than during normal eye-head saccades, suggesting that the EOMR had been reduced by effort of will. Larger reductions were possible with altered visual input: when subjects donned pinhole glasses, the EOMR immediately shrank by 80%. But even with its reduced EOMR, the eye still moved into the "blind" region beyond the pinhole aperture during eye-head saccades. Then, as the head movement brought the saccade target toward the pinhole, the eyes reversed their motion, anticipating or roughly matching the target's motion even though it was still outside the pinhole and therefore invisible. This finding shows that the backward rotation of the eye is timed by internal computations, not by vision. When subjects wore slit glasses, their EOMRs shrank mostly in the direction perpendicular to the slit, showing that altered vision can change the shape as well as the size of the EOMR. A recent, three-dimensional model of eye-head coordination can explain all these findings if we add to it a mechanism for adjusting the EOMR.

    INTRODUCTION
Abstract
Introduction
Methods
Results
Discussion
References

In an eye-head saccade, a combined motion of the eye and head carries the gaze line rapidly to a new target. This paper examines two ways in which the neural control system for these movements constrains the motion of the eye.

The first constraint involves the kinematic rules governing three-dimensional (3-D) eye movements. One of these rules, called Donders' law, states that the torsional component of eye position relative to the head is determined by the horizontal and vertical components (Donders 1848). If we use quaternion vectors to represent eye positions, then Donders' law implies that these quaternion vectors will be confined to a 2-D surface. Listing's law defines the shape of this surface, stating that the vectors are confined to a head-fixed plane (Von Helmholtz 1867).

During head-fixed saccades between distant targets, the eye obeys Listing's law (e.g., Ferman et al. 1987b,c; Haustein 1989; Tweed and Vilis 1990; Von Helmholtz 1867). But what about eye-head saccades? Does the eye then follow Listing's law relative to space or relative to the head? Hypotheses proposed by Von Helmholtz (1867) and Hering (1868) to explain the functional significance of this law imply that it should hold for the eye in space (Glenn and Vilis 1992; Radau et al. 1994). In contrast, the one existing 3-D model of eye-head saccades (Tweed 1997) requires that the eye in head obey Listing's law and therefore predicts systematic violations of Listing's law for the eye in space. Statistical analysis in a previous study indicated that Donders' law holds somewhat better for the eye in head than for the eye in space (Radau et al. 1994). Here, we use a more straightforward paradigm, where the same space-fixed targets are fixated but with the head in different static positions, to show that subjects systematically violate Donders' law of the eye in space to maintain Listing's law of the eye in head.

The second neural constraint examined here is the "saturation" of desired eye-position commands. Guitton and Volle (1987) found that during large gaze shifts by human subjects, the eye is never driven to the edge of the oculomotor range, ±55°. Instead, eye position is saturated neurally or limited to eccentricities less than ~45° horizontally. This range of neurally allowed eye-in-head positions is called the effective oculomotor range (EOMR). Recent results suggest that neural saturation works in all three dimensions, so that the EOMR is a 3-D volume (Tweed 1997; Tweed et al. 1995).

During large eye-head saccades, the eye moves toward the target as far as the EOMR allows; e.g., if the target object is 65° right, the eye moves swiftly to a position ~45° right. When head and eye motion have brought the gaze line to the target, the eye then rotates back under the influence of the vestibuloocular reflex (VOR) until the head ends its movement (e.g., Guitton and Volle 1987; Laurutis and Robinson 1986; Tweed et al. 1995).

The fact that the eye overshoots its final position in the head and then rotates back has been interpreted to mean that it is being driven to a desired position defined in a space-fixed reference frame rather than in a head-fixed frame (Tweed 1997). We tested this idea, which is embodied in several eye-head models (Galiana and Guitton 1992; Goossens and Van Opstal 1997; Phillips et al. 1995; Tweed 1997), by having subjects attempt large, head-only saccades: saccades where the eyes maintain a fixed position in their orbits. If the eye is in fact driven to a desired position in space, it should travel to the edge of the EOMR despite the subject's efforts to keep it stationary. Our results show that, as predicted, head-only saccades are impossible: the eye seeks the target despite all efforts to hold it still.

Unexpectedly, though, we found that subjects can voluntarily reduce the amount of eye-in-head motion by a small amount; i.e., they can slightly shrink their EOMRs. We explored the flexibility of the EOMR by having subjects wear pinhole and slit spectacles, the former for 6 h, to see if altered visual input and practice led to larger changes in its size and shape.

    METHODS
Abstract
Introduction
Methods
Results
Discussion
References

Movement recording and tasks

Experiments were performed on seven adult human subjects (5 male, 2 female) without known eye or head movement disorders. Search coils were used to measure 3-D positions of the left eye and the head (Robinson 1963; Tweed et al. 1990). The position of the eye was monitored using the Skalar annulus: a silicone rubber ring containing two effectively orthogonal search coils that adhered to the sclera by suction (Ferman et al. 1987a). Head position was measured using another annulus attached to a knitted hat that fitted snugly to the head and was secured further by bands of tape wrapped under the chin. The subject sat in three orthogonal alternating magnetic fields (frequencies 62.5, 100, and 125 kHz) that were generated by Helmholtz coils of 2-m diam arranged so that the fields were uniform to within 10% throughout a 1-m cube centered on the subject's head. Three voltages from each search coil (i.e., 6 signals per annulus) were sampled at 100 Hz.

Saccade targets were red dots, 8-mm across, on a yellow background ~1 m from the subject's left eye. They were viewed binocularly, so that the vergence angle during static fixation was constant and <3.5°. Subjects sat on a chair with a firm back support and kept their bodies still.

In the experiments dealing with Donders' and Listing's laws, subjects held their heads stationary in different horizontal positions and made eye-only saccades between space-fixed targets: one center target and four eccentric ones, at 15 or 20° right, left, up, and down. This procedure was performed twice for each of two different head positions.

In the remaining experiments, dealing with saturation, subjects made gaze shifts between a central target and eight radially distributed visual targets at 63.5° eccentricity. These saccades were sequenced randomly in response to verbal commands (using the "clock convention," i.e., 12:00 = up, 1:30 = up and right,3:00 = right, etc.) read off a computer-generated random list. Subjects performed four different tasks, each task twice 1) Gaze shifts with the head stationary (eye-only paradigm). For these trials, subjects were instructed to keep their heads still and use only their eyes for the gaze shifts, even though the targets could not be reached because of their 63.5° eccentricity. We monitored the3-D components of head in space positions and verified that they were <3° horizontally and vertically and <1.5° torsionally. Because of prior training, the measured eye-only saccades were usually very accurate in direction. 2) Large gaze shifts with the head free to move (eye-and-head). This task mapped the EOMR during normal eye-head saccades. 3) Gaze shifts with the instruction to keep the eyes stationary in the head (head-only). 4) Repeat of task 2 with the subject wearing pinhole or slit glasses. The pinhole glasses restricted the visual field radially to ±10°, the glasses with a horizontal slit restricted it vertically to ±9°. Both types of glasses therefore blocked the view of the targets so that the subject had to saccade to their remembered locations. To test for adaptive changes, three subjects were reexamined after wearing the pinhole glasses for 6 h. To promote rapid adaptation, the subjects spent these 6 h on activities needing visual guidance in rich visual environments.

Quaternions and coordinate systems

Three-dimensional eye and head positions are represented as quaternions, which express angular positions in terms of the angle and axis of a rotation away from some reference position (Tweed et al. 1990; Westheimer 1957). When an object rotates alpha ° away from reference position, about an axis parallel with the unit vector n, then its 3-D orientation is represented by the quaternion vector q:
q = sin (α/2)<B>n</B> (1)
Here alpha  is the rotation angle between the reference orientation and the orientation represented by q; n is a unit vector parallel to the rotation axis. The direction of n is specified by the right-hand rule: if the right thumb is parallel to the rotation axis, then the fingers will curl in the direction of the rotation. In this study, the reference orientations of the eye and head were defined when the subject looked at the center target with the head upright and facing straight ahead.

All orientations are expressed relative to some reference frame. For example, eye position can be described relative to the head or space frame. Thus eh, es, and hs denote the angular positions of the eye relative to the head, of the eye relative to space, and of the head relative to space, respectively. Analogous terminology is used when describing angular velocities.

When eh and es are plotted as quaternion vectors in this paper, they are always expressed in magnetic field coordinates. The vector components and corresponding coordinate axes are named q1, q2, and q3. Following convention, rotations about these axes are torsional, vertical, and horizontal, respectively, with the positive directions clockwise (CW), left and down.

First- and second-order surfaces were fitted to the es and eh quaternion data by least-squares minimization. The second-order surface function is
q<SUB>1</SUB><IT>= a</IT><SUB>1</SUB><IT>+ a</IT><SUB>2</SUB>q<SUB>2</SUB><IT>+ a</IT><SUB>3</SUB>q<SUB>3</SUB><IT>+ a</IT><SUB>4</SUB>q<SUP>2</SUP><SUB>2</SUB>+ <IT>a</IT><SUB>5</SUB>q<SUB>2</SUB>q<SUB>3</SUB><IT>+ a</IT><SUB>6</SUB>q<SUP>2</SUP><SUB>3</SUB> (2)
First-order surface fits use only the first three terms. The shape of a first-order surface is planar, whereas for higher orders the surface can be curved or twisted (Glenn and Vilis 1992; Radau et al. 1994).

Size of the effective oculomotor range

To measure how different gaze shift tasks influence the size and shape of the EOMR in the horizontal-vertical dimensions, we quantified the relative distribution of the eh positions as follows. First, the data-analysis program found the start and end of each centrifugal eh saccade using an acceleration threshold. The program then computed and stored the eh quaternion vectors at the start and end of the saccade as well as the magnitude and the direction of the saccade. Using these saccade parameters, the eh positions then were grouped corresponding to the eight target directions, and the eh quaternion vectors at the end of each saccade were averaged for each group. These eight averaged position vectors SD were connected with lines yielding an octagonal area (Fig. 1). This area allowed us to quantify the size of the EOMR in different tasks. In Fig. 1, as in all figures plotting eye and head position vectors, the locations of the peripheral targets are indicated by stars.


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FIG. 1. Quantifying the area of the effective oculomotor range (EOMR) in the horizontal-vertical plane. Subjects made 4-7 centrifugal saccades toward each of 8 peripheral targets (*). Point of maximum eccentricity (in the horizontal-vertical plane) achieved by the eye in head was marked for each saccade. These points were averaged for each of the 8 targets, and the averages (eccentric dots) were connected (- - -), enclosing an octagon. ------, connects dots located 1 SD beyond the average maximum eccentricity for each of the 8 targets. Area enclosed by the solid lines was used to compare the size of the EOMR in various tasks. Central dots are the quaternion vectors at the start of each saccade. This figure depicts data from the eye-only task. Subject DT.

    RESULTS
Abstract
Introduction
Methods
Results
Discussion
References

Donders' law fails for the eye in space

To test whether the eye in space obeys Donders' law, we asked the subjects to look at five space-fixed targets (straight ahead and either 15 or 20° right, left, up, or down) with the head stationary, facing a target at either 20° (for 6 subjects) or 40° (for 1 subject) to the left and right. If the eye followed Donders' law in space, its 3-D orientations would be identical when looking at the same space-fixed targets with the head in two different positions. If Donders' law held for the eh, the es vectors would fill out two distinct surfaces: one for each head position. Moreover, if eh followed Listing's law and the head were turned exactly 20° right and 20° left, the es vectors would fill out two planes, tilted at 20° relative to one another.

Figure 2 shows es positions represented as the tips of quaternion vectors. In Fig. 2A, the targets were at center and 20° eccentric (right, left, up, or down) and the subject's head (as measured) was 21° left and 21° right. In Fig. 2B, the targets were at center and 15° eccentric and the subject's head was 41° left and 35° right. As indicated by the cartoon head, the quaternion vectors are seen from above the subject so that q1 and q2 are plotted along the ordinate and abscissa, respectively. For example, the quaternion vector plotted as a white square marked by an arrow in Fig. 2B, for fixation of a target 15° up when the head is turned 35° right, indicates an eye rotation with components of ~15° upward and ~7° counterclockwise.


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FIG. 2. Eye positions relative to space violate Donders' law. Eye-in-space quaternion vectors (black-square) are viewed from above the subject so that their torsional and vertical components (q1 and q2) are plotted along the ordinate and abscissa. In A, subject DT made eye-only saccades between 5 earth-stationary targets placed at center and 20° up, down, right, or left with the head stationary at 21° left or 21° right. In B, subject NN made saccades between the center and 15° eccentric, earth-fixed targets with the head stationary at 41° left or 35° right. Corresponding eye-in-space positions (for fixation of the same target, here: with the same q2 component) show markedly different torsional components up to ~9° when fixating the 20° up target in A and up to ~16° when fixating the 15° down target in B.

As illustrated in Fig. 2, corresponding eye positions for the two head positions fill out two surfaces that differ significantly in torsion, and this difference depends on how far the head is turned. For example, in Fig. 2B, when subject NN fixates the target 15° up, the torsional orientation of es changes from ~5.5° clockwise when the head is 41° left to ~6.7° counterclockwise when the head is 35° right. When fixating the target at 15° down, es is 8.8° counterclockwise when the head is 41° left and 7.7° clockwise when the head is 35° right. Moreover, the es vectors are confined to two different planes, tilted relative to one another. The angle between these two planes is ~26° when the angle between the two head positions is 42° in subject DT (Fig. 2A) and ~51° when the head angle is 76° in subject NN (Fig. 2B).

The rotation of the two planes was almost purely horizontal. On average, the tilt in the sagittal plane was only0.9 ± 1.0° and not significantly different from zero (t-test, P < 0.05, n = 7). The shift of the es surfaces along the torsional (q1) axis, averaged over all subjects, was only1.4 ± 1.1° and not consistent in any one direction.

To quantify the horizontal rotation, we fitted second-order surfaces to the es vectors by least-squares minimization (Glenn and Vilis 1992; Radau et al. 1994). Then we computed the normal vectors to these surfaces, at the point where they intersect the naso-occipital axis. We projected these normal vectors into the horizontal plane and found the angle between the projected vectors. Dividing this angle by the horizontal angle between the two head positions then yielded the rotation ratio, which indicates how far the fitted surfaces were rotated, in the horizontal plane, relative to the head's rotation. This rotation ratio will be zero if the orientations of es follow Donders' law, filling a single surface. On the other hand, if eh obeys Listing's law, there will be two planes of es vectors tilted at about half the angle between the two eccentric head positions, i.e., the rotation ratio will be ~0.5. The reason the expected ratio is 0.5 rather than 1---i.e., the planes turn only half as far as the head---is related to the half-angle rule of eye motion: if the eye obeys Listing's law, then its rotation axes tilt when the eye moves, but only half as far. The geometry underlying these half angles is discussed in several publications (e.g., Tweed and Vilis 1990; Von Helmholtz 1867).

 
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TABLE 1. Rotation ratios

Rotation ratios for all subjects are listed in Table 1. The averaged value is 0.71 ± 0.10. This value is greater than zero, which means that es violates Donders' law. However, the rotation ratio is also higher than the 0.5 value expected if eh obeyed Listing's law. We consider this discrepancy in the DISCUSSION.

Eye-in-head motion

To check directly whether eh obeyed Listing's law during these gaze shifts, we examined eye position relative to the head. Figure 3 shows data from the same subject and task as in Fig. 2A, but this time plotting eh rather than es vectors, together with a second-order surface of best fit. To quantify the scatter of the vectors about this best-fit surface, we measured the distance, in the torsional dimension, from each vector to the surface and computed the standard deviation. This measure of scatter was 0.81° for this subject, proving close agreement with Donders' law. But the twist score, quantifying surface curvature, amounted to 0.29, indicating a systematic departure from Listing's law, which requires a twist score of zero. These values of scatter and twist were consistent: averaged across the six subjects in this task, scatter was 0.78 ± 0.30 and twist was 0.43 ± 0.15. 


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FIG. 3. Eye positions relative to the head violate Listing's law. If we pool eye-in-head quaternion vectors recorded while a subject viewed the same space-fixed targets but in different head positions, we find that they lie in a twisted surface, not in a plane, violating Listing's law. Twist may indicate that the vectors are confined to a curved surface rather than a plane, or it may mean that they lie in a plane but the plane is not fixed in the head. Same view, subject and task as in Fig. 2A.

Can subjects make head-only saccades?

Most current models of eye-head saccades (e.g., Galiana and Guitton 1992; Goossens and Van Opstal 1997; Phillips et al. 1995; Tweed 1997) assume that the eye is driven to a desired position defined in a space-fixed reference frame, not in a head-fixed frame. If this assumption is correct, then subjects should be unable to make head-only saccades, in which the eye is held still in the head, because the eye always will be driven away from its start position, toward the target.

We instructed our subjects to make head-only saccades to eight radially distributed targets at 63.5° eccentricity. Figure 4 shows a comparison of eh (left) and hs (right), represented as quaternion vectors, with the positive q2 and q3 axes labeled down and left, respectively, in this behind view. Subjects performed three saccade tasks, each involving centrifugal gaze shifts toward the eight targets (indicated by stars). At the top of the figure are shown eye-only saccades; in the middle, normal eye-head saccades; and at bottom, attempted head-only gaze shifts. As can be seen in Fig. 4, top, the subject can perform voluntary eye-only saccades with virtually no contribution of the head. Although the eye moves well in the direction of the targets, it always falls short, limited by the EOMR. During normal eye-head saccades (Fig. 4, middle), the distribution of eh corresponds to the EOMR in the horizontal-vertical plane in this task. Note that this subject's EOMR is larger vertically than horizontally as indicated by the larger position range along the abscissa.


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FIG. 4. Eye-in-head and head-in-space positions during eye-only (top), normal eye-head (middle), and attempted head-only saccades (bottom). black-square, tips of quaternion vectors plotted at 0.01-s time intervals (as in Figs. 2 and 3). Here, the position vectors are viewed from behind the subject so that their vertical and horizontal components (q2 and q3) are plotted along the abscissa and ordinate. Contribution of the head to the overall gaze shift is negligible in the eye-only task. During normal eye-head saccades in this subject, the range of eye-in-head positions (i.e., the effective oculomotor range, EOMR) is larger vertically than horizontally whereas the range of head motion is mostly horizontal. During attempted head-only saccades, eye rotation still occurs, although with reduced magnitude and is still larger vertically than horizontally. At the same time, head rotations increase in this task so that the targets still can be foveated. Between 3 and 5 saccades were recorded for each target direction. Subject DT.

Figure 4, bottom, shows attempted head-only saccades. Clearly, the attempts fail: the eye still moves considerably in the head. This is as predicted by the models and supports the notion that the eye is driven to a target in space. More surprisingly, though, the range of eye motion does decrease slightly, and the head's contribution to the overall gaze shift increases compared with their values during normal eye-head saccades.

Can the size of the EOMR be changed voluntarily?

To quantify this change, we measured the area of the EOMR in the horizontal-vertical plane using the octagon method described in METHODS (see Fig. 1). Because each gaze-shift task was performed twice, we averaged the two measurements of the EOMR, expressed in deg2, for each subject. Figure 5 shows the magnitudes of these areas during normal eye-head saccades (black bars) and attempted head-only saccades (white bars) for each subject, average and SD. The average area of the EOMR was 4,697.5 ± 569.2 deg2 during normal eye-head saccades and 3,250.4 ± 323.9 deg2 in the head-only task, a reduction of 30.8 ± 6.9%. There was no significant difference between the first and second trials. Clearly, if the subjects had succeeded in making head-only saccades, the area of the EOMR would have been zero. Thus such saccades cannot normally be made, but subjects do have a limited ability voluntarily to reduce the magnitude of the eye component in a combined eye-head gaze shift.


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FIG. 5. Area of the EOMR in the horizontal-vertical plane for all subjects and average in different gaze shift tasks. Compared with its area during normal eye-head saccades (black-square), the EOMR is reduced during attempted head-only saccades (square ), and eye-head saccades wearing pinhole glasses (), on average by 30.8 and 80.2%, respectively.

Can the size of the EOMR be changed by altered vision?

Can the EOMR be reduced further when the visual field is restricted? We had subjects wear pinhole glasses that blocked all vision >10° from straight ahead, so that eye movements >10° would be of no help in fixating visual targets. As seen in Fig. 6, the range of eh with these glasses (right) is clearly shrunken as compared with the range during normal eye-head saccades (left), although it is still larger than the ±10° visible field. The average EOMR in the pinhole task (striped bars in Fig. 5) is 932.3 ± 170.2 deg2. Compared with normal eye-head saccades, this is a reduction of 80.2 ± 3.6%. Averaged horizontal and vertical ranges were 34.3 ± 2.6° and 34.7 ± 6.7°, respectively.


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FIG. 6. Eye-in-head positions during eye-head saccades with pinhole glasses before and 6 h after adaptation as compared with normal eye-head saccades. With the glasses on, the EOMR in the horizontal-vertical plane is reduced drastically and roughly circular. Reduction was immediate, with little further decrease after 6 h wearing the glasses. Same view and conventions as in Fig. 4. Visible range in the pinhole task lies within the circles. Subject DT.

This reduction of the EOMR was seen immediately in the first motor task after the pinhole glasses were put on. After 6 h wearing the glasses, there was a further small reduction of the EOMR in the pinhole task compared with the eye-head task (Fig. 6, right). But as Fig. 7 shows, after 6 h of adaptation to pinhole glasses the EOMR was reduced in all three tasks (eye-head saccades without glasses, head-only without glasses, and eye-head with pinhole glasses). In the three subjects tested for adaptation, the EOMR during normal eye-head saccades, without spectacles, was on average 4,304.4 deg2 before and 3,267.3 deg2 after the 6-h adaptation time, a highly significant decrease of 24.1% (paired t-test, P < 0.01, n = 6). Before adaptation, the EOMR was reduced by 77.7% in the pinhole task and by 23.4% in the attempted head-only task, both compared with its value during normal eye-head saccades before adaptation. After adaptation, the EOMR was decreased by 77.8% and by 22.3% compared with normal eye-head saccades after adaptation. Thus the relative shrinkage of the EOMR caused by donning pinhole glasses or attempting head-only saccades was the same before and after adaptation (t-test, P < 0.05, n = 6).


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FIG. 7. Horizontal-vertical area of the EOMR during normal eye-head saccades (black-square), attempted head-only saccades (square ), and eye-head saccades wearing pinhole glasses () before and after 6 h wearing pinhole glasses. After adaptation to the restricted visual field, the absolute size of the EOMR is smaller in all tasks. However, relative to the eye-head task, the ranges of eye-in-head positions in the head-only and pinhole tasks are not significantly different before and after adaptation.

Why does the range of eye motion decrease?

Is the reduction in the eye's range really due to shrinkage of the EOMR or might it be caused by some other factor? One possibility is that the border of the EOMR was not reached in the pinhole task, perhaps because the eye started moving much later than the head or because the eye saccades were very slow. To determine whether the edge of the EOMR in the pinhole task had actually been reached, we examined the trajectories of the eye in head. Phases where the eye was stationary relative to the head ("plateaus"), were regularly found at times when the motor error (the quotient of current desired eh and actual eh) driving the saccadic pulse generator was still large (15-35°), indicating that the eye had reached a saturation limit.

Figure 8 shows an example of such a plateau during a leftward gaze shift, with horizontal positions of eh and hs (------) and target relative to the eye (···) plotted against time. The eye moves leftward for ~105 ms and then stops for 220 ms (at 17° left) when the motor error is ~35°. The head, which started moving ~20 ms after the eye, rotates leftward throughout the gaze saccade, thereby shifting the target's location relative to the head (···) rightward until it is equal to current eh. At that moment, the eye is on target, even though it does not see anything because it is outside the pinhole (radius 10°, - - -). While the head continues to rotate leftward, the VOR rotates the eye rightward to keep it on target. Note that the VOR starts at a moment when the target is not visible, meaning that visual input is not needed to initiate compensatory VOR eye movements. Rather, it seems that the brain combines information about the current positions of the eye in the orbit and the head in space to predict when the target would be foveated, if vision were not blocked.


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FIG. 8. Plateau of eye-in-head position during a leftward gaze shift wearing pinhole glasses. After an initial saccadic movement, the eye stays stationary relative to the head while dynamic motor error, i.e., the difference between current eye-in-head position and target relative to the head position (···), is still large (~35°). - - -, edge of the pinhole glasses; right-arrow, onset of the VOR eye movement. Note that VOR eye movement starts when the target is outside the visible range. Subject TS.

Figure 9 shows the horizontal and vertical distribution of plateaus in the pinhole task, i.e., of the positions where the eye's motion in the head stops and then reverses. Dots mark positions where the eye remained stationary in the orbit for >= 70 ms, for the same subject as in Fig. 8. Most of these plateau positions lie outside the pinhole (dashed circle). Thus wearing pinhole glasses shrinks the EOMR but leaves it larger than the restricted visual field.


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FIG. 9. Eye-in-head positions during plateaus while the subject made gaze shifts to all targets wearing pinhole glasses. Position vectors are viewed from behind the subject. In most cases, the plateaus occur outside the pinhole (dotted circle). Eye-in-head eccentricities in the horizontal-vertical plane are much smaller than during normal eye-head saccades, indicating a shrinkage of the EOMR. Same subject as in Fig. 8.

Shape of the EOMR

The ranges of horizontal and vertical eh positions during normal eye-head saccades, averaged over all subjects, were 77.9 ± 10.0° and 78.5 ± 5.5°. Three of the six subjects showed significantly larger vertical than horizontal eh ranges (t-test, P < 0.01, n = 6), indicating that the eye rotated farther vertically than horizontally. But in one subject, the EOMR was equally large in the horizontal and vertical dimensions, while the other two subjects had significantly larger horizontal than vertical ranges (t-test, P < 0.05, n = 4). In the head-only task, the averaged horizontal and vertical eh position ranges were 59.9 ± 7.4° and 69.3 ± 8.2°, respectively. Here, four subjects showed eh ranges significantly larger in the vertical than in the horizontal dimension (t-test, P < 0.01, n = 8), one subject showed no difference, and in another subject the eye rotated farther horizontally than vertically.

Can the shape of the EOMR be changed?

When a subject is wearing pinhole glasses, the EOMR is roughly disk-shaped in the horizontal-vertical plane (Fig. 6). Does this shape change when subjects wear horizontal slit glasses? Comparing the EOMR with slit glasses (Fig. 10B) to during normal eye-head saccades without glasses (Fig. 10A), one can see that in the control condition the eh vector distribution is roughly equal horizontally and vertically, but when the world is seen through a horizontal slit, the range of vertical eh (orthogonal to the direction of the slit) is reduced markedly. In accordance with the right-hand rule, this means that the distribution of the eye-position vectors while wearing slit glasses is shrunken along the abscissa, the axis representing vertical position components. As in the pinhole task, the eh positions still spread beyond the ±9° vertical limits of the visual field, indicated by the dashed lines.


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FIG. 10. Horizontal-vertical shape of the EOMR is changed by altered visual input. Compared with normal eye-head saccades with roughly equal-sized horizontal and vertical components (A), eye-in-head position vectors during eye-head saccades with (horizontal) slit glasses (B) show a reduction in the vertical component, corresponding to the vertical reduction of the visible visual field. Same view and conventions as in Figs. 4 and 6. Dashed lines enclose visible range. Subject PR.

The averaged distribution of horizontal and vertical eh in the three subjects tested for gaze shifts wearing slit glasses were 59.0 ± 6.4° and 30.7 ± 7.3°, respectively (Fig. 11). During normal eye-head saccades, the corresponding ranges in these subjects were 86.0 ± 5.4° and 75.7 ± 5.7°. This means that the ratio of horizontal to vertical eh range increased from 1.2 ± 0.1 during normal eye-head saccades to 2.0 ± 0.4 during eye-head saccades with horizontal slit glasses. Thus the form of the visual restriction influences the shape of the EOMR.


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FIG. 11. Horizontal and vertical ranges of eye-in-head positions (in degrees) during normal eye-head saccades (black-square) and during eye-head saccades with horizontal slit glasses (square ). Range of vertical eye positions is much more drastically reduced by the effects of altered vision than the range of horizontal eye positions.

    DISCUSSION
Abstract
Introduction
Methods
Results
Discussion
References

Donders' and Listing's laws

It is known that eh obeys Listing's law during fixation of distant targets with the head upright and stationary, and during head-fixed saccades (Haustein 1989; Ferman et al. 1987b,c; Straumann et al. 1991, Tweed and Vilis 1990; Von Helmholtz 1867). More controversial is whether eh obeys Listing's law after eye-head saccades. Glenn and Vilis (1992) described static eh vectors after large eye-head gaze shifts lying not in Listing's plane but in warped surfaces. They concluded that Listing's law fails. But Radau et al. (1994) showed statistically that, although eh surfaces were thicker after eye-head-torso saccades (average 1st-order SD = 2.6°) than after head-fixed saccades (Straumann et al. 1991: 1.3°; Tweed and Vilis 1990: 1.5°), there was no significant change in shape. In other words, eh vectors after large eye-head-torso saccades still lay in a "plane," albeit a thicker one. The increase in thickness may be due to the tilt of the head and trunk relative to gravity, as Listing's plane of eh shifts along the torsional axis during static body roll (Crawford and Vilis 1991) and changes pitch during static body pitch (Haslwanter et al. 1992).

It is known that head position in space, hs, obeys Donders' law, but not precisely Listing's law, during and after most eye-head gaze shifts (Glenn and Vilis 1992; Tweed and Vilis 1992). Geometrically, Donders' law of hs and Listing's law of eh are incompatible with Donders' law of es if the eye and head move at all independently. The reason is that the planes formed by the es vectors in different head positions cannot fit together into a single surface. This failure to mesh is clear in our data: the es vectors for the two head positions, ~20° or 40° right and left, lie in distinct planes and not in one surface. Actually, not only Listing's law of eh but even Donders' law of eh is incompatible with Donders' law of hs and es. In other words, geometry dictates that, given Donders' law of hs, we can have Donders' law of eh or Donders' law of es but not both.

Which law holds? Radau et al. (1994) showed, by statistical analysis of eye-position surfaces, that Donders' law holds somewhat better for the eye in head than for the eye in space. In the present study, we showed directly that Donders' law of the eye in space fails utterly. When the head was held stationary in two different positions and the same space-fixed targets were viewed, the es vectors lay in two distinct surfaces (Fig. 2). The angle between these surfaces increased with increasing angle between the two head positions. Qualitatively, at least, this is the pattern one would expect if the system were sacrificing Donders' law of es to preserve Listing's law of eh.

Quantitative data on Listing's law

If the head were turned exactly ±20° and if eh obeyed Listing's law and Listing's plane were head-fixed, one would expect an angle of 20° between the es planes, yielding a "rotation ratio" of 0.5. The computed averaged rotation ratio in our experiments was 0.71, clearly different from the zero value required for Donders' law of the eye in space, but also different from the 0.5 expected for Listing's law of the eye in head.

One possible explanation is that Listing's plane rotates slightly, with respect to the head, in the direction that the head is facing. But if this explanation were correct, one would expect torso movements to affect Listing's plane. That is, if a subject scanned a space-fixed target array, once with the torso rotated left and once with the torso rotated right but always with the head facing forward, one would expect Listing's plane to rotate slightly in the direction opposite the torso position. When this experiment was done, however, there was no consistent movement of Listing's plane (unpublished observation). This negative result makes it less likely that Listing's plane moves whenever the head turns on the torso.

Another possibility is that Listing's plane turns toward the center of attention; i.e., when all the targets in a visual or saccade task are to the left, relative to the head, maybe Listing's plane turns slightly left in the head. Such behavior might serve a useful purpose, shifting the primary gaze direction toward an object of interest so that radial saccades, toward and away from this object, would follow the shortest possible path. Radau et al. (1994) reported a related finding for vertical head rotations: subjects hold their heads so that the primary gaze direction points at the center of the visual scene. Similarly, Haslwanter et al. (1992) found that the primary gaze direction rotates in the opposite direction to the head during pitch, albeit with a low gain, thereby helping to keep primary gaze direction close to the horizon.

A third possible explanation for the large rotation ratios in our experiment is that Listing's "plane" is not quite flat. Surface twist can be quantified by the parameter a5 (Eq. 2), called the twist score. If this twist score were positive, then the rotation ratio would be >0.5. Indeed, DeSouza and Vilis (1997) report that Listing's surface consistently is twisted positively during head-fixed saccades by normal subjects, showing an average twist score of 0.24. Based on this value, one would predict a rotation ratio of 0.62 if Listing's surface were preserved perfectly relative to the head in our experiment.

When we fitted second-order surfaces to our eh data as in Fig. 3, the twist score, averaged across all subjects, was 0.41. This large value may indicate that our subjects' Listing's surfaces were more twisted than those in DeSouza and Vilis's study, perhaps because we used a larger range of eye positions. Or it may indicate that the surfaces move: if Listing's plane were perfectly flat but moved in the head, we would get a large twist score if we pooled eh data from different head positions, as in Fig. 3. With our data we cannot distinguish these two possibilities---surface twist or surface rotation---but either way, we have a systematic violation of Listing's law of eh: Listing's surface is likely curved, and it may turn toward the center of visual attention. On the other hand, Donders' and Listing's law still are preserved better for the eye in head than for the eye in space; e.g., averaged across our six subjects, the scatter of eye positions about their best-fit, second-order surface averaged 0.78° for eh and 1.59° for es.

Implications for theories of Listing's law

The fact that es violates Donders' law has implications for the functional purpose of Listing's law. Last century, Von Helmholtz (1867) and Hering (1868) suggested that the purpose of the law was to optimize certain aspects of retinal-image flow. They knew that retinal flow depends on the eye's motion in space, not in the head, and that most gaze shifts involve both eye and head. Thus they must have assumed either that the eye follows Listing's law with respect to space or that the law was developed specifically for head-fixed scanning. The present study indicates that the former assumption is false. Regarding the latter possibility, it is true that we sometimes hold our heads still when carefully examining a visual scene, but by no means always, and when the head moves, it is Listing's law of the eye in head that holds, and Listing's law of the eye in space that fails, as our result here shows for saccades. The pursuit system, too, obeys Listing's law of the eye in head whether the head is moving or not (Haslwanter et al. 1991; Misslisch et al. 1996; Tweed et al. 1992). Therefore theories that suggest a purpose for Listing's law of the eye in head (e.g., Fick 1858; Tweed 1997; Wundt 1859) explain more than do eye-in-space theories like Von Helmholtz's and Hering's, and they need not propose completely distinct optimization strategies for head-fixed versus head-moving scanning.

Size of the EOMR

Guitton and Volle (1987) reported that during natural eye-head gaze shifts the range of eye positions is usually smaller (±45°) than the mechanical limits (±55°) of the extraocular muscles. They suggested that if the target is far eccentric, then eh is driven to a saturated version of target position within a central effective oculomotor range, EOMR. Thus in their 1-D model, the desired eh signal passes through a saturation element before reaching the saccadic pulse generator. A target position 65° right relative to straight ahead, for example, would emerge as a desired eh signal of 45° right.

In a recent study of eye-head saccades, Tweed et al. (1995) showed that a 3-D version of the EOMR explains many features of eye trajectories. For instance, in radial saccades, the eye initially moves too vertically in the head and then curves, tracing systematic loops in centrifugal and centripetal eye trajectories. This looping is explained by the fact that the eye is driven to a point where the visual target is predicted to enter the EOMR, a strategy that allows foveation of the target with a minimum of time and ocular motion. Another finding explained by 3-D saturation is the curvature in the torsional dimension observed in es trajectories during horizontal gaze shifts. This likely occurs because a straight path of es during horizontal saccades requires large violations of Listing's law for eh. A curved path is needed to keep eh within the torsional boundaries of the EOMR.

The present study indicates that the saturation function is, to at least some extent, under voluntary control and that it is changed drastically by altered visual input. In other words, the size and shape of the EOMR are not fixed but taskdependent. Thus when subjects tried not to move their eyes in the head-only paradigm, the area of the EOMR was reduced on average by ~30% (Figs. 4 and 5). As a result, the target was reached with a smaller eye movement and a larger head movement than usual (Fig. 4).

When a subject performs gaze shifts wearing pinhole glasses, the EOMR is reduced by ~80% (Figs. 5-7). The purpose of this reduction may be to save energy: if vision is restricted to a small central area, why waste muscular effort driving the eye into the "blind" periphery? However, the eye was actually driven a considerable distance across the border of the restricted visual field (Figs. 6, 8, and 9) even after 6 h of adaptation to the pinhole glasses (Figs. 6 and 7). Clearly there is more to this motor strategy than just energy saving.

One reason the eye moves into the dark zone may be to get a running start. That is, when the visual target comes into the restricted visual field, it will be moving relative to the head. If the eye simply sat at the edge of the pinhole and waited for the target to emerge, it would have to lurch into motion abruptly when the target appeared. Inevitably, there would be a catch-up interval while the eye accelerated. It may be to avoid this lag time that the eye instead crosses into the dark zone, there to turn around and begin its centripetal acceleration, driven by the VOR, so as to keep pace with the target when the latter comes into view.

These experiments make it clear that the VOR begins to act when the visual target is still invisible (Fig. 8). Thus VOR onset must be triggered by an internal estimate that the eye is pointing at the unseen target. Similarly, Misslisch et al. (1994) found that the VOR can adjust itself in other ways to the motion of an invisible target: the axis of slow-phase eye rotation tilts systematically depending on current eye-in-head position so as to decrease deviations from Listing's law and reduce optic flow over the fovea. Surprisingly, these axis tilts were also seen in complete darkness, when the subject was asked to imagine earth-fixed targets at various locations. Thus the brain can compute the retinal consequences of any given head movement, in any eye position, and produces a motor command that would stabilize a foveal image even if no such image is present.

Shape of the EOMR

During normal eye-head and attempted head-only saccades, some of our subjects rotated their eyes more vertically than horizontally (Fig. 4). In other subjects, however, there was no difference or the eye moved farther horizontally than vertically (Fig. 10). This finding contrasts with Glenn and Vilis's (1992) report that in general hs rotated mainly horizontally and eh mainly vertically. That behavior was interpreted as minimizing energy expenditure because the eye, with its relatively small, balanced mass, would perform the main work against gravity during a vertical or oblique gaze shift. The disagreement between our findings and Glenn andVilis's may be due to the fact that their targets were more eccentric than ours. Perhaps the head rotates more horizontally during larger gaze shifts.

We also found that the shape of the EOMR is changed by altering the visual input. With horizontal slit glasses, eh vectors no longer are distributed uniformly horizontally and vertically but show a reduced vertical range (Fig. 10). As in the pinhole task, this effect occurs immediately when the slit glasses are put on. With the pinhole glasses, a 6-h adaptation to the reduced visual input caused only a small further reduction of the EOMR, indicating that most of the adjustment occurs quickly. Moreover, the adaptation equally affects all tasks tested, suggesting a single, shared locus of adaptation.

Implications for theories of eye-head control

Most current models of eye-head control (e.g., Galiana and Guitton 1992; Goossens and Van Opstal 1997; Phillips et al. 1995; Tweed 1997) assume that the eye is driven toward a target in space and therefore predict our finding that head-only saccades are impossible. And although none of these models implies the size and shape changes we saw in the EOMR, at least two of them could be altered readily to do so. In the models by Goossens and Van Opstal (1997) and Tweed (1997), a desired eye-in-head position signal passes through a saturation box that defines the EOMR, and so the findings obviously can be mimicked by making the saturation function adjustable by effort of will or altered visual input.

Our other main findings---the failure of Donders' law of the eye in space and the (rough) preservation of Listing's law of the eye in head---are predicted by only one model (Tweed 1997) because it is the only 3-D theory in the lot. In one- or two-dimensional models, Donders' and Listing's laws do not come up. In a 3-D context, and only there, we can draw a further conclusion from the above findings: given that the eye is driven toward a desired position in space and given that eye position in space does not obey Donders' law, it follows that the desired eye position does not obey Donders' law; i.e., its torsional component is not a function of its gaze direction. In other words, the desired-eye-position command is not fully determined by the direction of the visual target. Therefore the brain does not compute its desired eye-position commands based on target location alone but also uses information about the planned head movement.

In summary, the 3-D model depicted in Fig. 12 can explain our findings on human eye-head saccades if we assume that its saturation function (i.e., the brain's definition of the EOMR) is adjustable: it can be influenced to some extent by effort of will and more markedly by altered vision.


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FIG. 12. Three-dimensional model of the eye-head saccadic system in humans. A 2-D signal coding the desired gaze direction in space, g*s, passes through the Donders operator to yield a desired 3-D head position, h*s, which obeys Donders' law. Within the head pulse generator, Ph, this h*s is compared with actual head position, hs, to produce the head-velocity command, &hdot;s. At the same time, g*s and h*s interact within the Listing operator to yield 3-D desired eye-in-head position, e*h, which obeys Listing's law. This signal combines with desired head position to yield desired eye position in space, e*s, which then interacts with current head position, hs, resulting in current desired eye-in-head position. This signal in turn passes through the saturation box to yield saturated current desired eye-in-head position, esath. In the eye pulse generator, Pe, this signal is compared with actual eye position, eh, to produce a saccadic eye-velocity command that, together with the VOR, determines eye-in-head velocity, ėh. This model can account for the findings in this paper if we assume that the computations within the saturation box are influenced by cognitive factors (e.g., the wish to make a head-only saccade) and by the structure of the visual field (e.g., restrictions caused by pinhole or slit glasses).

    ACKNOWLEDGEMENTS

  We thank S. Watts and L. Van Cleeff for technical assistance. H. Misslisch thanks the motor control group at University of Western Ontario for the warm welcome.

  This study was supported by the Deutsche Forschungsgemeinschaft (Sonderforschungs bereich 307/A2) and by the Medical Research Council (MRC) of Canada. During this study D. Tweed was a Scholar of the MRC.

    FOOTNOTES

  Present address and address for reprint requests: H. Misslisch, Dept. of Neurology, University Hospital Zürich, Frauenklinikstrasse 26, CH-8091 Zurich, Switzerland.

  Received 11 March 1997; accepted in final form 3 October 1997.

    REFERENCES
Abstract
Introduction
Methods
Results
Discussion
References

0022-3077/98 $5.00 Copyright ©1998 The American Physiological Society