Abstract
purpose. The kinematics of eye rotation is not entirely elucidated despite two centuries of fascination with the deceptively simple yet geometrically complex nature of the movement. Recently, the traditional view that oculorotatory muscles except the superior oblique muscle exert straight pull on the globe has been challenged by the claim that the muscles also go through a connective tissue pulley-like structure that holds them steady during eye rotation. Although earlier studies failed to observe sideslippage at the posterior part of muscles, a finding supportive of the pulley hypothesis, the conclusions should not be taken as conclusive given short-comings in the techniques used in the studies.
methods. The authors developed a novel method of image analysis to improve spatial resolution and applied the method for investigating the medial rectus muscle, the entire length of which can easily be identified in magnetic resonance images.
results. Contrary to previous reports, vertical sideslippage was observed at the posterior part of the muscle during vertical eye rotation between two tertiary eye positions. Furthermore, the sideslip varied as a function of horizontal eye position, in accordance with the half-angle rule of Listing’s law.
conclusions. These findings are more consistent with the traditional view of the restrained shortest-path model than with the pulley model and have further implications for basic and clinical understanding of ocular kinematics.
Demer and colleagues
1 put forth the proposal that all oculorotatory muscles, other than the superior oblique, go through connective tissue pulleys. The idea sprang from observations that the posterior part of muscles did not shift whereas the anterior part moved along with the globe.
2 3 However, methodological limits in the latter studies require caution in accepting them as conclusive. Given that expected sideslips were small—no larger than a few millimeters
3 —they might have been obscured by the techniques used for image analysis, which involved free-hand drawings on computed tomography/magnetic resonance imaging (MRI).
2 3 Moreover, tertiary eye positions that would have maximized the sideslip were not tested in one of the studies, and the other did not report on comparisons for individual subjects.
The pulley hypothesis
1 and traditional views, such as the (restrained) shortest-path model,
4 5 6 differ in their predictions about how the medial rectus (MR) muscle would change its position during vertical ocular rotations. The difference is schematically depicted in
Figure 1 . For vertical rotation of the eye, the axis of rotation lies in a horizontal plane, and the MR insertion draws an arc about the axis. The pulley hypothesis predicts that the muscle behind the pulley would not move vertically and would be held by the pulley, whereas the shortest-path model predicts vertical displacement at all parts of the muscle, with the amount proportional to proximity to the insertion.
The two models also differ regarding whether vertical sideslip would depend on horizontal eye position: The shortest-path model predicts such a dependency, but the pulley hypothesis does not. This difference is illustrated by the rows of panels in
Figure 1 . When vertical eye movements take place at different horizontal eye positions, for example, in abduction versus adduction, the rotational axis for the vertical rotations lies within the horizontal plane and tilts to the side by half the amount of the horizontal deviation of the eye from the primary position (the half-angle rule, a corollary of Listing’s law).
7 Now, because of this rule, the relative position of the MR insertion and the axis for vertical rotation changes as a function of horizontal eye position. The insertion, because it is attached to the globe, rotates fully with it, whereas the rotation axis rotates only half as much; the separation between the two, therefore, becomes greater as the eye assumes a more abducted position. Because the separation equals the radius of the arc the insertion draws during a vertical rotation, the size of the arc and the vertical shift of the MR will also be greater when the eye is more abducted. Dictated by these geometric considerations, the shortest-path model predicts that vertical sideslip is dependent on horizontal eye position (
Fig. 1 , left panels). In contrast, the pulley model would not predict such dependence on horizontal eye position because the pulleys are supposed to assume a constant vertical position during ocular rotation (
Fig. 1 , right panels). (More recent versions of the hypothesis, namely, the active pulley hypotheses, suggest a coordinated anterior–posterior movement of the pulley with the muscle contraction, but they still suppose the pulley to be fixed in the perpendicular direction, i.e., the vertical direction in the MR.)
In this study, we tested the two models by imaging orbital contents with high-resolution MRI while subjects maintained tertiary eye positions. Specifically, we asked whether the MR muscle shifted perpendicularly between tertiary eye positions that only differ vertically and whether the shifts varied with the horizontal component of the eye positions.
T2-weighted images by 3D RARE (Turbo-SE) sequences were acquired with a 1.5-T scanner (Siemens, Munich, Germany) and a four-phase array surface coil while five healthy volunteers fixated a target at tertiary positions (30° in horizontal and vertical deviations from the center, at a distance of approximately 30 cm). All procedures were carried out in strict adherence to the Declaration of Helsinki with informed consent obtained from each subject. Image acquisition was set in axial planes, and the field of view (108 mm × 108 mm) included the orbit on the right side, the nasal cavity, and the retro-orbital intracranial structures, including parts of the temporal cortex. In-plane resolution of the images was 0.42 mm × 0.42 mm (matrix size of 256 × 265), with slices separated by 0.375 mm.
Image volumes were registered to correct against head motion using an algorithm
8 as implemented in SPM2 (The Wellcome Department of Imaging Neuroscience, UCL, London, UK), a software package widely used for functional MRI data processing. The registration was performed after the intra-orbital portion in the volumes was masked out. Masking was performed because only head motion was to be corrected, though orbital contents had obviously moved between scans because of eye movements as well. The resultant transformation matrices correcting against head motion were then applied to the whole volumes for further analysis of changes caused by eye movements only.
To compute the amount of expected sideslip predicted by the shortest-path model,
4 5 the following measurements were made using individual MRI data: horizontal and vertical eye positions at each MRI volume, axis for vertical rotation, location of MR insertion, and length of MR muscle (in front and back of the point of tangency). First, eye positions were deduced from the location of the lens with respect to the globe center, after the globe and lens were segmented out by taking advantage of the high contrast between the sclera and lens and the vitreous in the images. Second, because the torsion of the globe could not be measured from the MRI data, we made the assumption that the rotation axis was perpendicular to the midline for vertical rotations from the primary position. For rotations between two tertiary positions on the same side, the axis was assumed to tilt to the side by the half amount of horizontal components of the tertiary positions. Third, we presumed that the MR insertion laid 34° anterior to the globe equator.
5 (The equator was identified from the globe segmented as described.) Fourth, the length of the MR muscle was measured from the origin near the orbital apex to the insertion through the point of tangency on the globe. Given these measurements, we computed the expected sideslip through steps of trigonometric calculations described by Robinson.
5 We followed his suggestion that the bend at the insertion, because of the width of the muscle, be corrected by multiplying the cosine of vertical rotation angle to the vertical shift of the insertion. After such correction, the vertical translation of the MR insertion was then proportioned for a point on the muscle according to the proximity of the point to the insertion. In particular, we computed the expected amount of vertical shift at the part of the muscle on the plane tangential to the posterior pole of the globe and compared it with what was observed in the real MRI data for each individual subject.
Observed Sideslips and Predictions According to the Restricted Shortest-Path Model
Contrary to previous reports,
2 3 we observed that the MR indeed shifted sideways during vertical eye movements because of the high spatial resolution achieved in our study. Furthermore, we found that the amount of shift varied as a function of horizontal eye position, which was in accordance with the restrained shortest-path model, taking Listing’s law of ocular kinematics into account.
Given the current findings, an alternative interpretation, in support of the pulley hypothesis, is that pulleys may reduce rather than abolish sideslip of the MR. Such an ad hoc interpretation poses difficulties in two aspects. First, the reduction of sideslip was not enacted by a localized restraint. No inflection by such a restraint—i.e., a pulley—was observed in the images. Instead the reduction appeared to be distributed along the whole course of the muscle path. Second, the fact that the sideslip was larger when the eyes were in abduction was contrary to the idea that a pulley held the muscle, even if it did so imperfectly. The MR is in least tension during abduction. Therefore, if it were restrained by a pulley at all, the sideslip would have been smallest here, and an inflection would have been observed. In fact, the sideslip was larger in abduction than in adduction.
Vertical sideslips demonstrated in our study must have occurred under distributed resistance from the surrounding tissue, such as the orbital fat and septal meshwork of connective tissue,
9 10 rather than under localized restraint as the pulley model suggested. The amount of shift was graduated over the muscle length with no discernible inflection point, as was well demonstrated when the eye was in abduction and the shift was maximal. Since the MR is fully relaxed in abduction, a pulley would have restricted the muscle from sideslipping by making it bend around the pulley, but we did not observe this.
The revision of the shortest-path model by Miller and Robinson
6 considered elastic connective tissue coverings, at and around the insertional end of the muscle, that reduce the slippage of muscle against the sclera (hence, the restraint shortest-path model). This is clearly different from the pulley concept in that the coverings move with the globe, whereas the pulley is supposed to maintain its position in the orbit despite the rotations. A more recent active pulley hypothesis claims that the pulley may move in the direction parallel to the muscle length, but it still precludes any shifts perpendicular to it.
1 The distinction between these two kinds of connective tissue restraints may perhaps be clearer when one thinks of the former (i.e., covering restraints over the insertion) as changing the functional insertion, whereas the latter (i.e., pulleys) assumes a change in the functional origin.