EOM Pulleys and Sequelae: A Critical Review

Abstract

Purpose: The discovery of extraocular muscle (EOM) pulleys resolved long-standing issues in oculomotor physiology, revived interest in EOM function generally, and led to several new theories. We describe the pulley concept of Miller and Demer (M-D Pulleys) and briefly review evidence, distinguishing this well-supported notion from the Active Pulley Hypothesis (APH) and the EOM Compartments hypothesis, and critically reviewing the methodologies and evidence on which the latter are based.

Methods: We analyze evidence on mechanical independence of individual EOM fibers, implications of nerve tracing for functional independence of EOM layers and compartments, validity of image-based methods of assessing EOM contraction, and data analysis issues.

Conclusions: M-D Pulleys are well-supported by several lines of evidence from several labs. The APH, which predicts relative movements of EOM lamina sufficient to alter muscle actions, has been effectively disproved. The width-wise articulations of EOM Compartments, in contrast, might produce significant contractile oculorotary force gradients across muscle tendons, although existing evidence is unconvincing. We suggest how this hypothesis could be effectively tested.

Orbital connective tissues perform a complex function once thought to require the brain: extraocular muscle (EOM) pulleys, condensations of connective tissue elastically stabilized to the orbital wall, solve the problem of controlling 3-dimensional (3D) eye rotation according to Listings Law.^1–4 This discovery was unexpected in a field that supposed extraocular anatomy and muscle actions to be basically understood, stimulated research in anatomy, physiology, mathematical analysis and modeling, and prepared ground for further theorizing. 

We review the pulley concept of Miller and Demer,^1,5,6 and distinguish it from related proposals that followed. The Active Pulley Hypothesis (APH) and the notion of independently controlled EOM Compartments are then discussed, and their evidence is reviewed. 

Longitudinally-Dragged EOM Pulleys

Condensations of midorbital connective tissue stabilized relative to the orbit and determining muscle paths were predicted by biomechanical modeling,^1,7,8 and confirmed by magnetic resonance imaging (MRI) before and after muscle transposition surgery.^1,5 Subsequent imaging studies estimated pulley positions and movements,^9–11 immunohistochemical studies showed that elastin and smooth muscle were concentrated in pulley tissues,^12–14 electron microscopic studies revealed an unusual, cross-layered structure,¹⁵ and studies in nonhuman species showed that pulleys were evolutionarily conserved.^12,16 

Neurophysiologists had long assumed that Listing's Law (the kinematic principle that determines torsion for each gaze position), and coping with noncommutativity of 3D rotation (such as how independent horizontal and vertical gaze centers could control nonadditive rotation) must be implemented in the brainstem, although no such center could be found.^17–20 Mathematical analyses then showed that EOM pulleys could solve these problems mechanically, in the orbit.^2–4 

Demer and colleagues observed that rectus muscles could not slide freely through their connective tissue pulleys because they were attached on their orbital faces,²¹ such that the pulleys would be dragged longitudinally with the contracting and relaxing muscles while remaining stabilized in other directions, and showed that this arrangement extended pulley kinematic functions to nonprimary gaze positions.^6,22 Originally named “Pulleys of Miller,”^23–25 we propose to recognize the contribution of Demer's group by calling these longitudinally-dragged connective tissue structures Miller-Demer Pulleys (M-D Pulleys). 

Compelling confirmation of M-D Pulley kinematics was provided by Ghasia and Angelaki,²⁶ who showed that cyclovertical motoneurons do not modulate their firing during eccentric pursuit as would be necessary if the brainstem implemented Listing's Law, and by Klier et al.,^27,28 who stimulated the abducens nerve and nucleus downstream of any neural circuit that might implement Listing's Law and found that eye movements nevertheless had Listing kinematics, demonstrating that extraocular mechanics, that is M-D Pulleys, were capable of implementing Listing's Law without neural assistance. 

However, Demer et al.⁶ went beyond these data to claim support for the APH, the notion that orbital layer (OL) EOM fibers controlled pulley positions independently of global layer (GL) fibers, which rotated the eye. The APH was never plausible in its strong form,²⁹ and nerve tracing, microanatomy, immunohistochemistry, and experimental surgical manipulations have since rendered it untenable. The subsequently proposed notion of EOM Compartments, in contrast, remains a viable, if unproven, hypothesis. We review the evidence on both theories. 

APH and EOM Compartments

The APH is the claim that orbital and global EOM layers independently control longitudinal pulley position and globe rotation, respectively. The EOM Compartments hypothesis proposes that the two half-width parts of most muscles are independently controlled, thereby endowing, for example, horizontal recti with vertical and torsional actions. Together, these ideas distinguish actions, not of six EOMs, but of some 17 independent extraocular “mini-muscles” (11 GL compartments and six OLs). Such complication of the oculomotor plant must be justified with clear evidence that the proposed mini-muscles have independent neural control and sufficient mechanical independence to function differentially. 

Mechanical Independence of EOM Fibers

The APH was born of the well-known microanatomic fact that mammalian EOMs generally have a thin layer of small myofibers facing the orbital wall, with different type distribution than the bulk of the muscle (the GL). The microanatomic study of Lim et al.²¹ usefully describes the merging of OL connective tissue with adjacent pulley tissue, but then struggles to characterize this fusion of neighboring connective tissues as a “tendon.” In support of fiber independence, they report being unable to find the myomyous junctions linking adjacent fibers that are reported commonly in EOMs of many species, including human,^30–33 which failure may have been due to their reliance on muscle cross-sections or their use of formalin-fixed tissue, which suffers significant shrinkage, breaking protein crosslinks and creating artefactual spaces. 

From in-vitro experiments on bovine EOM, Shin et al.^34,35 report that differential passive stretching of OL or GL, and chemically-induced contraction of GL, were almost completely uncoupled from unmanipulated layers. They also stretched lateral halves of muscles, corresponding to compartments suggested by nerve tracing (see below), and found similarly weak coupling to the unstretched halves. Interestingly, Shin et al.³⁴ found that any group of EOM fibers was only loosely coupled to adjacent fibers, which is to say that the particular division into compartments suggested by nerve tracing was not found. 

The extraordinary fiber independence reported by Shin et al. could be due to epimysium having been stripped off, damaging the connective tissue matrix that normally couples fibers,³⁶ and to the experimental procedure itself, in which connective tissues joining adjacent fibers were subjected to shear forces far exceeding those they normally sustain. A related study of tendon fiber independence³⁷ drew a similar, independent critique, complaining that muscle samples had been denuded of “key surrounding structures” and subjected to supraphysiologic forces, also citing surgical Z-tenotomy data inconsistent with fiber independence.³⁸ If EOMs were composed of parallel independent fibers their total force would be the sum of forces of the individual fibers, which several lines of evidence show is not the case.^33,39–41 

McLoon et al.³⁶ showed that epimysium, perimysium, and endomysium of human EOMs form a dense and continuous collagen matrix, with no separations between any muscle regions, limiting relative fiber movements of any kind. Alan B. Scott (personal communication, 2018) sought to selectively ablate OL to weaken primary position forces without impairing eccentric gaze or saccades, but could find no natural laminar cleavage in the horizontal recti of cats, rabbits, or monkeys, even with sharp dissection and laser ablation. It generally is accepted that neither histologic sections²¹ nor MRI⁴² show any boundary or separation between OL and GL. 

The finding of Maas and Sandercock⁴³ that the connective tissue matrix of skeletal muscles permits small fiber movements, but not large, potentially damaging ones, suggests a clarifying distinction: differential contractile forces can be developed across a muscle's width, but substantial differential movements cannot. Thus, EOM Compartments might function by producing a force gradient across the tendon, balancing opposing forces isometrically, whereas the APH implausibly requires relative movements of OL and GL sufficiently large to translate pulleys and alter the actions of muscles passing through them. 

Innervational Independence of Layers and Compartments

Different oculomotor functions generally are associated with distinct brainstem nuclei or regions, but the anatomic studies cited in support of EOM Compartments only traced motor axons downstream of the entry into their muscles. Absent full axon tracing (e.g., using brainstem lesioning, stimulation, or retrograde tracers) there is no evidence that the branches identified contain axons from distinct brainstem centers. It has been shown only that the abducens nerve, the medial rectus (MR) and inferior rectus (IR) divisions of the oculomotor nerve, and the trochlear nerve bifurcate as they enter, and then branch to fill more-or-less separate regions of their respective muscles.^44–46 

These nerve tracing studies are at the root of the EOM Compartment notion, but what do they imply about function? Arborization is a fractal process in which a compact trunk branches out to fill a large volume while preserving its basic structure. Trees arborize to expose leaves to sunlight, and bronchi to increase contact of air from the trachea with circulating blood. Motor nerves traverse long distances in compact bundles, and then branch repeatedly to synapse effectively throughout the volumes of target muscles. Once a trunk branches into, say, left and right limbs, the starting points of subsequent branchings already tend to be lateralized. To minimize inefficient overlap with domains of neighboring branches that would occur with such purely random growth, active processes exist, such as molecular self-avoidance, that help achieve “innervational tiling.”⁴⁷ Branching into nonoverlapping neighborhoods is an efficient way to fill space and does not imply differential function. 

How do the nerve tracing studies bear on the APH and its assumption of independent OL and GL control? Although anatomically separate nerve branches do not imply independent control, an intermixed nerve supply does mean that independent control is impossible. Earlier studies showed that many abducens motor neurons innervate OL and GL,^48,49 and now, Peng et al.⁴⁴ and da Silva Costa et al.⁴⁵ report finding no separation of nerve branches to OL and GL in any muscle. The absence of neural support for independent control clearly disconfirms the APH. 

Posterior Partial Volume (PPV) Does Not Measure Muscle Contraction

The neurophysiologic studies needed to demonstrate differential functioning of mini-muscles have not been done. In their place, we are offered MRI measurements of Posterior Partial Volumes. Are PPVs reliable measures of EOM contraction, or indeed measures of muscle contraction at all? 

When an EOM contracts, its maximum cross-section (MaxCS) increases, so that a reasonable measure of contraction would be the volume of a few MRI slices centered on MaxCS. However, MaxCS also moves posteriorly with contraction,^1,50 and this movement must be tracked to avoid conflating different contractile states with different parts of the muscle. A MaxCS-centered region of interest (ROI) also would have a defined location in any gaze position for any muscle that had a MaxCS, and as the muscle contracted volume would flow, so to speak, similarly into both ends, making such a measure robust to positioning errors. 

PPV, in contrast, was defined as the volume in an 8 mm thick ROI posterior to MaxCS in central gaze. It was chosen from many candidate measures for its high correlation with duction.^51,52 Therefore, PPV is a measure of eye position, not of muscle contraction. Eye position results from contractile and elastic actions of multiple muscles and elastic tissues, and is not interchangeable with the contractile state of an individual muscle. Indeed, nontrivial mathematical models are needed to relate the two.^8,53,54 

Clark and Demer⁵² summarize the centrality of their PPV measurements: “Using change in PPV as the measure of contractility, differential compartmental activity has been demonstrated for the LR during ocular counterrolling,⁵⁶ for the MR during asymmetric convergence,⁵⁰ and for the LR, inferior rectus (IR), and superior oblique (SO) during vertical fusional vergence.” ⁵⁷ 

What does PPV actually measure? Admittedly, it reflects not only contractile thickening of the muscle, but also the contraction-related posterior movement of its MaxCS⁵¹ (Fig. 1). Unhappily, the ROI is defined relative to the globe-optic nerve junction (G-OJ),^51,52 which moves anteriorly in eccentric gaze (Fig. 2). When we introduced orbital MRI to study muscle function,¹ resolution was insufficient to resolve the orbital apex and it was necessary to reference the G-OJ, but thanks to improvements in resolution, such unstable orbital referents have long been obsolete. A consequence of using a G-OJ referent is that in experiments using gaze to determine contractile state, the part of the muscle analyzed is contingent on gaze. Offered as a general measure of muscle contraction, PPV actually measures duction, is complexly contaminated, and is vulnerable to error and bias due to the critical positioning of its ROI. 

Figure 1

 

PPV is a complex measure. As the MR contracts and the eye adducts, the data of Clark and Demer⁵⁰ show MaxCS increasing and tissue distributions moving posteriorly (blue => green and yellow => red), the movement causing more anterior tissue to enter the ROI than posterior tissue leaves. Compounding this problem, the ROI is referenced to the G-OJ (Image Plane 0), which moves anteriorly in adduction (see Fig. 2), so that posterior tissue movement is exaggerated, and contraction is doubly overestimated. Redrawn with permission from Demer et al.⁵⁰

Figure 2

 

PPV sampling depends on eye position. For the adducted gaze pictured, the ROI (green box) referenced to the G-OJ (green dot) encloses four MRI slices (horizontal dashed lines, separated by 2 mm), located 10 to 16 mm anterior to the orbital apex. In central gaze, the G-OJ moves to the red dot and the ROI to the red box, sampling different parts of muscles and introducing a systematic gaze-related sampling error. Redrawn with permission from Clark and Demer.⁵⁵

MRI Quantification Issues

Muscles visualized by MRI must be manually segmented (outlined) because judgment is required to distinguish adjacent nerves, vessels, connective tissues, and bone. Since introducing MRI techniques to study human EOMs in vivo,¹ we have learned that bias must be controlled with multiple readers from whom experimental conditions are obscured.⁵⁸ No such controls are described in MRI studies from the Demer lab. 

Although scan planes generally cut muscles obliquely, the Demer lab calculates muscle volumes by multiplying slice areas by slice thickness, without correcting projection errors, and then stacking these blocks to estimate volume.⁵¹ This process introduces errors that could have been avoided using well-described methods (Fig. 3).⁵⁸ 

Figure 3

 

MRI volume calculation. Left: Muscle paths are not straight and scan planes are not generally perpendicular to the muscle's long centerline, so simply stacking individual slice “blocks”⁵¹ gives a poor estimate (green) of muscle volume (red). Center: Both problems can be solved by stacking slice contours to form a ring model, fitting a smooth surface, and reslicing normal to the midline.⁵⁸ Right: This 3D reconstruction technique estimates true cross-sections with high longitudinal resolution.

Published images illustrate the difficulty of unbiased segmentation. Figure 4, for example, shows an image from Clark and Demer's⁵² study of vertical duction, in which it is clear that the shape change claimed in the MR cross-section is the result of biased segmentation. 

Figure 4

 

Biased image segmentation. Clark et al.⁵² present these image segmentations as evidence that, from supraduction (top-right) to infraduction (bottom-right), the inferior part of MR enlarges differentially because compartment MR_I contracts more than MR_S. However, the raw images on the left clearly show that the supposed shape change is an artifact of excluding MR_I tissue where it abuts the curved orbital wall in the upper image, and excluding MR_S tissue in the less clear lower image (red arrows). EOM compartment theory would also predict LR_I > LR_S but this is not seen, and no explanation is given. The “stretching-bunching” theory (see text), in contrast, might explain that the LR pulley inflection fell outside of the slices shown. Redrawn with permission from Clark and Demer.⁵²

In an experiment involving head tilt, Clark and Demer⁵⁶ measured ocular counterrolling relative to the interhemispheric sulcus, a soft tissue referent likely to be unstable with head tilt, and which can be seen in Figure 5 to have misaligned orbits in the two tilt conditions, creating the appearance of counterrolling where there was actually little or none. Because the head tilt manipulation evidently failed, this experiment provides no support for compartmental contraction during ocular counterrolling. 

Figure 5

 

Biased image comparison. Left: Images, modified from Clark and Demer,⁵⁶ aligned by the interhemispheric sulcus and claiming to show the pulley array counterrolling against head tilt, are rotationally misaligned. Right: The “left tilt” image is rotated to align the two images on the visible orbital bone, showing that there was actually little or no counterrolling.

Clark and Demer⁵⁹ offered an alternative to existing biomechanical strabismus models, which likened eye muscles to inextensible bicycle chains, and supported it with an MRI study claiming to show that the globe's axis of rotation was highly eccentric. However, the analysis was so clearly mistaken⁶⁰ that the published paper was retracted. The representative MRI image shown⁵⁹ is worrisome on its own, picturing a globe with geometric center far from the point marked “globe center,” and a distance between global landmarks before rotation different from after, which cannot be correct unless the globe changed shape. 

Cause or Effect?

Changes in the shapes of EOM cross-sections have been assumed to reflect differential contraction of compartments and to be causal with respect to eye position, but are more parsimoniously explained as passive consequences of eye movement. When a muscle (or any such soft object) bends “sideways” (e.g., vertical eye rotation for horizontal recti), tissue on the outside of the curve distributes along a lengthened path, reducing its cross-section, and tissue inside the curve “bunches-up,” increasing its cross-section. Therefore, observed cross-sectional shape changes are likely a result of eye movement, occurring precisely because the muscle is not contracting differentially to relax outside fibers and take-up slack inside. Midorbital M-D Pulleys sharpen and confine the bend to a small region, increasing the “stretching-bunching” difference, and predicting that the asymmetry would be seen only in slices through pulleys, but not elsewhere (Fig. 6). Clark and Demer⁵⁶ dismiss the relevance of passive changes in cross-section. 

Figure 6

 

Sharp deflection of muscle path due to pulleys. Positions of area centroids of the LR relative to globe center are shown as a function of vertical gaze. The muscle's path bends sharply in elevation and depression at the location of the pulley (dashed box). Passive changes to the shape of the muscle's cross-section would be confined to the region of the pulley. Redrawn with permission from Clark et al.¹¹

Sampling Bias

Studies from the Demer lab typically use multiple eye movement types, eye positions, mini-muscle segmentations and measures of contraction to generate many potential comparisons. These are evaluated with t-tests and correlations to find those yielding the largest differences, which then are reported as either confirming and extending previous claims or as suggesting new and unexpected EOM capabilities. However, simple pairwise contrasts give correct error rates only for single hypotheses stated before analysis. Multiple a-posteriori tests on complex data sets—referred to as “data dredging” or “p-hacking”—are problematic, because as the number of comparisons increases, so does the probability of finding a “significant difference” by chance where none exists. There are many ways the multiple comparison problem might have been dealt with. 

Clark and Demer,⁵² for example, collected data in central and six eccentric gaze positions. Some comparisons pooled all infraductions, others all supraductions, and still others changes from maximum infraduction to maximum supraduction. A small 4% compartmental PPV difference pooled across infraductions is reported for LR, although there was no difference across supraductions or across maximal gaze changes (which included infraductions), and nevertheless, was taken as support for EOM Compartments and the broad conclusion that all EOMs have complex actions. 

Clark and Demer^52,56 wished to show differential compartmental contraction during ocular counterrolling and vertical duction. Although nerve tracing^45,46,61 predicts particular compartment boundaries, they created multiple segmentations—12 in the case of the SO—with the expressed aim of finding the “most likely intercompartmental border,” but actually finding segmentations yielding the largest differences, regardless of whether they corresponded to nerve tracing predictions.⁵² These differences were then tested with paired comparisons. 

Conclusions

•  
  Nerve tracing, experimental surgical manipulations, and connective tissue studies—given that relative movements and not just force gradients are required—have effectively disproven the APH.
•  
  Nerve tracing raises the possibility that LR, MR, SO, and possibly IR might have differentially controlled half-width compartments, and it is possible that they strain the connective tissue matrix sufficiently to exert differential oculorotary forces at their tendons, although there is no good evidence that they do so.
•  
  MRI studies from the Demer lab use incorrect measures of muscle contraction that are dominated by artifacts, use statistics that do not reasonably account for overall error rates, show evidence of bias, are unconvincing about cause and effect, and lack confirmation from other labs.
•  
  It is unwarranted to state as if proven that eye position is controlled by some 17 extraocular mini-muscles, and to urge tests, diagnoses, and treatments on the basis that it is.^62–64

Future Directions

The EOM Compartments hypothesis remains viable, though unproven. EOMs certainly develop elastic force gradients across their tendons, which helps stabilize eye position,^7,8,65 and it is possible that they develop contractile force gradients as well. Testing this idea would require new studies with better design and analysis: 

•  
  To establish that EOM motor nerve branching is functionally significant, tracing must extend back to the motor nuclei. Brainstem lesioning and stimulation studies should be performed, and effects on putative compartmental contractions measured.
•  
  Techniques must be used that specifically measure muscle contraction, uncontaminated by muscle movement or eye rotation, and robust to variation in ROI position. We described the desirable properties of an imaging measure that tracks MaxCS. Direct measurement with force transducers is another possibility.^66,67
•  
  It is essential to control bias and error in quantifying orbital MRI images. We found it sufficient to have images segmented by three trained readers who are naive about experimental conditions. When the three reads are not consistent, all are repeated.⁵⁸
•  
  MRI studies must distinguish passive muscle cross-section shape changes due to “stretching-bunching” from hypothetical changes due to differential compartmental contraction. This could be done by taking advantage of the fact that the former would be confined to the region of the pulleys.
•  
  Experiments must be designed so that potential comparisons are clear in advance, and are amenable to analysis using acceptable statistical methods.

Acknowledgments

Supported by Eidactics (eidactics.com) and The Strabismus Research Foundation (srfsf.org). 

Disclosure: J.M. Miller, None