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Through a Scanner Darkly
Misrepresentations and Confusion in the Oculomotor Plant
False Differential Predictions in Lee, Lai, Brodale & Jampolsky (2007)
Reply to the Letters on "Sideslip of the Medial Rectus Muscle during Vertical Eye Rotation"
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Joseph Demer
Send letter to journal:
jld{at}ucla.edu Joseph Demer
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The recent paper by Lee, Lai, Brodale, and Jampolsky in IOVS claims absence of rectus extraocular muscle (EOM) pulleys in humans.1 Readers will naturally wonder how these authors can make a claim contradicting two decades of persuasive scientific evidence. The explanation lies in both methodological and technical errors, as well as in the paradigm embraced by the Jampolsky laboratory. The errors may be grouped into four types. Error 1. Misunderstanding of Ocular Kinematics. Lee et al. misunderstand Listing's Law (LL), which states that with the head upright and stationary, any secondary or tertiary eye position can be reached by rotation from a primary position about a single position axis, and that all possible position axes of the eye lie in a single plane, Listing's plane (LP).2 Lee et al. failed to appreciate the crucial fact that the three-dimensional (3-D) eye velocity axis differs from the position axis.3 Tweed demonstrated that in the position domain, LL is mathematically equivalent to changing the 3-D ocular velocity axis by half of eye position.4 In Lee et al.'s "model" of EOM paths in their Figure 1, the position axis for vertical eye movements was incorrectly assumed to shift by half of horizontal eye position. The shifts in ocular position axis illustrated in Lee et al.'s Figure 1 would permit only axes lying in a grossly non-physiological horizontal plane. A valid position axis for supraducted adduction in a physiologic LP would have to lie in something approximating the frontoparallel plane, but angled from inferonasal to superotemporal. Thus, Lee et al. have arbitrarily assumed rotational axes violating LL for modeling their data. Lee et al.'s Figure 1B models medial rectus paths in the presence of pulleys rigidly-fixed in the orbit. This is a straw-man comparison, since no one believes that the orbitally-stabilized pulleys assumed in Figure 1B could implement LL,5 and the pulleys were always supposed to have soft, elastic suspensions capable of small deformations. Instead, in 2000 the active pulley hypothesis (APH) proposed that pulleys shift anteroposteriorly so that each EOM's pulling direction changes by half of eye position to implement LL.6 A large body of quantitative MRI data has since accumulated to support the APH (detailed reviews5,7-11 summarize primary publications). Lee et al.'s comparison of observed vs. model data is invalid, as they compared their path model with an old pulley model not supposed to implement LL mechanically. Lee et al. offer as an alternative the "restrained shortest-path model," an oxymoron analogous to mixing oil with water. Their Figure 6 actually uses the inaccurate label "shortest path model" to depict sideslip limited to 2.5 mm.1 A true shortest path assumption would require medial rectus sideslip exceeding 8 mm for the gaze positions studied by Lee et al., rather than the 0.2 – 1. 5 mm mean values they reported. Robinson12 and Miller and Robinson13 assumed constraint on rectus EOM sideslip because computational models assuming a shortest (great circle) path were inconsistent with any eye position except for flipping of the cornea back toward the orbital apex. Miller and Robinson were careful to distinguish the constrained path assumption that limited EOM sideslip, from the shortest path hypothesis that permitted sideslip freely, but these modeling pioneers acknowledged that they had merely guessed the constraints in order to implement workable computer models.12,13 Assumption of any constraints on EOM sideslip already defeats the shortest path hypothesis as portrayed by Lee et al. Error 2. Inadequate Imaging Technique. While criticizing imaging studies from the 1980's for low resolution, Lee et al. claim superior imaging technique.1 In fact, the MRI resolution of Lee et al. is inferior to that employed by most investigators since the early 1990's. Lee et al. imaged axially, and reformatted into coronal and sagittal planes, with rotational and translational shifting to compensate for head motion. Reformatting alone reduced Lee et al.'s in-plane resolution to the diagonal of the primary image plane voxel, in this case 0.705 mm. Additional resolution loss due to rotational and translational effects of head motion also explain the blurriness of the images published by Lee et al. in their Figures 2 – 4. By comparison, data at in-plane resolution 0.312 mm or better support the existence of pulleys.14,15 Lee et al. did not specify how they determined EOM positions from their images, but their figures suggest use of gross estimation from EOM borders in sagittal reconstructions. Such technique is susceptible to partial volume averaging and slight changes in EOM shape, and has a resolution no better than ±1 pixel (0.7 mm in Lee et al.'s case). Miller first proposed that EOM centroids in transverse planes represent the best measure of path,16 because centroids reflect EOM force direction and can be determined more precisely at subpixel resolution. Until Lee et al., all subsequent quantitative MRI of the EOMs has employed Miller's rigorous technique. Error 3. Reported Data Do Not Support Claims. The average medial rectus sideslip claimed by Lee et al. is 0.2 - 1.5 mm, which is only 66% of the prediction of their flawed geometrical model and a tiny fraction of the more than 8 mm anticipated from the shortest path hypothesis. Some of the subjects studied by Lee et al. exhibited zero to 1.0 mm sideslip over the range of 70° horizontal and 60° vertical eye movements. Even at face value, Lee et al.'s findings hardly refute the idea of constraint on EOM sideslip. Although Lee et al. claim to have found gradual changes in EOM path, the sagittal images in their Figure 2A show parallel offsets in the entire medial rectus path that would have required implausible sideslip even at the annulus of Zinn. Such a result is not only incompatible with the model in their Figure 1A, but also easily explained as an artifact of image translation or its correction by the SPM2 software. Lee et al. were emphatic of the negative finding that their sagittal images showed no medial rectus path inflections. That negative result could constitute evidence only if Lee et al.'s low resolution MRIs were capable of resolving inflections. Superior MRI technique has demonstrated clear inflections in paths of all four human rectus EOMs in secondary14 and tertiary gazes,15 quantitatively consistent with the APH. Moreover, in eccentric vertical gaze, the lateral rectus path shifts slightly in a direction opposite the prediction of the shortest path hypothesis.14 It is notable that the images collected by Lee et al. should also have permitted analysis of the paths of the superior, lateral, and inferior rectus EOMs. Is it possible that this data was not presented because these EOMs do not exhibit sideslip consistent with the notions of Lee et al.? Lee et al. did not even claim any appreciable sideslip except for the medial rectus in abduction. It seems insufficient to challenge the existence of pulleys based on an isolated observation for only the medial rectus in abduction, particularly if this observation were inconsistent with the behavior of the other three EOMs and for other gaze directions. Lee et al. should publish their data for the other EOMs. Error 4. Discussion Emphasizes Abandoned Theories. Lee et al.'s discussion ignores long-recognized findings contradicting their conclusion, while repeating alternative hypotheses now abandoned by even their authors. For example, Lee et al. propose that rectus EOM sideslip may be limited by musculo-global tissue connections, an idea assumed by Miller and Robinson as the possible anatomic basis for restricted sideslip,13 and plausible until 1993. In that year, high resolution MRI scans before and shortly after large transpositions of rectus EOM insertions demonstrated continued EOM path stability and the presence of path inflections.17 Since pulley effects persisted after all musculo-global tissue connections had been severed by surgery, it is untenable to maintain, as do Lee et al., that such connections could provide rectus path stability. Lee et al.'s presentation of the electrophysiology literature is inaccurate. They avidly cited Angelaki and Hess’s early skepticism that pulleys, rather than explicit neural commands, could be the basis of LL.18 However, Lee et al. then went on to dismiss as conceptually misguided the elegant experiments later performed in the Angelaki lab in behaving monkeys that have decisively settled this issue in favor of mechanical, rather than neural, factors. First, electrical stimulation of the abducens nerve evokes eye movements conforming to LL, absent any other changes in EOM innervation patterns.19 That implies that LL must be mechanically implemented. Second, direct recordings from the motoneurons that innervate all of the vertical rectus and oblique EOMs failed to demonstrate the torsional signal for LL that would be required if LL were neurally specified.20 Finally, Lee et al. ignore high resolution MRI evidence indicating that the oblique EOMs reposition the rectus pulleys to implement eye movements not conforming to LL, such as convergence21 and the vestibulo-ocular reflex.22 In their discussion, Lee et al. inaccurately denied that the APH allows for the pulley shifts we have described in the foregoing detail. Why Do Lee et al. Ignore the Evidence? The reader may be perplexed by the Jampolsky lab's denial of voluminous evidence that other scientists find compelling. Pulley action on EOMs was first proposed in 1989 by Joel M. Miller.16 The noted philosopher of science, Thomas Kuhn,23 has provided an explanation of Lee et al's behavior. Dr. Jampolsky and his colleagues are adherents to a traditional paradigm of EOM function built on the basis of strabismus surgical experience. This traditional paradigm is a self-contained approach to conceptualizing EOM actions, but beset by internal and external inconsistencies, and largely unvalidated against other sources of evidence. Over the last two decades, Joel Miller initiated a different paradigm of the EOMs and connective tissues that is consistent with considerable external evidence. Dr. Jampolsky and colleagues reject that modern paradigm. Thomas Kuhn has explained that the development of a novel paradigm represents a "scientific revolution."23 So many concepts change in a scientific revolution that adherents to the old and new paradigms find communication impossible, and cannot agree on mutually acceptable evidence. Kuhn has explained that this mis-communication arises because paradigms constrain the sort of observations that might be considered "evidence" in the first place. Thomas Kuhn has provided historical examples illustrating times of scientific revolutions, when competing paradigms briefly coexisted.23 Kuhn showed that competing scientific paradigms cannot coexist indefinitely. Eventually, new paradigms prevail if they offer advantages to practitioners of science, including better and more elegant abilities to explain existing observations, internal consistency, and the capacity to predict novel observations. A new paradigm ultimately succeeds if it is more useful than the older paradigm. It is anticipated that students of orbital and EOM anatomy, ocular motility and the neurosciences, as well as clinicians interested in the correction of strabismus, will find the concept of pulleys useful to them. Joseph L. Demer References 1. Lee K-M, Lai AP, Brodale J, Jampolsky A. Sideslip of the medial rectus muscle during vertical eye rotations. Invest Ophthalmol Vis Sci. 2007;48:4527-4533. |
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Eliana Klier
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eliana{at}cabernet.wustl.edu Eliana Klier
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The debate surrounding the implementation of Listing's law and the half-angle rule has become heated over the last decade with strong support on different fronts. One issue of contention surrounds the function of the oculomotor pulleys themselves and whether or not they are innervated in such a way to implement the half-angle rule. Support for pulley innervation has largely stemmed from magnetic resonance imaging studies that demonstrate how pulleys alter their orientation with different eye positions and how certain eye muscle fibers terminate, and perhaps innervate, the pulleys themselves.1,2 In contrast, others have found that destruction of the lateral rectus pulley does not affect the amplitude or velocity profiles of stimulation-induced eye movements, indicating no role for the pulleys.3 Thus, the debate over pulley innervation persists without a solution. Another issue of dispute surrounds the neural versus mechanical realization of the half-angle rule. On one side, proponents support a neural basis of implementation in which the brain determines ocular torsion and sends these commands to the eye via the nuclei and nerves that control it (cranial nerves III, IV and VI). The other side favors a mechanical implementation in which the ocular pulleys that surround and guide the eye change their orientation with changes in eye position. Part of the reason that this debate has become so contentious is that three-dimensional ocular kinematics and the mathematics that are inherent to rotating objects such as the eye are extremely complex to grasp, even to many close to the field. Our lab set out to investigate what the brain tells eye muscles to do by recording from cyclovertical4 and stimulating horizontal5 oculomotoneurons. It was to our dismay that we read the paper by Lee, Lai, Brodale and Jampolsky entitled "Sideslip of the medial rectus muscle during vertical eye rotation,"6 especially concerning their erroneous summary and critique of our recent work. While misquoting our papers,4,5 the authors state that "if one wants to find out how Listing's law or, equivalently, the half-angle rule is implemented in horizontal eye movements…the abducens neurons and the lateral rectus muscle are the last place to look because implementing the law for horizontal eye movements requires changing the rotation axis vertically; for this, the lateral rectus muscle is an insignificant player." This statement both misrepresents what our experiments were about and partially misguides what should be done. First, we agree that single-unit recording from horizontal motoneurons like those in the abducens nuclei would not yield fruitful results since changes in motoneuron firing should be observed in the nuclei that control torsion (i.e., the vertical eye muscles). But even a simple scan through the Ghasia and Angelaki paper4 would indicate that we did indeed record from the vertical motorneurons (i.e., oculomotor and trochlear nerves and nuclei) and not the horizontal motoneurons as Lee et al. mistakenly claim. Second, we assert that stimulating the nuclei/nerves that innervate the horizontal muscles is precisely what should be done in order to determine if three-dimensional kinematics are implemented neurally or mechanically. The fact that Klier et al.5 found that the half-angle rule was still implemented when the horizontal system was activated, while the normal neural pathways for cyclovertical rotations were bypassed, most convincingly indicates a mechanical implementation of Listing's law. The only way in which a half-angle rule could emerge in our electrical stimulation experiment is if the plant implemented it itself. Stimulation of the cyclovertical motoneurons and nerves is precisely the incorrect approach since one can no longer distinguish between neural or mechanical factors when stimulation evokes vertical and torsional eye movements simultaneously. The complexities of ocular anatomy and physiology are indeed difficult to grasp; however, their understanding is key to helping those with strabismus and other eye muscle-related deficits. Unfortunately, this goal is only made more difficult by blatant misquotes and the condemnations of correct experiments. In the last several years there has been great stride in uniting the two disparate views and recognizing that both neural and mechanical factors play important roles in three- dimensional kinematics. This progress should not be undone. Eliana M. Klier and Dora E. Angelaki References 1. Demer JL, Oh SY, Poukens V. Evidence for active control of rectus extraocular muscle pulleys. Invest Ophthalmol Vis Sci. 2000;41:1280-1290. |
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Joel Miller
Send letter to journal:
jmm{at}eidactics.com Joel Miller
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This paper from Jampolsky's group1 reports two results of an MRI study: [1] that the posterior medial rectus muscle sideslips slightly upward relative to the orbit when the eye elevates and slightly downward when it depresses, and [2] that this movement is greater when the eye moves vertically in abduction (1.5 mm at the posterior pole of the eye) than in adduction (0.2 mm). They believe that these findings disprove the notion of EOM pulleys. Actually, they do not bear on the existence of EOM pulleys at all, even if uncritically accepted. Finally, Lee et al.1 state that to account for their data they must assume that orbit-relative muscle paths are determined by "distributed resistance from the surrounding tissue," which is exactly the pulley theory of Miller,2 which they claim to have disproved. Imaging Although they used modern imaging facilities, the methodology chosen by Lee et al. is problematic. It has been assumed by other workers that elongated muscles surrounded by contrasting fat and connective tissue are best imaged in cross-section (i.e., quasi-coronal sections for rectus EOMs), because: [1] muscles in such images have clear, sharp boundaries, and [2] muscle cross-sections vary little through the thickness of each such image slice, so that slice positioning is not critical, and artifacts due to partial volume averaging are minimal. Lee et al. are alone in having attempted to measure paths of horizontal recti in sagittal view, in which muscles tend to move from one image plane to another as the eye rotates or if the head moves, and are seen against the poorly contrasting globe and optic nerve. They dismiss proven methodology with the criticism that muscles were manually outlined on MR images (a reasonable method when borders are clear), rather than being delineated by some automatic technique, or as in their case, in an unspecified way. Image registration algorithms must be used with data such as theirs, in which precise location of image planes drastically alters image contents (see, e.g., Lee et al., Figs. 2, 4), but has the side effect of reducing image resolution: the fuzzy indistinctness of Lee et al.'s images is not an artifact of the publication process. Some close-cropped coronal images are shown (Lee et al., Fig. 3), but they do not seem to have been used in their analysis. It is difficult to accept findings about millimeter-sized muscle movements, when they could easily result from sub-millimeter variations in the positions of image planes relative to a muscle moving against the spheroidal globe. Having acquired images in axial planes, Lee et al. must have data for the lateral rectus muscle, as well as the medial rectus, but they do not report it. In what follows, however, for the sake of argument, we will accept Lee et al.'s results as presented and ask only whether such results have any bearing on the existence or function of EOM pulleys. Models Almost 20 years ago I performed the first MRI study of EOM paths as a function of gaze, a study which Lee et al. have essentially repeated using modern equipment. A fundamental problem interpreting the data of both studies is that plausible pulley and non-pulley models do not predict different EOM paths. Thus, in my 1989 paper2 I could only suggest that a pulley theory might account as well as the traditional model for the muscle paths measured. Subsequent studies, quite different from those of Miller2 and Lee,1 were necessary to distinguish the two types of model, and show that the traditional model was wrong.
Figure 1. Muscle paths are the same according to pulley and non-pulley models (compare panels in center row), but the mechanics are critically different. The blue sleeve is a schematic representation of the pulley sleeve, and the blue coils suggest the elastic coupling to the orbital wall (anatomically, both tissues are distributed and, of course, look quite different). All pulley models other than that of Lee et al.1 have specified that transverse constraints on muscle paths are elastic (not rigid), and are distributed along the muscle’s length (not applied at a point). The coordinated pulley model further specifies that EOMs translate their pulleys longitudinally (compare Tertiary Gaze for the passive and coordinated models). Non-pulley models have evolved from the "shortest path model" to what we call the "traditional model": 1. The shortest path model supposes EOMs to be constrained only at points of origin and insertion.3,4 This oldest model allows the muscle to assume any "angle of departure" from its insertion, predicts catastrophic, uncontrollable muscle "flipping," and is obviously incorrect.5 Standing against these developments, the non-pulley model Lee et al. choose to compare with their data is principally a "(restricted) shortest path model" that lies somewhere between models "1" and "2," above. Pulley models too have evolved: the original "passive" model2 and the subsequent "strong differential" model7 have both yielded to the current, well-supported, "coordinated" model.7-9 In Figure 1 we schematize the original passive pulley model and the currently accepted coordinated pulley model. The pulley model Lee et al. favor for comparison with their data is none of these. Instead they evaluate a rigid, localized pulley model no one had previously proposed. Which models would have made more reasonable choices? The "traditional model"6 is certainly the most realistic of the non-pulley models. It supposes that muscles are constrained by musculo-global connective tissue bands that function like distributed springs along the muscle's arc of contact with the globe.6 Imagine the forces at play in the left column of Figure 1 as the eye elevates. The anterior path of this horizontal muscle is shaped by elastic connective tissues that tend to hold it to its primary position arc of contact with the globe, and opposing forces related to muscle tension that tend to pull it towards the top of the globe, to where the muscle would follow the shortest path from insertion to origin. The path that results from the balance of these forces may allow the posterior muscle belly to move slightly upwards in the orbit as the eye elevates. Such orbit-relative movement of the muscle belly is called sideslip.
Pulley Models, in contrast, suppose musculo-orbital coupling to be dominant, such as would exert transverse forces on the muscles and so determine their paths, while allowing them to contract and relax longitudinally (see center and right columns of Figure 1). The coordinated pulley model (right column) is currently the best supported, and differs from the passive pulley model (center column) in that its muscle origin-determining connective tissues are pulled longitudinally by the EOM passing through them (schematized by the small yellow lines connecting pulley sleeve and EOM in Fig. 1). For the rectus muscles, the musculo-orbital coupling is thought to consist of a spatially distributed matrix of elastic tissues: the reflected sleeves of Tenon's capsule (pulley "sleeves") and associated intermuscular and musculo-orbital connective tissue (pulley "suspensions"), stiffened by smooth muscle, and probably supplemented by fascially compartmentalized orbital fat. Muscle paths in a pulley model therefore result from a balance of musculo-orbital elasticities against shortest path sideslipping forces. As with non-pulley models, if stabilizing elasticities are weak, muscle tensions are high, or geometry determines that a large component of muscle tension acts in an appropriate direction (Fig. 2), the muscle sideslips towards its shortest path (upward in Figs. 1, 2). Lee et al.1 correctly distinguish pulley from non-pulley models when they explain that the connective tissue constraints in non-pulley models would determine a muscle's functional insertion, whereas pulley constraints would determine its functional origin. But then, they propose that their muscle path findings both disprove the existence of pulleys, and support exactly the distributed, origin-determining, elastic constraints of the passive pulley model: "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."1 Lee et al. correctly dismiss their localized, rigid pulley model, but then, as though anything called a "pulley" must be like the cartilaginous trochlea of the superior oblique muscle, suppose that they have disproved all pulley models, despite the fact that all but theirs suppose distributed, elastic pulleys. If rectus muscle pulleys were hard and compact, how could they possibly have escaped the notice of ancient anatomists (see discussion in Miller et al.10)? Predictions Lee et al. compare a version of Robinson's5 obsolete "permitted sideslip model" to a trochlea-like localized rigid pulley model. It is apparent from their Figure 1 that their differential predictions of medial rectus sideslip rely on a pulley model that constrains the muscle sharply, at the point labeled "presumed pulley location," and rigidly, allowing no muscle sideslip at all. A realistic, distributed, elastic pulley, would predict muscle paths that could not be distinguished from those in the left, "shortest path," column of their Figure 1. Conversely, paths drawn in the left column of their figure are completely dependent on details of the non-pulley model assumed. In terms of the traditional model (our Fig. 1, left column), Lee et al.'s non-pulley predictions only follow if all of the musculo-global elasticities are bunched up near the insertion, and consequently act, unphysiologically, as an extremely stiff torsional spring. In contrast, non-pulley models that incorporated physiologically possible, distributed musculo-global coupling could be made to predict the paths in the "pulley model" column of their Figure 1. Thus, Lee et al.'s differential predictions for pulley and non-pulley models with the eye on the midline do not follow from reasonable pulley and non-pulley models, and are therefore unconvincing. Next consider Lee et al.'s finding of greater medial rectus sideslip with the eye moving vertically in abduction compared to in adduction. Here, they propose two effects: an insertion movement effect that tends to increase, and a muscle tension effect that tends to decrease medial rectus sideslip in abduction. They then fabricate agreement between their findings and their non-pulley model by applying the first, sideslip increasing effect, only to the non-pulley model, although it actually applies to both, and the second, sideslip reducing effect, only to their pulley model, although it too applies to both. The muscle tension effect is due to medial rectus muscle tension being lower in abduction than in adduction. Although they otherwise suppose pulleys to be rigid, Lee et al. here predict reduced sideslip by allowing that sideslip is determined by the balance of muscle tension, which tends to increase it, against musculo-orbital elasticity, which tends to hold the muscle path fixed. However, they fail to apply the corresponding argument to their non-pulley model, although they otherwise assume sideslip in that model to be elastically restrained. Under both models, then, less muscle tension means less sideslip. The insertion movement effect is explained in terms of a claim about Listing's Law that is incorrect.1 Listing's law determines a plane for each position shown in Lee et al.'s Figure 1, not an axis line; any destination position determines another plane, and fixed-axis eye movements are made about the linear intersection of two such planes (see Tweed and Vilis11). To proceed nevertheless, we will take Lee et al. to mean that the axes shown are the axes of rotation for their particular vertical movements (although they do not describe the coordinate system of their fixation targets or the vergence state of their subjects, both of which influence eye position). The essence of Lee et al.'s claim is then simply that the medial rectus wraps further around the globe in abduction than in adduction, which positions its insertion more anteriorly with respect to the axis of rotation, so that globe elevation, for example, moves the insertion higher. Thus, in abduction and elevation, the shortest path (see Robinson,5 Fig. 4) passes nearer the top of the globe, directing the path of a muscle upwards, against the restraints of musculo-global connective tissues. Such paths are suggested in the left column of Lee et al.'s Figure 1. However, a similar effect occurs in pulley models, except that the elastically restrained movement is at the pulley rather than at the insertion (Fig. 2). Thus, under both models a higher muscle insertion means more sideslip. If Lee et al. wish to avoid pulley movement by supposing that EOM pulleys are fixed and rigid, they should do the same for the angle of departure from the insertion of their non-pulley model, and then neither model would reflect the abduction-elevation effect in their data. Conclusions The imaging method used by Lee et al. is unreliable, but even accepting their empirical claims as presented, none provide any evidence against EOM pulleys. Although Lee et al.'s interpretations are unconvincing, their results themselves may be new. It does not seem that anyone has studied sideslip in tertiary gaze since the study of Miller,2 who did not find an abduction-adduction difference in sideslip. This issue should probably be revisited using methodology that preserves the exquisite resolution possible with modern imaging equipment. Jampolsky's group has opposed the notion of EOM pulleys (see also McClung et al.12) that has evolved over the past 20 years based on broad evidence of many types (reviewed in Miller2), including recently, the compelling findings of Ghasia and Angelaki13 and Klier and Angelaki,14 which Lee et al. misrepresent and dismiss. Here, they use unproven, artifact-vulnerable, poorly specified methodology, where suitable broadly accepted methodology exists, and report only selected data. Lee et al. interpret their results with respect to an obsolete non-pulley model and a "straw man" pulley model, the latter having trochlea-like, localized, rigid pulleys, unlike anything previously proposed. Even with these biases, Lee et al. cannot explain their data without accepting the notion of distributed, elastic, origin-determining EOM pulleys, which they claim to have disproved. Joel M. Miller References 1. Lee K-M, Lai AP, Brodale J, Jampolsky A. Sideslip
of the medial rectus muscle during vertical eye rotation. Invest Ophthalmol Vis Sci. 2007;48:4527-4533.
2. Miller JM. Functional anatomy of normal human rectus muscles. Vision Res. 1989;29:223-240. |
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Arthur Jampolsky
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aj{at}ski.org Arthur Jampolsky
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We here respond to the letter from Klier and Angelaki, and thank them for their many thoughtful comments, expressed with expected civility. We entirely agree with their concluding comments that both neural and mechanical factors play important roles in three-dimensional ocular kinematics. This is a reasonable expression from the laboratory view, and it is so patently obviously true from the strabismus clinical management view that it feels almost awkward and unnecessary to agree that it is so. Clinical scientists managing strabismus have long observed and quantified the following important points: 1) Patients with cerebral palsy (and other neural deficits) may have as much as 70 prism diopters of esotropia, which completely and totally disappears under general anesthesia. That the basis of this must be mostly neural rather than mechanical appears to be self-evident. 2) Many patients with congenital malformation, trauma to the orbit, or acquired diseases of the orbit often have overriding mechanical factors to consider in their management. A vast majority of strabismus patients have a combination of both neural and mechanical factors. We heartily agree with the remarks by Klier and Angelaki regarding this. It is from this standpoint that we suggested the following in our paper, regarding their electrical stimulation results1: The finding that the half-angle rule was implemented when the horizontal ocular nuclei/nerves were electrically activated could also have arisen because the stimulation bypassed the normal neural pathways for cyclovertical rotations. All oculo-rotatory muscles participate at the same time in maintaining any given eye position. It is quite conceivable then that, when one delivers electrical pulses to the horizontal system, the whole ensemble of muscles including cycloverticals must be exerting tension in such a configuration that resists yet allows the evoked eye movement to follow the half-angle rule. In other words, the half-angle rule behavior of evoked eye movements may have emerged from the passive mechanical reaction of other muscles that are actively maintaining the eye position at the time of electrical stimulation. Their comments on our discussion of the work by Ghasia and Angelaki2 are correct, and our published erratum3 acknowledges this: We here again apologize for the unintended mis-reference. We here address the letters from Demer and Miller. Whether the medial rectus muscle sideslips during vertical eye rotation is of utmost significance to their pulley hypothesis because the presence of sideslip at both anterior and posterior portions of the muscle speaks against the fundamental premise of the hypothesis. Two technical improvements in our experiments4 allowed us to demonstrate the sideslip, which they failed to observe. First, we chose tertiary eye positions and thereby maximized the sideslip in vertical rotations between abduction-elevation and abduction-depression. Second, we employed modern image analysis techniques to remove head motion artifacts that otherwise would have degraded spatial resolution and obscured the sideslip. Both of these points were discussed in some detail in our paper but ignored in the letters from Demer and Miller, and we feel compelled to belabor them again here. Their criticisms on our model of ocular rotations are incorrect in the facts and reveal their misunderstanding. For instance, the sideslip was the greatest during a vertical rotation between two tertiary eye positions in abduction, and the smallest in adduction. This was not only what we observed but also a logical derivation from the fundamental laws of ocular kinematics (Fig. 1). Furthermore, the vertical rotations in our comparisons did not start from, end at, or go through the primary eye position. Hence, contrary to Demer's erroneous statements in his letter, the axes for the vertical rotations were not a position axis for the tertiary positions. Instead, one may consider the axes as a velocity axis for a secondary eye position between two tertiary positions, because the single rotations went through the secondary position in the middle of the trajectory. Therefore, in our study we correctly modeled the rotation axes as tilted according to the half-angle rule. As depicted in Figure 1 here as well as Figure 1 of our paper,4 a corollary of the axis tilt by the half angle was that the muscle insertion became geometrically farther from the axis for the rotation between abduction-elevation and abduction-depression than for that between adduction-elevation and adduction-depression. Consequently, the muscle insertion drew a larger excursion in the former case, necessitating a greater sideslip of the muscle (Fig. 1B here, left panel). This logical deduction from the laws of ocular kinematics contributed much to our success in visualizing the sideslips in the first place, and also found a strong empirical substantiation in our data that the amount of sideslip varied depending on the horizontal eye position. Demer and Miller's criticisms on our imaging methods are also unfounded and misleading. The spatial resolution of an imaging study depends not only on how images are acquired, but also on how they are analyzed afterwards. A smaller voxel size at initial acquisition will help, but only with a sufficiently high signal-to-noise ratio which tends to go down as the voxel size gets smaller. More important to spatial resolution is the post-processing by which various noises and unwanted signals are filtered out. Head motion in particular is often a major hindrance that seriously degrades spatial resolution. It is one of the most basic lessons learned in functional neuroimaging that MRI volumes acquired in separate times and under different experimental conditions should be realigned so that the deleterious effects of head motions in-between are removed. We applied this lesson to our imaging study to examine the movements of interest, i.e., the sideway translations of the medial rectus muscle, free from the obscuring head movements between MRI scans. Doing so has rewarded us with a spatial resolution better than ever to visualize sideslips as small as less than a millimeter in amplitude. Our improvements may be best appreciated by a comparison with old techniques used in previous studies where the muscle boundaries in MR images were outlined by visual inspection and hand-drawing, and the muscle trajectory was then only inferred from the drawings. An example of the old techniques by the Demer group5 is redrawn in Figure 2A, and rescaled in Figure 2B for a comparison with our direct visualization of the medial rectus muscle in Figures 2C and D. Three points are worth noting in this comparison. First, why do we have to trust the indirect convoluted methods any longer, when muscle paths can be compared directly in the images themselves? Moreover, the spatial resolution of their old techniques was not good enough to demonstrate sideslips: notice the variability in the muscle trajectories, which looks large enough to obscure sideslips observed in our experiment. (One would like to know variance at each data-point to assess the measurement errors, but none reported by the authors.) Second, in their experiments, the elevation and depression was from the primary gaze, and the sideslip was therefore expected to be smaller than the maximum (compare the center and left panels in Fig. 1B). Both geometric predictions (Fig. 1B) and our observations (Figs. 2C and D) concur in that the sideslip was maximal when two tertiary eye positions in abduction are compared and it was minimal in adduction. Therefore, their failure to observe sideslips is not totally surprising, given their misunderstanding of basic ocular kinematics and testing it sub-optimally. Finally, seeing Figure 2B and appreciating how tiny the alleged inflections are even in their data when shown in real dimensions, readers may now wonder what the diagrams in Miller's letter (especially, that in Fig. 2 of his letter) represent: A reality in the orbital space or an imaginative distortion of it to support their pulley story? On a final note, some of Demer and Miller's many remarks are accusative, impugning of motives, and unbefitting space in a reputable journal. The editor requested a substantive response this time, but we wish not to engage in conversation at that level any longer. Rather, we will publish papers with scientific evidence supporting further elucidation in this area of biomedical research. Kyoung-Min Lee1,2 and Arthur Jampolsky1 1The Smith-Kettlewell Eye Research Institute, San Francisco, California,
USA References 1. Klier EM, Meng H, Angelaki DE. Three-dimensional kinematics at the level of the oculomotor plant. J Neurosci. 2006;26:2732-2737.
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