The coordination of binocular eye movements: Vertical and ... · ular occlusion lasting from...

Vision Research 46 (2006) 3537–3548www.elsevier.com/locate/visres

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The coordination of binocular eye movements: Vertical and torsional alignment

James S. Maxwell ¤, Clifton M. Schor

University of California, 360 Minor Hall, Berkeley, CA 94720-2020, USA

Received 8 December 2005; received in revised form 2 June 2006

Abstract

Precise binocular alignment of the visual axes is of utmost importance for good vision. The fact that so few of us ever experience dip-lopia is evidence of how well the oculomotor system performs this function in the face of changes due to development, disease and injury.The capacity of the oculomotor system to adapt to visual stimuli that mimic alignment deWcits has been extensively explored in labora-tory experiments. While the present paper reviews many of those studies, the primary focus is on issues involved in maintaining good ver-tical and torsional alignment in everyday viewing situations where the parsing of muscle forces may vary for the same horizontal andvertical eye positions due to changes in horizontal vergence and head posture.© 2006 Elsevier Ltd. All rights reserved.

Keywords: Phoria; Adaptation; Binocular; Skew; Ocular counterroll; Torsion; Cyclovergence; Hering; Listing; Eye alignment; Phoria adaptation;Otolith-ocular reXex; Vergence

1. Introduction

This review concerns the seemingly simple yet complextask of keeping the two eyes in good alignment. This is animportant function of the oculomotor system since pooralignment produces retinal disparities and disparities ofmore than 0.25° can result in double vision and a degrada-tion of stereopsis (Schor & Tyler, 1981). It is also desirableto keep the lines of sight of the two eyes converged on anobject of interest even if the view of one eye is temporarilyoccluded as often occurs. Torsional alignment of the eyes isimportant for achieving optimal stereo-depth perception(Schreiber, Crawford, Fetter, & Tweed, 2001). The presentreview will be limited to a discussion of the adaptation andcoordination of vertical and torsional eye movements sincethe literature concerning horizontal coordination is far tooextensive to cover in a relatively short review. In addition,we have focused most of our own adaptation experimentson vertical and torsional eye movements because they are

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free from the confounding issue of voluntary vergence as isthe case with horizontal vergence.

The terms vergence and skew will be used to signify thediVerence in position between the two eyes regardless of view-ing condition whereas fusion indicates that viewing is binocu-lar and phoria indicates that binocular alignment is tested inthe absence of a fusible stimulus for the dimension being mea-sured. For example, a bulls-eye pattern viewed binocularlyhas fusible stimuli for horizontal and vertical eye alignmentbut not for torsion and could be used to measure cyclophoria.

1.1. Vertical vergence and coordinate systems

Until fairly recently, slight regard has been paid tospecifying coordinate systems when reporting oculomotormeasurements. Of late, however, the desire to record three-dimensional eye movements has resulted in greater atten-tion to coordinate systems since torsional measurementsare inherently coordinate-system dependent. Specifying acoordinate system for horizontal and vertical eye move-ments is also important, however, especially when present-ing visual targets that require convergence, since tertiary

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3538 J.S. Maxwell, C.M. Schor / Vision Research 46 (2006) 3537–3548

eye position measurements will have diVerent horizontaland vertical values depending on the coordinate systemused. The three most widely used coordinate systems formeasuring eye movements are those named for Fick, Helm-holtz and Listing. These coordinate systems are often illus-trated as a series of rotations in which the rotational axesare gimbaled so that they either move with the eye (eye-Wxed) or are stationary with respect to the orbit (head-Wxed). Fig. 1A shows that if the eye were to rotate about ahead-Wxed vertical axis, the line of sight projected onto atangent screen describes a curved line. From the oppositepoint of view, a point projected from the screen to the backof the globe would inscribe a minor circle (like the lines oflatitude on a globe). If the eye were to rotate about an eye-Wxed axis, on the other hand (Fig. 1B), then the line of sightdescribes a straight line when projected onto a Xat screen,or again, from the opposite point of view, a point projectedonto the back of the eye describes a great circle (like thelines of longitude) when the globe rotates. Measured inFick coordinates, the eye appears to move as though it weregimbaled so that horizontal rotations were about a head-Wxed axis and vertical rotations were about an eye-Wxedaxis. Measured in Helmholtz coordinates, the eye appears

Fg. 1. (A and B) Illustrate the eVect of horizontal globe rotations aboutvertical axes for near targets on a tangent screen. DiVerent reference sys-tems produce diVerent measurements when the eyes are converged and intertiary positions.

to move as though horizontal rotations were about an eye-Wxed axis and vertical rotations were about a head-Wxedaxis. It is clear from the illustration why some authorsadvocate the use of Helmholtz coordinates for describingvertical eye movements because horizontal eye movementsdo not change the elevation of the eyes relative to eachother. If the eyes were actually gimbaled this way, therefore,no vertical vergence would be required to track near targetsin tertiary eye positions, that is, they would automaticallybe aligned. If, on the other hand, the eyes were gimbaled ina Fick-like fashion, then vertical vergence would berequired in order to binocularly foveate near, tertiarytargets.

Just how well aligned vertically are the two eyes? Fortargets placed directly in front of normal subjects, verticalalignment with one eye covered is quite good: on the orderof 0.10–0.16° of vertical phoria (Kapoula, Eggert, & Bucci,1996; van Rijn, ten Tusscher, de Jong, & Hendrikse, 1998).Vertical alignment is a more diYcult problem for near tar-gets in tertiary positions, where the target is closer to oneeye than the other thereby creating vertical disparities andone might expect that good alignment would suVer. In anextraordinary coincidence, three papers concerning the bin-ocular coordination of vertical eye movements during hori-zontal vergence were presented at a single meeting(Collewijn, 1994; Schor, Maxwell, & Stevenson, 1994; Ygge& Zee, 1995). The essence of each of these experiments wasto have subjects Wxate targets at near, tertiary eye positionsand measure vertical eye alignment open loop, i.e., withoutbinocular feedback for vertical vergence, to see whether ornot the lines of sight of the two eyes still intersected. Allthree groups found that the vertical axes did intersectmeaning that there was no vertical vergence error. Interest-ingly, the three groups of researchers interpreted essentiallysame data in three diVerent ways: Collewijn et al., notedthat vertical eye position is expressed best using Helmholtzcoordinates and in Helmholtz coordinates the eyes werewell aligned vertically during horizontal vergence. Yggeand Zee presented their results in Fick coordinates, and inFick coordinates, a horizontal rotation about the verticalaxis into a tertiary eye position results in a vertical mis-alignment of the two lines of sight if left uncompensated.The fact that the lines of sight intersected at tertiary targetsindicated to these authors that the oculomotor systemautomatically corrects for such potential misalignments.Schor, Maxwell & Stevenson essentially avoided dealingwith coordinate system issues by simply comparing the ver-tical alignment of the eyes with and without feedback forvertical vergence (horizontal vergence was always closed-loop) for both near and far tertiary targets. They found thatvertical eye alignment was nearly identical (within 0.25°)whether eye movements were between far, tertiary targetsor between near, tertiary targets and whether the targetswere open-loop (only one eye could see the vertical targets)or closed-loop for vertical vergence. Whether the accuratealignment of the eyes was the result of mechanical gimbal-ing or the result of adaptive mechanisms could not be

J.S. Maxwell, C.M. Schor / Vision Research 46 (2006) 3537–3548 3539

determined by these three experiments, all that can be saidwith certainty is that binocular feedback is not required tomaintain good vertical alignment.

Predicting the vertical vergence compensation requiredfor near viewing depends on how one assumes the eyesrotate. Are the eyes in any sense gimbaled? In a series ofgroundbreaking experiments, Miller, Demer, and theirassociates (Demer, Miller, Poukens, Vinters, & Glasgow,1995; Miller, 1989; Miller et al., 2003; Miller, Demer, &Rosenbaum, 1993) have shown that the extraocular mus-cles slide through Wbroelastic sleeves that are attached tothe wall of the orbit and act as pulleys thereby moving theeVective origin of the muscles from the rear of the orbit to apoint just behind the coronal equator. The presence of pul-leys drastically alters what is expected from a given set ofmuscle contractions so that predictions concerning theeyes’ responses to given innervations cannot be worked outin a back-of-the-napkin-like manner but rely on sophisti-cated simulations of orbital mechanics such as are providedby Orbit (Orbit 1.8, Eidactics, San Francisco), which isbased on the models of Robinson (1975) and Miller andRobinson (1984). Such simulations indicate that the pulleyscause the axes of rotation to lie half way between head-Wxed and eye-Wxed angles and recent MRI studies seem tobear this out (Clark, Miller, & Demer, 2000). This suggeststhat part, but not all, of good vertical eye alignment is theresult of orbital mechanics.

Vertical eye movements, to some extent at least, areinherently conjugate in that some vertical premotor neu-rons simultaneously drive both eyes (McCrea, Strassman,& Highstein, 1987a, 1987b). Moschovakis, Scudder, andHighstein (1990) traced the axons of individual neurons invertical premotor areas and found that many bifurcated soas to innervate vertical motor neurons for both eyes. Theauthors presented their results as evidence for Hering’s lawof equal innervation that presupposes that the two eyesmove together because they are driven by a commonsource, an assumption supported by the analysis of saccadedynamics by Bains, Crawford, Cadera, and Vilis (1992).

1.2. Adaptation of vertical eye alignment

While it is true that the activation of the premotor neu-rons described by Moschovakis et al., would result in bin-ocular vertical eye movements and that pulleys maydecrease the vergence compensation required, it seemsunreasonable to suppose that these mechanisms alonewould result in the exquisite coordination observed in thestudies described above (see also, Collewijn, Erkelens, &Steinman, 1988). Instead, the near-perfect alignment islikely to be the result of adaptive mechanisms. This suppo-sition is supported by the experimental Wnding that monoc-ular occlusion lasting from several hours to several daysresults in a vertical misalignment of the eyes (Graf, Max-well, & Schor, 2002; Liesch & Simonsz, 1993; Viirre,Cadera, & Vilis, 1987). Viirre et al. (1987) reported thatmonkeys consistently developed heterophorias wherein the

occluded eye elevated when abducting. Human subjects, onthe other hand, tended to develop an elevation of theoccluded eye on adduction (Graf et al., 2002; Liesch &Simonsz, 1993). Whatever the case, nearly all subjects lostthe precise vertical alignment typically measured. Presum-ably, monocular occlusion reveals the nonadapted state ofalignment (the latent phoria) for each subject and reXectsthe “hardwiring” of the system. Interestingly, some patientswith cerebellar abnormalities acquire a horizontal-eye-posi-tion-dependent vertical skew deviation that has much thesame pattern as that observed following long-term monoc-ular occlusion (Moster et al., 1988). This too, then, mightrepresent a loss of adaptation (Zee, 1996; Versino, Hurko,& Zee, 1996) and, indeed, patients with cerebellar dysfunc-tion show a decreased ability to adapt their phorias to verti-cal prism (Kono, Hasebe, Ohtsuki, Kashihara, & Shiro,2002). Versino et al. (1996) examined disconjugate controlin patients with cerebellar dysfunction and speculated thatdiVerent areas of the cerebellar cortex are responsible forcalibrating the conjugate and disconjugate components ofsaccades (the vermis and the Xocculus/paraXocculuscomplex, respectively).

An abundance of experiments have shown that the verti-cal alignment of the two eyes is easily modiWed. The sim-plest form of adaptation is often called concomitant (orcomitant) adaptation wherein the adaptive system is chal-lenged with either a uniform vertical disparity at multipleeye positions or by a single disparity given at a single eyeposition. Concomitant disparities are readily produced witha prism and, much to the dismay of clinicians who wouldlike to correct misalignments using a prism, the eyes realignwithin a short period of time and the patient ends up withthe same disparity that existed before the prism was intro-duced, hence, the alternative name of prism adaptation(Bagolini, 1976). In the laboratory, concomitant disparitiescan be introduced by either a prism or by introducing avertical oVset between identical images in a haploscope orany other device that allows targets to be presented sepa-rately to each eye. When a single disparate target of a fewdegrees diameter is presented at a single eye position, theadaptation spreads to all other eye positions just as thougha prism were used. DiVerent laboratories have measureddiVerent amounts of spread. Henson and Dharamshi(1982), for example, found that the adaptive response wasmaximal at the eye position at which training occurred anddropped oV by half that value 20° away from the traininglocation. Other investigators observed very little if anydecay in the adaptive response at other eye positions(Maxwell & Schor, 1994; Schor, Gleason, Maxwell, &Lunn, 1993). Whichever the case, it is clear that concomi-tant adaptation does not require training at every eye posi-tion but spreads broadly over the normal range of eyepositions. In the natural world, of course, the adaptive sys-tem would have experience at innumerable eye positionsand adaptation would be reinforced by experience at eachposition. The ability to adapt to prisms decreases with age(Kono, Hasebe, Ohtsuki, Furuse, & Tanaka, 1998).


Nonconcomitant adaptation (also called incomitant ornoncomitant adaptation) is required when the vertical misa-lignments that elicit the adaptive response vary with eyeposition (Lemij & Collewijn, 1991; Lemij & Collewijn,1992; Maxwell & Schor, 1994; Oohira & Zee, 1992; Oohira,Zee, & Guyton, 1991). Such nonconcomitant deWcits can bethe result of palsies of a single muscle. For example, Fig. 2Awas created from data obtained from a model of orbitalmechanics (Orbit) where a single superior rectus muscle wasweakened by 25%. The simulated muscle palsy results invertical diVerences in the positions of the two eyes (one eyeis assumed to be occluded in the simulation) that varymonotonically with eye elevation but are fairly constantacross horizontal positions.

Experimentally, nonconcomitant adaptation can bestimulated in two ways: one is to use a magniWer on one eyethat, due to the prismatic characteristic of the lens, createsvertical disparities, the magnitudes of which increase witheccentricity. The other method is to use just two diVerentdisparities at two spatially separated eye positions. Theresults of the second method, somewhat surprisingly, arecomparable to the Wrst in that the adapted vertical phoriaincreases smoothly between and beyond the adaptationpositions even though only two discrete disparities werepresent during training (Maxwell & Schor, 1994). In thisand other respects, the adaptation has the appearance of again change. Fig. 2B shows the results of training subjectsfor 40 min with oppositely directed vertical disparities (1.0°and ¡1.0°) at two vertical eye positions (up 9° and down9°). There is a graded spread of adaptation along the verti-cal axis and a fairly constant spread in the horizontal direc-tion. We and others (Erkelens, Collewijn, & Steinman,1989) have noted that adaptation tends to spread to all eyepositions unless there is a stimulus to do otherwise. Notethe similarity in the pattern of adaptation to this stimulusto the pattern of vertical misalignments shown in Fig. 2A.The graded spread of vertical phoria in the simulationshown in Fig. 2A is the result of orbital mechanics so it ispossible that orbital mechanics are also responsible for thepattern of adaptation observed following nonconcomitant

adaptation shown in Fig. 2B. Although nonconcomitantvertical phoria adaptation might seem more complex thanprism adaptation, orbital mechanics probably simpliWes theprocess.

There are limits to how large a disparity can be correctedby the adaptation mechanism. When selecting vertical dis-parities for our experiments we usually selected the largestdisparities that a subject could fuse or nearly fuse withsome eVort. While we have not rigorously tested thisassumption, anecdotally, we have observed that if fusion isnot possible, then adaptation does not occur. Therefore, itmight beneWt patients with large misalignments to start outwith lenses or prisms that do not completely compensatefor the vergence error but that will allow the patient to fusethe targets with eVort. For nonconcomitant experiments,the magnitude of the adaptive response depends not onlyon the size of the training disparities but on the rate ofchange of the training disparities over the oculomotorrange used. So, for example, if a right-over-left disparity of0.5° is given at a vertical position of up 5° and a left-over-right disparity of 0.5° is presented at a vertical position ofdown 5°, then the rate of change would be 0.1° of disparity/degree of elevation. It turns out that the adaptive responseincreases almost linearly with disparity size up to a stimulusrate of about 0.18° of disparity per degree of conjugate ele-vation where the response rapidly rolls oV (Schor et al.,1993). Conceivably, larger disparities could be adapted ifgiven in steps of smaller disparities that are within range ofthe adaptive system. This method has been shown to workwith prism adaptation (Sethi & North, 1987).

Why would decreasing the rate of change increase theadaptive response? In an attempt to answer this question,McCandless, Schor, and Maxwell (1996) constructed amodel of vertical phoria adaptation that used model neu-rons that had the discharge characteristics of certain ocularpremotor neurons. These included the threshold (the eyeposition at which the neuron becomes active) and eye posi-tion sensitivity (the rate of change of the Wring rate witheye position) typical of these neurons. The output of theseeye-position-sensitive neurons in the model drove vertical

Fig. 2. (A) Orbit simulation of a superior rectus palsy. (B) Change in vertical phoria due to nonconcomitant adaptation (adapted from Maxwell and Schor,1994).

SO Palsy Nonconcomitant adaptation

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vergence neurons that were given the characteristics of hor-izontal near response cells (no vertical vergence neuronshave ever been reported) as described by Mays and Porter(1984). With proper weighting, the model could reproducethe stimulus gradient eVect as well as all of the patterns ofadaptation that have been reported for both nonconcomi-tant and concomitant adaptation. This includes a case ofnonmonotonic adaptation wherein the vertical phoria wastrained to change from a right hyperphoria at the extremeupper and lower eye positions to a left hyperphoria in thecenter (McCandless et al., 1996), a result that we have notbeen able to model with simple gain changes (as with Orbit,for example). The model proposed that the reason adapta-tion increases when the stimulus gradient is low is thatmore eye-position-sensitive neurons are uniquely active fora particular vertical vergence response. For example, if a1.0° vertical disparity were given at an elevation of 10° anda ¡1.0° vertical disparity were given at an elevation of 0(straight ahead) then there would be many more eye posi-tion neurons uniquely active at each of these two locationsthan if the same two disparities were given at elevations of§2.0° where the majority of neurons would be abovethreshold for both positions. If this cross-adaptation modelwere correct, then there may be an intrinsic limitation tovergence adaptation that could not be exceeded even byslowly introducing stronger lenses or prisms.

1.3. Comparison of nonconcomitant and concomitant adaptation

Do adaptations to lenses and prisms utilize the sameadaptive mechanism? Based largely on anecdotal reportsfrom experimental subjects, we and others (Sethi & Henson,1984) had believed that concomitant adaptation is fasterthan nonconcomitant adaptation. In addition, it seemed logi-cal enough to suppose that a simple pattern would be easierto adapt than a more complex one. This turned out not to betrue as was discovered when the acquisition and decay ratesof concomitant and nonconcomitant adaptation weremethodically examined (Graf, Maxwell, & Schor, 2003). Itwas found that there was little diVerence in the rate of adap-tation between the two paradigms. The authors speculatedthat the reason most subjects feel that prism adaptation iseasier is not because adaptation is faster (as measured withopen-loop testing methods) but because binocular fusionduring training (with binocular targets) is easier when thevertical vergence requirement is the same at all eye positions.

While the time constants for the acquisition of concomi-tant and nonconcomitant adaptation were similar, the timeconstants for the decay were found to be quite diVerent(Graf et al., 2003). The decay of vertical phoria adaptationfollowing 60 min of training to either a prism or a lens wassigniWcantly faster for the prism. Of course, it is diYcult tofully equate the two training conditions quantitatively sincethey are so diVerent in nature but the authors attempted tostandardize the stimuli by using the largest disparities thatthe subjects could fuse with some eVort for each condition.

The decay of adaptation had a time constant of 31 min foradaptation to the prism and 83 min for adaptation to thelens. The diVerent decay periods for the two types of stimulisuggest that diVerent mechanisms are involved fornonconcomitant and concomitant adaptation.

1.4. Adaptation of vertical eye alignment with respect to horizontal vergence

When the two eyes Wxate a near target, the changes inmuscle force and innervation required to converge are morecomplex than might Wrst meet the eye: The discharge ratesof superior oblique motor neurons decrease (Mays, Zhang,Thorstad, & Gamlin, 1991), the thresholds of many abdu-cens neurons decrease, meaning that more neurons areactive for a given eye position (Maxwell, 1991), and thepopulation discharge rate is higher for convergence thanfor divergence for the same eye position (Gamlin, Gnadt, &Mays, 1989). In addition, during convergence, the inferiorrectus contracts (Demer, Kono, & Wright, 2003) and therelationship between torsion and horizontal and verticaleye position changes (Mok, Ro, Cadera, Crawford, & Vilis,1992; van Rijn & van den Berg, 1993). Given the multitudeof changes in innervation and muscle force that occurs dur-ing convergence, one might suspect that the oculomotorsystem would need the capacity to Wne tune the relativeparticipation of the various muscles during horizontalvergence. This supposition has been veriWed by experimentsin which vertical eye alignment was trained to vary as afunction of horizontal disparity vergence (Schor &McCandless, 1995a). The resulting adaptation was relatedto the horizontal vergence angle and not to the angle ofeither eye alone and the adaptation was manifested whetherhorizontal vergence was symmetrical or asymmetrical andwhether it was driven by horizontal disparities or byaccommodative demand. It is important to note thatvertical vergence cannot be adapted in relation to just anytype of cue. For example, Schor and McCandless (1995b)tried to adapt vertical vergence in relation to perceptualdistance cues either alone or in combination with changesin horizontal disparity vergence. The perceptual cuesincluded loom, overlap, relative size, and motion parallax.The addition of perceptual cues did not increase the magni-tude of the adaptive response over that obtained when hor-izontal disparity alone was the cue and no subject adaptedto the training stimulus when it was presented in conjunc-tion with a perceptual cue by itself. Our general observationis that vertical phoria and cyclophoria cannot be modiWedin relation to high-level cues but they can be trained inrelation to any set of naturally occurring low-level cues andsometimes in very complex ways as is discussed in moredetail below.

2. Torsion

The eye rotates not only about horizontal and verticalaxes but about its line of sight with the top of the eye


moving either temporally (extorsion) or nasally (intorsion).Van Rijn, van der Steen, and Collewijn (1994) have shownthat there is signiWcant variance in cycloversion (equalamplitude torsional movements of the eyes in the samedirection) with a standard deviation of about 0.21° duringWxation but there is much less variance in cyclovergence(torsional movements of the eyes in opposite directions)with an average standard deviation of about 0.07° if a back-ground is visible and 0.14 if one is not. Evidently, there is nocost for instability in cycloversion but cyclovergence needsto be tightly controlled. The good alignment of cyclover-gence is in all likelihood the result of adaptive mechanisms.

2.1. Listing’s law

Listing’s law prescribes the torsional position of the eyesfor any combination of vertical and horizontal eye position.The torsion of the eye equals the eye orientation that wouldresult if the eye had rotated from primary position to thenew position in one movement, about a single axis (Fig. 3).The axes of all such rotations are constrained to lie in a sin-gle plane that is approximately parallel to the frontal planealthough the actual tilt of the plane is idiosyncratic andmay be diVerent for the two eyes (Bruno & van den Berg,1997; Haslwanter, Curthoys, Black, & Topple, 1994). Inpractice, Listing’s plane is determined by measuring torsionover a broad range of horizontal and vertical positions.Commonly, horizontal, vertical, and torsional eye positionsare expressed as rotation vectors (Haslwanter, 1995), orsomething similar, and the endpoints of the vectors form aplane when plotted in three-dimensions.

2.2. Cyclovergence and monocular occlusion

We argued above that if good vertical alignment werethe result of adaptive mechanisms then long-term monocu-lar occlusion might reveal the extent of each subject’s adap-tation. Using the same reasoning, Graf et al. (2002) testedchanges in the orientation and translation of Listing’s planefollowing the occlusion of one eye in each of severalsubjects for eight hours. Four of Wve subjects developedconcomitant excyclophorias and the fourth subject’s cyclo-

phoria did not change appreciably. All of the subjects whodeveloped excyclophorias also demonstrated a left hyper-phoria on right gaze. Simulations with Orbit showed thatthe excyclophorias and the nonconcomitant vertical pho-rias that developed with respect to horizontal eye positionmight be related, since a decrease in superior oblique mus-cle force or an increase in inferior oblique muscle forcelarge enough to account for the changes that were mea-sured in cyclophoria, also produced nonconcomitantchanges in vertical phoria quantitatively similar to thosemeasured by Graf et al. (2002) and by Liesch and Simonsz(1993) in their monocular patching experiments.

It is interesting that the system so easily reverts to adiVerent phoria state following a relatively short period ofmonocular occlusion. This would suggest that good align-ment requires constant recalibration using binocular feed-back. Conceivably, vertical and cyclotorsional alignmentremain in a relative state of Xux because the various associ-ations are so numerous and complex that it is not worth-while making them more permanent. It may also speak tothe nature of adaptive processes in general, i.e., that theyare incapable of long lasting modiWcation.

2.3. Adaptation of Listing’s plane

Saccades are often adapted in the laboratory by jumpingthe target during the eye movement. Since initially the eyelands oV-target, and because detection of the displacementis suppressed during the saccade, the system assumes anerror has been made and within a few minutes it recali-brates to make the saccades appropriately longer or shorterin amplitude. Melis and Van Gisbergen (1995) attempted toadapt cycloversion in the same way, i.e., by stepping the tor-sional position of the target during horizontal saccades.They observed no change in the amplitude of cycloversionand concluded that Listing’s Law is not adaptable. Wepointed out above, that signiWcant variations in cyclover-sion are well tolerated so it is possible that the stimulus inthis study did not appear to the oculomotor system as anerror that needed correction. Unlike cycloversion, however,cyclovergence variance is small and we assume that it is anadaptive mechanism that keeps it this way.

Fig. 3. According to Listing’s law, the static torsional position of an eye is as though the eye rotated from primary position about an axis that is perpendic-
ular to the desired direction of sight.


The plasticity of cyclovergence has been tested by pre-senting cyclodisparities that varied as a function of verticalpursuit (Maxwell, Graf, & Schor, 2001) and, as hypothe-sized, all subjects showed substantial adaptation of cyclo-vergence in response to this novel association betweenvertical eye position and torsion. Subjects not only adaptedtheir cyclophorias, as shown by open-loop torsion measure-ments, but they increased their closed-loop cyclofusionalresponses by 50% when both eyes viewed the targets. Acomparison of open and closed loop adaptive responsesindicated that the closed-loop fusional responses mightadapt independently of, or in addition to, the open-loopchanges in cyclophoria since the increase in the closed-loopresponse was greater than that contributed by the open-loop adaptation. A consistent Wnding is that subjects tendto adapt better to incyclodisparities than excyclodisparities(Maxwell et al., 2001; Taylor, Roberts, & Zee, 2000). Sincethe default state of cyclophoria seems to be excyclophoria,as demonstrated by monocular occlusion, it is possible thatit is easier to adapt to incyclodisparities because the systemis used to adapting in this direction.

A study of the dynamics of saccades was not possiblewith the 60 Hz sampling rate used in the experiment justdescribed but the changes in torsion were not completed bythe ends of the saccades and it appeared as though cyclo-vergence movements were added to the end of saccades.Whether or not cyclovergence movements such as theseshould be construed as “adapting Listing’s law” is debat-able. It is possible that the adapted torsional component ofthe eye movement had nothing to do with a three-dimen-sional Listing’s law controller but was due to the additionof a cyclovergence movement from a separate cyclover-gence system. We should point out that the three-dimen-sional eye recordings typically used for calculating Listing’splanes often include the periods between Wxations andseveral seconds after the end of saccades. Also, it has beenshown that torsion can be unequal in the two eyes duringsaccades between tertiary positions resulting in transientexcyclovergence movements (Bruno & Van den Berg, 1997;Straumann, Zee, Solomon, Lasker, & Roberts, 1995) thatare then corrected by torsional drifts that can last longerthan a second after the saccade. If Listing’s planes had beengenerated from the data of Maxwell et al. in such a waythen the planes would have been modiWed by adaptation,and so, in that sense, it can be said that Listing’s planeswere adapted.

It is important to remember that not all cyclodisparitiesrepresent errors in binocular alignment, and the correctivesystem needs to be able to distinguish errors in cyclofusionfrom the disparities that normally arise from viewingslanted objects (Howard, 1993; Kertesz, 1983). Kertesz andSullivan (1978) and Howard et al. (1994) speculated thathorizontal contours (horizontal shear with vertical dispari-ties) drive the motor cyclofusional (and adaptive) responsesince vertical shear can result from either stereo-slant orocular misalignment. These authors also showed that cyclo-fusion increases with stimulus diameter and suggested that

cyclodisparities in the center of the visual Weld are fused bythe sensory system whereas those in the periphery drivecyclofusion (Howard, Sun, & Shen, 1994; Kertesz &Sullivan, 1978; see also van Rijn, van der Steen, & Colle-wijn, 1992, for a comparison of visually induced cyclover-sion and cyclovergence). According to van Rijn et al. (1992)cyclovergence is a truly binocular process and, unlike cyclo-version, requires correspondence of the images presented tothe two eyes.

2.4. Convergence and Listing’s law

If a subject were set up so that the reference position formeasuring three-dimensional eye position coincides withtrue primary position (the direction orthogonal to Listing’splane), then the rotation vectors for all eye positions wouldlie in a plane with a torsional value of zero. If the subjectnow converges on a near target, torsion is no longer foundto be zero everywhere. All of the rotation vectors are still ina plane but the plane for each eye is rotated temporally fromits position before convergence (an analogy to saloon doorshas been made; Tweed, 1997). This rotation of the twoplanes occurs even if vergence is asymmetrical, for example,if the near and far targets are aligned with one eye(Kapoula, Bernotas, & Haslwanter, 1999; SteVen, Walker, &Zee, 2000). The outward rotation of Listing’s planes meansthat torsion varies as a function of vertical eye position butnot horizontal eye position. The change in the orientation ofListing’s plane is often called L2 or the binocular extensionof Listing’s law (Tweed, 1997). It has been suggested that L2evolved alongside horizontal vergence to help keep corre-sponding points in the retina aligned during near viewing,that is, to avoid large cyclodisparities from occurring due totorsional misalignment of the two eyes (Tweed, 1997) withthe beneWt of preserving high stereo-acuity at near viewingdistances (Schreiber et al., 2001). If this were the case, itmight be possible to adapt L2 by purposely introducing thetorsional disparities that would occur if L2 were incorrect.Normally during convergence the eyes excyclorotate whenlooking up and incyclorotate when looking down. The plas-ticity of L2 was tested by presenting subjects with cyclodis-parities that either exaggerated this pattern or that reversedthe normal pattern by presenting incylodisparites to the sub-jects when they looked up and excyclodisparities when theylooked down (Schor, Maxwell, & Graf, 2001). All subjectsadapted appropriately for each of these conditions. Simula-tions with Orbit suggest that orbital mechanics couldaccount for L2 in that changes in oblique and vertical rectusmuscle tensions in one direction automatically results ineye-position-speciWc changes in torsion during horizontalconvergence that correspond to those observed with L2(Schor, 2003).

2.5. Relationship between torsion and vertical fusion

Several groups have shown that torsion changes in con-junction with vertical fusion. Given that the vertical rectus


muscles and obliques work together and are controlled bythe same neural structures such as the rostral interstitialnucleus of the MLF and the interstitial nucleus of Cajal(Crawford, Cadera, & Vilis, 1991; Helmchen, Rambold, &Buttner, 1996) it is not too surprising that changing oneaVects the other. Enright (1992) concluded from hisexperiments that vertical fusion is mediated by the superiorobliques but further investigation by van Rijn andCollewijn (1994) indicated that, while there is an associa-tion between vertical vergence and torsion, it is not alwaysin the direction predicted by Enright’s hypothesis (though,the eVect of muscle pulleys might be a complicating issue).Listing’s planes have been measured during vertical fusionwith somewhat mixed results. Mikhael, Nicolle, and Vilis(1995) and SteVen, Walker, and Zee (2002) found that List-ing’s planes rotated in the same direction as the eye duringprism-induced vertical vergence whereas Straumann andMuller (1994) found no consistent rotation. The rotation ofListing’s plane about a vertical axis was also observed to bediVerent by diVerent groups: It was determined to be out-ward by Mikael et al., inward by Straumann and Müller,and not to occur by SteVen et al. The diVerence in resultsbetween these groups could possibly be accounted for bythe diVerent paradigms and the amount of time that thesubjects experienced the prisms (from four seconds in vanRijn and Collewijn to four days in SteVen et al.) and to thesize of the prisms employed.

3. Binocular coordination during head tilt

When the head tilts to one side, dynamic rotation istransduced by the semicircular canals and head positionwith respect to gravity is sensed by the otolith organs: theutricle and saccule. When the head tilts about a naso-occip-ital axis (roll) and the eyes are parallel to the rotation axis,the eyes counterroll in the opposite direction by about 10%of the amplitude of the roll angle for static positions(Diamond & Markham, 1983) and much greater than thatfor dynamic roll where the canals are also activated(Collewijn, Van der Steen, Ferman, & Jansen, 1985;Jauregui-Renaud, Faldon, Clarke, Bronstein, & Gresty,1998; Kori, Schmid-Priscoveanu, & Straumann, 2001). Interms of Listing’s law, the planes do not change their orien-tation but simply translate along the torsion axis, that is tosay, torsion changes by the same amount at all horizontaland vertical eye positions (Bockisch & Haslwanter, 2001;Haslwanter, Straumann, Hess, & Henn, 1992). For headtilts about an interaural axis (pitch) Listing’s plane tilts inthe opposite direction and by about half the angle of thehead pitch in monkey (Haslwanter et al., 1992) althoughthis is reported to be less pronounced in humans (Bockisch& Haslwanter, 2001). A pure pitch rotation of Listing’splane means that torsion changes for horizontal eyemovements but not for vertical.

There is ample potential for vertical misalignment of theeyes during head roll. Ocular counterroll is mediated largelyby the superior and inferior obliques and the changes in mus-

cle force resulting from OCR may aVect the innervationrequired by the other muscles in order to perform the sameaction as with the head upright (Klier & Crawford, 1998;Scherberger et al., 2001). The secondary action of the supe-rior oblique is depression and that of the inferior oblique iselevation. Therefore, when the eyes counterroll, the eye ispi-lateral to the direction of the roll might be expected todepress and the opposite eye would elevate thereby resultingin a vertical skew. Another possible source of vertical mis-alignment is the utricles: Both of the eyes are driven by eachof the two utricles during counterroll and stimulation of eachutricle results in vertical skew (Curthoys, 1987; Fluur & Mell-strom, 1970; Suzuki, Goto, Tokumasu, & Cohen, 1969). Athigher frequencies of head tilt, the anterior and posteriorsemicircular canals excite the obliques for one eye and thevertical rectus muscles on the other, and this too must becoordinated in order to avoid vertical skew. Despite thepotential for vertical misalignment, most authors have foundonly a relatively small vertical skew with the intorted eyemore elevated than the extorted one (Jauregui-Renaud et al.,1998; Kori et al., 2001) although skew may increase withsymmetrical convergence (Migliaccio, Della Santina, Carey,Minor, & Zee, 2006). As for ocular counterroll (OCR), moststudies have described OCR as being nearly conjugate (e.g.,Diamond & Markham, 1983; Kori et al., 2001) although oth-ers have measured signiWcant disconjugacy (Bergamin &Straumann, 2001). OCR and vertical skew are normallywithin fusible limits but certain midbrain lesions (Corbett,Schatz, Shults, Behrens, & Berry, 1981; Gresty, Bronstein,Brandt, & Dietrich, 1992) result in a triad of responsesreferred to as the ocular tilt reaction (OTR) which consists ofhead tilt, conjugate ocular torsion, and vertical skew. Like-wise, OTR can be produced by electrical stimulation of themidbrain (Lueck et al., 1991; Westheimer & Blair, 1975). Thecerebellum is implicated in maintaining good eye alignmentduring head tilt in that vertical skew deviation has beenshown to accompany cerebellar deWcits in humans (Walker& Zee, 2005; Wong & Sharpe, 2005) and is associated withasymmetrical torsional VOR gains (Wong & Sharpe, 2005).Experimental unilateral lesions of the Xoccular lobe in the catleads to intorsion of the eye ispilateral to the lesion (Chin,Fukushima, Fukushima, Kase, & Ohno, 2002).

The abovementioned observations suggest that verticalskew is under adaptive control and experimental evidencesupports this (Maxwell & Schor, 1996). Vertical skew is eas-ily adapted with respect to head tilt when vertical dispari-ties are coupled to either head pitch or roll so long as thehead tilts about an earth-horizontal axis. In principle, a ver-tical vergence adaptation mechanism could exist that cor-rects for any vertical misalignment despite its source. Theexperimental evidence, however, indicates that head-posi-tion-related adaptation involves the otoliths (Maxwell &Schor, 1996) either directly or indirectly. In fact, when thesame training that elicits adaptation about an earth-hori-zontal axis is performed about an earth-vertical axis (whereotolith output does not vary) no adaptation occurs. Ofcourse, with static changes in head position, there is no


cycloversion when head rotation is about an earth-verticalaxis, so it remains to be tested whether the vertical vergenceadaptation that was measured in relation to head positionwas linked directly to an otolith signal or to the ensuingcycloversion.

Empirical evidence also indicates that head-position-dependent and eye-position dependent adaptation are notindependent processes but occur at a location where thetwo signals intersect. Maxwell and Schor (1997) presentedtraining stimuli that were contingent on both eye positionand head position. For example, if the head were rolled tothe left, a right-hyperdisparity stimulus was presented inthe upper Weld and a left hyperdisparity was presented inthe lower Weld just as with the nonconcomitant adaptationdescribed above. When the head was rolled to the right, theopposite set of eye-position-related disparities were pre-sented, i.e., a left hyperdisparity in the upper Weld and aright hyperdisparity in the lower. Subjects had no troubleadapting to these potentially conXicting stimuli. The resultsindicate that head-related and eye-position-related verticalvergence adaptation are not independent processes but thatcombinations of head and eye position are taken intoaccount. It also reinforces the conclusion that adaptation isnot at the level of the Wnal common pathway since in thisexperiment the eye-position-speciWc demands were inopposite directions at the two head positions.

3.1. Cyclovergence adaptation with respect to head roll

It was mentioned earlier that variation in cycloversion isfairly well tolerated (Van Rijn et al., 1994) and this seemsalso true for OCR in the sense that the world appears stableeven though OCR only compensates for about 10% of headtilt. For this reason, it might be diYcult to experimentallymodify the relationship between conjugate OCR and statichead tilt, although this has not been speciWcally tested andthere is some evidence that conjugate OCR does adapt inthat patients with cerebellar lesions sometimes have OCRthat is less than normal (Wong & Sharpe, 2005). Given thatcyclovergence is precisely controlled, it is not surprising toWnd that it is readily modiWed in relation to head roll inorder to avoid the cyclodisparities that would be evoked byunbalanced vestibular signals (Maxwell & Schor, 1999).The post-training right eye and left eye torsional move-ments in these experiments looked like scaled versions ofthe pre-trained eye movements with the maximal change incyclophoria occurring at a head tilt of 60° (where OCR wasmaximal) even though training was received at 45° to theleft and right. In other words, the adaptation had theappearance of a gain change in otolith-ocular pathways.

As with everything pertaining to torsion, predicting theeVect of OCR on vertical eye alignment is not straightfor-ward and depends on what the eVective axis of rotation fortorsion is assumed to be. If the axes of rotation were head-Wxed during head roll, then the eyes would develop avertical skew during convergence (Misslisch, Tweed, &Hess, 2001). If the axes were eye-Wxed, so that the eyes spin

about their lines of sight, then skew would not occur but asMisslisch, Tweed and Hess (Misslisch et al., 2001) haveshown, a vertical disparity develops nevertheless becausethe cycloversion causes images to fall on vertically dispa-rate locations on the retina. These authors speculated thatthe system partly avoids these correspondence problems byreducing ocular counterroll during convergence, a phenom-enon that has been demonstrated by several groups(Averbuch-Heller et al., 1997; Bergamin & Straumann,2001; Misslisch et al., 2001; but see Migliaccio et al., 2006).This would render the vertical disparities small enough tobe easily corrected by vertical fusion (although, seeBergamin & Straumann, 2001, who observed an increase invertical skew with convergence). While this argument isvery appealing, the fact that vertical skew and cyclover-gence are so easily modiWed with respect to both head posi-tion and to horizontal vergence makes it more diYcult tounderstand why the system would Wnd it necessary todecrease the gain of OCR. Perhaps the decrease in OCRgain reduces skew to a level where the residual disparity canbe eliminated by vertical fusion that then stimulates theadaptation mechanism.

4. Conclusion

Vertical and torsional binocular eye alignment can beadapted with respect to orbital eye position, horizontal ver-gence, and head tilt with respect to gravity and virtually anycombination of the above. The vertical and torsional align-ment of the eyes can be signiWcantly changed within20–30 min but even long-term adaptation can be lostquickly without periodic reinforcement, as monocularpatching studies have shown. Adaptation can take the formof a change in open-loop alignment, an increase in theclosed-loop fusional range, and increase in the speed ofmotor fusion, and, possibly, an increase in sensory fusion.

Oftentimes, phoria adaptation is discussed as though itwere a single process and this is almost certainly a mistake.There could be diVerent adaptive sites involved for correct-ing binocular misalignment due to saccades, post-saccadicdrift, canal responses, otolith responses, pursuit and so on.For example, it has been shown that vertical vergenceaccompanying pursuit can be adapted independently fromvertical vergence accompanying saccades (Schor, Gleason,& Horner, 1990) and vertical vergence can be adapted withrespect to pursuit in a direction-speciWc manner (Gleason,Schor, Lunn, & Maxwell, 1993) which means that noncon-comitant phoria adaptation is not simply tied to an eyeposition signal but perhaps a velocity or phase signal aswell. We have shown that vertical phoria and cyclophoriaadaptation can be very context speciWc and, seemingly,wherever one signal is dependent on another, the cross-cou-pled weights can be modiWed. We have never observedadaptation of vertical vergence or cyclovergence in the con-text of higher-level cues such as loom or gaze in the worldbut we have always obtained adaptation with low-level,naturally intersecting cues such as eye position, head


position, and horizontal vergence angle. More often thannot, vertical disconjugate adaptation has the appearance ofa slow vertical vergence added onto a conjugate movementbut it is hard to look at eye movement records resultingfrom longstanding disconjugacy such as occurs with aniso-metropic spectacles (Erkelens et al., 1989), cerebellar dys-function (Versino et al., 1996), or muscle recession (Viirreet al., 1987) and not think that they represent truly discon-jugate saccades. If this is correct (and it should be methodi-cally tested), it lends support the notion that, at least insome instances, the two eyes can be independently con-trolled (Zhou & King, 1998; King & Zhou, 2000; but seealso Mays, 1998).

Good alignment is a multi-stage process. Neural connec-tivity between motor and premotor areas serving horizontal,vertical and torsional eye movement serves as a substrate forcoordinated movements (McCrea et al., 1987a, McCrea,Strassman, & Highstein, 1987b; Belknap & McCrea, 1988).The required parsing of muscle force between the extraocu-lar muscles varies with head tilt, conjugate eye position, andvergence angle so that the interactions between horizontal,vertical, and torsional pathways need to be Xexible. Musclepulleys may simplify the neural control required and mightalso be involved in the adaptive process. It is likely thatgiven the complexity of the alignment problem it might beunreasonable to expect the system to be inherently accurateand to be able to maintain accuracy over a lifetime withoutthe use of adaptive mechanisms. Such plasticity relies onexperience to vary the weight of contacts between diVerentsystems to achieve binocular alignment that is withinPanum’s area for fusion. The fusional system may keep theeyes aligned in the short term but if these fusional move-ments persist, they stimulate adaptive mechanisms thatresult in modiWcation that lasts from hours to days.

Acknowledgments

This research was supported by NIH Grant EYO-3532.We thank Kai Schreiber for his helpful comments on themanuscript.

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