Functional anatomy of extraocular muscles during human vergence compensation of horizontal heterophoria

Abstract

We employed magnetic resonance imaging to quantify human extraocular muscle (EOM) contractility during intermittent convergent and divergent strabismus with each eye viewing monocularly at 20 cm compared with centered target fusion. Contractility, indicated by posterior partial volume change, was analyzed in transverse rectus and in medial and lateral superior oblique (SO) muscle compartments. In five subjects with intermittent esotropia, abduction of the deviated eye to monocular target fixation was associated with significant whole lateral rectus (LR) contraction, but with medial rectus (MR) relaxation that was significantly greater in the superior than inferior compartment. Esotropic eye abduction to binocular fusion was associated with similar relaxation in the two MR compartments, but with greater contraction in the LR’s superior than inferior compartment. The whole diverging eye SO muscle relaxed. In three subjects with intermittent exotropia, converging eye fusional adduction was associated with significant whole LR relaxation and with MR contraction attributable to significantly greater contraction in the superior than inferior compartment. In adduction of the exotropic eye to monocular target fixation but not fusional adduction, the whole SO exhibited significant relaxation. Rectus pulley positions were not significantly altered by fusion of either form of intermittent strabismus. Globe rotational axis was eccentric in intermittent strabismus, rolling the eye so that rectus EOM lever arms facilitated vergence. These results confirm, and extend to fusion of intermittent horizontal strabismus, differential compartmental function in horizontal rectus EOMs and suggest a novel role for the SO in compensation of both intermittent esotropia and exotropia.

NEW & NOTEWORTHY Disjunctive eye movements normally permit binocular fixation in near visual space but also compensate for mechanical imbalances in binocular alignment developing over the life span. Magnetic resonance imaging of the extraocular muscles demonstrates important differential function in muscle compartments during compensation of large-angle intermittent convergent and divergent strabismus in humans. Eye translation during rotation also enhances vergence compensation of intermittent strabismus.

INTRODUCTION

Normal binocular function requires identical horizontal rotations of the two eyes for infinitely distant targets. When targets are proximally located, the two eyes cannot rotate equally; the required inequality of horizontal rotations is known as “convergence” (Fray 2017; Judge 1996). Extensive behavioral studies have been conducted of convergence in normal humans (Allen 1954; Bharadwaj et al. 2007; Fray 2017; Kapoula et al. 1999; Steffen et al. 2000; Yang et al. 2009) and nonhuman primates (Gamlin et al. 1989a, 1989b; Hess and Misslisch 2016; Mays 1984; Mays and Gamlin 1995; Miller et al. 2011; Nitta et al. 2008). Fusional convergence is clinically tested by placing in the viewing path of one eye a prism with its base oriented to the temporal side, which requires that eye to adduct to achieve single binocular vision. Under such conditions, fusional convergence is robust; normal adult humans can converge to compensate for prisms that maximally deviate the geometrically appropriate visual direction by an average of 18° for near targets within haptic visual space (arm’s length) and 15° for remote targets at distances approximating optical infinity (Fray 2017).

Disjunctive horizontal ocular rotation opposite convergence is known as “divergence.” Divergence is physiologically required to reduce convergence when fixation is shifted from near to distant targets, but normal divergence range is less than for convergence. When targets are located in near visual space, divergence can be achieved by the relaxation of convergence so that the lines of sight can become even nearly parallel as geometrically appropriate for targets at optical infinity. However, under some conditions, divergence can exceed parallelism so that the lines of sight of each eye never intersect. Fusional divergence is clinically tested by placing in the viewing path of one eye a prism with its base oriented to the nasal side, which requires that eye to abduct to achieve single binocular vision. Normal human adults can for a few seconds diverge to compensate for prisms that maximally deviate the geometrically appropriate visual direction by an average of 9° for near and 4° for remote targets (Fray 2017), but can sustain such divergence of only an average maximum of ~3° for near and 2° for remote targets (Demer and Clark 2018). Prior convergence effort diminishes subsequent divergence amplitude (Fray 2017). Divergence is typically (Hung et al. 1997; Semmlow and Wetzel 1979), but not always (Tyler et al. 2012), slower than convergence.

Beyond its geometric necessity for binocular fixation of targets in near visual space, horizontal vergence also corrects for the effects of neural and mechanical imbalances in binocular alignment that are collectively termed “heterophorias” when compensation is fully effective and “heterotropias” when failure of compensation leads to occasional manifest misalignments, known as “strabismus” (von Noorden 1990). Strabismus occurs naturally in ~2% of Macaca nemestrina monkeys (Kiorpes and Boothe 1981). In humans, strabismus, most commonly horizontal, is present in ~3.6% of Asian (McKean-Cowdin et al. 2013), 3.2% of non-Hispanic white (McKean-Cowdin et al. 2013), and ~2.5% of the Black and Latino population under 6 yr of age (Multi-ethnic Pediatric Eye Disease Study Group 2008). In such children, 25–29% of all divergent strabismus for near targets is intermittent and is known as “intermittent exotropia” (McKean-Cowdin et al. 2013; Multi-ethnic Pediatric Eye Disease Study Group 2008). Seven to 24% of convergent strabismus in these children is intermittent and is known as “intermittent esotropia” (McKean-Cowdin et al. 2013; Multi-ethnic Pediatric Eye Disease Study Group 2008). Esotropia also occurs spontaneously in monkeys (Quick et al. 1992; Tychsen et al. 2004).

A latent tendency toward binocular divergence, termed “exophoria,” is commonly present in healthy adult humans and also occurs in monkeys (Kiorpes and Boothe 1981; Quick et al. 1992). Exophoria is present in 93% of Japanese adults, of whom 2.9% have latent divergences of 11–40° but 1.6% have intermittent exotropia with manifest divergences of 11–22° (Goseki and Ishikawa 2017). In latent horizontal strabismus comprising esophoria and exophoria, as well as in intermittent esotropia and intermittent exotropia, the deviations are compensated during periods of binocular alignment by fusional divergence and convergence, respectively. Moreover, the amplitudes of these vergences in long-standing cases can greatly exceed those of healthy humans who do not have imbalances in binocularity (von Noorden 1990). The functional value of fusional vergences, beyond the obvious geometrical requirements for normal binocular convergence to near targets, is that fusional vergences prevent widely prevalent latent imbalances in binocular alignment from manifesting as strabismus, which in humans causes double vision and amblyopia (von Noorden 1990), and in monkeys who do not report their perceptions is at least a cause of amblyopia (Quick et al. 1992). It thus is important to understand the mechanisms of horizontal vergences that compensate for binocular imbalances that would otherwise create visual problems over the life span.

Magnetic resonance imaging (MRI) of the extraocular muscles (EOMs) can provide a window into their actions during vergence, including their contractile states as assessed by posterior partial volume (PPV) changes (Clark and Demer 2016a) and their force directions as assessed by locations of their pulleys (Clark et al. 1997, 2000; Demer et al. 1999, 2000). Our early human MRI study of convergence to a target aligned with one eye found reciprocal lateral rectus (LR) relaxation and medial rectus (MR) muscle contraction, along with rectus pulley array extorsion (Demer et al. 2003a). It was later recognized that the intramuscular innervations of the LR (Peng et al. 2010) and MR are anatomically distinct within corresponding halves of each EOM that are composed of generally parallel fibers (Demer et al. 2010; Lim et al. 2007), conferring mechanical independence to these two compartments (Shin et al. 2012, 2013, 2015). Under in vitro conditions, forces in bovine EOM compartments have been shown to be mechanically independent both under passive loading (Shin et al. 2012) and during active contraction (Shin et al. 2015). We have recently reviewed evidence for independent neural control of EOM transverse compartments (Clark and Demer 2016b; Demer 2015; Demer and Clark 2014; Suh et al. 2016a), including the frequent clinical occurrence of partial LR palsy selectively impairing the superior (LRs), and sparing the inferior (LRi), LR compartment (Clark and Demer 2014). Applying the asymmetrical convergence paradigm of Miller et al. (2002, 2011) during MRI scanning (Demer and Clark 2014), we found similar relaxation of both LRi and LRs compartments during aligned convergence, but both MR compartments in the aligned eye also relaxed, consistent with EOM force recordings (Miller et al. 2002, 2011). Threefold greater superior MR compartment (MRs) contraction than inferior MR compartment (MRi) contraction in conjugate adduction than during convergence provides further evidence for differential compartmental innervation and function in the MR (Demer and Clark 2014).

The functional anatomy of the EOMs during normal fusional divergence evoked by base-in prism viewing has also been studied using MRI (Demer and Clark 2018). In this paradigm, the target was centered between the eyes, either 20 or 400 cm away, and maximum base-in prism was imposed that could be compensated by divergence in healthy, young adults having excellent vision. For the nearer target to which normal convergence could merely be relaxed, 3° diverging eye abduction was associated with uniform contraction in the entire LR and with a smaller overall MR relaxation attributable to compartmentally selective relaxation in the superior compartment without change in the inferior compartment, and without contractile change in the LR and MR of the non-prism-viewing eye (Demer and Clark 2018). At 400 cm, ~2° diverging eye abduction in nine subjects was associated with ~6% whole LR PPV increase but no change in MR, with compartmentally similar corelaxation in the aligned eye LR and MR; this divergence represented more than relaxation of convergence, because the visual axes diverged beyond parallel (Demer and Clark 2018). In contrast with convergence, there was no change in rectus pulley positions during fusional divergence to targets at either 20 or 400 cm.

The foregoing MRI studies of EOM function during horizontal vergence have involved relatively small vergence angles but revealed surprising phenomena, including differential compartmental function in the MR, cocontraction of the MR and LR in the verging eye, and corelaxation of the MR and LR in the aligned eye. So far, there has been no study of the EOM mechanisms that implement fusional vergence to compensate large horizontal heterophoria or intermittent heterotropia. It seems possible that this vergence might be implemented by novel EOM mechanisms, exaggeration of normal mechanisms, or both. Such mechanisms are important, because they probably operate on an ongoing basis to avert strabismus in the majority of individuals over the life span as EOM paths and lengths change during aging (Chaudhuri and Demer 2013). Therefore, to elucidate such mechanisms, the current study of the functional anatomy of EOMs during horizontal convergence and divergence was extended to include a rare group of otherwise normal humans who have been identified to exhibit large-angle latent binocular imbalances.

MATERIALS AND METHODS

Subjects.

Healthy adults were selected from volunteers to a study of strabismus under a protocol conforming to the Declaration of Helsinki and approved by the Institutional Review Board for Protection of Human Subjects at the University of California, Los Angeles. Volunteers, who were financially compensated for participation, gave written informed consent and underwent eye examinations by an author who is a clinical strabismus specialist, verifying normal ocular versions, ocular health, and refractive error permitting excellent, optically uncorrected near visual acuity with each eye. These individuals had history of progressively decompensating intermittent horizontal strabismus, having presented for surgical treatment, with the exception of one man who had volunteered for the study as a normal control subject but was found on qualification examination to have a large exophoria. No subject had vertical strabismus or dissociated vertical deviation. Experimental procedures were performed before surgical correction of strabismus that was sought by all of the other subjects. Subjects underwent alternate cover testing in an examining room to verify that they could sustain fusional vergence to a near target at 20 cm. Nine subjects participated in the fusional divergence of intermittent esotropia experiment; however, four of these failed to maintain divergence during the more demanding conditions of MRI scanning, so interpretable data were obtained in three female and two male subjects of average age 42 ± 8 yr (mean ± SD; range 23 - 62 yr). Six subjects participated in the fusional convergence of intermittent exotropia experiment; three of these failed to maintain convergence during MRI scanning, so interpretable data were obtained in three male subjects of average age 29 ± 6 yr (range 19–39 yr). Two interpretable subjects had frank intermittent exotropia intermittently manifesting as strabismus, whereas the third had a large latent exophoric deviation that was not symptomatic.

Visual stimuli.

As published elsewhere (Demer and Clark 2014, 2018; Demer et al. 2003a), during MRI the subjects wore a facemask containing an embedded surface coil array (Medical Advances, Milwaukee, WI) while supine. The target consisted of a fine central black cross on a white background measuring 3 × 3 mm with 0.75-mm stroke width surrounded by five concentric squares with ~0.25-mm stroke width (innermost 9 × 9 mm, outermost 20 × 20 mm) designed to promote accommodation. The indirectly illuminated target was affixed above the subject, midway between the eyes of all subjects with intermittent esotropia and one with exophoria. The target for the two subjects with intermittent exotropia was a scaled version of the near target, with the fine central black cross measuring 40 × 40 mm with 10-mm stroke width, placed 400 cm distant and viewed via an acrylic mirror above the subject’s eyes to make the target appear straight ahead (Demer and Clark 2018). The distant target was illuminated by a floodlight in an otherwise dark room.

The ability of each subject to binocularly fuse the target was initially verified subjectively by monocularly covering each eye in the scanner and querying subjects before and after every imaging sequence, but definitively by verification in MRI of geometrically appropriate eye positions. Scans were first performed during binocular fusion, then during monocular fixation by the right eye, and finally during monocular fixation by the left eye.

The subjective visual direction (line of sight) in humans does not generally correspond to the line of anatomical symmetry of the eyeball. The angular difference between these two lines is termed in physiological optics to be the “angle kappa” (Basmak et al. 2007; Gharaee et al. 2014). Angle kappa is individually variable but usually positive, which means that the eyes may appear anatomically diverged when in fact the visual directions are parallel or slightly converging. Whereas changes in an eye’s angular direction can be measured with high precision from MRI, absolute gaze direction cannot be determined except by “calibrating” under the assumption that cooperative normal subjects will foveate a designated target under monocular conditions. We therefore employed this standard assumption for each eye during MRI when the eye was designated as “aligned” and fixating the target while its fellow was occluded. In every experiment, each eye individually served as an aligned eye when it fixated the target monocularly during one set of MRI scans as the fellow eye was occluded. Because each subject had intermittent or latent strabismus, the eye under occlusion when its fellow was aligned was a “deviated” eye that exhibited abnormal adduction in esotropia or abnormal abduction in exotropia. The angle of the strabismus was determined relative to the angle evident for that eye in the MRI scan when the eye viewed the target and was therefore aligned. During conditions of “fusion,” both eyes fixated the target simultaneously; validation measurements were performed in axial MRI to compare ocular orientations during fusion with those in monocular alignment. As will be shown, eye positions were, on average, identical during alignment and fusion.

Magnetic resonance imaging.

MRI was as previously published for study of normal fusional divergence (Demer and Clark 2018). High-resolution, T2-weighted fast spin-echo (Demer and Dushyanth 2011) MRI was performed at 1.5 Tesla (General Electric Signa, Milwaukee, WI) using a surface coil array (Medical Advances) and techniques detailed elsewhere (Clark and Demer 2012a; Demer and Clark 2014; Demer et al. 2003a). For each viewing condition, the following image sets were obtained using a 256 × 256 matrix and 2-mm-thick contiguous planes: 9–11 axial images of both eyes with a 10- to 11-cm field of view to verify vergence (Figs. 1 and 2); 17–19 contiguous quasi-coronal images perpendicular to the long orbital axis with an 8-cm² field of view (313-μm pixels) for determination of rectus and superior oblique (SO) EOM volumes; and 9–11 quasi-sagittal images parallel to the long orbital axis for determination of inferior oblique (IO) muscle cross section.

Fig. 1.

Axial (top row) and quasi-coronal (middle and bottom rows) MRI of orbits of a subject with intermittent esotropia during binocular fusion of a 20-cm distant centered target (middle columns) and during monocular viewing by the right eye (right columns) or left eye (left columns). Images in middle row are near the globe-optic nerve junction, and images in bottom row in mid-orbit. Presumed compartmental borders are indicated by superimposed white lines based on half transverse dimensions of the rectus muscles; anatomical demarcations of compartments are not generally visible in MRI. IRl, lateral compartment of inferior rectus muscle; IRm, medial compartment of inferior rectus muscle; LRi, inferior compartment of lateral rectus muscle; LRs, superior compartment of lateral rectus muscle; MRi, inferior compartment of medial rectus muscle; MRs, superior compartment of medial rectus muscle; ON, optic nerve; SO, superior oblique muscle; SRl, lateral half of superior rectus muscle; SRm, medial half of superior rectus muscle.

Fig. 2.

Axial (top row) and quasi-coronal (middle and bottom rows) MRI of orbits of a subject with intermittent exotropia during binocular fusion of a 400-cm distant centered target (middle columns) and during monocular viewing by the right eye (right columns) or left eye (left columns). Presumed compartmental borders are indicated by superimposed white lines based on half transverse dimensions of the rectus muscles; anatomical demarcations of compartments are not generally visible in MRI. IRl, lateral compartment of inferior rectus muscle; IRm, medial compartment of inferior rectus muscle; LRi, inferior compartment of lateral rectus muscle; LRs, superior compartment of lateral rectus muscle; MRi, inferior compartment of medial rectus muscle; MRs, superior compartment of medial rectus muscle; ON, optic nerve; SO, superior oblique muscle; SRl, lateral half of superior rectus muscle; SRm, medial half of superior rectus muscle.

Analysis.

Images were quantified using ImageJ64 and customized analysis programs in MATLAB (The MathWorks, Natick, MA). Horizontal eye position was determined from axial MRI by the projection of a line from corneal apex through the anteroposterior axis of the lens to the foveal region of the retina, as done previously (Demer and Clark 2014; Demer et al. 2003a). It was assumed that during monocular fixation, each fixating eye was aligned on the target, and its direction was set nominally to zero for analysis. Vergence was defined to be the difference in horizontal gaze positions between the two eyes.

The remainder of the MRI analysis was as published previously (Demer and Clark 2018), relying on published histological demonstrations of stereotypic, compartmentally selective intramuscular innervation in the LR, MR, inferior rectus (IR) (da Silva Costa et al. 2011), and SO (Le et al. 2015). Briefly, rectus EOMs and SO bellies were outlined in quasi-coronal views (Clark and Demer 2012a), the line of the maximum transverse dimension of each rectus EOM was determined (Clark and Demer 2012a, 2016b), and superior and inferior horizontal rectus compartmental areas were calculated above and below the perpendicular bisector of the maximum transverse dimension, omitting a band ±10% about the line as a safeguard against undetected variations in the compartmental border. Medial and lateral vertical rectus compartmental areas were correspondingly calculated (Clark and Demer 2012a, 2016b). For the SO, bootstrap analysis has determined that a line 30° or 60° to the long axis of the SO cross section optimally discriminates compartmental function, again omitting the central 20% (Demer and Clark 2015). As done previously (Demer and Clark 2018), data for the SO were analyzed for both angles.

Under other conditions, IO contractility can be determined from changes in its cross section in quasi-sagittal images at the center of the IR muscle (Demer and Clark 2015; Demer et al. 2003b). However, in the present case, the large changes in horizontal eye position due to horizontal vergence were confounding because large changes in IO path altered both the point at which cross section was evaluated and IO path orientation there. Data on the IO were therefore considered unreliable and are not reported.

As an indicator of contractility, we employed change in PPV, which correlates closely with duction angle for horizontal (Clark and Demer 2012b) and vertical rectus EOMs (Clark and Demer 2016b). We computed PPV as the summed cross sections of each EOM compartment in the four contiguous image planes from 8 to 14 mm posterior to the globe-optic nerve junction (Clark and Demer 2012b), including contributions from both the global and orbital layers. We compared three PPV differences: 1) between the misaligned state and the monocular fixation state, corresponding to the duction required to correct the strabismic angle without binocular interaction; 2) between monocular fixation by the fellow eye and the fusing state, again corresponding to the duction required to correct the strabismic angle but with binocular interaction; and 3) between monocular fixation by the same eye and the fusion state, with the latter representing little or no duction but specific to binocular fusion rather than merely monocular fixation in the same eye position. As in the prior study (Demer and Clark 2018), the unit of sampling was generally taken to be the individual eye, for which parametric statistical comparisons and linear regressions were performed using GraphPad Prism (GraphPad Software, La Jolla, CA).

Although MRI was not performed in secondary gaze positions that would have permitted three-dimensional localization of the rectus pulleys from inflections of EOM paths, the anteroposterior location of pulleys is both stereotypical and minimally influential on coronal plane pulley coordinates. Assumed normal anteroposterior positions, rectus EOM centroid coordinates at these locations were taken to represent the coronal plane locations of the pulleys in the published coordinate system (Clark et al. 2000; Kono et al. 2002a). This approach was employed in prior MRI studies of fusional vergence (Demer and Clark 2018; 2014; Demer et al. 2003a).

Horizontal and vertical components of globe translation during rotation were determined at subpixel resolution from shifts of area centroids of the globe cross section in image planes spaced across the globe’s diameter (Clark and Demer 2006; Clark et al. 2000; Kono et al. 2002a; Suh et al. 2016b). Anteroposterior globe shifts were determined because of the locally linear variation in the cross-sectional area of the bony orbit (Demer et al. 2017). With the assumption that the globe is rigid, we determined the coordinates of its rotational axis from axial images before and after rotation using linear algebra derived by Eric M. Demer (Demer and Clark in press). For a point (x, y) on an eye that rotates about axis $\left(\begin{array}{c}{x}_c\\ y_c\end{array}\right)$ through angle α from initial point $\left(\begin{array}{c}{x}_1\\ y_1\end{array}\right)$ to final point $\left(\begin{array}{c}{x}_2\\ y_2\end{array}\right)$,

$$x_c=\frac{\left[x_1+x_2+\sin \left(\alpha \right)\left(y_1-y_2\right)-\cos \left(\alpha \right)\left(x_1+x_2\right)\right]}{2\left[1-\cos \left(\alpha \right)\right]}$$ (1)

$$y_c=\frac{\left[y_1+y_2+\sin \left(\alpha \right)\left(x_2-x_1\right)-\cos \left(\alpha \right)\left(y_1+y_2\right)\right]}{2\left[1-\cos \left(\alpha \right)\right]}$$ (2)

The angle of rotation α can be determined by knowing the change in coordinates of a second point on the eye that moves during rotation from initial $\left(\begin{array}{c}{x}_3\\ y_3\end{array}\right)$ to final $\left(\begin{array}{c}{x}_4\\ y_4\end{array}\right)$ coordinates:

$$\cos \left(\alpha \right)=\frac{\left(x_3-x_1\right)\left(x_4-x_2\right)+\left(y_3-y_1\right)\left(y_4-y_2\right)}{\sqrt{\left[{\left(x_3-x_1\right)}^2+{\left(y_3-y_1\right)}^2\right]\left[{\left(x_4-x_2\right)}^2+{\left(y_4-y_2\right)}^2\right]}}$$ (3)

$$\sin \left(\alpha \right)=\frac{\left(x_3-x_1\right)\left(y_4-y_2\right)-\left(y_3-y_1\right)\left(x_4-x_2\right)}{\sqrt{\left[{\left(x_3-x_1\right)}^2+{\left(y_3-y_1\right)}^2\right]\left[{\left(x_4-x_2\right)}^2+{\left(y_4-y_2\right)}^2\right]}}$$ (4)

Lever arms were computed as the distances between the ocular rotational center and muscle insertions (Demer and Clark in press).

RESULTS

Reliable vergence achieved.

Although all participants could maintain brief binocular fusion of their latent binocular misalignments during normal viewing, only about half of them could do so during the extended periods of up to 2.5 min required for MRI. Care was taken to ensure that data were interpreted only for subjects who maintained the required fusional vergence in all of the MRI views for each eye in each of the three imaging conditions, as illustrated in Fig. 3. All data reported are limited to these subjects.

Fig. 3.

Mean individual eye gaze changes (wide lines) and vergence for both eyes of 4 subjects with intermittent esotropia (A) and 3 subjects with intermittent exotropia (B). The aligned eye fixated monocularly during fellow eye occlusion, whereas the fusing eye fixated binocularly along with the fellow eye. Convergence is the difference between the horizontal angles of the converging and aligned eyes. Each symbol represents one eye. Geometric required angle is shown in gray. Error limits represent 95% confidence interval.

Vergence in intermittent esotropia.

On reaching binocular fusion, the formerly esotropic eye diverged an average of 9.2 ± 1.3° from its position in monocular fixation, not significantly different from its 8.6 ± 1.3° change in vergence state relative to the aligned fellow eye, whose position did not change significantly (Fig. 3A). Mean change in vertical positions of the diverging and aligned eyes did not differ significantly from zero.

Vergence in intermittent exodeviation.

These subjects included the subject with exophoria. On reaching binocular fusion, the eye that was formerly exotropic converged an average of 22.6 ± 2.4° from its position in monocular fixation, not significantly different from its 21.0 ± 3.5° change in vergence state relative to the aligned fellow eye, whose position did not change significantly (Fig. 3B). Mean change in vertical positions of the converging and aligned eyes did not differ significantly from zero.

Horizontal rectus function in intermittent esotropia.

Data interpretation allowed for the possibility that monocular refixation correcting the strabismic deviation might not necessarily involve the same EOM mechanisms that operate during binocular fusion. We therefore examined both cases quantitatively.

During simple divergence averaging 9.2° from the esotropic position when the eye was monocularly occluded to monocular fixation by the same eye as its fellow was occluded, there was significant contractile PPV increase in the whole LR by ~10%, similar in both LRs and LRi (Fig. 4A). In contrast, relaxational PPV decrease in the MR was compartmentally selective, being significantly greater in MRs at ~11% compared with ~3% in MRi. These trends were similar during fusional (binocular) divergence of ~8.6° (Fig. 4B). Not significantly different from zero were the position change of the aligned eye and PPV changes in the aligned eye’s LR and MR, yet a small contraction in the aligned eye’s MRs was significantly greater than a very small relaxation in MRi (Fig. 4C).

Fig. 4.

Compensation of intermittent esotropia. A–C: mean (±SE) horizontal rectus muscle contractility during fusional divergence, indicated by change in posterior partial volume, of the total medial rectus (MR) muscle and its inferior and superior compartments, and of the total lateral rectus (LR) muscle and its inferior and superior compartments. Note that in the diverging eye, both LR compartments contracted similarly, whereas the superior MR compartment relaxed more than the inferior MR compartment. P values indicate significance of differences from zero. N.S., not significantly different from zero. Statistical levels were determined by 2-tailed t-tests.

Cyclovertical muscle function in intermittent esotropia.

No changes in vertical eye position were required for target fixation or fusion. Vertical rectus muscles exhibited no significant contractile changes during abduction to the target or fusion of intermittent esotropia (Fig. 5).

Fig. 5.

Compensation of intermittent esotropia. A–C: mean (±SE) vertical rectus muscle contractility, as assessed by percent change in posterior partial volume, during fusional divergence, of the total inferior rectus (IR) muscle and its lateral and medial compartments, and of the total superior rectus (SR) muscle and its lateral and medial regions. Scale is half that for horizontal rectus muscles in Fig. 4, yet there were no significant changes for any muscle or compartment. N.S., not significantly different from zero. Statistical levels were determined by 2-tailed t-tests.

Changes in PPV of putative medial and lateral SO compartments were computed for presumed demarcation lines varying at 30° and 60° from the long axis of the ellipse best fitting the SO cross section, but for neither such angle was there a statistically significant difference between behaviors of the putative compartments for diverging abduction or fusional divergence. For the 60° compartmental demarcation angle, Fig. 6 illustrates nonsignificant trends to SO relaxation during compensation of intermittent esotropia that argue against SO contraction; effects were similarly nonsignificant for the 30° compartmental demarcation angle.

Fig. 6.

Mean (±SE) superior oblique (SO) muscle contractility, as assessed by change in posterior partial volume (PPV), during fusional divergence of intermittent esotropia. There were no significant contractile changes in PPV in either the total or medial or lateral SO compartments of either the aligned or abducting eyes for a 60° demarcation between compartments. Statistical levels were determined by 2-tailed t-tests.

Kinematics of intermittent esotropia.

The initial rotational axis was computed for the rotation from the fusion position to the esotropic position (Fig. 7A). The initial rotational axis was located 4.3 ± 0.9 mm medial to globe center, significantly more medial to globe center than the published 0.8 ± 0.9-mm axis location for adduction in normal subjects (Demer and Clark in press). However, the axis reported for the normal subjects was for a larger abduction averaging 34° rather than the divergence of ~14°; this difference might influence axis location. The anteroposterior location of the rotational axis in intermittent esotropia was similar to that in normal abduction (Fig. 7A).

Fig. 7.

Mean (±SE) ocular rotational axis location relative to globe center during fusion (A) and computed mean lever arms for the medial and lateral rectus muscles (B) during rotation from fusing to deviated positions in intermittent esotropia, and exodeviation, including intermittent exotropia and exophoria. Medial and anterior axes are positive. Comparison data are as published for 34° mean adduction and 23° aligned convergence by normal subjects (Demer and Clark in press). N = no. of orbits contributing data, applicable to both A and B. N.S., not significantly different. Statistical comparisons were performed using Student’s t-test.

The effect of eccentric rotational axis on lever arms of the MR and LR is illustrated in Fig. 7B for ocular rotation from the fusing to the esotropic positions. The MR lever arm in intermittent esotropia was similar to control adduction at 9–10 mm (Fig. 7B). However, the LR lever arm in intermittent esotropia was significantly greater at 16.2 ± 0.8 mm than the control adduction arm at 12.5 ± 0.6 mm.

Pulley positions in intermittent esotropia.

As illustrated in Fig. 8A, the coronal plane coordinates of the rectus pulleys were tightly clustered according to their anatomical designations and exhibited no evidence of torsional reconfiguration during esotropic deviation or fusion. The LR pulley was located slightly inferior to the MR pulley.

Fig. 8.

Mean (±SD) rectus pulley coordinates for all analyzed eyes in the study relative to globe center for intermittent esotropia (A) and for exodeviation, including intermittent exotropia and exophoria (B). Pulley coordinates did not significantly differ among the conditions of monocular fixing with fellow eye occluded, binocular fusion, or manifest strabismus with the eye occluded.

Horizontal rectus function in intermittent exotropia.

During simple adduction averaging 21.9° from the exotropic position when the eye was monocularly occluded to monocular fixation by the same eye as its fellow was occluded, there was a significant contractile increase in PPV in the whole MR of 24.0 ± 2.9%%, but not quite significantly greater in MRs at 32.1 ± 5.0% than 17.9 ± 4.9% in MRi (P = 0.06; Fig. 9A). The entire LR relaxed uniformly by 21.2 ± 1.3%. During fusional convergence, however, there was an overall contractile PPV increase in the MR of 18.4 ± 2.4%, driven by a 31.1 ± 6.7% increase in MRs that was significantly greater than the 10.2 ± 3.5% increase in MRi (P < 0.02; Fig. 9B). Mean convergence in the aligned eye did not differ significantly from zero, associated with absence of PPV changes in the LR and MR (Fig. 9C).

Fig. 9.

Horizontal rectus muscle contractility in compensation of intermittent exotropia, including the subject with exophoria. A–C: mean (±SE) horizontal rectus muscle contractility during fusional divergence, indicated by change in posterior partial volume, of the total medial rectus (MR) muscle and its inferior and superior compartments, and of the total lateral rectus (LR) muscle and its inferior and superior compartments. Note that in the converging eye, both LR compartments relaxed similarly, whereas the superior MR compartment contracted more than the inferior MR compartment. P values indicate significance of differences from zero. N.S., not significantly different from zero. Statistical levels were determined by 2-tailed t-tests.

Cyclovertical muscle function in intermittent exotropia.

No changes in vertical eye position were required for fixation or fusion of the target. With one exception, the vertical rectus muscles exhibited no significant contractile changes during abduction to the target or fusion of intermittent exotropia (Fig. 10). In comparison with monocular target fixation, the superior rectus (SR) muscle in the fusing eye exhibited a 6.3 ± 1.7% PPV increase, mainly attributable to a 6.4 ± 1.7% increase in the medial region (P < 0.0003). Fusion was not associated with any significant change in vertical eye position.

Fig. 10.

Compensation of exodeviation, combining intermittent exotropia and exophoria. A–C: mean (±SE) vertical rectus muscle contractility during fusional convergence, as assessed by percent change in posterior partial volume, of the total inferior rectus (IR) muscle and its lateral and medial compartments, and of the total superior rectus (SR) muscle and its lateral and medial regions. There was no significant contractile change in any muscle region, except for contraction associate with fusion in comparison with target alignment for the SR, principally in its medial region. P values indicate significance of differences from zero. N.S., not significantly different from zero. Statistical levels were determined by 2-tailed t-tests.

Changes in PPV of putative medial and lateral SO compartments were computed for presumed demarcation lines varying at 30° and 60° from the long axis of the ellipse best fitting the SO cross section, but only for 60° was there any statistically significant difference between behaviors of the medial and lateral compartments for converging adduction or fusional convergence (Fig. 11). In the diverging eye, there was significant 5.7 ± 1.6% relaxational reduction in PPV of the whole SO, mainly driven by the lateral (predominantly vertically acting) SO compartment (P < 0.0005). There were no significant PPV changes in either compartment of the aligned eye or in the entire SO.

Fig. 11.

Mean (±SE) superior oblique (SO) muscle contractility, as assessed by change in posterior partial volume (PPV), during fusional convergence of exodeviation, including intermittent exotropia and exophoria. The SO of the converging eye exhibited significant relaxational reduction in PPV, driven by the lateral compartment. The SO of the aligned eye exhibited significant relaxational reduction in PPV in the lateral compartment only. P values indicate significance of differences from zero. N.S., not significantly different from zero. Statistical levels were determined by 2-tailed t-tests.

Kinematics of intermittent exotropia.

The rotational axis was computed for the rotation from the exotropic position to fusion (Fig. 7A). The rotational axis was located −0.1 ± 0.5 mm lateral to globe center, not significantly different from the published 0.8 ± 0.3-mm lateral axis location for abduction in normal subjects (Demer and Clark in press). The anteroposterior location of the rotational axis in intermittent exotropia was not significantly different than in normal adduction (Fig. 7A). The reported axis in the normal subjects was for a 29° mean abduction, similar to the divergence of ~26°.

The effect of eccentric rotational axis on lever arms of the MR and LR is illustrated in Fig. 7B for ocular rotation from the fusing to the exotropic positions and in comparison with published data during 23° aligned convergence by normal subjects (Demer and Clark in press). The LR lever arm in intermittent exotropia was similar to control convergence at 12–14 mm, yet the LR lever arm was lower in intermittent exotropia than in intermittent esotropia (Fig. 7B). However, the MR lever arm in intermittent exotropia was significantly greater at 14.0 ± 0.3 mm than the control arm at 10.5 ± 0.4 mm (P < 10⁻⁴).

Pulley positions in intermittent exotropia and exophoria.

Similar to intermittent esotropia (Fig. 8B), the coronal plane coordinates of the rectus pulleys were tightly clustered according to their anatomical designations and exhibited no evidence of torsional reconfiguration during exotropic deviation or fusion. Again, similar to intermittent esotropia, the LR pulley was located slightly inferior to the MR pulley.

DISCUSSION

Novel findings.

The current investigation is a novel demonstration of EOM function during fusional vergence compensation of imbalances in horizontal binocular alignment that greatly exceed the vergence amplitudes of the normal human population. An average of ~10° sustained fusional divergence, approximately five times the normal maximum, was achieved for compensation of intermittent esotropia. An average of 23° sustained convergence was achieved for compensation of exodeviations, equivalent to the normal convergence required to view a target at ~10 cm and approximately the limit of what can be briefly sustained by healthy subjects.

Several important findings emerge in this work through use of MRI to evaluate EOM contractile function in intermittent strabismus. First, the activity of horizontal rectus EOMs typically differed according to transverse compartment. For example, divergence from the esotropic state to monocularly aligned state was associated with significantly greater relaxation in MRs than in MRi (Fig. 4A), whereas during fusional divergence, correcting the esotropic state was associated with significantly greater contraction in LRs than in LRi (Fig. 4B). Contractility of MRs was more than threefold that of MRi during divergence (Fig. 4A), although this difference was smaller and not statistically significant during divergent fusion (Fig. 4B). During fusional convergence correcting the exotropic aligned state, there was significantly greater contraction in MRs than in MRi (Fig. 9B), although the two compartments of LR relaxed to a similar degree (Fig. 9, A and B). During convergent fusion of exodeviation, contractility in MRs was more than threefold that of MRi (Fig. 9B), although this difference was smaller and not statistically significant during convergence (Fig. 9A). Although differences in significance level may result from limited sample size or individual variations in the severity of strabismic imbalance rather than a fundamental property of fusion, this overall pattern is consistent with the known greater role of the MRs in both normal convergence (Demer and Clark 2014) and divergence (Demer and Clark 2018).

The two LR compartments have been observed to contract similarly, without differential behavior, in normal subjects during convergence (Demer and Clark 2014) and divergence (Demer and Clark 2018). However, in the current subjects with intermittent esotropia, the much larger fusional divergence movements were associated with ~30% greater contractility in LRs than LRi that was statistically significant. Fusional divergence was not associated with significant cyclovertical EOM activity in the fusing or aligned eye, nor with cocontraction or corelaxation of EOMs in the aligned eye or torsional shifts in rectus pulley positions.

Relaxation of the LR in compensation of intermittent exotropia or large exophoria was very similar in LRs and LRi, suggesting absence of differential compartmental function in this muscle for this behavior. This compensation was also generally not associated with cyclovertical EOM activity, with exception in the aligned eye of significant contraction in the medial part of the SR and in the converging eye relaxation in the lateral part of the SO that is considered to have predominantly vertical action.

The ocular rotational axis during compensation of intermittent exotropia was significantly more posterior than for convergence in normal subjects, and much more lateral than the rotational axis in intermittent esotropia (Fig. 7). Unlike physiological convergence to a near target (Demer et al. 2003a), compensation of intermittent exodeviation was not associated with extorsional reconfiguration of the rectus pulley array.

The magnitudes of PPV changes in whole muscle MR and LR observed during fusional vergence compensation of both intermittent esotropia and exotropia were comparable to those for similar angles of adduction at ~1–2%/deg (Clark and Demer 2012b). This argues for generally similar EOM contractile function.

Historical theories of vergence.

Controversy about the neural control of vergence has simmered since the 19th century, when Helmholtz argued for the separate direction of each eye to targets in visual space so that resulting conjugacy in binocular positions would merely be learned in relationship to optical geometry (King 2011). Consistent with Helmholtz are the paramedian pontine reticular formation burst neuron recordings of King and Zhou (2000) showing that the majority encode the position of only one eye. An alternate theory of vergence is Reid’s 18th century postulate (Westheimer 2014), later popularized as Hering’s Law, that both eyes are innervated as a yoked pair, with EOMs for each eye receiving innervation symmetrically for conjugate movements but antisymmetrically for vergence (Semmlow and Wetzel 1979). Our earlier study of EOM contractility during prism-induced fusional divergence in normal subjects was supportive of neither the Helmholtz nor Hering theories, because imaging demonstrated geometrically unnecessary corelaxation of the MR and LR in the aligned eye as its fellow diverged to view the distant target (Demer and Clark 2018). However, the required fusional divergence was geometrically unrealistic in the sense that real targets never require divergence beyond parallelism of the visual axes.

The current experiment, involving vergence movements much larger than normal yet still geometrically appropriate to real target fixation, does not distinguish between the Hering vs. Helmholtz theories. However, there was contractile activity in the SR of the aligned eye during fusion and in the SO of both eyes in the absence of vertical eye position change. Such cyclovertical EOM activity is likely to have been required for torsional movement that is kinematically necessary for convergence in real visual space (Hess and Misslisch 2016). No torsional changes in the rectus pulley array were observed in either eye in the current experiment, unlike the extorsion of the pulley array of the eye aligned on target when its fellow executed normal convergence to a near target (Demer et al. 2003a).

Eccentric ocular rotational center.

As early as 1862, Donders recognized that the eye does not rotate about its geometric center (Donders 1999), an eccentricity confirmed by optical methods a century later (Fry and Hill 1962). With the exception of the Orbit 1.8 model by Miller et al. (1999) that permits limited globe translation during rotation, this insight of eccentric rotation has until very recently been largely ignored by ocular motor physiologists and modelers, who first for convenience and then presumably out of habit assumed oculocentric rotation. The center of ocular rotation can be substantially eccentric relative to the normal eye’s roughly 12-mm radius (Demer and Clark in press). This means that the eye translates as it rotates, “rolling” nasally in adduction and temporally in abduction. The location of the ocular center of rotation thus depends to some extent on the particular rotational eye positions under consideration, so the kinematic consequences of eccentric rotation can be both complex and dependent on both the directions and starting angles of ocular rotation. Although the data in Fig. 7 should thus be interpreted cautiously given that the initial conditions and rotational angles were not precisely matched, certain implications seem plausible. For example, the computed ocular rotational center was ~1 mm anterior and 1 mm medial to initial globe center in conjugate adduction, implying lever arms for the MR and LR of ~8 and 12.5 mm, respectively. Rotational torque is the product of the tension and lever arm of each EOM, with a cosine correction for nontangential force application at the insertion. Total torque is strongly dominated for horizontal eye rotation by the torques of the LR and MR. For rotational equilibrium in which LR and MR torques are assumed equal, this requires MR tension to be ~56% greater than LR tension but, during rotation, MR length change to be only 64% of LR length change.

The rotational axis for fusional divergence in intermittent esotropia was much more medial to globe center, ~4 mm, than was the case for adduction, increasing MR lever arm slightly to ~9 mm but LR lever arm markedly to ~16 mm (Fig. 7). Such an increase in LR lever arm enhances the relative abducting torque of LR contraction, requiring the MR to develop 78% more tension to balance it; the situation is greatly to the advantage of divergence. If the same shift in rotational axis occurred in normal fusional divergence for distant targets, it might at least in part explain how the LR can achieve this abduction despite failure of any relaxation by the MR (Demer and Clark 2018).

In normal convergence, the MR lever arm is ~10 mm and the LR lever arm ~12 mm (Fig. 7), requiring that the MR develop ~20% more tension than the LR to balance it. During fusional convergence of intermittent exotropia, however, the ocular rotational center shifted ~3 mm posteriorly (Fig. 7A), increasing the MR more than the LR lever arms so that both became about equal at 14 mm (Fig. 7B). The relative increase in MR lever arm would have enhanced adducting torque without additional MR tension.

Overall, changes in ocular rotational center appear to augment EOM contractility and thus promote fusional vergence in both intermittent esotropia and intermittent exotropia. Such changes in rotational center are equivalent to coordination of ocular translation with rotation and must be under active control by muscle effectors. Such muscle effectors might include the striated orbital layers of the rectus and oblique EOMs that insert on the connective tissue system that suspends the globe (Demer et al. 2000). However, the shift in ocular rotational center may not be actuated by the striated EOMs. Another candidate actuator may be the smooth muscle (SM) present in the pulley suspensions of the medial orbit, particularly in a band from the IR to MR pulleys (Demer et al. 1997; Kono et al. 2002b; Miller et al. 2003) and extending from the MR pulley superiorly toward the SR pulley (Demer et al. 1997). Most SM between the MR and IR pulleys is composed of 30- to 40-μm-diameter bundles oriented anteroposteriorly, whereas most SM between the MR and SR pulleys has a superior-to-inferior orientation in 10-μm-diameter bundles (Kono et al. 2002b). The SM receives autonomic innervation (Demer et al. 1997). Relaxation of SM tonus near the MR pulley could loosen the MR pulley’s elastic suspensions mediolaterally so as to increase nasal globe translation during adduction, or directly translate the globe’s rotational center medially as observed. To date, it has not been possible to study the contractility of the SM in vivo, and its central innervational control is unknown. It seems possible that the physiological mechanisms responsible for control of ocular rotational axis might be capable of changing state in anticipation of a future ocular rotation or consensually in an aligned eye during rotation by its fellow. The actual kinematic effect in such cases could not be measurable, because a rotational center cannot be determined empirically until some rotation has in fact occurred. However, measurable changes in EOM tensions to maintain torque balance might be necessary in the event of a change in ocular rotational center. This phenomenon might explain the mysterious observation of co-relaxation of the horizontal rectus EOMs in the aligned eyes of monkeys during asymmetrical convergence (Miller et al. 2002, 2011).

GRANTS

This work was supported by National Eye Institute Grant EY008313. J. L. Demer received an unrestricted award from Research to Prevent Blindness and is Arthur L. Rosenbaum Chair of Pediatric Ophthalmology.

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the authors.

AUTHOR CONTRIBUTIONS

J.L.D. conceived and designed research; J.L.D. performed experiments; J.L.D. and R.A.C. analyzed data; J.L.D. interpreted results of experiments; J.L.D. prepared figures; J.L.D. drafted manuscript; J.L.D. and R.A.C. edited and revised manuscript; J.L.D. and R.A.C. approved final version of manuscript.