Neural plasticity lies at the heart of orthoptics rehabilitation of neuromuscular disorders of the visual system. These disorders include many forms of strabismus, sluggish ocular focusing, or accommodation. Neural plasticity also compensates for natural aging of the ocular lens (incipient presbyopia), growth of the cranium and separation of the two eyes during childhood, environmental factors including spectacles that magnify retinal images unequally in the two eyes (aniseikonia), and mismatched stimuli for accommodation and convergence that are presented by virtual reality (volumetric) computer displays. Many of these conditions are compensated with a natural calibration process that occurs automatically and without effort to optimize visual performance. However, some of them present a difficult challenge, and they require the assistance of orthoptics to facilitate adaptation of natural reflex interactions that coordinate voluntary and involuntary binocular motor responses.
The near-reflex oculomotor interactions are analogous to the body's postural reflexes that maintain the balance when we walk. We take voluntary steps while our hips and shoulders reflexively counter rotate. If we pick up a bag of groceries with one hand, we automatically adjust the postural cross-coupling between voluntary steps and involuntary torso reflexes while walking in response to the increased load and change in body's center of gravity. Throughout life, the oculomotor system makes similar adjustments of binocular reflex interactions in response to the natural challenges in ordinary conditions such as the effects of development, aging, optical environmental factors, and acquired disorders including disease and trauma.
The Role of Orthoptics in Calibrating Ocular Postural Reflex Interactions
Some developmental conditions, environmental conditions, and acquired disorders disrupt the normal cross-coupled motor responses to an extent that the reflexes cannot be calibrated on their own by adaptation under natural conditions. Under these circumstances, orthoptics is prescribed to perform repetitious exercises to adjust and reinforce Hebbian-like synapses1 that control the cross-coupling interactions between voluntary and involuntary eye movements.2 Orthoptics exercises are similar to the repetitive training required for athletes to excel in a sport. Orthoptics facilitates the body's natural adaptive mechanisms to correct mismatches between motor responses and environmental stimuli. The scope of this aspect of orthoptics is determined by the range of natural adaptive processes that are available to the visuomotor system. The exploitation of these adaptive mechanisms by orthoptics is limited to our awareness of them, possible critical periods for their development, their range of plasticity, effects of aging, and some understanding of how they operate. This information provides the field of orthoptics with the means to rehabilitate and manage sensory-motor anomalies of the visual system.
The Near Response
Most motor calibration processes work thorough a cross-coupling of involuntary responses with voluntary motor systems as observed with postural spinal reflexes. Effective orthoptics procedures calibrate cross-coupled interactions between voluntary and involuntary motor functions that are associated with one another. Binocular alignment is controlled by several cross-coupled interactions between voluntary and involuntary motor systems, which are collectively referred to as the near response.3 The two eyes automatically focus to near distances when they voluntarily converge (convergence accommodation, Ref. 4) and they automatically converge when they voluntarily focus to a near distance (accommodative convergence, Ref. 5). Similarly, when we voluntarily fixate in a tertiary direction of gaze, we automatically make involuntary vertical vergence adjustments of our two eyes even when one eye is occluded.6,7 This vertical adjustment is necessary because objects at finite viewing distances in tertiary gaze lie at unequal distances from the two eyes, and they subtend unequal retinal image sizes and vertical disparity (Fig. 1). For example, if we look at a near target that is up and to the left, it is closer to the left than the right eye, and it subtends a larger angle at the left eye. The left eye needs to rotate up more than the right eye in Fick coordinates to align the two eyes. Similarly, when we look up and down while converging at a near distance, the two eyes need to twist in opposite directions about the visual axes to keep the horizontal meridians of the two retinas aligned, so that we can sense binocular disparity and have good stereopsis.8 The involuntary twist or torsion of the eyes varies with voluntary eye elevation and azimuth, and it occurs to keep stereo images formed on matched or corresponding regions of the two retinas.9 This change in torsion with convergence and gaze elevation is described as a modification of Listing's law, which is necessary to keep the horizontal retinal meridians aligned (coplanar) in the visual plane.10 Similarly, when the head is tilted (rolled from side to side), there are vertical and torsional adjustments of the eyes stimulated by the otoliths that transduce head position and keep the eyes aligned and oriented near earth vertical. The ocular counter roll is only about 10% of head tilt. A more important calibration is of binocular torsion to minimize cyclodisparities. When these reflexes are abnormal, a head tilt can cause one eye to move downward and the other upward (skew movement), such as in the ocular tilt response and in the superior oblique palsy.11 In these cases, the cross-coupled interactions among otolith activity, vertical vergence, and cyclovergence need to be kept calibrated (Fig. 1).7
Optimal Cross-Coupled Interactions of the Near Response for Three-Dimensional Viewing Geometry
Cross-coupled interactions between voluntary and involuntary components of the near response are based on predictable relationships between version and vergence components of eye position that reduce retinal image disparity in the fixation plane to nearly zero. Vergence has 3 dF described by horizontal, vertical, and cyclovergence. Two of these, vertical and cyclovergence, are involuntary responses, whereas horizontal vergence is under both voluntary and involuntary control.
Coupling interactions between voluntary and involuntary oculomotor responses have been described for all three components of vergence.3 Scale factors are used to describe the couplings quantitatively. The predictable relationship between viewing geometry and binocular disparity determines the linear scaling of cross- coupling interactions between involuntary vergence responses and voluntary version and horizontal vergence. Horizontal, vertical, and torsional disparities are determined by the target location and the coordinate systems that describe the control of horizontal and vertical eye position.7 The main benefit of the cross-coupling is to synchronize motor responses to achieve simultaneous, clear, and single binocular vision.
Horizontal Vergence Coupling
The horizontal component of vergence is under both involuntary and voluntary control and can be guided by voluntary accommodation to selected targets (accommodative convergence). This is useful under conditions where an occluder, such as the nose, blocks one eye's view of a target. The linear coupling between accommodation and convergence is a consequence of both the motor systems, responding to optical-geometric properties of a common viewing distance. The coupling between horizontal convergence (C) with the accommodation response (A) to defocus is described by the accommodative vergence ratio (Kc), which is also referred to as the AC/A ratio.
A Kc of 1.0 for symmetrical convergence, expressed in meter angles and accommodation in diopters, represents an ideal situation where the magnitude of responses by convergence and accommodation is matched to the same viewing distance. Empirical measures demonstrate a normal Kc = 0.66 MA/D.5 Accommodation (A) can also follow convergence responses (C) to binocular disparity (convergence accommodation) with a different empirical scalar value (Ka) of 1.0, as described by the CA/C ratio.4
The ideal Kc and Ka change with gaze azimuth.12 Ideal Kc is lower and ideal Ka is higher for targets viewed in eccentric horizontal gaze than in symmetrical convergence, because the amplitudes of stimuli for accommodation and convergence change unequally when gaze is shifted laterally from straight ahead. Different circles describe constant stimuli with gaze azimuth for accommodation and convergence. Fig. 2 illustrates the isovergence circle and isoaccommodation circle that intersect one another in the midsagittal plane, but differ elsewhere. Iso-vergence refers to a constant vergence angle with azimuth, and iso-accommodation refers to a constant mean accommodative stimulus to the two eyes with azimuth.12 Empirical measures of Kc follow these changes in the ideal Kc with azimuth. The empirical Kc reduces and a bias of Ka (a DC elevation in convergence accommodation without changing the CA/C ratio) increases with increasing horizontal eccentric gaze in asymmetric convergence.12 The low empirical value of Kc is also a compromise of several different gaze azimuths.
Vertical Vergence Coupling
Binocular vertical alignment of foveal images is controlled by vertical vergence. In a Fick coordinate system, which is often used to describe vertical disparity,13 the amplitude of vertical vergence is scaled proportionally with the vertical image size ratios of the two ocular images of a target viewed in a tertiary direction.7,14,15 In this application, vertical vergence is quantified as the ratio of vertical positions of the left and right eyes (Vl/Vr) that is necessary for bifoveal fixation of elevated targets in tertiary directions of gaze. In symmetrical convergence, the ratio equals 1.0, and in asymmetric convergence, it depends on both convergence (C) and horizontal gaze eccentricity or azimuth (H). Convergence is positive after a sign convention where left and down are positive values and where convergence equals R-L eye position. In left gaze, the ratio of left over right eye position is described by
where Hl and Hr represent the azimuth of the left and right eye, respectively, relative to primary position, and Vl and Vr represent the elevation of the left and right eye in Fick coordinates, respectively, and Kv equals the gain of vertical vergence. Empirical measures demonstrate a normal scalar value of Kv = 1.0.7 Note that when vertical vergence is described in a Helmholtz coordinate system, then the relationship is simplified and Vl/Vr is independent of convergence or gaze angle.7
Kv = 1.0 for both the Fick or Helmholtz coordinate systems where the vertical rotation of the two eyes is equal. As stated above, a Kv of one alone aligns the two eyes at zero disparity in the Helmholtz coordinate system, but not in the Fick coordinate system in which the abducting eye must elevate more than the adducting eye to achieve binocular alignment in tertiary gaze.
Nearly one and a half centuries ago, Donders16 recognized that the torsional orientation of the eyes in any given direction of gaze was independent of the path the eyes took to reach that position. This was noteworthy because spherical rotations of physical objects like satellites are normally non-commutative, i.e., the twist about the primary depth axis depends on the path taken to reach a tertiary direction.17 Thus, rotating a satellite camera to view the moon with an earth perspective, from a given orbital position, requires 3 dF. The amount of ocular torsion was quantified by Listing as though the eye had rotated from a primary position about an axis that was in a common plane with other axes of rotation from primary position (Fig. 3, top). The orientation of the axis is orthogonal to a plane containing the primary position and the direction of eccentric gaze. Rotations about these polar axes are referred to as rotation vectors.16 Helmholtz18 referred to this as Listing's plane and, as shown in Fig. 3 (top), the plane lies in the facial plane, orthogonal to primary position. Listing's law describes a coupling between cyclotorsion and versional eye position that makes spherical rotations of the eye appear commutative (i.e., eye position and orientation can be described with only 2 dF-horizontal and vertical position). Normally, rotation vectors and the orientation of Listing's planes are used to describe ocular torsion and cyclovergence with only 2 dF (axis orientation in Listing's plane and magnitude of rotation).
Horizontal and vertical vergences are better described by Cartesian coordinate systems, referred to Fick and Helmholtz, respectively; however, these coordinate systems use 3 dF (vertical rotation about an ocular horizontal axis, horizontal rotation about a vertical ocular axis, and torsional rotations about the visual axis). Because Fick and Helmholtz coordinate systems are non-commutative, the order of rotations determines the resulting eye position. Helmholtz rotations start with a vertical rotation from primary position about the horizontal axis, followed by a horizontal rotation about the ocular vertical axis, and then a torsional rotation about the visual axis. The result is that all horizontal Helmholtz movements (version and vergence) at a constant gaze elevation lie in a flat plane and a straight horizontal line in the tangent screen (iso-elevation line), so that single points in space can fall on corresponding retinal points without introducing vertical disparity.19 Note that iso- azimuth lines, corresponding to a constant gaze azimuth, are curved on the tangent screen. Another advantage of the Helmholtz system is that equal amplitude vertical rotations of the two eyes are used to fixate any target in tertiary gaze. The imaging of tertiary targets on corresponding points without vertical disparity and equality of vertical eye rotations to fixate targets in tertiary gaze are not possible in a Fick system. Fick rotations are customarily used to describe eye position, perhaps because they are more intuitive than Helmholtz coordinates because they are the same as the coordinate system that moves the head horizontally about an earth-fixed vertical axis (the neck) and vertically about a head-fixed horizontal axis (interaural axis). Fick rotations start with a horizontal rotation from primary position about the vertical axis, followed by a vertical rotation about the horizontal ocular axis, and then a torsional rotation about the visual axis. The result is that all vertical Fick movements at a given gaze azimuth lie in a flat plane and along a straight vertical line in the tangent screen (iso-azimuth line). This makes measurement of vertical movements on the tangent screen convenient; however, at near-viewing distances, binocular fixation of elevated points on the tangent screen require different amplitude elevations of the left and right eye in Fick coordinates. Iso-elevation lines, corresponding to a constant gaze elevation, are curved on the tangent screen. Schreiber and Schor19 published a web-based graphic tool that illustrates these characteristics of the Listing, Fick, and Helmholtz coordinate systems with binocular eye movements.
The orientation of Listing's planes changes with convergence (Fig. 3, bottom). Hering20 first observed a binocular coupling among horizontal vergence, eye elevation, and cyclovergence. He observed that during convergence in upward gaze, the eyes were intorted, and in downward gaze, they were extorted, which is relative to the orientations predicted by the orientation of Listing's planes located in the facial plane.21 In a Fick coordinate system, incyclovergence forms an “A” pattern between the vertical meridians of the retinas, and excyclovergence forms a “V” pattern. This coupling between cyclovergence and eye elevation during convergence is part of the near response.3
During convergence, ocular torsion is still described as commutative, as though the eyes had rotated about axes in two fixed Listing's planes, one for each eye, from their respective primary positions. However, the orientation of the empirically measured Listing's planes is different from the orientation of the classical or theoretical Listing's planes that lie in the facial plane when the eyes view distant targets. During near fixation, ocular torsion has a different pattern in which the eyes incycloverge in upward gaze and excycloverge in downward gaze. These changes follow Listing's law for Listing's planes that are diverged for the right and left eye by approximately the amount that the eyes have converged (Fig. 3, bottom).10,22–25 The benefit of this change in cyclovergence with vertical gaze and convergence is to enhance stereopsis by keeping the horizontal retinal meridians coplanar within the visual plane.
Coupling between cyclovergence and the combination of vertical gaze and convergence is optimized to match 3-D viewing geometry. During symmetrical convergence, the torsional alignment of the horizontal meridians of the retinas is controlled by cyclovergence (T) that is scaled proportionally by Kt with combinations of convergence (C) and vertical eye position (V). Following a right-hand rule sign convention, left, down, and clockwise ocular rotations are positive, and convergence equals R–L eye position. Eye position is described in Helmholtz coordinates so that foveal alignment is achieved by equal elevation of the two eyes. The cyclovergence necessary for coplanar alignment of the planes of regard is described by24
When expressed in radians, it is24
The coupling between the diverged orientation of Listing's planes and convergence can be described by the scalar Kt as a ratio of the change in divergence difference between the two eyes' Listing's planes (ΔY) over the change in convergence (ΔC).
To What Degree Can the Near-Response Couplings Be Modified in Response to Sensory Demands Placed on Binocular Vision?
Plasticity has been demonstrated for all three components of vergence couplings. The gain of the accommodative-vergence coupling can be increased or decreased by adapting to appropriate mismatches between the stimulus to accommodation and convergence.26–29 Mismatches between accommodation and vergence stimuli have been produced with a telestereoscope (Fig. 4) that increases the stimulus to convergence and decreases the stimulus to accommodation by using mirrors that optically widen the interpupillary distance. The stimulus to convergence increases proportionally with the effective interpupillary distance, whereas the stimulus to accommodation is not appreciably affected. After wearing this apparatus for 1 h, the scalar (Kc) relating convergence and accommodation in Eq. 1 increases 75% from 0.66 to 1.16.26 The ratio has also been lowered by reducing the stimulus for convergence, whereas increasing the stimulus to accommodation in a binocular head-mounted video display28 and with a telestereoscope that optically narrowed the interpupillary distance.29 However, note that adapting to decrease the AC/A ratio is much more difficult than adapting to increase the AC/A ratio.26 This asymmetry could result from a developmental bias that adjusts interactions between accommodation and convergence to compensate for the increase of the interpupillary distance during childhood.
Vertical vergence can be adapted to either increase or decrease in tertiary gaze and to vary with convergence in response to appropriate optical distortions.30,31 Vertical disparity, produced by optical geometry in tertiary gaze (Fig. 5), can be exaggerated by placing a magnifier over the abducting eye in asymmetric convergence. Schor and McCandless30 used an apparatus that introduced a 6% magnifier over the right eye in right gaze and over the left eye in left gaze. Subjects alternated fixation for 1 h between targets that were separated horizontally and vertically by 28°. The magnifiers produced vertical disparities, whose sign depended on both horizontal and vertical eye position (Fig. 5). The magnifier stimulated an increase in Kv in the right field of gaze and a decrease in Kv in the left field of gaze. Consistent with these stimuli, after adapting to the 6% magnifiers, the ratio of vertical (right/left) eye positions (Kv), measured under open-loop conditions, changed in the predicted direction from 1.0 (Helmholtz coordinates) by 2.6% (Fig. 6). The result demonstrates that vertical vergence, measured subjectively under open-loop conditions, can be modified to vary with specific combinations of horizontal and vertical eye position.
In another experiment, Schor and McCandless30 varied vertical disparity by placing an 8% vertical magnifier over the right eye when viewing two targets separated vertically by 28° and an 8% vertical magnifier over the left eye when the eyes viewed the same two targets through 15 base-out prism that stimulated approximately 8.5° of convergence (Fig. 7). The stimulus produced an aftereffect that was measured under open-loop conditions for vertical vergence. Vertical vergence was rendered open loop to control horizontal vergence with long vertical lines, presented binocularly to control convergence and gaze azimuth and a small cross, and presented monocularly to control elevation of the right eye without any fusion cues for vertical vergence. The vertical position of the left eye was measured subjectively with a flashing-foveal probe (point source) presented monocularly to the left eye. The elevation of the point source was adjusted to appear at the same elevation as the fixation-cross presented to the right eye. Targets to the two eyes were isolated with anaglyphic red-green filters. The ratio of Vl/Vr for open-loop measures of vertical eye position varied with convergence. The ratio was <1.0 without convergence and >1.0 with convergence (Fig. 8). In both the experiments, the vertical phoria changed by approximately one-half of the optically induced vertical disparity. The results demonstrate plasticity in the coupling between vertical vergence and specific combinations of vertical and horizontal eye position and horizontal convergence.32
Variations of open-loop cyclovergence responses (cyclophoria) with gaze elevation and convergence also exhibit plasticity in response to environmental factors such as the natural variation of torsional disparities with changes in vertical eye position.33 Two adaptation procedures were conducted; one that exaggerated the normal pattern of distance-dependent cyclovergence changes in cyclophoria with gaze elevation and another that reversed the pattern. In the exaggerated condition, 5° cyclodisparities were presented in the midsagittal plane with excyclodisparity in 10° upward gaze and incyclodisparity in 10° downward gaze during far fixation (zero convergence), and the opposite pattern of cyclodisparity with vertical eye position was presented in near fixation (10° convergence). In the reversed condition, the pattern of cyclodisparities was opposite to that in the exaggerated condition. The two patterns of cyclodisparity are shown schematically in Fig. 9 (top and bottom). The disparate fusion patterns, inset in Fig. 9, consisted of a 53° rectangular grid with three concentric circles superimposed on its center. The subject viewed the targets sequentially from one position to theother, approximately at 10-s intervals for a 2-h period.
Fig. 10 illustrates an example of preadapted front and top-down (plan) views of displacement planes for a straight-ahead reference direction of the right and left eye. The planes represent Listing's planes, they are roughly frontoparallel and do not diverge from one another. Changes in the horizontal yaw rotations about the vertical axes of Listing's planes were used to quantify the changes produced by the two training procedures. Fig. 11 plots preadapted and postadapted measures of yaw-tilt differences (YTD) in Listing's planes for the reversed and exaggerated conditions. The light lines connect premeasures and postmeasures for individual subjects, and the solid line plots the mean result. Positive YTDs between primary positions represent an increase in excyclovergence in down gaze and a divergence of the right and left Listing's planes. Results after training that conformed to the torsional disparity pattern presented in the reversed training condition would be expected to have an increased positive or decreased negative YTD at the far distance and a decreased positive or increased negative YTD at the near convergence distance.
The changes in the YTD between Listing's planes can be described as gain changes, where the change in primary position vergence angle (YTD) is divided by the change in horizontal vergence angle (see Eq. 7). On an average, the exaggerated adaptation condition increased K by half as much as it was decreased in the reversed adaptation condition. The smaller average change in K in the exaggerated than reversed condition is likely due to the difference in spread of cyclophoria aftereffects from trained to non-trained horizontal directions of gaze. In the exaggerated condition, aftereffects were seen mainly in the trained center direction, whereas in the reversed condition they spread to non-trained horizontal gaze eccentricities of 5° and 10°. The gain of the aftereffects measured in the exaggerated and reversed conditions was similar in the trained directions of gaze. However, in the displacement plane analysis, all horizontal positions are included resulting in a smaller aftereffect for the exaggerated condition. There is also a bias to adapt more readily to incyclovergence than excyclovergence stimuli, perhaps in response to an excyclophoria bias at birth.33 The results of the exaggerated condition clearly demonstrate that it is possible to selectively adapt the vertical-cyclophoria gradient in a specific horizontal direction of gaze.
What Mechanisms Underlie Adapted Changes in the Near Response?
Convergence and Accommodation
The coupling between accommodation and convergence can be modified by interactions between the various subcomponents of these two motor systems. Both accommodation and convergence have dual modes of control (Fig. 12).34 A rapid phasic component responds to both perceptual and retinal cues to distance, and adaptable tonic components store activity of the phasic systems.35 The phasic element enables rapid changes in motor responses to obtain clear and single binocular vision at selected viewing distances. However, the phasic system lacks durability and fatigues easily. It also has a very limited range of a few diopters or a few degrees that it can comfortably sustain. The slower tonic system extends the range of the fast system, so that we can accommodate or converge over larger amplitudes and maintain these large responses to static or slowly changing stimuli for long periods of time. Phasic and tonic mechanisms are described as a serial arrangement in a negative feedback loop that keeps their summed response from exceeding the stimulus amplitude. There is a trade-off between phasic and tonic responses such that when the tonic adaptation increases, the stimulus to the phasic systems is reduced, and its response is lowered.
The coupling between the two systems is stimulated principally by the phasic component, and adaptable tonic responses do not directly stimulate the cross-couplings.34,36,37 Consequently, the cross-coupled activity between accommodation and convergence is greater in response to rapid (phasic) than gradual (tonic) dynamic responses.34 In addition, the tonic adapters respond to both direct and cross-coupled phasic activity of accommodation and convergence. Factors that reduce tonic activity of one system (accommodation or convergence), such as fatigue after rapid alternating changes in viewing distance (flipper exercises), cause cross-coupled activity of the fatigued system to be elevated and the cross-coupled activity of the non-fatigued system to be reduced.38 For example, fatigue of adaptable tonic accommodation, produced by repeated stimulation of accommodation, causes the AC/A ratio to increase and the CA/C ratio to decrease.38 It is also possible for repeated stimulation of accommodation to cause greater fatigue of tonic vergence than tonic accommodation because the cross-links activate the tonic component of the receiving system (i.e., convergence).38 In this case, the AC/A would be reduced and the CA/C ratio increased. Which system gets fatigued (if not both) could depend on many factors, including the number of near response neurons mediating tonic vergence and accommodation. It is only when susceptibility to fatigue of accommodation and convergence are imbalanced, fatigue can influence the cross-coupling gains, and these conditions are usually earmarked by abnormally high or low gains before fatigue. The effect of fatigue is to normalize both the directions of the cross-link interaction.38 Thus, the magnitude of the cross-coupled interaction can be modulated by the relative activity of the adaptable tonic components of accommodation and convergence.
How might the changes in orientation of Listing's planes be accomplished? Physiological studies indicate that simple gain changes of the extraocular obliques and perhaps the vertical recti might be involved. Mays et al.39 found that convergence-dependent changes of cyclovergence with gaze elevation were associated with a reduced discharge rate of trochlear motor neurons and an implied relaxation of the superior oblique muscle during convergence. The modulation of trochlear activity with convergence varies systematically with gaze elevation and is largest in downward gaze. The fact that these authors observed no net increase in trochlear activity when the eyes incyclorotated with eye elevation during convergence indicates that the forces of other vertical ocular muscles were modulated during convergence to account for torsional adjustments in upward directions of gaze. Enright's40 measures of ocular translation also suggested that the superior oblique relaxes during convergence.
This model was tested by simulating 3-D eye position with Orbit, a biomechanics model that simulates binocular eye position based on the relationships of the six extraocular muscles, their tendons and supportive connective tissues including muscle sheaths or pulleys, innervation level, and motor nucleus connection weights (innervation gain) according to equations given, in part, by Miller and Robinson,41 Robinson,42 and Miller and Demer.43 Orbit was designed to follow both Hering's and Listing's laws for distance viewing, but currently does not automatically implement the binocular extension of Listing's law observed during convergence. Simulations were conducted with 15% gain reductions to the obliques and 15% gain increases to the vertical recti. In this simulation, the bilateral innervation to the medial recti was increased and that to the lateral recti was decreased to produce 20° of convergence. Hering's law was simulated by finding the innervation to an assumed normal-following eye that would produce the same gaze direction as that of the fixating eye. Orbit simulates binocular alignment when the two eyes are dissociated (i.e., vergence is open-loop), such that one eye fixates various target directions, whereas the following eye is guided by Listing's and Hering's innervations. Parameters of either eye or both the eyes may be modified, and torsion is allowed to deviate from Listing's law in both the fixating and following eye.
Eye positions were simulated during 20° of convergence, whereas versional gaze position was varied over +30° horizontally and vertically from the point of fixation. The simulated eye positions were converted from Fick coordinates to rotation vectors and fit to planes. Without any gain adjustments, the resulting orientation of Listing's plane at the near convergence distance was frontoparallel. With gain adjustments for obliques and vertical recti, the primary positions diverged by 20° for a simulated convergence of 20° (Fig. 13).
These gain changes might be modified to describe the adaptive plasticity of Kt (Eqs. 5 and 6). The empirical adaptation results of the exaggerated condition could be simulated with greater gain changes of obliques and vertical recti, and the results of the reversed condition could be simulated with smaller gain changes. The simulation demonstrates that simple convergence-related gain changes of the vertical ocular muscles are sufficient to transform the innervation pattern appropriate for torsion at far-viewing distances into ones consistent with Listing's extended law at near-viewing distances. These results strongly suggest that Listing's extended law for near-viewing conditions responds to perceptual demands of binocular vision and that these modifications result from the combination of a central neural process and passive forces determined by biomechanical properties of the orbit.
Vertical Vergence in Tertiary Gaze
In the simulations of Listing's extended law described in the previous Cyclovergence section, vertical eye alignment was preserved in tertiary gaze during the gain adjustments to the vertical recti and obliques, which produced the binocular extension of Listing's law. The simulation suggests that for normal eye alignment, it is not necessary to alter the innervation to vertical vergence to obtain binocular alignment of tertiary targets at near- and far-viewing distances,14 because orbital mechanics automatically produces vertical eye alignment. In this simulation, the yoked innervation for vertical eye position to the following eye is the same as during distance fixation with parallel lines of sight, but orbital mechanics produces a different elevation of the two eyes when horizontal position of the following eye is modified by asymmetric convergence. As a consequence, the same innervation aligns the lines of sight with distant or near tertiary targets when the fixing eye is aimed in a direction common to both target distances. For normal eye alignment, it is not necessary to alter the innervation to vertical vergence to obtain binocular alignment of tertiary targets at near- and far-viewing distances.7,15 The simulation suggests that binocular vertical eye alignment is primarily a consequence of Hering's law and the passive biomechanics of the oculomotor system.40,43,44
Vertical Vergence Adaptation
As described above in the adaptation section, the normal pattern of vertical eye alignment in tertiary gaze can be exaggerated by adapting to magnification differences between the two ocular images that varies with convergence and azimuth gaze direction.30,32 Adaptation of vertical vergence could be the consequence of convergence-dependent gain alterations of the vertical extraocular muscles without regard to position of the eye in the orbit. Changes in vertical vergence can be simulated with Orbit by altering the gains of the vertical ocular muscles. For example, if the gains of the left and right superior obliques are decreased 15% and the gains of the left and right superior recti are increased 15%, the normal changes of vertical phoria, described in Fick coordinates as a ratio of Vl/Vr, increase by 5%.
It is possible for vertical phoria to adapt to a non-monotonic change in vertical disparity with vertical version-gaze elevation (e.g., right-hyper in up gaze, right-hypo in central gaze, and right-hyper in down gaze). Vertical phoria can also adapt to non-monotonic changes in vertical disparity with convergence (distance of gaze).45 Non-linear couplings have been modeled with lookup tables or an association matrix that, for example, can be used to describe vertical vergence innervation driven by various combinations of horizontal and vertical eye position that are coded by neurons in the nucleus prepositus and in the nucleus of Cajal, respectively (Fig. 14).30,32,45 Such a computation could occur in the cerebellum. This adaptive mechanism could calibrate vertical eye alignment and compensate for changes in orbital biomechanics. Similarly, it is possible to adapt vertical vergence to specific combinations of head roll and eye elevation. For example, it is possible to adapt a left-hyper vertical phoria in up gaze and a left-hypo vertical phoria in down gaze when the head is rolled to the left, and the opposite pattern of vertical phorias with gaze elevation when the head is tilted to the right.46 This illustrates that head position dependence and eye position dependence of vertical skew are not independent processes, but that combinations of otolith-related head position and eye position are taken into account in determining binocular vertical eye alignment.
Neural Control Is Simplified by the Organization of the Physical Plant (Orbital Mechanics)
Binocular control of cyclovergence and vertical vergence results from a calibrated neuromuscular interface. Binocular eye alignment is achieved by matching the innervation for horizontal, vertical, and cyclovergence to the physical constraints set by the extraocular muscles and orbital connective tissues. Orbital mechanics are organized to simplify the neural control needed to achieve precise cyclovergence and vertical vergence. Although cyclovergence varies with convergence and vertical eye position, the gain of the vertical muscles only needs to be modified with convergence, and orbital mechanics automatically constrain cyclovergence with eye elevation. Similarly, in tertiary gaze, vertical vergence varies with both convergence and horizontal gaze direction to null vertical disparity in different gaze elevations. In natural viewing conditions, orbital mechanics constrains vertical vergence in tertiary gaze and achieves binocular alignment during convergence with the same innervation patterns used to align the eyes when viewing distant targets that do not subtend vertical disparities. In cases of pathology or optical distortion, it is possible to modify the open-loop innervation to vertical vergence to achieve binocular alignment.
Implications for Orthoptic Rehabilitation of Oculomotor Disorders
Orthoptics can rehabilitate several binocular disorders by adaptive recalibration of cross-coupled interactions that characterize the near response. Many orthoptics techniques are already well established whereas others are suggested by adaptation research and yet to be fully applied. Examples of the application of adaptation techniques to rehabilitation of several disorders are discussed below.
Anisometropic spectacle corrections magnify the two ocular images unequally and result in non-concomitant variations in horizontal and vertical phorias with direction of gaze (anisophoria).47 Initially, anisometropes corrected with spectacles make vergence errors during versional movements to eccentric targets, because the eyes follow Hering's law of equal innervation to the extra ocular muscles, but one eye views a larger image. The resulting binocular disparity errors can be easily corrected in horizontal gaze by horizontal disparity-vergence eye movements. However, vertical disparity-vergence eye movements are too slow to effectively correct binocular disparities produced by vertical anisophoria, and recalibration is necessary.48,49
Normally, the oculomotor system is capable of recalibrating Hering's law to compensate for optically induced anisophoria. For example, anisometropic patients wearing bifocal spectacle corrections with the lens addition below the optic center do not exhibit the predicted change in vertical heterophoria while near-viewing in down gaze.50,51 Adjustments of vertical heterophoria in all directions of gaze occur in approximately 2.5 h for unequal ocular magnification up to 10%.52,53 Differential ocular magnification that exceeds 10%, such as observed in monocular aphakia corrected with spectacles or spectacle-contact lens combinations,54 are extremely difficult to adapt. These magnification differences set an upper limit to the degree of optically corrected anisometropia that will not disrupt binocular eye alignment. It is likely that patients with symptoms of aniseikonia, when corrected with spectacle lenses, are simply unable to adapt to restore conjugate eye alignment when viewing through the spectacles. Indeed, Charnwood55 observed that aniseikonia patients preferred prism incorporated into their spectacle corrections to reduce anisophoria, and Field56 reported that nearly all of his 25 patients with clinically significant aniseikonia had oculomotor imbalance without prism corrections.
Accommodative esotropia, convergence excess, and convergence insufficiency share a common abnormality of their accommodative- convergence interactions. When the AC/A ratio is too high esophoria results, mainly because binocular disparity vergence is very limited in the divergence direction.57 As described above, it is very difficult to reduce the AC/A ratio with techniques using a telestereoscope that optically reduces the interpupillary distance.26 Our studies of adaptation of accommodation and convergence illustrate that high cross-coupled interactions can result from imbalanced capacity to adapt tonic accommodation and tonic convergence.38,58 The AC/A ratio tends to be elevated when vergence is more adaptable than accommodation because insufficient adaptation causes increased phasic activity, the excessive phasic accommodation stimulates accommodative vergence, and tonic vergence adapts in response to accommodative convergence.58 The elevated AC/A can be reduced by restoring the balance of adaptation gain of accommodation and vergence using accommodative and vergence flipper exercises.38 Fatigue caused by repeated stimulation of accommodation and vergence with Flipper exercises reduces the more adaptable response and causes the cross-coupled ratios to become more like the norm. If the fatigue effects can be sustained, this could be a promising approach to treat abnormal accommodative-vergence interactions.
Non-concomitant variations of strabismus and heterophoria are common with oculomotor paresis involving either the extraocular muscles or their cranial nerve innervations. Trochlear palsy is one of the more common forms of paresis resulting from head trauma. Trochlear or superior oblique palsy is characterized by a non- concomitant vertical deviation (elevation of the affected eye) that increases in magnitude when gaze is directed toward the tip of the nose. Patients can reduce the magnitude of the deviation by unconsciously tilting (rolling) their head to the opposite side as the eye with the affected muscle (ocular torticollis), and the vertical deviation increases when the head is rolled to the same side as the affected eye. These variations of vertical deviation with head tilt are part of the Parks'59 diagnostic sequence (Hering-Bielchowsky head-tilt test). Interestingly, the magnitude of vertical skew deviation that occurs with head tilt (positive Bielchowsky sign) increases with time after the initial traumatic insult, suggesting that it is exacerbated by an attempted adaptation.60 The interaction of the vertical deviation with head roll results from an interaction between the superior rectus and superior oblique of the affected eye that normally occurs during ocular counter-roll to prevent skew movements. When the head is rolled to the left, the left superior oblique contracts to in-tort the left eye toward earth vertical. Depression is the secondary action of the superior oblique, and this is counteracted or nulled by co-contraction of the superior rectus. However, when the superior oblique is paretic, the reflexive co-contraction of the superior rectus is unchecked, and it increases the hyperdeviation. The increase in the vertical deviation with head roll toward the paretic side could reflect an increase in the cross-coupled gain between the superior rectus and superior oblique, which can allow very small head tilts away from the paretic side to control and neutralize the vertical deviation.
Our studies of vertical vergence adaptation associated with head roll illustrate that it is possible to differentially adapt vertical vergence coupled with head roll and eye elevation, depending on the direction the head is rolled.7 This demonstration indicates that it is possible to reduce ocular torticollis as well as vertical deviation in some forms of trochlear palsy by training vertical disparity vergence in different combinations of head and eye position. Patients could be trained to control vertical eye alignment with small head rolls away from the side of the affected eye without exaggerating vertical skew deviation with head rolls toward the same side as the affected eye. Similar training techniques could be used to control torsional deviations of the two eyes.
These are only a few examples of how adaptable cross-coupled interactions can be facilitated by orthoptics in the process of rehabilitating disorders of binocular alignment. The main goals of research on neural plasticity of the near response are to identify reflex interactions between voluntary and involuntary motor responses, quantify the degree to which they can be modified with adaptation, determine the effects of aging on their plasticity, and gain some understanding of how these adaptive processes work. The practice of orthoptics is only limited by existing natural adaptive properties of the visuomotor system. The more that is known about these near-response interactions, the greater is the scope of orthoptics for correcting disorders of binocular alignment.
I thank James Maxwell for his comments on this manuscript.
Clifton M. Schor
School of Optometry
University of California, Berkeley
Berkeley, CA 94720-2020
1. Hebb DO. The Organization of Behavior: A Neuropsychological Theory. New York: Wiley; 1949.
2. Schlund MW, Rosales-Ruiz J, Vaidya M, Glenn SS, Staff D. Experience- dependent plasticity: differential changes in activation associated with repeated reinforcement. Neuroscience 2008;155:17–23.
3. Allen MJ, Carter JH. The torsion component of the near reflex. A photographic study of the non-moving eye in unilateral convergence. Am J Optom Arch Am Acad Optom 1967;44:343–9.
4. Fincham EF, Walton J. The reciprocal actions of accommodation and convergence. J Physiol 1957;137:488–508.
5. Alpern M, Ellen P. A quantitative analysis of the horizontal movements of the eyes in the experiment of Johannes Mueller. I. Method and results. Am J Ophthalmol 1956;42:289–96.
6. Maxwell JS, Schor CM. The coordination of binocular eye movements: vertical and torsional alignment. Vision Res 2006;46:3537–48.
7. Schor CM, Maxwell JS, Stevenson SB. Isovergence surfaces: the conjugacy of vertical eye movements in tertiary positions of gaze. Ophthalmic Physiol Opt 1994;14:279–86.
8. Schreiber KM, Tweed DB, Schor CM. The extended horopter: quantifying retinal correspondence across changes of 3D eye position. J Vis 2006;6:64–74.
9. Schreiber KM, Hillis JM, Filippini HR, Schor CM, Banks MS. The surface of the empirical horopter. J Vis 2008;8:7.1–20.
10. Van Rijn LJ, Van den Berg AV. Binocular eye orientation during fixations: Listing's law extended to include eye vergence. Vision Res 1993;33:691–708.
11. Zee DS. Considerations on the mechanisms of alternating skew deviation in patients with cerebellar lesions. J Vestib Res 1996;6:395–401.
12. Nguyen D, Vedamurthy I, Schor C. Cross-coupling between accommodation and convergence is optimized for a broad range of directions and distances of gaze. Vision Res 2008;48:893–903.
13. Howard IP, Rogers BJ. Binocular Vision and Stereopsis. Oxford: Oxford University Press; 1995.
14. Collewijn H. Vertical conjugacy: what coordinate system is appropriate? In: Fuchs AF, Brandt T, Buttner U, Zee DS, eds. Contemporary Ocular Motor and Vestibular Research: A Tribute to David A. Robinson. Stuttgart, Germany: Thieme; 1994:296–303.
15. Ygge J, Zee DS. Control of vertical eye alignment in three-dimensional space. Vision Res 1995;35:3169–81.
16. Donders FC. Beitrag zur Lehre von den Bewegungen des menschlichen Auges. Holland Beitr Anat Physiol Wiss 1848;1:105–45.
17. Haslwanter T. Mathematics of three-dimensional eye rotations. Vision Res 1995;35:1727–39.
18. Helmholtz H. Helmholtz's Treatise on Physiological Optics, 3rd ed (1910). [Translated by Southall JPC]. Rochester, NY: The Optical Society of America; 1924.
19. Schreiber KM, Schor CM. A virtual ophthalmotrope illustrating oculomotor coordinate systems and retinal projection geometry. J Vis 2007;7:4.1–14.
20. Hering E. The Theory of Binocular Vision (1868). [Translated by Bridgeman B, Stark L, eds.]. New York: Plenum Press; 1977.
21. Nakayama K. Kinematics of normal and strabismic eyes. In: Schor CM, Ciuffreda K, eds. Vergence Eye Movements: Basic and Clinical Aspects. Boston: Butterworth; 1983:543–64.
22. Tweed D. Visual-motor optimization in binocular control. Vision Res 1997;37:1939–51.
23. Somani RA, DeSouza JF, Tweed D, Vilis T. Visual test of Listing's law during vergence. Vision Res 1998;38:911–23.
24. Bruno P, van den Berg AV. Relative orientation of primary positions of the two eyes. Vision Res 1997;37:935–47.
25. Mok D, Ro A, Cadera W, Crawford JD, Vilis T. Rotation of Listing's plane during vergence. Vision Res 1992;32:2055–64.
26. Judge SJ, Miles FA. Changes in the coupling between accommodation and vergence eye movements induced in human subjects by altering the effective interocular separation. Perception 1985;14:617–29.
27. Bobier WR, McRae M. Gain changes in the accommodative convergence cross-link. Ophthalmic Physiol Opt 1996;16:318–25.
28. Eadie AS, Gray LS, Carlin P, Mon-Williams M. Modelling adaptation effects in vergence and accommodation after exposure to a simulated virtual reality stimulus. Ophthalmic Physiol Opt 2000;20:242–51.
29. Jiang BC, Ramamirtham R. The adaptive effect of narrowing the interocular separation on the AC/A ratio. Vision Res 2005;45:2704–9.
30. Schor CM, McCandless JW. Context-specific adaptation of vertical vergence to correlates of eye position. Vision Res 1997;37:1929–37.
31. Maxwell JS, Schor CM. Mechanisms of vertical phoria adaptation revealed by time-course and two-dimensional spatiotopic maps. Vision Res 1994;34:241–51.
32. McCandless JW, Schor CM. An association matrix model of context-specific vertical vergence adaptation. Netw Comput Neural Syst 1997;8:239–58.
33. Schor CM, Maxwell JS, Graf EW. Plasticity of convergence-dependent variations of cyclovergence with vertical gaze. Vision Res 2001;41:3353–69.
34. Schor CM, Kotulak JC. Dynamic interactions between accommodation and convergence are velocity sensitive. Vision Res 1986;26:927–42.
35. Schor CM, Alexander J, Cormack L, Stevenson S. Negative feedback control model of proximal convergence and accommodation. Ophthalmic Physiol Opt 1992;12:307–18.
36. Jiang BC. Accommodative vergence is driven by the phasic component of the accommodative controller. Vision Res 1996;36:97–102.
37. Hasebe S, Graf EW, Schor CM. Fatigue reduces tonic accommodation. Ophthalmic Physiol Opt 2001;21:151–60.
38. Schor CM, Tsuetaki TK. Fatigue of accommodation and vergence modifies their mutual interactions. Invest Ophthalmol Vis Sci 1987;28:1250–9.
39. Mays LE, Zhang Y, Thorstad MH, Gamlin PD. Trochlear unit activity during ocular convergence. J Neurophysiol 1991;65:1484–91.
40. Enright JT. Unexpected role of the oblique muscles in the human vertical fusional reflex. J Physiol 1992;451:279–93.
41. Miller JM, Robinson DA. A model of the mechanics of binocular alignment. Comput Biomed Res 1984;17:436–70.
42. Robinson DA. A quantitative analysis of extraocular muscle cooperation and squint. Invest Ophthalmol 1975;14:801–25.
43. Miller JM, Demer JL. Biomechanical analysis of strabismus. Binoc Vis Eye Muscle Surg Q 1992;7:233–48.
44. Porrill J, Warren PA, Dean P. A simple control law generates Listing's positions in a detailed model of the extraocular muscle system. Vision Res 2000;40:3743–58.
45. McCandless JW, Schor CM, Maxwell JS. A cross-coupling model of vertical vergence adaptation. IEEE Trans Biomed Eng 1996;43:24–34.
46. Maxwell JS, Schor CM. Head-position-dependent adaptation of nonconcomitant vertical skew. Vision Res 1997;37:441–6.
47. Friedenwald JS. Diagnosis and treatment of anisophoria. Arch Ophthalmol 1936;15:283–307.
48. Perlmutter AL, Kertesz AE. Measurement of human vertical fusional response. Vision Res 1978;18:219–23.
49. Houtman WA, Roze JH, Scheper W. Vertical motor fusion. Doc Ophthalmol 1977;44:179–85.
50. Ellerbrock V, Fry GA. Effects induced by anisometropic corrections. Am J Optom Arch Am Acad Optom 1942;19:444–59.
51. Cusick PL, Hawn HW. Prism compensation in cases of anisometropia. Arch Ophthalmol 1941;25:651–4.
52. Henson DB, Dharamshi BG. Oculomotor adaptation to induced heterophoria and anisometropia. Invest Ophthalmol Vis Sci 1982;22:234–40.
53. Schor CM, Gleason J, Horner D. Selective nonconjugate binocular adaptation of vertical saccades and pursuits. Vision Res 1990;30:1827–44.
54. Enoch JM. A spectacle-contact lens combination used as a reverse galilean telescope in unilateral aphakia. Am J Optom Arch Am Acad Optom 1968;45:231–40.
55. Charnwood JRB. An Essay on Binocular Vision. London: Hatton Press; 1950.
56. Field HB. A comparison of ocular imagery. Arch Ophthalmol 1943;29:981–8.
57. Morgan MW. The analysis of clinical data. Optom Wkly 1964;55:27–34.
58. Schor C, Horner D. Adaptive disorders of accommodation and vergence in binocular dysfunction. Ophthalmic Physiol Opt 1989;9:264–8.
59. Parks MM. Ocular Motility and Strabismus. Hagerstown, MD: Harper and Row; 1975.
60. Kommerell G, Klein U. Adaptive changes of the otolith-ocular reflex after injury to the trochlea. Neuro Ophthalmol 1986;6:101–7.
Keywords:© 2009 American Academy of Optometry
neuromuscular plasticity; adaptation; near response; accommodation; vergence; orthoptics; anisophoria; esotropia; trochlear palsy; convergence excess; convergence insufficiency; non-concomitant strabismus