Negativefeedback Path

FIGURE 12.13. Block diagram of the cross-links between a dual control model of accommodation and convergence.

1986) (Figure 12.13). A rapid phasic component responds to both spatiotopic and retinal cues to distance, and an adaptable tonic component stores activity of the phasic systems (Schor et al., 1992). The phasic element enables rapid changes in viewing distance to obtain clear and single binocular vision. However, the phasic system lacks durability and it fatigues easily. It also has a very limited range of a few diopters or a few degrees that it can sustain comfortably. The slower tonic system extends the range of the fast system so that we can accommodate or converge large amplitudes and maintain these large responses to static or slow changing stimuli for long periods of time. Phasic and tonic mechanisms are arranged serially 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 as tonic adaptation increases, the stimulus to the phasic systems is reduced by negative feedback 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 crosslinks (Schor and Kotulak, 1986; Jaing, 1996; Hasebe et al., 2001). Consequently, the cross-link activity is greater in response to rapid (phasic) than gradual (tonic) dynamic responses. In addition, the tonic adapters respond to both direct and cross-linked phasic activity of accommodation and convergence (Schor and Kotulak, 1986). Factors that reduce tonic activity of one system (accommodation or convergence), such as fatigue following rapid alternating changes in viewing distance, cause cross-link activity of the fatigued system to be elevated and the cross-link activity of the non-fatigued system to be reduced (Schor and Tsuetaki, 1987). For example, fatigue of adaptable tonic accommodation causes the AC/A ratio to increase and the CA/C ratio to decrease. Thus, the magnitude of the cross-link interaction can be modulated by the activity of the adaptable tonic components of accommodation and convergence.

12.6.2 Cyclovergence and Eye Elevation During Convergence

How might the changes in orientation of Listing's planes be accomplished? Physiological studies indicate that simple gain changes of the obliques and perhaps the vertical recti might be involved. Mays et al. (1991) 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 varied systematically with gaze elevation, and was largest in downward gaze. The fact that these authors observed no net increase in trochlear activity when the eyes incyclorotate 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's measures of ocular translation also suggested that the superior oblique relaxes during convergence (Enright, 1992).

This hypothesis was tested by simulating 3-D eye position with OrbitTM, a biomechanics model that simulates binocular eye position based upon 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 Robinson (1975) and Miller and Robinson (1984). 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. 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 rectus was increased and the innervation to the lateral rectus was decreased to produce 20 deg 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 while the following eye is guided by Listing's and Hering's innervations. Parameters of either eye or both 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 deg of convergence while lateral gaze was varied over ±30 deg 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 fronto-parallel. With gain adjustments, the primary positions diverged by 20 deg for a simulated convergence of 20 deg (Figure 12.14). These gain changes might be modified to describe the adaptive plasticity of Kt. The adaptation results of the exaggerated condition could be simulated with greater gain changes, 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

Displacement Plane Rotations with 20° Convergence

FIGURE 12.14. A top-down view of simulated displacement planes for a straight-ahead reference direction are shown the right and left eye during 20 deg of convergence. Planes were derived from Orbit simulations of three-dimensional eye position with modified gains of the obliques and vertical recti. The Orbit simulations are for a 15% decreased gain of the obliques and 15% increased gain of the vertical recti. Torsion, plotted in degrees, is simulated for vertical and horizontal changes in eye positions over a 60 deg horizontal and vertical range. Fifteen test points ranged from the near central fixation point in 30 deg horizontal increments and 15 degree vertical increments in a 3 x 5 rectangular matrix. YTD of the two displacement planes equals 9 deg, which corresponds to a YTD between primary positions of 18 deg and a K value equal to 0.9.

FIGURE 12.14. A top-down view of simulated displacement planes for a straight-ahead reference direction are shown the right and left eye during 20 deg of convergence. Planes were derived from Orbit simulations of three-dimensional eye position with modified gains of the obliques and vertical recti. The Orbit simulations are for a 15% decreased gain of the obliques and 15% increased gain of the vertical recti. Torsion, plotted in degrees, is simulated for vertical and horizontal changes in eye positions over a 60 deg horizontal and vertical range. Fifteen test points ranged from the near central fixation point in 30 deg horizontal increments and 15 degree vertical increments in a 3 x 5 rectangular matrix. YTD of the two displacement planes equals 9 deg, which corresponds to a YTD between primary positions of 18 deg and a K value equal to 0.9.

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 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.

12.6.3 Vertical Eye Alignment in Tertiary Gaze

Vertical eye alignment in tertiary gaze was preserved during the gain adjustments to the vertical recti and obliques that produced the binocular extension of Listing's law. Figure 12.15 plots the simulated open-loop vertical position of the following eye against closed-loop vertical position of the fixating eye during 20 deg of convergence while vertical and lateral gaze varied over a ±30 deg range of eye positions. Results from all horizontal test positions are combined into a single plot. Vertical eye position is specified in Helmholtz coordinates such that equal vertical position of the following eye and fixating eye (slope =1.0) corresponds to binocular vertical eye alignment with the fixation target. The top plot shows an amplitude ratio of (following eye)/(fixating eye) of Kv = 1.0 indicating that changes in cyclophoria that were consistent with Listing's extended law did not disrupt vertical eye alignment in tertiary gaze. The bottom plot shows a similar amplitude ratio of the two eyes with normal (unaltered) gains to the vertical recti and obliques. In this simulation, the yoked innervation for vertical eye position

(20 degrees convergence: Vertical recti increased15%, Obliques reduced 15%)

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