The first and second order dynamics of accommodative convergence and disparity convergence

Abstract

Main sequences, the function describing the relationship between eye movement amplitude and velocity, have been used extensively in oculomotor research as an indicator of first-order dynamics yet it is difficult to find main sequence analyses for accommodative vergence or for disparity vergence in isolation when all mitigating factors have been well controlled and there are no studies in which accommodative vergence and disparity vergence main sequences have been generated for the same group of subjects. The present study measured main sequences in: (1) accommodative vergence with disparity vergence open loop, (2) disparity vergence with accommodation open loop, and (3) combinations of accommodative and disparity vergence. A dynamic AC/A ratio was defined and was found to be similar to the traditional static AC/A ratio. Vergence acceleration was measured for all conditions. A pulse-step model of accommodation and convergence was constructed to interpret the dynamics of the crosslinked interactions between the two systems. The model supports cross-coupling of both the pulse and step components and simulates the primary empirical findings that: (1) disparity vergence has a higher main sequence slope than accommodative vergence, (2) both accommodative and disparity vergence acceleration increase with response amplitude whereas accommodation acceleration does not.

Figure 1

Targets. A. Modified Maltese cross with a diameter of 10 degrees. B. Horizontal lines with a width of approximately 22 degrees (spanning the aperture) and a height of 1.6 degrees. C. Low-pass filtered hourglass-shaped target with a width of 6 degrees and a height of 22 degrees. D. Unfiltered hourglass-shaped target.

Figure 2

Example of Aligned trials for subject JK showing vergence (black lines) and accommodation (gray lines) amplitude, velocity and acceleration. Vergence was converted to meter angles (MA) so that it could be plotted on the same scale as accommodation. Traces are the average of 15 trials.

Figure 3

Main sequence for convergence for subject SG Blur + Disparity trials. Circles represent all data and squares represent trials having saccades occurring within50 msec of peak vergence velocity.

Figure 4

A. Main sequences for subject AB for the three accommodative vergence trial types (Aligned, Binocular and Monocular H. Line), the disparity vergence trial (Disparity) and the trials in which both cues were given (Disparity + Blur). The lines were fit by second order polynomial equations. The regression lines are ordered as indicated by the legend to the right, e.g., the Blur + Disparity at the top and Aligned at the bottom line. B. Convergence acceleration for the same subject (AB). Format the same as in A.

Figure 5

A. Mean second order polynomial fits for six subjects for the three accommodative vergence trial types (Aligned, Binocular and Monocular H. Line), the disparity vergence trial (Disparity) and the trials in response to both cues (Disparity + Blur). The error bars show the standard deviation of the means between subjects for Aligned and Disparity trials. Standard errors for other conditions were similar but not shown for clarity. B. Mean vergence acceleration for six subjects. Same format as A.

Figure 6

Accommodation velocity (A) and acceleration (B) for the Aligned trials for seven subjects (different symbols). A polynomial was fit to each subject’s data and the coefficients were averaged to obtain a mean polynomial equation. The accommodation velocity data were fit with a third order polynomial and the acceleration data were fit with a second order polynomial.

Figure 7

Dynamic AC/A ratio as a function of static AC/A ratio for each subject as measured by the stigmascope (circles) or the Purkinje eye tracker (squares). All AC/A values are response ratios.

Figure 8

Average vergence velocity for three subjects for the three conditions of the control experiment. Monocular H. Line trial (solid gray line) and Disparity trial data (solid black lines) were measured as before and Control trials (stippled line) were measured with the right eye constantly occluded.

Figure 9

Pulse-step model for accommodation and vergence. The dashed lines indicate two sites where signals from the accommodation system may cross over to drive the vergence system. .See text for details.

Figure 10

Pulse signals for the feed-forward loops for accommodation and vergence labeled “acceleration pulse” and “disparity vergence pulse”, respectively, in Figure 9.

Figure 11

Pulse-step model simulations of accommodation and vergence main sequences. Symbols in C also pertain to figure D.