Accommodation and induced myopia in marmosets

Abstract

Accommodation may indirectly influence visually guided eye growth by affecting the retinal defocus signal used to guide growth. Specifically, increased lags of accommodation associated with low stimulus-response (S-R) function slopes will impose increased hyperopic blur on the retina and may induce axial elongation and myopia. The purpose of this study was (1) to measure accommodation in awake, free viewing marmosets and (2) compare accommodation behavior in marmosets before and after inducing different amounts of myopia with binocular spectacle lenses. In untreated marmosets, the average accommodation S-R slope approached one, but showed considerable inter-individual variability (mean+/-SD: 0.964+/-0.249 for monocular viewing; 0.895+/-0.235 for binocular viewing; monocular and binocular measures not significantly different). The monocular S-R slopes were significantly reduced following a period of lens rearing that produced axial myopia (change in slope=-0.30+/-0.30, p<.01) and the reduction in slope was proportional to the amount of myopia induced (p<.01). The S-R slopes measured either under monocular or binocular conditions before induction of myopia were not well correlated with the degree of myopia induced (monocular: r=-.240, p=.453; binocular: r=-.060, p=.824). These results support the hypothesis that the reduction in S-R slope in myopes is a consequence of the myopia induced. The alternative hypothesis-that low S-R slope increases susceptibility to the development of myopia--is not supported by the weak correlation between the pre-manipulation S-R slopes and the magnitude of the myopic shift.

Figure 1

A schematic of the set-up for measuring accommodation in marmosets. Marmosets viewed video stimuli at varying distances from a window in an observation chamber. The video stimuli were alternately presented on two video monitors to determine when the marmoset was attending to the accommodative stimulus (see text for details). An infrared videorefractor (PowerRefractor) was used to measure accommodation to targets at different distances. The videorefractor was aligned with the accommodative stimulus and the window in the observation chamber using an infrared hot mirror.

Figure 2

Examples of S-R functions illustrating the procedure to objectively determine the average S-R slope (dy/dx) across the range of changing responses using the first derivative of a polynomial. The diagonal dashed line has a slope = 1 and is shown for reference. Black circles show measures of the subject's refraction response (left y-axis) for a given accommodative demand (x-axis). A 3^rd order polynomial is fit to the data and is indicated by a solid line. White circles give the values of the first derivative (right y-axis) taken from the polynomial function. The polynomial derivative was used to remove flat regions from the function before calculating the average slope. (A) An example of a S-R function in which the function is nearly linear. A linear regression fit to the data (r²=0.936) gives a slope of 0.66. The average change in response for a given change in accommodative demand derived from the polynomial fit to the data (r=0.938) has a slope of 0.63 in this example. (B) An example of a saturating S-R function from a different animal. A linear regression fit to these data (r=0.951) gives a slope of 0.859. The polynomial fit (r=0.977) shows response saturation indicated by flat region on the right end of the function. By accepting only the data corresponding to derivatives <−0.1 (indicated by the horizontal line extending from the right y-axis) the flat portion of the function is ignored and only those derivatives corresponding to the data highlighted within the grey box are used to determine the accommodation S-R slope. The S-R slope of the function calculated in this way yields a value of 0.905.

Figure 3

Comparison of methods to estimate accommodation S-R slopes. (A) Slopes of linear regressions fit to the S-R data are plotted on the x-axis. Estimates from averaging the first derivative of 3^rd order polynomial fits are plotted on the y-axis (see Figure 2 and text for a complete explanation). The solid lines gives the Model II reduced major axis regression and the dashed line has a slope=1. (B) Bland-Altman plot (Bland & Altman, 1986) showing the 95% confidence interval (shaded area) for the difference between the accommodation S-R slopes measured from polynomial derivatives or linear regressions. The method of polynomial slope derivation omits flat regions in the accommodation S-R function due to sub-threshold responses at low demands or response saturation at high demands and so tends to give steeper slopes than simple linear in data sets exhibiting those characteristics.

Figure 4

Accommodation S-R functions of the individual eyes of six untreated marmosets. Data are fit with 3^rd order polynomials. Black circles fit with solid lines are data collected during binocular viewing. White circles with dashed lines are data collected during monocular viewing. Data from right eyes are shown in the right hand column and data from left eyes are shown in the left hand column. Diagonal lines indicate S-R slopes of 1 and are shown for reference. The total range of stimulus and response values is 0 to 16 D for each graph.

Figure 5

The effect of lens rearing on refractive state and vitreous chamber depth. Data are the differences between the post-manipulation measurement and the pre-manipulation measurement. The change in refractive state (y-axis) and vitreous chamber depth (x-axis) are significantly correlated (p<0.01).

Figure 6

Accommodation S-R slope is significantly correlated with refractive state. Black circles, fit with the solid linear regression line, show slopes measured during binocular viewing following lens treatment. White circles, fit with the dashed linear regression line, show slopes measured under monocular conditions in the same marmosets. Accommodation S-R slopes for untreated marmosets (diamonds) are shown for comparison, black symbols show S-R slopes measured under binocular conditions, white symbols show S-R slopes measured under monocular conditions.

Figure 7

Accommodation S-R functions from both eyes of six marmosets measured during monocular viewing before and after induced changes in refractive state. Data from right eyes are shown in the right hand column and data from left eyes are shown in the left hand column. Data are fit with 3^rd order polynomials. White circles fit with solid lines are data collected before visual manipulations, crosses fit with dashed lines show data collected after the manipulation. Diagonal lines indicate S-R slopes of 1 and are shown for reference. The total range of stimulus and response values is 0 to 16 D for each graph.

Figure 8

Accommodation S-R functions from eight marmosets measured during binocular viewing before and after induced changes in refractive state. Data collected before visual manipulations are shown as black circles fit with solid lines, all other details are same as in Figure 7.

Figure 9

Changes in individual accommodation S-R slope measured under monocular (white circles) and binocular (black circles) conditions are represented in this scatter plot of slopes measured before (x-axis) and after (y-axis) lens-induced changes in eye size and refractive state. The diagonal dashed line has a slope of 1. Points below the line indicate reduced slopes following lens wear. Points above the line indicate increasing slopes.

Figure 10

The change in accommodative slope (post lens wear – pre lens wear) plotted against the change in refractive state (A) and vitreous chamber depth (B) induced in experimental marmosets raised with binocular spectacle lenses. Black circles show slopes measured under binocular conditions and are fit with solid linear regression lines. White circles show slopes measured under monocular conditions and are fit with dashed regression lines.

Figure 11

Induced change in refractive state (A) and vitreous chamber depth (B) plotted against the accommodative slope measured in experimental marmosets before being treated with binocular spectacle lenses. Black circles show slopes measured under binocular conditions and white circles show slopes measured under monocular. There are no statistically significant correlations between S-R slopes measured before lens rearing and the induced change in either refractive state or vitreous chamber depth.