Hara et al.
4 showed that the increase in VFA with convergence is brought about by an increase in the motor component of vertical vergence. The exact reason for the increase in the motor component of VFA with convergence remains unanswered. Although the experiments that we performed do not provide an answer, they exclude three plausible explanations that are worth considering. First, it has been shown by several authors that the VFA increases with the size of the fusion target.
8 20 21 22 23 It is plausible that the concurrent increase in angular size of the fusion target with the target proximity, as was the case in experiment II, was responsible for the increase in VFA with convergence. However, the increase of VFA with convergence also occurred when the angular size of the fusion target remained independent of the convergence stimulus, as was the case in experiment I. Hence, it is unlikely that the increase in angular size of the fusion target with convergence is responsible for the increase in VFA. Second, because both experiments I and II delayed the increase in vertical disparity until subjects reported fusion, the adaptable component of the vertical vergence system could have increased the VFA.
33 39 46 Larger VFAs have been observed by Ogle and Prangen
33 after vertical prism adaptation. Control experiment II was performed on three subjects to rule out this factor. At each convergence position, the VFA was estimated by incrementing the vertical vergence stimulus once every 6 seconds, thus providing minimal time for any short-term adaptation to occur. No statistically significant differences were observed between the results of control experiment II and the main experiment I (
P > 0.05). The results of both control experiment II and main experiment I also compare well with the results obtained by Hara et al.
4 who estimated the VFA by incrementing the vertical vergence stimulus once every 6 seconds. These results suggest that the adaptable component of the vertical vergence system could play only a minor role in increasing the VFA with convergence angle. Third, since naturally occurring vertical disparities (in Fick coordinates) are encountered more often during near viewing than during distance viewing,
2 it is plausible that the increase in VFA at near viewing is related to accommodation or to the sense of proximity of the fusion targets.
15 In experiment I, the accommodative stimulus was held constant and the horizontal disparities were generated by changing the horizontal separation between the red-green circles on a computer monitor placed at 50 cm in front of the subject. The increase in VFA with convergence in experiment I obtained with a constant accommodative stimulus suggests that accommodation is a minor determinant in the coupling between VFA and convergence. The sense of proximity was not explicitly controlled in either of our experiments. In experiment II, convergence was stimulated by changing the physical distance between the subject and the horizontal fusion targets. The increase in physical proximity and the increase in retinal image size of the fusion targets could provide a proximal cue to the vertical vergence system. In experiment I, the horizontal disparities were generated on a computer monitor that was placed at 50 cm in front of the subject. Although weak and ineffective in the presence of other visual and nonvisual cues,
55 56 57 it is plausible that the proprioceptive signals generated by the horizontal recti muscles during convergence could have provided the desired sense of proximity to the vertical vergence system. Prior studies have shown that proximal cues such as motion parallax and overlap are ineffective in stimulating vertical vergence.
39 Whether the sense of proximity plays a role in the increase in VFA with convergence remains a question; however, given the robustness of the effect observed here, it seems unlikely that the sense of proximity could solely account for the coupling between VFA and convergence. Vertical vergence eye movements that have been trained to change in association with convergence are thought to be preprogrammed (and under adaptive recalibration), based on an internally generated three-dimensional motor map.
2 15 38 The increase in VFA with convergence could result from a similar preprogrammed cross-link whose gain is analogous to the cross-link gains between accommodation and convergence (AC/A
58 59 and CA/C
60 61 ratios).