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  • Title: The variation of torsion with vergence and elevation.
    Author: Porrill J, Ivins JP, Frisby JP.
    Journal: Vision Res; 1999 Nov; 39(23):3934-50. PubMed ID: 10748926.
    Abstract:
    Two recently developed kinematic models of human eye movements predict systematic departures from Listing's law which are associated with changes in vergence. This vergence-dependent torsion t is proportional to elevation e and vergence v, that is t = kev/2. The proposed value for k is either 1 (Van Rijn, L. J., & Van den Berg, A. V. (1993). Vision Research, 33, 691-708) or 1/2 (Minken, A. W. H., Gielen, C. C. A. M., & Van Gisbergen, J. A. M. (1995). Vision Research, 35, 93-102). One implication of both models is that an eye with a constant fixation direction should exhibit systematic torsional variation during movements of the other eye. This paper therefore examines the torsion produced by moving a fixation target inwards and outwards along the line-of-sight of the right eye at five different viewing elevations (0, +/- 15 and +/- 30 degrees). In a monocular analysis, each eye generally showed intorsion during convergence at positive elevation angles, whereas extorsion occurred at negative elevations; the opposite was true during divergence. However, the torsion response was visibly different between the five subjects, and depended on the direction of target motion. In a binocular analysis, cycloversion (mean of left and right eye torsion) varied dramatically both between subjects and between convergence and divergence; however, cyclovergence (torsional difference) was much less variable. Least-squares methods were used to estimate the constant k from monocular torsion, yielding values between 0.2 and 1.0; however, corresponding estimates based on cyclovergence were all close to 1/2. These findings support suggestions that a binocular control system couples the three-dimensional movements of the eyes, and that an existing model of monocular torsion should be generalised to the binocular case.
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