The variation of torsion with vergence and elevation

Vision Res. 1999 Nov;39(23):3934-50. doi: 10.1016/s0042-6989(99)00102-9.


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.

MeSH terms

  • Convergence, Ocular / physiology*
  • Eye Movements / physiology*
  • Fixation, Ocular / physiology
  • Humans
  • Vision, Binocular / physiology
  • Vision, Monocular / physiology