Dynamical version--vergence interactions for a binocular implementation of Donders' law.

Recent investigations of the three-dimensional (3D) binocular eye positions in near vision have shown that a full characterization of vergence requires incorporation of its torsional component. The latter has a proportional relationship with horizontal vergence and elevation, causing the eyes to have intorsion in near upgaze but extorsion in near downgaze. In this study, we focus on the dynamical implementation of the torsional vergence component in both pure vergence and combined direction-depth binocular eye movements. We report on experiments in five subjects whose eye movements were recorded binocularly with the 3D magnetic search-coil technique. In pure vergence movements at a given elevation, torsional vergence increased with almost the same time course as horizontal vergence. In addition, the dynamic relationships among torsional vergence, horizontal vergence and elevation were close to static results in all subjects. In combined direction-depth movements a similar relationship held for the complete movements, but we could not firmly establish a straight-line relationship during the saccadic portion of the movement. Possible factors determining these responses are discussed. We computed the angular velocity profiles of pure vergence movements to see how tilting of the vergence angular velocity axis relative to Listing's plane generates torsional vergence. It is widely held that both saccadic and vergence movements are controlled by dedicated pulse generators specifying velocity signals. Little thought has been given to the question of how these controllers can be coordinated to yield realistic eye movements in 3D. Our finding that this tilt was close to full-angle, suggests a model in which version and vergence velocity signals are combined before the 3D neural integrator proposed by Tweed and Vilis. The implications of this scheme for the control of binocular eye movements in three dimensions are discussed, along with possible neural correlates.