An analysis of curvature in fast and slow human saccades

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Abstract
In order to study the cooperation of peripheral motor subsystems, the degree of curvature of human saccades along cardinal (right, up, left, down) and oblique directions was computed from an extensive set of experimental data. Our curvature measure allows comparison of fast and slow saccade trajectories elicited in different experimental conditions, independent of the speed of execution. Although we found clear and consistent subject-specific differences, the most common pattern in oblique visually-guided (i.e., fast) saccades reflected early dominance of the horizontal velocity signal as expressed in saccade trajectories curving away from the horizontal axis. Plots of curvature against direction yielded consistent idiosyncratic patterns with periodical increases and decreases in saccade curvature which were largely independent of saccade amplitude. At the cardinal axes, mean saccade curvature was generally less, but rarely entirely absent, and fitted smoothly into the curvature pattern of neighbouring quadrants. Memory-guided saccades, which have been shown earlier to be considerably slower than visually-guided saccades and to be more variable in their dynamic properties, showed a strikingly similar dependence of curvature on saccade direction, although some small but consistent differences were noticed. This finding suggests that saccade curvature is determined by mechanisms residing in the final common pathway for both saccade types. The curvature data were compared with quantitative predictions from three different models for the generation of oblique saccades. By quantifying the curvature of human saccades and thereby revealing the shortcomings of these models, the present paper documents new constraints with which future models of the saccadic system must comply and allows certain suggestions on how these might be developed.