Eye movements are commutative

Abstract

Purpose: To provide evidence that all eye movements are commutative and to use that evidence to establish a coherent theory of ocular kinematics. Methods: Fixation targets and two miniature video cameras, one to record eye movements and the other to record head movements, were suspended from a head band. The apparatus (VOG) keeps the eyes stable in the orbits during head yaw, pitch, and tilt while allowing the head to move freely. It was also used for tracking eye movements with the head held stationary. Ocular orientation was determined from downloaded video clips by superimposing serial frames. Results: Video frame analysis reveals that all eye movements are commutative. The eye has one fixed axis within its substance, which serves eye movements to and from the midsagittal orbital plane. Brow-up and chin-down eye movements occur around an axis fixed in the orbit. Oblique movements consist of alternating arcs of great and small circles. The vertical extraocular muscles act synergistically when the head is held stationary producing slope and reciprocally during head tilt producing transient torsional movements. Conclusions: The globe rotates around two axes when the eye is stationary and one axis when the head tilts. The orientation of the eye can be calculated using the formula for the derivative of an ellipse. The results suggest a coherent theory of ocular movement: The function of the extraocular muscles is to maintain the fixation plane of each eye in equilibrium with the brain and coplanar with the fixation plane of the other eye in all gaze directions and head positions.