Listing's law is a term used to describe the three-dimensional orientation of the eye and its axes of rotation. Listing's law has been shown to hold when the head is stationary and upright and gaze is directed toward far targets, i.e., when the eyes are either fixating, making saccades, or pursuing moving visual targets.
Definition
Listing's law states that all eye orientations can be reached from one common reference orientation about an axis that lies within a unique plane. This is true for any arbitrary reference position, and each has its own associated plane. However, the gaze direction at one, and only one, reference position is orthogonal to its associated plane. This reference position is called the primary position and the associated plane of axes is called Listing's plane.
One can simplify the expression of Listing's law by creating a coordinate system where the origin is primary position, the vertical and horizontal axes of rotation are aligned in Listing's plane, and the third (torsional) axis is orthogonal to Listing's plane. In this coordinate system, Listing's law simply states that the torsional component of eye orientation is held at zero. (Note that this is not the same description of ocular torsion as rotation around the line of sight.)
Common Misconceptions
1) It is often assumed the primary position is at the mechanical center of the eye's range of movement. Direct measurements show that the location of primary position (and thus the orientation of Listing's plane) varies between subjects. Primary position is generally close to center, but it may be rotated slightly up or down, left or right.
2) It is often misunderstood that Listing's law says that the eye only rotates about axes in Listing's plane. This is incorrect. Listing's plane only provides the orientations of the eye relative to primary position, expressed as an angle of rotation about some axis in Listing's plane (normally using the right-hand rule, where one curls the fingers of the right hand in the direction of rotation and the thumb then points in the direction of the rotation vector). This is not the same as the axes that the eye actually rotates about. These axes of rotation only stay in Listing's plane for movements that head toward or away from primary position. For all other eye movements, the eye must rotate about an axis of rotation that tilts out of Listing's plane, i.e., has a torsional component. (This apparent contradiction is one of the most difficult aspects of Listing's law to understand, but it follows directly from the non-commutative laws of physical rotation). How do the axes tilt? A good 'rule of thumb' is to take the shortest angle between primary position and the path of a saccade. The saccade axis will tilt by half this angle away from Listing's plane. This is called 'the half angle rule'.
Modifications and Violations
Listing's law is not obeyed when the eyes counter-rotate during head rotation to maintain gaze stability, either due to the VOR or the optokinetic reflex. Here the eye simply rotates about approximately the same axis as the head (which could even be a pure torsional rotation). This generally results in slow movements that drive the eye torsionally out of Listing's plane. However, when the head translates without rotating, gaze direction remains stable but Listing's law is still maintained.
Listing's law persists but takes on a torsional bias when the head is held at a tilted posture and the eyes counter-roll. The Listing's planes of the two planes tilt outward, opposite to the eyes, when they converge on a near target.
When larger 'gaze saccades' are accompanied by a head movement, Listing's law cannot be maintained constantly because VOR movements occur during or toward the end of the movement sequence. In this case, saccades take on torsional components equal and opposite to the oncoming torsional movements such that Listing's law is transiently violated, but the eye ends up at zero torsion in the end.
Discovery and History
Listing's law was named after German mathematician Johann Benedict Listing (1808–1882).
References
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