Listing's law: Difference between revisions

'''Listing's law''' describes the [[Three-dimensional space|three-dimensional]] orientation of the [[human eye|eye]] and its [[rotation|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.

 

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Listing's law states that the eye does not achieve all possible 3D orientations and that, instead, all achieved eye orientations can be reached by starting from one specific "primary" reference orientation and then rotating about an axis that lies within the plane orthogonal to the primary orientation's gaze direction (line of sight / visual axis). This plane is called Listing's plane.

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Listing's law is the specific realization of the more general 'Donders' law', which states that for any one gaze direction the eye's 3D spatial orientation is unique and independent of how the eye reached that gaze direction (previous gaze directions / eye orientations / temporal movements).

 

There has been considerable debate for over a century whether the purpose of Listing's law is primarily motor or perceptual. Some modern neuroscientists -who have tended to emphasize optimization of multiple variables- consider Listing's law to be the best compromise between motor factors (e.g., taking the shortest possible rotation path) and visual factors (see below for details).

 

# It is often assumed the primary position is at the mechanical center of the eye's range of movement. Primary position can only be determined by measuring Listing's plane. 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.

 

The axes of rotation associated with Listing's law are only in Listing's plane for movements that head toward or away from primary position. For all other eye movements towards or away from some non-primary position, the eye must rotate about an axis of rotation that tilts out of Listing's plane. Such axes lie in a specific plane associated with this non-primary position. This plane's normal lies halfway between the primary gaze direction and the gaze direction of this non-primary position. This is called 'the half angle rule'. (This complication is one of the most difficult aspects of Listing's law to understand, but it follows directly from the non-[[Commutative property|commutative]] laws of physical rotation, which specify that one rotation followed by a second rotation does not yield the same result as these same rotations performed in the inverse order.)

 

Listing's law is not obeyed when the eyes counter-rotate during head rotation to maintain gaze stability, either due to the [[Vestibulo-ocular reflex]] (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, and when the head is held steady upward or downward Listing's plane tilts slightly in the opposite direction when.{{clarify|date=July 2013}}

 

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.

 

Since Listing's law and its variants determine the orientation of the eye(s) for any particular gaze direction, it therefore determines the spatial pattern of visual stimulation on the retina(s). For example, since Listing's law defines torsion as zero about a head-fixed axis, this results in 'false torsional' tilts about the line of sight when the eye is at tertiary (oblique) positions, which the brain must compensate for when interpreting the visual image. Torsion is not good for binocular vision because it complicates the already difficult problem of matching images from the two eyes for [[stereopsis]] (depth vision). The binocular version of Listing's law is thought to be a best compromise to simplify this problem, although it does not completely rid the visual system of the need to know current eye orientation.

 

In the 1990s there was considerable debate about whether Listing's law is a neural or mechanical phenomenon. However, the accumulated evidence suggests that both factors play a role in the implementation of different aspects of Listing's law.

 

Higher gaze control centers in the frontal cortex and superior colliculus are only concerned with pointing gaze in the right direction and do not appear to be involved in 3-D eye control or the implementation of Listing's law. However the brainstem reticular formation centers that control vertical eye position (the interstitial nucleus of Cajal; INC) and saccade velocity (the rostral intersitial nucleus of the medial longitudinal fasciculus; riMLF) are equally involved in torsional control, each being divided into populations of neurons that control directions similar to those of the vertical and torsional pulling eye muscles. However, these neural coordinate systems appear to align with Listing's plane in a way that probably simplifies Listing's law: positive and negative torsional control is balanced across the midline of the brainstem so that equal activation produces positions and movements in Listing's plane. Thus torsional control is only needed for movements toward or away from Listing's plane. However, it remains unclear how 2-D activity in the higher gaze centres results in the right pattern of 3-D activity in the brainstem. The brainstem premotor centers (INC, riMLF, etc.) project to the motoneurons for eye muscles, which encode positions and displacements of the eyes while leaving the 'half angle rule' to the mechanics of the eyes itself (see above). The cerebellum also plays a role in correcting deviations from Listing's plane.

 

 

Listing's law was named after German [[mathematician]] [[Johann Benedict Listing]] (1808–1882). (It is not clear how Listing derived this idea.) Listing's law was first confirmed experimentally by the 19th century polymath [[Hermann von Helmholtz]], who compared visual [[afterimage]]s at various eye positions to predictions derived from Listing's law and found that they matched. Listing's law was first measured directly, with the [[Scleral lens#Use for eye movement measurement|use of 3-D eye coils]] in the 1980s by Ferman, Collewijn and colleagues. In the late 1980s Tweed and Vilis were the first to directly measure and visualize Listing's plane, and also contributed to the understanding of the laws of rotational kinematics that underlie Listing's law. Since then many investigators have used similar technology to test various aspects of Listing's law. Demer and Miller have championed the role of eye muscles, whereas Crawford and colleagues worked out several of the neural mechanisms described above over the past two decades.