Listing's law: Difference between revisions

|last=Tweed |first=D. |author2=W. Cadera |author3=T. Vilis

| pmid=2321369

| doi=10.1016/0042-6989(90)90130-D

| s2cid=1555793 }}</ref>

The expression of Listing's law can be simplified 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: whereas movements that start or end at the primary position can indeed be performed without any rotation about the line of sight, this is not the case for arbitrary movements.) Listing's law can also be formulated in a [[coordinate-free]] form using [[geometric algebra]].<ref>[[David{{cite Hestenes]]:journal |doi=10.1016/0893-6080(94)90056-6 ''|title=Invariant body kinematics: I. Saccadic and compensatory eye movements'', Neural|year=1994 Networks,|last1=Hestenes Vol.|first1=David 7,|author-link1=David No.Hestenes 1|journal=Neural (1994),Networks pp.|volume=7 |issue=1 |pages=65–77 ([http|url=https://davidhestenes.net/geocalc.clas.asu.edu/pdf-preAdobe8/InvarBK1.pdf PDF])}}</ref>

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{{snd}} -who have tended to emphasize optimization of multiple variables-{{snd}} 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 that 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.

# 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; in fact, Listing's law requires that the rotation axis of most saccades lies ''outside'' of Listing's plane,<ref>D.{{cite Tweed,journal T|doi=10.1152/jn.1987.58.4.832 Vilis: ''|title=Implications of rotational kinematics for the oculomotor system in three dimensions'', J|year=1987 |last1=Tweed |first1=D. Neurophysiol|last2=Vilis |first2=T. 58|journal=Journal (1987),of pp.Neurophysiology |volume=58 |issue=4 |pages=832–849 |pmid=3681398}}</ref> more specifically, the rotation axis lies in Listing's plane only if the movement starts or ends at the primary position or if it is a prolongation of such a movement.

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.)

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.

The horizontal recti muscles of the eyes only contribute to horizontal eye rotation and position, but the vertical recti and oblique muscles each have approximately equal vertical and torsional actions (in Listing's plane coordinates). Thus, to hold eye position in Listing's plane, there needs to be a balance of activation between these muscles so that torsion cancels to zero.

The [[Extraocular muscles|eye muscles]] may also contribute to Listing's law by having position-dependent pulling directions during motion, i.e., this might be the mechanism that implements the '"half -angle' rule" described above.

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-D3D 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 intersitialinterstitial 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-D2D activity in the higher gaze centres results in the right pattern of 3-D3D 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.

Damage to any of the physiology described above can disrupt Listing's law, and thus have negative impacts for vision. Disorders of the eye muscles (such as [[strabismus]])<ref name="LiversedgeGilchrist2011">{{cite book |author1=Simon Liversedge |author2=Iain Gilchrist |author3=Stefan Everling |title=The Oxford Handbook of Eye Movements |url=httphttps://books.google.com/books?id=Hiof9gzHPNoC&pg=PA348 |accessdate=7 July 2013 |date=18 August 2011 |publisher=Oxford University Press |isbn=978-0-19-162661-6 |pages=348}}</ref> often cause torsional offsets in eye position that are particularly troublesome when they differ between the two eyes, as the resulting [[cyclodisparity]] may lead to cyclodisplopia (double vision due to relative torsion) and may prevent binocular fusion. Damage to the vestibular system and brainstem reticular formation centres for 3-D3D eye control can cause torsional offsets and/or torsional drifting motion of the eyes that severely disrupts vision. Degeneration of the Cerebellumcerebellum causes torsional control to become '"sloppy'". Similar effects occur during alcohol consumption.

Listing's law was named after German [[mathematician]] [[Johann Benedict Listing]] (1808–1882). (It is not clear how Listing derived this idea, but apparently based on his geometric aesthetics.)<ref name="wong-2004" />

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-D3D 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.

* Crawford{{cite JD,journal|pmid=14662365|date=December 2003|last1=Crawford|first1=J. D.|last2=Martinez-Trujillo|first2=J. JC, C.|last3=Klier EM|first3=E. M.|title=Neural control of three-dimensional eye and head movements.|journal=Current CurrOpinion Opinin Neurobiol. 2003 Dec;Neurobiology|volume=13(|issue=6):655-62|pages=655–62|doi=10. Review1016/j.conb.2003.10.009|s2cid=353894 }}

* [http://schorlab.berkeley.edu/vilis/whatisLL.htm What is LinstingListing's law?], Schor Lab, University of California at Berkeley (with a graphical illustration of Listing's law)