How Listing's Law May Emerge from Neural Control of Reactive Saccades

We hypothesize that Listing's Law emerges as a result of two key properties of the saccadic sensory-motor system: 1) The visual sensory apparatus has a 2-D topology and 2) motor synergists are synchronized. The theory is tested by showing that eye attitudes that obey Listing's Law are achieved in a 3-D saccadic control system that translates visual eccentricity into synchronized motor commands via a 2-D spatial gradient. Simulations of this system demonstrate that attitudes assumed by the eye upon accurate foveation tend to obey Listing's Law.Office of Naval Research (N00014-92-J-1309, N00014-95-1-1409); Air Force Office of Scientific Research (90-0083

Theoretical explanations of Listing's law and their implication for binocular vision

AbstractWe shall discuss three theoretical explanations of Listing's law for conjugate eye movements with the head fixed: the original argument by Helmholtz, which is “sensorimotor” in its attempt to optimize vision by using internal feedback from the oculomotor system, and two comparatively simple recent explanations based on either visual or oculomotor performance. These geometrical demonstrations shed some light on recent generalizations of Listing's law to vergent eye movements

Eye mechanics and their implications for eye movement control

The topic of this thesis is the investigation of the mechanical properties of the oculomotor system and the implications of these properties for eye movement control. The investigation was conducted by means of computer models and simulations. This allowed us to combine data from anatomy, physiology and psychophysics with basic principles of physics (mechanics) and mathematics (geometry). In chapter 2 we investigate the degree to which mechanical and neural non-linearities contribute to the kinematic differences between centrifugal and centripetal saccades. On the basis of the velocity profiles of centrifugal and centripetal saccades we calculate the forces and muscle innervations during these eye movements. This was done using an inverted model of the eye plant. Our results indicate that the non-linear force-velocity relationship (i.e. muscle viscosity) of the muscles is probably the cause of the kinematic differences between centrifugal and centripetal saccades. In chapter 3 we calculate the adjustment of the saccadic command that is necessary to compensate for the eye plant non-linearities. These calculations show that the agonist and antagonist muscles require different net saccade signal gain changes. In order to better understand how this gain change is accomplished we use the inverted model of the eye plant (chapter 2) to calculate the muscle innervation profiles of saccades with different starting orientations. Based on these calculations we conclude that the saccade signal gain changes are accomplished primarily by changes in the magnitude of the saccade signal. In chapter 4 we examine the requirements that the oculomotor system must meet for the eye to be able to make desired gaze changes and fixate at various eye orientations. We first determine how the axes of action (i.e. unit moment vectors) of the muscles are related to eye orientation and the location of the effective muscle origin (i.e. the muscle pulleys). Next we show how this relation constrains muscle pulley locations if the eye movements are controlled by specific rules. The two control theories we investigate are: 1. Eye movements that obey Listing's law, and the binocular extension of Listing's law, actively use only the horizontal and vertical muscle pairs. 2. Oculomotor control involves perfect agonist-antagonist muscle alignment. In chapter 5 we test two assumptions that are commonly made in models of the oculomotor plant. The first is the assumption that the antagonistic muscles can be viewed as a single bi-directional muscle. The second is the assumption that the three muscle pairs act in orthogonal directions. On the basis of the geometrical properties governing the muscle paths we show how these assumptions give rise to incorrect predictions for the oculomotor control signals. Using the same muscle activation patterns for eye plant models with and without these assumptions we calculate the eye orientations that are reached. Finally in chapter 6 we discuss some general conclusions concerning the consequences of the mechanics of the eye for oculomotor control

Torsional eye movements in humans

If one has to give a description of eye movements, what first comes to mind is the possibility of the eyes to rotate in horizontal and vertical directions. It is generally less obvious that the eyes are capable of moving in a third. namely the torsional. direction. This capability is by no means hypothetical: humans, as well as other species, possess eye muscles that are pulling in torsional direction and orbital mechanics do allow for a certain amount of torsion. Definition of torsion Torsional eye movements can be defined in two different ways, namely as a rotation about the line of sight and as a rotation about an antero-posterior (forward-to-backward) axis that is fixed in the head

Decoding 3D search coil signals in a non-homogeneous magnetic field

We present a method for recording eye-head movements with the magnetic search coil technique in a small external magnetic field. Since magnetic fields are typically non-linear, except in a relative small region in the center small field frames have not been used for head-unrestrained experiments in oculomotor studies. Here we present a method for recording 3D eye movements by accounting for the magnetic non-linearities using the Biot-Savart law. We show that the recording errors can be significantly reduced by monitoring current head position and thereby taking the location of the eye in the external magnetic field into account

A geometric basis for measurement of three-dimensional eye position using image processing

AbstractPolar cross correlation is commonly used for determination of ocular torsion from video images, but breaks down at eccentric positions if the spherical geometry of the eye is not considered. We have extended this method to allow three-dimensional eye position measurement over a range of ±20 deg by determining the correct projection of the eye onto the image plane of the camera. We also determine the orientation of the camera with respect to the eye, allowing eye position to be represented in appropriate head-fixed coordinates. These algorithms have been validated using both in vitro and in vivo measures of eye position

Computational Study of Multisensory Gaze-Shift Planning

In response to appearance of multimodal events in the environment, we often make a gaze-shift in order to focus the attention and gather more information. Planning such a gaze-shift involves three stages: 1) to determine the spatial location for the gaze-shift, 2) to find out the time to initiate the gaze-shift, 3) to work out a coordinated eye-head motion to execute the gaze-shift. There have been a large number of experimental investigations to inquire the nature of multisensory and oculomotor information processing in any of these three levels separately. Here in this thesis, we approach this problem as a single executive program and propose computational models for them in a unified framework. The first spatial problem is viewed as inferring the cause of cross-modal stimuli, whether or not they originate from a common source (chapter 2). We propose an evidence-accumulation decision-making framework, and introduce a spatiotemporal similarity measure as the criterion to choose to integrate the multimodal information or not. The variability of report of sameness, observed in experiments, is replicated as functions of the spatial and temporal patterns of target presentations. To solve the second temporal problem, a model is built upon the first decision-making structure (chapter 3). We introduce an accumulative measure of confidence on the chosen causal structure, as the criterion for initiation of action. We propose that gaze-shift is implemented when this confidence measure reaches a threshold. The experimentally observed variability of reaction time is simulated as functions of spatiotemporal and reliability features of the cross-modal stimuli. The third motor problem is considered to be solved downstream of the two first networks (chapter 4). We propose a kinematic strategy that coordinates eye-in-head and head-on-shoulder movements, in both spatial and temporal dimensions, in order to shift the line of sight towards the inferred position of the goal. The variabilities in contributions of eyes and head movements to gaze-shift are modeled as functions of the retinal error and the initial orientations of eyes and head. The three models should be viewed as parts of a single executive program that integrates perceptual and motor processing across time and space

Design of a Humanoid Robot Eye

This chapter addresses the design of a robot eye featuring the mechanics and motion characteristics of a human one. In particular the goal is to provide guidelines for the implementation of a tendon driven robot capable to emulate saccadic motions. In the first part of this chapter the physiological and mechanical characteristics of the eyeplant1 in humans and primates will be reviewed. Then, the fundamental motion strategies used by humans during saccadic motions will be discussed, and the mathematical formulation of the relevant Listing\u2019s Law and Half-Angle Rule, which specify the geometric and kinematic characteristics of ocular saccadic motions, will be introduced