The "practical mathematics" of recording three-dimensional eye position using scleral coils.

The "gold standard" for recording the three-dimensional rotation of the eye involves placing two coils of wire, embedded in a soft plastic ring, on the sclera of the eye, then placing the subject inside a set of orthogonal oscillating magnetic fields, and using the currents induced in the eye coils to deduce the position of the coil, and hence of the eye, in space. Eye movements are actually eye rotations, which can be described mathematically by a special class of matrices, rotation matrices, or, alternatively, by a rotation vector related to the axis of the rotation. This article deals with the mathematical tools needed to implement the signal processing from such a multifield, dual-coil system and compute the precise rotational movement of the eye. One reason for making such careful measurements is to study an interesting constraint on eye movements, called Listing's law, which expresses ocular torsion, or rotation of the eye about its line of sight, in terms of the direction of gaze. Techniques for experimentally quantitating these constraints are also presented. Following a treatment of the "ideal" case, with coils and eye in perfect alignment, the additional techniques for dealing with various departures from ideality that are almost always encountered experimentally are examined. A final section deals with developing a validation protocol for eye movement analysis techniques using mechanical and computer simulations of eye movements.     

Dorsal premotor neurons encode the relative position of the hand, eye, and goal during reach planning

When reaching to grasp an object, we often move our arm and orient our gaze together. How are these movements coordinated? To investigate this question, we studied neuronal activity in the dorsal premotor area (PMd) and the medial intraparietal area (area MIP) of two monkeys while systematically varying the starting position of the hand and eye during reaching. PMd neurons encoded the relative position of the target, hand, and eye. MIP neurons encoded target location with respect to the eye only. These results indicate that whereas MIP encodes target locations in an eye-centered reference frame, PMd uses a relative position code that specifies the differences in locations between all three variables. Such a relative position code may play an important role in coordinating hand and eye movements by computing their relative position.     

Self-Organizing Task Modules and Explicit Coordinate Systems in a Neural Network Model for 3-D Saccades

The goal of this study was to train an artificial neural network to generate accurate saccades in Listing's plane and then determine how the hidden units performed the visuomotor transformation. A three-layer neural network was successfully trained, using back-prop, to take in oculocentric retinal error vectors and three-dimensional eye orientation and to generate the correct head-centric motor error vector within Listing's plane. Analysis of the hidden layer of trained networks showed that explicit representations of desired target direction and eye orientation were not employed. Instead, the hidden-layer units consistently divided themselves into four parallel modules: a dominant "vector-propagation" class (approximately 50% of units) with similar visual and motor tuning but negligible position sensitivity and three classes with specific spatial relations between position, visual, and motor tuning. Surprisingly, the vector-propagation units, and only these, formed a highly precise and consistent orthogonal coordinate system aligned with Listing's plane. Selective "lesions" confirmed that the vector-propagation module provided the main drive for saccade magnitude and direction, whereas a balance between activity in the other modules was required for the correct eye-position modulation. Thus, contrary to popular expectation, error-driven learning in itself was sufficient to produce a "neural" algorithm with discrete functional modules and explicit coordinate systems, much like those observed in the real saccade generator.     

Neural control of three-dimensional eye and head movements

Although the eyes and head can potentially rotate about any three-dimensional axis during orienting gaze shifts, behavioral recordings have shown that certain lawful strategies--such as Listing's law and Donders' law--determine which axis is used for a particular sensory input. Here, we review recent advances in understanding the neuromuscular mechanisms for these laws, the neural mechanisms that control three-dimensional head posture, and the neural mechanisms that coordinate three-dimensional eye orientation with head motion. Finally, we consider how the brain copes with the perceptual consequences of these motor acts.     

The composition of central programs subserving horizontal eye movements in man

A hypothesis is presented which describes, in biomechanical terms, the central programs underlying horizontal eye movements in man. It is suggested that eye movements are produced by means of programmed shifts of the so-called invariant muscle characteristics (static force vs angle of gaze). These shifts lead to a change of the equilibrium point resulting from the interaction of agnnist and antagonist muscles and, as a consequence, to movement and the attainment of a new position of gaze. A reciprocal or a coactivation command to agonist and antagonist muscles occurs when their characteristics shift with respect to the coordinate in the same or opposite directions, respectively. It is proposed that during pursuit and saccadic eye movements a supperposition of the both central commands occurs. During a saccade, the reciprocal command develops evenly up to a certain level. The initial and final levels of the reciprocal command dictate the respective position of gaze and therefore the size of the saccade. The coactivation command develops to a maximum level and is slowly switched off when the new position of gaze has been achieved. The magnitude of the coactivation command seems to be not connected with an absolute position of gaze. It provides probably a stability of the movement and, in particular, prevents overshoot and oscillation during the saccade. The same timing of these commands occurs during pursuit movements, but the magnitude of the coactivation command and the rates of the development of the both commands are less in this case and correlate with the velocity of the movement. This hypothesis enables the tension changes in the muscle during saccadic and pursuit movements to be simulated in qualitative accordance with unique experimental data obtained by Collins et al. (1975). The functional significance of superposition of these motor commands and similarity in the efferent organization of eye and limb movements are discussed.     

Three-dimensional vestibular eye and head reflexes of the chameleon: characteristics of gain and phase and effects of eye position on orientation of ocular rotation axes during stimulation in yaw direction

We investigated gaze-stabilizing reflexes in the chameleon using the three-dimensional search-coil technique. Animals were rotated sinusoidally around an earth-vertical axis under head-fixed and head-free conditions, in the dark and in the light. Gain, phase and the influence of eye position on vestibulo-ocular reflex rotation axes were studied. During head-restrained stimulation in the dark, vestibulo-ocular reflex gaze gains were low (0.1-0.3) and phase lead decreased with increasing frequencies (from 100 degrees at 0.04 Hz to < 30 degrees at 1 Hz). Gaze gains were larger during stimulation in the light (0.1-0.8) with a smaller phase lead (< 30 degrees) and were close to unity during the head-free conditions (around 0.6 in the dark, around 0.8 in the light) with small phase leads. These results confirm earlier findings that chameleons have a low vestibulo-ocular reflex gain during head-fixed conditions and stimulation in the dark and higher gains during head-free stimulation in the light. Vestibulo-ocular reflex eye rotation axes were roughly aligned with the head's rotation axis and did not systematically tilt when the animals were looking eccentrically, up- or downward (as predicted by Listing's Law). Therefore, vestibulo-ocular reflex responses in the chameleon follow a strategy, which optimally stabilizes the entire retinal images, a result previously found in non-human primates.     

Optimal response of eye and hand motor systems in pointing at a visual target

In a task requiring an optimal hand pointing (with regards to both time and accuracy) at a peripheral target, there is first a saccade of the eye within 250 ms, followed 100 ms later by the hand movement. However the latency of the hand movement is poorly correlated with that of the eye movement. When the peripheral target is cut off at the onset of the saccade, there is no correlation between the error of the gaze position and the error of the hand pointing. This suggests an early parallel processing of the two motor outputs. The duration of hand movement does not change significantly when subjects either see or not see their hand (closed or open loop). In the open loop situation, the undershoot of the hand pointing increases with target eccentricity, whatever the subjects are allowed or not to do a saccade toward the target. It suggests that the encoding of eye position by itself is a poor index for an accurately guided movement of the hand.     

Variables Contributing to the Coordination of Rapid Eye/Head Gaze Shifts

In this article results of several published studies are synthesized in order to address the neural system for the determination of eye and head movement amplitudes of horizontal eye/head gaze shifts with arbitrary initial head and eye positions. Target position, initial head position, and initial eye position span the space of physical parameters for a planned eye/head gaze saccade. The principal result is that a functional mechanism for determining the amplitudes of the component eye and head movements must use the entire space of variables. Moreover, it is shown that amplitudes cannot be determined additively by summing contributions from single variables. Many earlier models calculate amplitudes as a function of one or two variables and/or restrict consideration to best-fit linear formulae. Our analysis systematically eliminates such models as candidates for a system that can generate appropriate movements for all possible initial conditions. The results of this study are stated in terms of properties of the response system. Certain axiom sets for the intrinsic organization of the response system obey these properties. We briefly provide one example of such an axiomatic model. The results presented in this article help to characterize the actual neural system for the control of rapid eye/head gaze shifts by showing that, in order to account for behavioral data, certain physical quantities must be represented in and used by the neural system. Our theoretical analysis generates predictions and identifies gaps in the data. We suggest needed experiments.     

Kinematics of Visually-Guided Eye Movements

One of the hallmarks of an eye movement that follows Listing’s law is the half-angle rule that says that the angular velocity of the eye tilts by half the angle of eccentricity of the line of sight relative to primary eye position. Since all visually-guided eye movements in the regime of far viewing follow Listing’s law (with the head still and upright), the question about its origin is of considerable importance. Here, we provide theoretical and experimental evidence that Listing’s law results from a unique motor strategy that allows minimizing ocular torsion while smoothly tracking objects of interest along any path in visual space. The strategy consists in compounding conventional ocular rotations in meridian planes, that is in horizontal, vertical and oblique directions (which are all torsion-free) with small linear displacements of the eye in the frontal plane. Such compound rotation-displacements of the eye can explain the kinematic paradox that the fixation point may rotate in one plane while the eye rotates in other planes. Its unique signature is the half-angle law in the position domain, which means that the rotation plane of the eye tilts by half-the angle of gaze eccentricity. We show that this law does not readily generalize to the velocity domain of visually-guided eye movements because the angular eye velocity is the sum of two terms, one associated with rotations in meridian planes and one associated with displacements of the eye in the frontal plane. While the first term does not depend on eye position the second term does depend on eye position. We show that compounded rotation - displacements perfectly predict the average smooth kinematics of the eye during steady- state pursuit in both the position and velocity domain.     

Derivation of the angle of torsion of the eye.

The angle of torsion of the eye, that is the amount by which the eye rotates about its anterio-posterior axis, changes with the direction of the line of fixation. If the eye can be considered as a rigid body under an elaborate system for constraints its motion can be described by the laws of kinematics. The techniques of linear algebra can then be used to derive an explicit relationship between the angles defining the direction of fixation and the angle of torsion of the eye. The angle of torsion can then be expressed as a function of the angle of rotation of the eye and the direction cosines of the axis of rotation. However, under conditions in which Listing's Law holds these angles, are well defined functions of the angles defining the direction of fixation, and so the angle of torsion, in this case, can be expressed as an explicit function of this direction.     

Spatial modulation of primate inferotemporal responses by eye position

Background

A key aspect of representations for object recognition and scene analysis in the ventral visual stream is the spatial frame of reference, be it a viewer-centered, object-centered, or scene-based coordinate system. Coordinate transforms from retinocentric space to other reference frames involve combining neural visual responses with extraretinal postural information.

Methodology/Principal Findings

We examined whether such spatial information is available to anterior inferotemporal (AIT) neurons in the macaque monkey by measuring the effect of eye position on responses to a set of simple 2D shapes. We report, for the first time, a significant eye position effect in over 40% of recorded neurons with small gaze angle shifts from central fixation. Although eye position modulates responses, it does not change shape selectivity.

Conclusions/Significance

These data demonstrate that spatial information is available in AIT for the representation of objects and scenes within a non-retinocentric frame of reference. More generally, the availability of spatial information in AIT calls into questions the classic dichotomy in visual processing that associates object shape processing with ventral structures such as AIT but places spatial processing in a separate anatomical stream projecting to dorsal structures.     

Evidence for on-line visual guidance during saccadic gaze shifts.

Rapid orientating movements of the eyes are believed to be controlled ballistically. The mechanism underlying this control is thought to involve a comparison between the desired displacement of the eye and an estimate of its actual position (obtained from the integration of the eye velocity signal). This study shows, however, that under certain circumstances fast gaze movements may be controlled quite differently and may involve mechanisms which use visual information to guide movements prospectively. Subjects were required to make large gaze shifts in yaw towards a target whose location and motion were unknown prior to movement onset. Six of those tested demonstrated remarkable accuracy when making gaze shifts towards a target that appeared during their ongoing movement. In fact their level of accuracy was not significantly different from that shown when they performed a 'remembered' gaze shift to a known stationary target (F3,15 = 0.15, p > 0.05). The lack of a stereotypical relationship between the skew of the gaze velocity profile and movement duration indicates that on-line modifications were being made. It is suggested that a fast route from the retina to the superior colliculus could account for this behaviour and that models of oculomotor control need to be updated.     

Responses of collicular fixation neurons to gaze shift perturbations in head-unrestrained monkey reveal gaze feedback control

A prominent hypothesis in motor control is that endpoint errors are minimized because motor commands are updated in real time via internal feedback loops. We investigated in monkey whether orienting saccadic gaze shifts made in the dark with coordinated eye-head movements are controlled by feedback. We recorded from superior colliculus fixation neurons (SCFNs) that fired tonically during fixation and were silent during gaze shifts. When we briefly (相似文献   

Eye-Head Coordination for Visual Cognitive Processing

We investigated coordinated movements between the eyes and head (“eye-head coordination”) in relation to vision for action. Several studies have measured eye and head movements during a single gaze shift, focusing on the mechanisms of motor control during eye-head coordination. However, in everyday life, gaze shifts occur sequentially and are accompanied by movements of the head and body. Under such conditions, visual cognitive processing influences eye movements and might also influence eye-head coordination because sequential gaze shifts include cycles of visual processing (fixation) and data acquisition (gaze shifts). In the present study, we examined how the eyes and head move in coordination during visual search in a large visual field. Subjects moved their eyes, head, and body without restriction inside a 360° visual display system. We found patterns of eye-head coordination that differed those observed in single gaze-shift studies. First, we frequently observed multiple saccades during one continuous head movement, and the contribution of head movement to gaze shifts increased as the number of saccades increased. This relationship between head movements and sequential gaze shifts suggests eye-head coordination over several saccade-fixation sequences; this could be related to cognitive processing because saccade-fixation cycles are the result of visual cognitive processing. Second, distribution bias of eye position during gaze fixation was highly correlated with head orientation. The distribution peak of eye position was biased in the same direction as head orientation. This influence of head orientation suggests that eye-head coordination is involved in gaze fixation, when the visual system processes retinal information. This further supports the role of eye-head coordination in visual cognitive processing.     

Unequal saccades generated by velocity interactions in the peripheral oculomotor system

Experiments with precision eye movement recordings show binocularly unequal saccades to be present under several stimulus conditions having as a common theme ongoing low velocities at the times of the saccades. Simulations using a model of eye muscles and eyeball dynamics reproduce these unequal saccades in quantitative agreement with the experimental findings. The model uses equal innervation for the saccades, and demonstrates a peripheral interaction between the muscle forces and the eye velocities to be the cause of the large inequality of the simulated binocular saccades. Thus, the simulations provide evidence that Hering's law continues to describe the innervation patterns to corresponding muscles producing these binocularly unequal saccades found in the experimental situation.     

一个常染色体显性遗传先天性眼外肌 纤维化家系A

为寻找疾病相关基因,通过随访调查、体检、病理检查等手段,发现了一眼外肌纤维化家系4代中有15人患有眼外肌纤维化综合征,主要表现先天性上眼睑下垂、下颌上举、头后仰、双眼固定下转位和被动牵拉试验阳性,眼外肌病理检查结果为肌纤维化和玻璃样变性,所有阳性体征者除眼球运动限制程度有区别外,其他眼部症状基本相同。遗传分析表明,该疾病属常染色体显性遗传。该家系可作为寻找眼外肌纤维化疾病相关基因的宝贵资源。Abstract: To discover novel disease genes, a family with congenital fibrosis of the extraocular muscle was studied by a follow-up investigation, eye examinations and histo-pathological examination. There were fifteen cases suffering from congenital general fibrosis syndrome in four generations. They have congenital blepharoptosis, head tilt, chin lift, primary gaze fixed in a hypo- and exotropic position. The diagnosis is confirmed with positive forced duction testing in the affected eye. Furthermore, fibrosis of the extraocular muscles and hyaline degeneration was confirmed by histo-pathological examination. Except for different levels of restriction of the eyeball movements , other eye symptoms in positive patients are substantially identical. The genetic analysis showed that this disease was caused by autosomal dominant inheritance. The pedigree may be precious resource candidate for discovering disease gene related with congenital fibrosis of the extraocular muscle.     

Oculocentric frames of reference for limb movement

We have reviewed evidence that suggests that the target for limb motion is encoded in a retinocentric frame of reference. Errors in pointing that are elicited by an illusion that distorts the perceived motion of a target are strongly correlated with errors in gaze position. The modulations in the direction and speed of ocular smooth pursuit and of the hand show remarkable similarities, even though the inertia of the arm is much larger than that of the eye. We have suggested that ocular motion is constrained so that gaze provides an appropriate target signal for the hand. Finally, ocular and manual tracking deficits in patients with cerebellar ataxia are very similar. These deficits are also consistent with the idea that a gaze signal provides the target for hand motion; in some cases limb ataxia would be a consequence of optic ataxia rather than reflecting a deficit in the control of limb motion per se. These results, as well as neurophysiological data summarized here, have led us to revise a hypothesis we have previously put forth to account for the initial stages of sensorimotor transformations underlying targeted limb motions. In the original hypothesis, target location and initial arm posture were ultimately encoded in a common frame of reference tied to somatosensation, i.e. a body-centered frame of reference, and a desired change in posture was derived from the difference between the two. In our new scheme, a movement vector is derived from the difference between variables encoded in a retinocentric frame of reference. Accordingly, gaze, with its exquisite ability to stabilize a target image even under dynamic conditions, would be used as a reference signal. Consequently, this scheme would facilitate the processing of information under conditions in which the body and the target are moving relative to each other.     

Ciliary muscle contraction force and trapezius muscle activity during manual tracking of a moving visual target

Previous studies have shown an association of visual demands during near work and increased activity of the trapezius muscle. Those studies were conducted under stationary postural conditions with fixed gaze and artificial visual load. The present study investigated the relationship between ciliary muscle contraction force and trapezius muscle activity across individuals during performance of a natural dynamic motor task under free gaze conditions. Participants (N = 11) tracked a moving visual target with a digital pen on a computer screen. Tracking performance, eye refraction and trapezius muscle activity were continuously measured. Ciliary muscle contraction force was computed from eye accommodative response. There was a significant Pearson correlation between ciliary muscle contraction force and trapezius muscle activity on the tracking side (0.78, p < 0.01) and passive side (0.64, p < 0.05). The study supports the hypothesis that high visual demands, leading to an increased ciliary muscle contraction during continuous eye–hand coordination, may increase trapezius muscle tension and thus contribute to the development of musculoskeletal complaints in the neck–shoulder area. Further experimental studies are required to clarify whether the relationship is valid within each individual or may represent a general personal trait, when individuals with higher eye accommodative response tend to have higher trapezius muscle activity.     

Physiological tremor and control of limb position in 1 and 0 G

Muscle and skeletal mechanoreceptors play an important role for the regulation of muscular tone and the genesis of normal Physiological Tremor (PT). For example if a big limb as the arm or leg is kept against the gravity vector, the la afferent spindle discharges continuously control the load bearing flexor in a negative feedback manner in order to compensate the gravity vector and to the stabilize arm position. This servo-like action, denoted as 'stretch reflex', not only increases static postural stability (tonic stretch reflex) but also counteracts against external disturbances by dynamically increasing the muscle tone. Muscle spindles are very sophisticated sensory organs. They have an own innervation and the endings of the nuclear bag fibres are highly sensitive for small microstretches. EMG and microneurografic studies showed their importance in the mechanism of the 8-12 Hz component for PT. In a 0 G a limb becomes position controlled. In contrast to 1g, where control of limb position is a subordinated function of force compensation in the load bearing muscle, an antagonistic control scheme is necessary in 0 G to compensate the arm against positional drifts. As a consequence there is a shift from load dependent (muscular) to position dependent (skeletal) mechanoreceptors that become involved in the neural control process. As the control process is reflected in the tremor pattern, we investigated arm tremor in a constant limb position in 1 and 0 G.     

Enhancing Sensorimotor Activity by Controlling Virtual Objects with Gaze

This fMRI work studies brain activity of healthy volunteers who manipulated a virtual object in the context of a digital game by applying two different control methods: using their right hand or using their gaze. The results show extended activations in sensorimotor areas, not only when participants played in the traditional way (using their hand) but also when they used their gaze to control the virtual object. Furthermore, with the exception of the primary motor cortex, regional motor activity was similar regardless of what the effector was: the arm or the eye. These results have a potential application in the field of the neurorehabilitation as a new approach to generate activation of the sensorimotor system to support the recovery of the motor functions.