Modeling dynamical interactions between fast and slow movements: fast saccadic eye movement behavior in the presence of the slower VOR

An ongoing controversy has to do with the interactions between “fast” (saccadic, quick phase) and “slow” (all other) eye movements. By attacking such issues with both experimental and especially simulation studies using our nonlinear sixth order reciprocally innervated model of the eye mechanical system, insights can be gained into the nature of these nontrivial phenomena. In our present study we relied both (1) on simulation of saccades under a wide range of experimental conditions [vestibular ocular reflex (VOR) velocities from -100 to 100 deg/sec, VOR induced position ranges from -30 to 30 degrees, time-optimal saccades ranging from 2 to 40 degrees], and (2) on using a wide variety of computer simulation of eye movement models, ranging from nonlinear ones with first and especially second order multipulse step controller signal structures, to different controller signal interaction schemes, to simulation using linearized models. We have isolated two important nonlinear phenomena: a level I nonlinear mechanical interaction, dependent not only on the initial velocity but also on the “position effect,” a new finding; and a level II nonlinear neurological interaction, close to “squelching” of the VOR controller signals by the dominating saccadic signal. Furthermore, we have used our simulation findings to reinterpret others' experimental data on eye movement interactions, including saccadic-smooth pursuit, saccadic-vergence, and vestibular nystagmus.     

Computational principles underlying the recognition of acoustic signals in insects

Many animals produce pulse-like signals during acoustic communication. These signals exhibit structure on two time scales: they consist of trains of pulses that are often broadcast in packets—so called chirps. Temporal parameters of the pulse and of the chirp are decisive for female preference. Despite these signals being produced by animals from many different taxa (e.g. frogs, grasshoppers, crickets, bushcrickets, flies), a general framework for their evaluation is still lacking. We propose such a framework, based on a simple and physiologically plausible model. The model consists of feature detectors, whose time-varying output is averaged over the signal and then linearly combined to yield the behavioral preference. We fitted this model to large data sets collected in two species of crickets and found that Gabor filters—known from visual and auditory physiology—explain the preference functions in these two species very well. We further explored the properties of Gabor filters and found a systematic relationship between parameters of the filters and the shape of preference functions. Although these Gabor filters were relatively short, they were also able to explain aspects of the preference for signal parameters on the longer time scale due to the integration step in our model. Our framework explains a wide range of phenomena associated with female preference for a widespread class of signals in an intuitive and physiologically plausible fashion. This approach thus constitutes a valuable tool to understand the functioning and evolution of communication systems in many species.     

Afferent signals from pigeon extraocular muscles modify the vestibular responses of units in the abducens nucleus.

Although the extraocular muscles contain stretch receptors it is generally believed that their afferents exert no influence on the control of eye movement. However, we have shown previously that these afferent signals reach various brainstem centres concerned with eye movement, notably the vestibular nuclei, and that the decerebrate pigeon is a favourable preparation in which to study their effects. If the extraocular muscle afferents do influence oculomotor control from moment-to-moment they should exert a demonstrable effect on the oculomotor nuclei. We now present evidence that extraocular muscle afferent signals do, indeed, alter the responses of units in an oculomotor nucleus (the abducens, VI nerve nucleus, which supplies the lateral rectus muscle) to horizontal, vestibular stimulation induced by sinusoidal oscillation of the bird. Such stimuli evoke a vestibulo-ocular reflex in the intact bird. The extraocular stretch receptors were activated by passive eye movement within the pigeon's saccadic range; such movements modified the vestibular responses of all 19 units studied which were all, histologically, in the abducens nucleus. The magnitude of the effects, purely inhibitory in 15 units, depended both on the amplitude and the velocity of the eye movement and most units showed selectivity for particular combinations of plane (e.g. horizontal versus vertical) and direction (e.g. rostral versus caudal) of eye movement. The results show that an afferent signal from the extraocular muscles influences vestibularly driven activity in the abducens nucleus to which it carries information related to amplitude, velocity, plane and direction of eye movement in the saccadic range. They thus strongly support the view that extraocular afferent signals are involved in the control of eye movement.     

Reactions of male domestic chicks to two-dimensional eye-like shapes

There is considerable evidence that eye-shapes are aversive to the domestic chick but controversy remains over the relative importance of various features of the eyes in causing aversion. In this study the potency of various eye-like shapes in causing avoidance was evaluated. It was shown that monochromatic, two-dimensional eye shapes elicit avoidance and fear in young male domestic chicks, and that the eye shapes are not responded to merely as conspicuous objects. Horizontal orientation, pairedness and the presence of both an ‘iris’ and a ‘pupil’ are important recognition cues. The shape of the eye-like stimulus appears to be more important than its size. Circularity of the iris is not an essential feature but further work is necessary before conclusions can be drawn regarding the shape of the pupil although the available evidence does suggest that circularity is important.     

The Viscoelastic Properties of Passive Eye Muscle in Primates. III: Force Elicited by Natural Elongations

We have recently shown that in monkey passive extraocular muscles the force induced by a stretch does not depend on the entire length history, but to a great extent is only a function of the last elongation applied. This led us to conclude that Fung''s quasi-linear viscoelastic (QLV) model, and more general nonlinear models based on a single convolution integral, cannot faithfully mimic passive eye muscles. Here we present additional data about the mechanical properties of passive eye muscles in deeply anesthetized monkeys. We show that, in addition to the aforementioned failures, previous models also grossly overestimate the force exerted by passive eye muscles during smooth elongations similar to those experienced during normal eye movements. Importantly, we also show that the force exerted by a muscle following an elongation is largely independent of the elongation itself, and it is mostly determined by the final muscle length. These additional findings conclusively rule out the use of classical viscoelastic models to mimic the mechanical properties of passive eye muscles. We describe here a new model that extends previous ones using principles derived from research on thixotropic materials. This model is able to account reasonably well for our data, and could thus be incorporated into models of the eye plant.     

Sensitivity of control parameters in a model of saccadic eye tracking and estimation of resultant nervous activity

A model for the extraocular plant of the human visual eye tracking mechanisms is discussed. Its sensitivity to variation of controller signal nervous activity is studied in order to determine the type of activity that yields realistic simulations characteristic of typical saccadic eye movements.     

Analysis of an optimal control model of multi-joint arm movements

 In this paper, we propose a model of biological motor control for generation of goal-directed multi-joint arm movements, and study the formation of muscle control inputs and invariant kinematic features of movements. The model has a hierarchical structure that can determine the control inputs for a set of redundant muscles without any inverse computation. Calculation of motor commands is divided into two stages, each of which performs a transformation of motor commands from one coordinate system to another. At the first level, a central controller in the brain accepts instructions from higher centers, which represent the motor goal in the Cartesian space. The controller computes joint equilibrium trajectories and excitation signals according to a minimum effort criterion. At the second level, a neural network in the spinal cord translates the excitation signals and equilibrium trajectories into control commands to three pairs of antagonist muscles which are redundant for a two-joint arm. No inverse computation is required in the determination of individual muscle commands. The minimum effort controller can produce arm movements whose dynamic and kinematic features are similar to those of voluntary arm movements. For fast movements, the hand approaches a target position along a near-straight path with a smooth bell-shaped velocity. The equilibrium trajectories in X and Y show an ‘N’ shape, but the end-point equilibrium path zigzags around the hand path. Joint movements are not always smooth. Joint reversal is found in movements in some directions. The excitation signals have a triphasic (or biphasic) pulse pattern, which leads to stereotyped triphasic (or biphasic) bursts in muscle control inputs, and a dynamically modulated joint stiffness. There is a fixed sequence of muscle activation from proximal muscles to distal muscles. The order is preserved in all movements. For slow movements, it is shown that a constant joint stiffness is necessary to produce a smooth movement with a bell-shaped velocity. Scaled movements can be reproduced by varying the constraints on the maximal level of excitation signals according to the speed of movement. When the inertial parameters of the arm are altered, movement trajectories can be kept invariant by adjusting the pulse height values, showing the ability to adapt to load changes. These results agree with a wide range of experimental observations on human voluntary movements. Received: 4 December 1995 / Accepted in revised form: 17 September 1996     

A computational study of the passive mechanisms of eye restraint during head impact trauma

A finite element model of the eye and the orbit was used to examine the hypothesis that the orbital fat provides an important mechanism of eye stability during head trauma. The model includes the globe, the orbital fat, the extra-ocular muscles, and the optic nerve. MRI images of an adult human orbit were used to generate an idealized geometry of the orbital space. The globe was approximated as a sphere 12 mm in radius. The optic nerve and the sclera were represented as thin shells, whereas the vitreous and the orbital fat were represented as nearly incompressible solids of low stiffness. The orbital bone was modelled as a rigid shell. Frontal head impact resulting from a fall onto a hard floor was simulated by prescribing to the orbital bone a triangular acceleration pulse of 200 g (1962 m/s(2)) peak for a duration of 4.5 ms. The results show that the fat provides the crucial passive mechanism of eye restraint. The mechanism is a consequence of the fact that the fat is incompressible and that its motion is restricted by the rigidity of the orbital walls. Thus, the acceleration loads of short duration cannot generate significant distortion of the fat. In contrast, the passive muscles provide little support to the globe. When the connection between the orbital fat and the eye is absent the eye is held mainly by the optic nerve. We discuss the possible role that this loss of contact may have in some cases of the evulsion of the eye and the optic nerve.     

Evolution of genetic variation for condition-dependent traits in stalk-eyed flies

Sexual selection has been proposed to increase genetic variation for condition-dependent ornaments. The condition capture model predicts the genetic variance for a sexually selected trait from the genetic variance in condition and the slope of the relationship between the ornament and condition. Assuming that body size reflects condition we assess the efficacy of this model using six species of stalk-eyed flies (Diopsidae). Prior evidence indicates that male eye span exhibits strong condition dependence and is under sexual selection in sexually dimorphic but not monomorphic species. In contrast, thorax width is weakly related to condition and probably under stabilizing selection. We estimated additive genetic variances for eye span, body length and thorax width from half-sib breeding studies and found that the condition capture model explained 97% of the variation in eye span genetic variance but only 7% of thorax width genetic variance. Comparison of phylogenetically independent contrasts revealed that evolutionary change in male eye span genetic variance is due to evolutionary change in the allometric relationship between eye span and condition: not to evolutionary change in genetic variance for condition. These results suggest that sexual selection can accelerate evolutionary change in condition-dependent male ornaments by increasing the genetic variation available for selection.     

Computer simulation of the hydrostatic skeleton. The physical equivalent, mathematics and application to worm-like forms

The functional principles of a hydrostatic skeleton were combined to obtain a physical model which includes geometry, number and length-tension relationships of the elastic elements in the body wall, internal volume and internal pressure. The model skeleton with pre-set internal volume assumes a certain shape and develops a specific internal pressure in order to minimize the potential energy stored in the elastic elements. This shape is calculated as equilibrium state by using finite element methods and optimization techniques. This model is flexible enough to accommodate different geometries and length-tension-relationships of the elastic elements. Presently, the model is implemented with linear length-tension relationships and certain geometrical restrictions, such as uniform width over the entire animal, and rectangular cross sections; the general case is outlined. First simulations with the "unit-worm" yield stable solutions, i.e. stable shapes for all combinations of parameters tested so far. They define the conditions for bringing all muscles to an optimal operating point. We detected a pressure maximum with increasing volume, assessed the contribution of circular muscles to bending, and determined the shapes of animals with different muscle activations in each body half (Chapman-matrix). We summarize our results by the volume rule and stabilization rule, two simple concepts which predict changes in shape as the result of muscle activation.     

Size and shape in the phylum Phoronida

The lophophorate phylum Phoronida consists of about 13 species, which differ in body length and width, number of longitudinal muscles, lophophore geometry and number of lophophore tentacles. In absolute terms large species have a larger body width, more tentacles, more longitudinal muscles and greater coiling of the lophophore than small species. However, size and shape analyses suggest that with increasing size: (I) the body surface area to volume ratio increases because body length increases faster than body width; (2) the relative number longitudinal muscles decreases, and (3) the relative feeding surface area of the lophophore decreases because tentacle diameter is constant while tentacle number increases at the same rate as body length and tentacle length increases more slowly than tentacle number. Coiling and spiraling of the lophophore in large species may be an attempt to compensate for this last relationship. We suggest that the habits, mode of growth and feeding mechanism of phoronids constrain size-related changes in shape.     

Phenotypic plasticity in the Antarctic nototheniid fish Trematomus newnesi: a guide to the identification of typical, large mouth and intermediate morphs

Trematomus newnesi is a common inshore species with a circum-Antarctic distribution. It provides the only known example of phenotypic plasticity in Antarctic notothenioid fish, existing as populations of typical, large mouth and intermediate morphs that can be difficult to identify. Using specimens from both Potter Cove, King George/25 de Mayo Island, and from McMurdo Sound, we found that the morphometric measurements gape width/head length (HL), upper jaw length/HL and, to a lesser extent, orbit diameter/HL reliably separated the morphs. For use in a key, we converted the ratios into the qualitative characters head shape, head width and upper jaw length relative to middle of the eye. To increase the reliability of the key, we also assessed intra-morph variability in these characters. The key is supplemented with colour photographs illustrating the distinctive features for separation of the morphs. We discovered that, in the case of the specimens from Potter Cove, each morph had a distinct pattern of colouration: typical—trunk blotched, with yellow or orange-brown predominating especially on pectoral and caudal fins; large mouth—trunk blotched, with green predominating especially in pectoral and opercular regions; and intermediate—trunk less blotched, with homogeneous dark brown-grey on trunk, pectoral and caudal fins. We also discuss the ecological implications of colour in the morphs.     

Angle of gaze and optic flow direction modulate body sway

Optic flow is a crucial signal in maintaining postural stability. We sought to investigate whether the activity of postural muscles and body sway was modulated by eye position during the view of radial optic flow stimuli. We manipulated the spatial distribution of dot speed and the fixation point position to simulate specific heading directions combined with different gaze positions. The experiments were performed using stabilometry and surface electromyography (EMG) on 24 right-handed young, healthy volunteers. Center of pressure (COP) signals were analyzed considering antero-posterior and medio-lateral oscillation, COP speed, COP area, and the prevalent direction of oscillation of body sway. We found a significant main effect of body side in all COP parameters, with the right body side showing greater oscillations. The different combinations of optic flow and eye position evoked a non-uniform direction of oscillations in females. The EMG analysis showed a significant main effect for muscle and body side. The results showed that the eye position modulated body sway without changing the activity of principal leg postural muscles, suggesting that the extraretinal input regarding the eye position is a crucial signal that needs to be integrated with perceptual optic flow processing in order to control body sway.     

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.     

A pulse generator simulating slit-scan chromosome analysis signals

A simple circuit is described for generating a variety of electronic pulses to test hardware and software for slit-scan chromosome analysis in a flow cytometer. The pulse shape can be changed to have different numbers of local minima, thereby simulating fluorescence pulses from acrocentric, monocentric, and dicentric chromosomes. Long pulses simulate aggregates of chromosomes. The pulse repetition rate as well as the pulse amplitude is variable. Although the circuitry is built with only three integrated circuits, the pulse-to-pulse variation in shape and height is quite small. After digitization of the analog signals, the constructed histograms of pulse integrals show a relative coefficient of variation below 1%. This signal generator provides a valuable tool for a number of electronic test applications that would otherwise require expensive standard particles analyzed in a well-tuned flow cytometer.     

Control of neural synchrony using channelrhodopsin-2: a computational study

In this paper, we present an optical stimulation based approach to induce 1:1 in-phase synchrony in a network of coupled interneurons wherein each interneuron expresses the light sensitive protein channelrhodopsin-2 (ChR2). We begin with a transition rate model for the channel kinetics of ChR2 in response to light stimulation. We then define "functional optical time response curve (fOTRC)" as a measure of the response of a periodically firing interneuron (transfected with ChR2 ion channel) to a periodic light pulse stimulation. We specifically consider the case of unidirectionally coupled (UCI) network and propose an open loop control architecture that uses light as an actuation signal to induce 1:1 in-phase synchrony in the UCI network. Using general properties of the spike time response curves (STRCs) for Type-1 neuron model (Ermentrout, Neural Comput 8:979-1001, 1996) and fOTRC, we estimate the (open loop) optimal actuation signal parameters required to induce 1:1 in-phase synchrony. We then propose a closed loop controller architecture and a controller algorithm to robustly sustain stable 1:1 in-phase synchrony in the presence of unknown deviations in the network parameters. Finally, we test the performance of this closed-loop controller in a network of mutually coupled (MCI) interneurons.     

The Viscoelastic Properties of Passive Eye Muscle in Primates. II: Testing the Quasi-Linear Theory

We have extensively investigated the mechanical properties of passive eye muscles, in vivo, in anesthetized and paralyzed monkeys. The complexity inherent in rheological measurements makes it desirable to present the results in terms of a mathematical model. Because Fung''s quasi-linear viscoelastic (QLV) model has been particularly successful in capturing the viscoelastic properties of passive biological tissues, here we analyze this dataset within the framework of Fung''s theory.We found that the basic properties assumed under the QLV theory (separability and superposition) are not typical of passive eye muscles. We show that some recent extensions of Fung''s model can deal successfully with the lack of separability, but fail to reproduce the deviation from superposition.While appealing for their elegance, the QLV model and its descendants are not able to capture the complex mechanical properties of passive eye muscles. In particular, our measurements suggest that in a passive extraocular muscle the force does not depend on the entire length history, but to a great extent is only a function of the last elongation to which it has been subjected. It is currently unknown whether other passive biological tissues behave similarly.     

Afferent signals from the extraocular muscles of the pigeon modify the electromyogram of these muscles during the vestibulo-ocular reflex.

There is no general agreement on whether afferent signals from the extraocular muscles play any part in oculomotor control. However, we have previously shown that they modify the responses of cells in the oculomotor control system during the vestibulo-ocular reflex (VOR). If, as we suspect, these signals have an important role in the control of the VOR from moment-to-moment, we should be able to demonstrate similar, functionally significant, modifications at the output of the reflex. We have recorded the electromyographic activity of several extraocular muscles of the right eye during the VOR and while imposing movements on the left eye. We describe how the activity of the muscles, reflected in the electromyogram, is modified in specific ways depending on the parameters of the imposed eye movements. The effects of the extraocular afferent signals on the eye-muscle responses to vestibular drive during the slow phase of the VOR appear to be corrective. Thus the present results provide strong evidence that afferent signals from the extraocular muscles are concerned in the control of the reflex from moment-to-moment, and suggest that the wider question of their role in oculomotor control merits further consideration.