An improved neural-network model for the neural integrator of the oculomotor system: More realistic neuron behavior

The discharge rates of premotor, brain-stem neurons that create eye movements modulate in relation to eye velocity yet firing rates of extraocular motoneurons contain both eye-position and eyevelocity signals. The eye-position signal is derived from the eye-velocity command by means of a neural network which functioins as a temporal integrator. We have previously proposed a network of lateral-inhibitory neurons that is capable of performing the required integration. That analysis centered on the temporal aspects of the signal processing for a limited class of idealized inputs. All of its cells were identical and carried only the integrated signal. Recordings in the brain stem, however, show that neurons in the region of the neural integrator have a variety of background firing rates, all carry some eye-velocity signal as well as the eye-position signal, and carry the former with different strengths depending on the type of eye movement being made. It was necessary to see if the proposed model could be modified to make its neurons more realistic.By modifying the spatial distribution of afferents to the network, we demonstrate that the same basic model functions properly in spite of afferents with nonuniform background firing rates. To introduce the eye-velocity signal a double-layer network, consisting of inhibitory and excitatory cells, was necessary. By presenting the velocity input to only local regions of this network it was shown that all cells in the network still carried the integrated signal and that its cells could carry different eye-velocity signals for different types of eye movements. Thus, this model stimulates quantitatively and qualitatively, the behavior of neurons seen in the region of the neural integrator.     

Effect of boundaries on the response of a neural network.

The effect an abrupt boundary has upon the dynamical response of a neural network is investigated. The retina of the Limulus eye is used as a model system for studying this effect. A theoretical technique is presented for the quantitative prediction of the manner in which this neural network responds in the vicinity of its boundary. Corresponding experimental measurements of the response to moving stimuli by single optic neurons located near retinal boundaries are presented. Theory and experiment show detailed quantitative agreement.     

A model of visually-guided smooth pursuit eye movements based on behavioral observations

We report a model that reproduces many of the behavioral properties of smooth pursuit eye movements. The model is a negative-feedback system that uses three parallel visual motion pathways to drive pursuit. The three visual pathways process image motion, defined as target motion with respect to the moving eye, and provide signals related to image velocity, image acceleration, and a transient that occurs at the onset of target motion. The three visual motion signals are summed and integrated to produce the eye velocity output of the model. The model reproduces the average eye velocity evoked by steps of target velocity in monkeys and humans and accounts for the variation among individual responses and subjects. When its motor pathways are expanded to include positive feedback of eye velocity and a switch, the model reproduces the exponential decay in eye velocity observed when a moving target stops. Manipulation of this expanded model can mimic the effects of stimulation and lesions in the arcuate pursuit area, the middle temporal visual area (MT), and the medial superior temporal visual area (MST).     

Gene regulatory networks reused to build novel traits: co-option of an eye-related gene regulatory network in eye-like organs and red wing patches on insect wings is suggested by optix expression

Co-option of the eye developmental gene regulatory network may have led to the appearance of novel functional traits on the wings of flies and butterflies. The first trait is a recently described wing organ in a species of extinct midge resembling the outer layers of the midge's own compound eye. The second trait is red pigment patches on Heliconius butterfly wings connected to the expression of an eye selector gene, optix. These examples, as well as others, are discussed regarding the type of empirical evidence and burden of proof that have been used to infer gene network co-option underlying the origin of novel traits. A conceptual framework describing increasing confidence in inference of network co-option is proposed. Novel research directions to facilitate inference of network co-option are also highlighted, especially in cases where the pre-existent and novel traits do not resemble each other.     

Relative spike timing in stochastic oscillator networks of the Hermissenda eye

The role of relative spike timing on sensory coding and stochastic dynamics of small pulse-coupled oscillator networks is investigated physiologically and mathematically, based on the small biological eye network of the marine invertebrate Hermissenda. Without network interactions, the five inhibitory photoreceptors of the eye network exhibit quasi-regular rhythmic spiking; in contrast, within the active network, they display more irregular spiking but collective network rhythmicity. We investigate the source of this emergent network behavior first analyzing the role of relative input to spike–timing relationships in individual cells. We use a stochastic phase oscillator equation to model photoreceptor spike sequences in response to sequences of inhibitory current pulses. Although spike sequences can be complex and irregular in response to inputs, we show that spike timing is better predicted if relative timing of spikes to inputs is accounted for in the model. Further, we establish that greater noise levels in the model serve to destroy network phase-locked states that induce non-monotonic stimulus rate-coding, as predicted in Butson and Clark (J Neurophysiol 99:146–154, 2008a; J Neurophysiol 99:155–165, 2008b). Hence, rate-coding can function better in noisy spiking cells relative to non-noisy cells. We then study how relative input to spike–timing dynamics of single oscillators contribute to network-level dynamics. Relative timing interactions in the network sharpen the stimulus window that can trigger a spike, affecting stimulus encoding. Also, we derive analytical inter-spike interval distributions of cells in the model network, revealing that irregular Poisson-like spike emission and collective network rhythmicity are emergent properties of network dynamics, consistent with experimental observations. Our theoretical results generate experimental predictions about the nature of spike patterns in the Hermissenda eye.     

Eye Movement Deficits Are Consistent with a Staging Model of pTDP-43 Pathology in Amyotrophic Lateral Sclerosis

Background

The neuropathological process underlying amyotrophic lateral sclerosis (ALS) can be traced as a four-stage progression scheme of sequential corticofugal axonal spread. The examination of eye movement control gains deep insights into brain network pathology and provides the opportunity to detect both disturbance of the brainstem oculomotor circuitry as well as executive deficits of oculomotor function associated with higher brain networks.

Objective

To study systematically oculomotor characteristics in ALS and its underlying network pathology in order to determine whether eye movement deterioration can be categorized within a staging system of oculomotor decline that corresponds to the neuropathological model.

Methods

Sixty-eight ALS patients and 31 controls underwent video-oculographic, clinical and neuropsychological assessments.

Results

Oculomotor examinations revealed increased anti- and delayed saccades’ errors, gaze-palsy and a cerebellary type of smooth pursuit disturbance. The oculomotor disturbances occurred in a sequential manner: Stage 1, only executive control of eye movements was affected. Stage 2 indicates disturbed executive control plus ‘genuine’ oculomotor dysfunctions such as gaze-paly. We found high correlations (p<0.001) between the oculomotor stages and both, the clinical presentation as assessed by the ALS Functional Rating Scale (ALSFRS) score, and cognitive scores from the Edinburgh Cognitive and Behavioral ALS Screen (ECAS).

Conclusions

Dysfunction of eye movement control in ALS can be characterized by a two-staged sequential pattern comprising executive deficits in Stage 1 and additional impaired infratentorial oculomotor control pathways in Stage 2. This pattern parallels the neuropathological staging of ALS and may serve as a technical marker of the neuropathological spreading.     

Zur Theorie der lateralen Inhibition

Summary Recently it was shown (Reichardt 1961) that lateral neural inhibition, such as was found in the lateral eye of Limulus polyphemus by Hartline and Ratliff, can in principle compensate for the dioptric apparatus of the eye. The model of lateral inhibition in Limulus developed there is here considered further, with emphasis on the changes in the effective structure of the nerve network (and the associated vector transformation) resulting from the forced inactivity of fibers whose inhibition exceeds their excitation. The stability of the network model as a function of the inhibition coefficients is studied and two theorems regarding the stability are proven. The dependence of the properties of the network on the pattern of receptor excitation are investigated and it is shown by examples that the network could be used for form discrimination. This model's relationship to previously known pattern recognition systems is discussed and its possible application in computer technology is mentioned.     

Application of 3-Dimensional Printing Technology to Construct an Eye Model for Fundus Viewing Study

Objective

To construct a life-sized eye model using the three-dimensional (3D) printing technology for fundus viewing study of the viewing system.

Methods

We devised our schematic model eye based on Navarro''s eye and redesigned some parameters because of the change of the corneal material and the implantation of intraocular lenses (IOLs). Optical performance of our schematic model eye was compared with Navarro''s schematic eye and other two reported physical model eyes using the ZEMAX optical design software. With computer aided design (CAD) software, we designed the 3D digital model of the main structure of the physical model eye, which was used for three-dimensional (3D) printing. Together with the main printed structure, polymethyl methacrylate(PMMA) aspherical cornea, variable iris, and IOLs were assembled to a physical eye model. Angle scale bars were glued from posterior to periphery of the retina. Then we fabricated other three physical models with different states of ammetropia. Optical parameters of these physical eye models were measured to verify the 3D printing accuracy.

Results

In on-axis calculations, our schematic model eye possessed similar size of spot diagram compared with Navarro''s and Bakaraju''s model eye, much smaller than Arianpour''s model eye. Moreover, the spherical aberration of our schematic eye was much less than other three model eyes. While in off- axis simulation, it possessed a bit higher coma and similar astigmatism, field curvature and distortion. The MTF curves showed that all the model eyes diminished in resolution with increasing field of view, and the diminished tendency of resolution of our physical eye model was similar to the Navarro''s eye. The measured parameters of our eye models with different status of ametropia were in line with the theoretical value.

Conclusions

The schematic eye model we designed can well simulate the optical performance of the human eye, and the fabricated physical one can be used as a tool in fundus range viewing research.     

Identification of Retinal Transformation Hot Spots in Developing Drosophila Epithelia

Background

The retinal determination (RD) network is an evolutionarily conserved regulatory circuit that governs early events in the development of eyes throughout the animal kingdom. Ectopic expression of many members of this network leads to the transformation of non-retinal epithelia into eye tissue. An often-overlooked observation is that only particular cell-populations within a handful of tissues are capable of having their primary developmental instructions superseded and overruled.

Methodology/Preliminary Findings

Here we confirm that indeed, only a discrete number of cell populations within the imaginal discs that give rise to the head, antenna, legs, wings and halteres have the cellular plasticity to have their developmental fates altered. In contrast to previous reports, we find that all transformable cell populations do not lie within the TGFβ or Hedgehog signaling domains. Additionally neither signaling cascade alone is sufficient for non-retinal cell types to be converted into retinal tissue. The transformation “hot spots” that we have identified appear to coincide with several previously defined transdetermination “weak spots”, suggesting that ectopic eye formation is less the result of one network overriding the orders of another, as previously thought, but rather is the physical manifestation of redirecting cell populations of enormous cellular plasticity. We also demonstrate that the initiation of eye formation in non-retinal tissues occurs asynchronously compared to that of the normal eye suggesting that retinal development is not under the control of a global developmental clock.

Conclusions/Significance

We conclude that the subregions of non-retinal tissues that are capable of supporting eye formation represent specialized cell-populations that have a different level of plasticity than other cells within these tissues and may be the founder cells of each tissue.     

A computational remodeling approach to predict the physiological architecture of the collagen fibril network in corneo-scleral shells

Organized collagen fibrils form complex networks that introduce strong anisotropic and highly nonlinear attributes into the constitutive response of human eye tissues. Physiological adaptation of the collagen network and the mechanical condition within biological tissues are complex and mutually dependent phenomena. In this contribution, a computational model is presented to investigate the interaction between the collagen fibril architecture and mechanical loading conditions in the corneo-scleral shell. The biomechanical properties of eye tissues are derived from the single crimped fibril at the micro-scale via the collagen network of distributed fibrils at the meso-scale to the incompressible and anisotropic soft tissue at the macro-scale. Biomechanically induced remodeling of the collagen network is captured on the meso-scale by allowing for a continuous re-orientation of preferred fibril orientations and a continuous adaptation of the fibril dispersion. The presented approach is applied to a numerical human eye model considering the cornea and sclera. The predicted fibril morphology correlates well with experimental observations from X-ray scattering data.     

Spectral sensitivity of photoreceptors in insect compound eyes: Comparison of species and methods

Summary Three different methods were used to determine the spectral sensitivity of retinula cells in the compound eyes of three species of hymenopteran insects (Apis mellifera, Melipona quadrifasciata, Osmia rufa). The conventional flash method gives the least reliable results. Sensitivity is extremely sensitive to small fluctuations of the resting potential and long lasting changes induced by preceding test flashes. The ramp method, which speeds up a spectral scan to about 1 min and keeps effective illumination constant at every flash, determines S() much more reliably. The best results are obtained with the spectral scan method, which provides the experimenter with aS() function of high spectral resolution within 20 s. Using this method we demonstrate that the high observed variability inS() of individual receptors is the result of the inadequacy of the flash method, which was the only method used in earlier studies.Double microelectrode experiments and variations of the stimulus conditions reveal that field potentials and return flow of electric current produced by activated neighboring cells have no effect in the bee eye. We conclude that the model of Shaw (1975, 1981) of current flow in the locust and fly eye does not apply to the bee eye. Very rare recordings (about 1%) of UV receptors with hyperpolarizing responses to long wavelength light are interpreted as having a synaptic inhibitory connection to green receptors.The improvement of spectral measurements of single receptors allows us for the first time to model the spectral input to a color-coding network with great precision.     

A learning network model of the neural integrator of the oculomotor system

Certain premotor neurons of the oculomotor system fire at a rate proportional to desired eye velocity. Their output is integrated by a network of neurons to supply an eye positon command to the motoneurons of the extraocular muscles. This network, known as the neural integrator, is calibrated during infancy and then maintained through development and trauma with remarkable precision. We have modeled this system with a self-organizing neural network that learns to integrate vestibular velocity commands to generate appropriate eye movements. It learns by using current eye movement on any given trial to calculate the amount of retinal image slip and this is used as the error signal. The synaptic weights are then changed using a straightforward algorithm that is independent of the network configuration and does not necessitate backwards propagation of information. Minimization of the error in this fashion causes the network to develop multiple positive feedback loops that enable it to integrate a push-pull signal without integrating the background rate on which it rides. The network is also capable of recovering from various lesions and of generating more complicated signals to simulate induced postsaccadic drift and compensation for eye muscle mechanics.     

Determination of optical parameters of the porcine eye and development of a simulated model

The eye is a very sophisticated system of optical elements for the preeminent sense of vision. In recent years, the number of laser surgery to correct the optical aberration such as myopia or astigmatism has significantly increased. Consequently, improving the knowledge related to the interactions of light with the eye is very important in order to enhance the efficiency of the surgery. For this reason, a complete optical characterization of the porcine eye is presented in this study. Kubelka‐Munk and Inverse Adding‐Doubling methods were applied to spectroscopy measurement to determine the absorption and scattering coefficients. Furthermore, the refractive index has been measured by ellipsometry. The different parameters were obtained for the cornea, lens, vitreous humor, sclera, iris, choroids and eyelid in the visible and infrared region. Thereafter, the results are implemented in a COMSOL Multiphysics® software to create an eye model. This model gives a better understanding of the propagation of light in the eye by adding optical parts such as the iris, the sclera or the ciliary bodies. Two simulations show the propagation of light from the cornea to the retina but also from the sclera to the retina. This last possibility provides a better understanding of light propagation during eye laser surgery such as, for example, transscleral cyclophotocoagulation. Figure: Eye simulation models allow the development of new laser treatments in a simple and safe way for patients. To this purpose, the creation of an eye simulated model based on optical parameters obtained from experimental data is presented in this study. This model will facilitate the understanding of the light propagation inside the porcine eye.     

Microdissection of Zebrafish Embryonic Eye Tissues

Zebrafish is a popular animal model for research on eye development because of its rapid ex utero development and good fecundity. By 3 days post fertilization (dpf), the larvae will show the first visual response. Many genes have been identified to control a proper eye development, but we are far from a complete understanding of the underlying genetic architecture. Whole genome gene expression profiling is a useful tool to elucidate genetic regulatory network for eye development. However, the small size of the embryonic eye in zebrafish makes it challenging to obtain intact and pure eye tissues for expression analysis. For example, the anterior-posterior length of the eye between day 2 and 3 is only approximately 200-300 μm, while the diameter of the lens is less 100 μm. Also, the retinal pigment epithelium (RPE) underlying the retina is just a single-layer epithelium. While gene expression profiles can be obtained from the whole embryo, they do not accurately represent the expression of these tissues. Therefore pure tissue must be obtained for a successful gene expression profiling of eye development. To address this issue, we have developed an approach to microdissect intact retina and retina with RPE attached from 1-3 dpf, which cover major stages of eye morphogenesis. All procedures can be done with fine forceps and general laboratory supplies under standard stereomicroscopes. For retinal dissection, the single-layer RPE is removed and peeled off by brushing action and the preferential adherence of the RPE remnants to the surface of the culture plate for dissection. For RPE-attached retinal dissection, the adherence of RPE to the dissection plate is removed before the dissection so that the RPE can be completely preserved with the retina. A careful lifting action of this tissue can efficiently separate the presumptive choroid and sclera. The lens can be removed in both cases by a chemically etched tungsten needle. In short, our approach can obtain intact eye tissues and has been successfully utilized to study tissue-specific expression profiles of zebrafish retina^{1, 2} and retinal pigment epithelium³.Download video file.^{(105M, mp4)}     

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.     

Models of the saccadic eye movement control system

1. A sequence of four models is proposed for the saccadic eye movement control system. The models become increasingly complex as they are made to respond to increasingly more complicated target movements in accordance with experimental results. Compatibility with neurological structure and function is stressed in the formation of the models. In each case, the elements of the models are constructed to conform as closely as possible to neuroanatomical structures and behave in a way that has been established or suggested by neurophysiology.
2. The dynamic behavior of the mechanics of the extraocular muscles and eyeball suspensory tissues has been established by recording from oculomotoneurons in alert monkeys. The transfer function of this mechanical system is used in these models.
3. Recent experiments on the neural circuits in the brain stem that are responsible for saccadic eye movements suggest an arrangement of the premotor circuitry that contains two principal neural networks; an integrator and a pulse generator. This circuitry is used in the models.
4. When the above modifications are made to existing models of the saccadic system, they remove the necessity of supposing that the visual information is sampled by the nervous system. The models do not include a sampler although the saccadic pulse generator still makes the overall system behavior similar to that of a sampled-data system.
5. The basic model is modified to make its behavior agree with experimental eye movement responses to target ramps and step-ramps. This is done by using error and its rate of change to estimate the error that will exist one reaction time in the future.
6. Parallel processing of data is a well recognized property of the nervous system. By utilizing it in combination with a random decision threshold, the model is extended to produce results in agreement with experiments for double-step target movements in which the second step occurs less than 0.2 sec after the first.
7. Finally, a model is presented which incorporates a continuum of parallel processing to represent the retinotopic spatial organization of the visual system and the tecto-bulbar motor commands. The model is conceptual; it was not constructed or tested but is used to discuss more complex eye movement phenomena such as those that appear to occur when the decision process must shift between hemispheres and how the system might produce quick correcting saccades with latencies as short as 85 msec.