How neural interactions form neural responses in the salamander retina

Complete synchronization in fixed/preassigned time of multilayered heterogeneous networks

This paper is concentrated on the fixed/preassigned-time (FXT/PAT) synchronization of multilayered networks, in which the self-dynamics of nodes are heterogeneous and the synchronized state can be an arbitrary prescribed smooth orbit. Above all, the original network is augmented by involving the synchronized state as a virtual node, it is allowed to remove the topological connectivity limitations and reduce the conservatism of the synchronization conditions. Subsequently, several continuous control protocols have been developed to achieve FXT synchronization and some effective criteria are established by utilizing the theorem of FXT stability. Additionally, the relationship is revealed between the estimation of the synchronized time and the layer parameter. Moreover, the PAT synchronization is investigated for a preassigned synchronized time by proposing two control schemes with finite control gains. Eventually, the developed control designs and criteria are validated by some numerical simulations.

Simulating the impact of photoreceptor loss and inner retinal network changes on electrical activity of the retina

Objective.A major reason for poor visual outcomes provided by existing retinal prostheses is the limited knowledge of the impact of photoreceptor loss on retinal remodelling and its subsequent impact on neural responses to electrical stimulation. Computational network models of the neural retina assist in the understanding of normal retinal function but can be also useful for investigating diseased retinal responses to electrical stimulation.Approach.We developed and validated a biophysically detailed discrete neuronal network model of the retina in the software package NEURON. The model includes rod and cone photoreceptors, ON and OFF bipolar cell pathways, amacrine and horizontal cells and finally, ON and OFF retinal ganglion cells with detailed network connectivity and neural intrinsic properties. By accurately controlling the network parameters, we simulated the impact of varying levels of degeneration on retinal electrical function.Main results.Our model was able to reproduce characteristic monophasic and biphasic oscillatory patterns seen in ON and OFF neurons during retinal degeneration (RD). Oscillatory activity occurred at 3 Hz with partial photoreceptor loss and at 6 Hz when all photoreceptor input to the retina was removed. Oscillations were found to gradually weaken, then disappear when synapses and gap junctions were destroyed in the inner retina. Without requiring any changes to intrinsic cellular properties of individual inner retinal neurons, our results suggest that changes in connectivity alone were sufficient to give rise to neural oscillations during photoreceptor degeneration, and significant network connectivity destruction in the inner retina terminated the oscillations.Significance.Our results provide a platform for further understanding physiological retinal changes with progressive photoreceptor and inner RD. Furthermore, our model can be used to guide future stimulation strategies for retinal prostheses to benefit patients at different stages of disease progression, particularly in the early and mid-stages of RD.

A single retinal circuit model for multiple computations

Vision is dependent on extracting intricate features of the visual information from the outside world, and complex visual computations begin to take place as soon as at the retinal level. In multiple studies on salamander retinas, the responses of a subtype of retinal ganglion cells, i.e., fast/biphasic-OFF ganglion cells, have been shown to be able to realize multiple functions, such as the segregation of a moving object from its background, motion anticipation, and rapid encoding of the spatial features of a new visual scene. For each of these visual functions, modeling approaches using extended linear-nonlinear cascade models suggest specific preceding retinal circuitries merging onto fast/biphasic-OFF ganglion cells. However, whether multiple visual functions can be accommodated together in a certain retinal circuitry and how specific mechanisms for each visual function interact with each other have not been investigated. Here, we propose a physiologically consistent, detailed computational model of the retinal circuit based on the spatiotemporal dynamics and connections of each class of retinal neurons to implement object motion sensitivity, motion anticipation, and rapid coding in the same circuit. Simulations suggest that multiple computations can be accommodated together, thereby implying that the fast/biphasic-OFF ganglion cell has potential to output a train of spikes carrying multiple pieces of information on distinct features of the visual stimuli.

Real-time emulator for reproducing graded potentials in vertebrate retina

In most parts of the retina, neuronal circuits process visual signals represented by slowly changing membrane potentials, or so-called graded potentials. A feasible approach to speculate about the functional roles of retinal neuronal circuits is to reproduce the graded potentials of retinal neurons in response to natural scenes. In this study, we developed a simulation platform for reproducing graded potentials with the following features: real-time reproduction of retinal neural activities in response to natural scenes, a configurable model structure, and compact hardware. The spatio-temporal properties of neurons were emulated efficiently by a mixed analog-digital architecture that consisted of analog resistive networks and a field-programmable gate array. The neural activities on sustained and transient pathways were emulated from 128 × 128 inputs at 200 frames per second.

A continuum neuronal tissue model based on a two-compartmental representation of cells

Although significant advances have been made in continuum modeling of cardiac and smooth muscle tissue, the progress in neuronal continuum modeling has been slower. In this paper, a continuum neuronal tissue model based on a two-compartmental representation of cells is presented. Each neuron is described using both a somatic compartment modeled by the classical Hodgkin-Huxley current kinetics and a dendritic compartment based on a passive RC formulation. In addition, a synaptic current is fed into the dendritic compartment to account for the presynaptic influence of cells located within the dendritic field of each soma. A number of cases are simulated, including intracellular current injection into either the dendritic or somatic compartments, as well as extracellular current stimulation with and without synaptic input into neurons. The model incorporates a number of parameters controlling neuronal excitability which can be adjusted to validate each neuron's responses against experimental data, allowing for the modeling of different neuronal cell types and behaviors.

Convolution based method for calculating inputs from dendritic fields in a continuum model of the retina

Computational models are valuable tools that can be used to aid the design and test the efficacy of electrical stimulation strategies in prosthetic vision devices. In continuum models of retinal electrophysiology, the effective extracellular potential can be considered as an approximate measure of the electrotonic loading a neuron's dendritic tree exerts on the soma. A convolution based method is presented to calculate the local spatial average of the effective extracellular loading in retinal ganglion cells (RGCs) in a continuum model of the retina which includes an active RGC tissue layer. The method can be used to study the effect of the dendritic tree size on the activation of RGCs by electrical stimulation using a hexagonal arrangement of electrodes (hexpolar) placed in the suprachoroidal space.

A continuum model of the retinal network and its response to electrical stimulation

A continuum network model of the retina is presented, consisting of an active implementation of the retinal ganglion cell tissue layer and passive implementation of deeper cell layers. The retinal ganglion cell layer receives excitatory presynaptic inputs from the bipolar layer and inhibitory presynaptic inputs from the amacrine layer. Simulations were performed to investigate the behavior of retinal tissue activation with epiretinal and suprachoroidal electrode stimulation. The results indicated the presence of both early and late onset action potentials consistent with experimental findings.

A retinal circuit model accounting for wide-field amacrine cells

In previous experimental studies on the visual processing in vertebrates, higher-order visual functions such as the object segregation from background were found even in the retinal stage. Previously, the "linear-nonlinear" (LN) cascade models have been applied to the retinal circuit, and succeeded to describe the input-output dynamics for certain parts of the circuit, e.g., the receptive field of the outer retinal neurons. And recently, some abstract models composed of LN cascades as the circuit elements could explain the higher-order retinal functions. However, in such a model, each class of retinal neurons is mostly omitted and thus, how those neurons play roles in the visual computations cannot be explored. Here, we present a spatio-temporal computational model of the vertebrate retina, based on the response function for each class of retinal neurons and on the anatomical inter-cellular connections. This model was capable of not only reproducing the spatio-temporal filtering properties of the outer retinal neurons, but also realizing the object segregation mechanism in the inner retinal circuit involving the "wide-field" amacrine cells. Moreover, the first-order Wiener kernels calculated for the neurons in our model showed a reasonable fit to the kernels previously measured in the real retinal neuron in situ.

The temporal structure of transient ON/OFF ganglion cell responses and its relation to intra-retinal processing

A subpopulation of transient ON/OFF ganglion cells in the turtle retina transmits changes in stimulus intensity as series of distinct spike events. The temporal structure of these event sequences depends systematically on the stimulus and thus carries information about the preceding intensity change. To study the spike events' intra-retinal origins, we performed extracellular ganglion cell recordings and simultaneous intracellular recordings from horizontal and amacrine cells. Based on these data, we developed a computational retina model, reproducing spike event patterns with realistic intensity dependence under various experimental conditions. The model's main features are negative feedback from sustained amacrine onto bipolar cells, and a two-step cascade of ganglion cell suppression via a slow and a fast transient amacrine cell. Pharmacologically blocking glycinergic transmission results in disappearance of the spike event sequence, an effect predicted by the model if a single connection, namely suppression of the fast by the slow transient amacrine cell, is weakened. We suggest that the slow transient amacrine cell is glycinergic, whereas the other types release GABA. Thus, the interplay of amacrine cell mediated inhibition is likely to induce distinct temporal structure in ganglion cell responses, forming the basis for a temporal code.

How the retinal network reacts to epiretinal stimulation to form the prosthetic visual input to the cortex

We considered the problem of determining how the retinal network may interact with electrical epiretinal stimulation in shaping the spike trains of ON and OFF ganglion cells, and thus the synaptic input to first-stage cortical neurons. To do so, we developed a biophysical model of the retinal network with nine stacked neuronal mosaics. Here, we describe the model's behavior under (i) electrical stimulation of a retina with complete cone photoreceptor loss, but an otherwise intact circuitry and (ii) electrical stimulation of a fully-functional retina. Our results show that electrical stimulation alone results in indiscriminate excitation of ON and OFF ganglion cells and a patchy input to the cortex with islands of excitation among regions of no net excitation. Activation of the retinal network biases the excitation of ON relative to OFF ganglion cells, and in addition, gradually interpolates and focuses the initial, patchy synaptic input to the cortex. As stimulation level increases, the cortical input spreads beyond the area occupied by the electrode contact. Further, at very strong stimulation levels, ganglion cell responses begin to saturate, resulting in a significant distortion in the spatial profile of the cortical input. These findings occur in both the normal and the degenerated retina simulations, but the normal retina exhibits a tighter spatiotemporal response. The complex spatiotemporal dynamics of the prosthetic input to the cortex that are revealed by our model should be addressed by prosthetic image encoders and by studies that simulate prosthetic vision.

Effective Electrode Configuration for Selective Stimulation With Inner Eye Prostheses

The quality of visual perception with retinal prostheses strongly depends on the local selectivity. Electrode arrays at the surface of the retina should excite exclusively cells within a local area but they are expected to co-stimulate bypassing axons originating from ganglion cells of the outer regions. Long electrodes parallel to these axons are shown to be good candidates for avoiding the co-stimulation phenomenon. Efficiency of focal excitation depends on the length and resistance of the electrodes.

A model of high-frequency oscillatory potentials in retinal ganglion cells

High-frequency oscillatory potentials (HFOPs) have been recorded from ganglion cells in cat, rabbit, frog, and mudpuppy retina and in electroretinograms (ERGs) from humans and other primates. However, the origin of HFOPs is unknown. Based on patterns of tracer coupling, we hypothesized that HFOPs could be generated, in part, by negative feedback from axon-bearing amacrine cells excited via electrical synapses with neighboring ganglion cells. Computer simulations were used to determine whether such axon-mediated feedback was consistent with the experimentally observed properties of HFOPs. (1) Periodic signals are typically absent from ganglion cell PSTHs, in part because the phases of retinal HFOPs vary randomly over time and are only weakly stimulus locked. In the retinal model, this phase variability resulted from the nonlinear properties of axon-mediated feedback in combination with synaptic noise. (2) HFOPs increase as a function of stimulus size up to several times the receptive-field center diameter. In the model, axon-mediated feedback pooled signals over a large retinal area, producing HFOPs that were similarly size dependent. (3) HFOPs are stimulus specific. In the model, gap junctions between neighboring neurons caused contiguous regions to become phase locked, but did not synchronize separate regions. Model-generated HFOPs were consistent with the receptive-field center dynamics and spatial organization of cat alpha cells. HFOPs did not depend qualitatively on the exact value of any model parameter or on the numerical precision of the integration method. We conclude that HFOPs could be mediated, in part, by circuitry consistent with known retinal anatomy.

Limulus vision in the marine environment

Horseshoe crabs use vision to find mates. They can reliably detect objects resembling potential mates under a variety of lighting conditions. To understand how they achieve this remarkable performance, we constructed a cell based realistic model of the lateral eye to compute the ensembles of optic nerve activity ("neural images") it transmits to the brain. The neural images reveal a robust encocding of mate-like objects that move underwater during the day. The neural images are much less clear at night, even though the eyes undergo large circadian increases of sensitivity that nearly compensate for the millionfold decreasein underwater lighting after sundown. At night the neurral images are noisy, dominated by bursts of nerve impulses from random photon events that occur at low nighttime levels of illumination. Deciphering the eye's input to the brain begins at the first synaptic level with lowpass temporal and spatial filtering. Both neural filtering mechanisms improve the signal-to-noise properties of the eye's input, yielding clearer neural images of potential mates, especiallyat night. Insights about visual processing by the relatively simple visual system of Limulus may aid in the designof robotic sensors for the marine environment.

Cell-based model of the Limulus lateral eye

We present a cell-based model of the Limulus lateral eye that computes the eye's input to the brain in response to any specified scene. Based on the results of extensive physiological studies, the model simulates the optical sampling of visual space by the array of retinal receptors (ommatidia), the transduction of light into receptor potentials, the integration of excitatory and inhibitory signals into generator potentials, and the conversion of generator potentials into trains of optic nerve impulses. By simulating these processes at the cellular level, model ommatidia can reproduce response variability resulting from noise inherent in the stimulus and the eye itself, and they can adapt to changes in light intensity over a wide operating range. Programmed with these realistic properties, the model eye computes the simultaneous activity of its ensemble of optic nerve fibers, allowing us to explore the retinal code that mediates the visually guided behavior of the animal in its natural habitat. We assess the accuracy of model predictions by comparing the response recorded from a single optic nerve fiber to that computed by the model for the corresponding receptor. Correlation coefficients between recorded and computed responses were typically >95% under laboratory conditions. Parametric analyses of the model together with optic nerve recordings show that animal-to-animal variation in the optical and neural properties of the eye do not alter significantly its response to objects having the size and speed of horseshoe crabs. The eye appears robustly designed for encoding behaviorally important visual stimuli. Simulations with the cell-based model provide insights about the design of the Limulus eye and its encoding of the animal's visual world.

Spatiotemporal patterns at the retinal output

Edge enhancement in the retina is thought to be mediated by classical center-surround antagonism, first encountered as the interactions between horizontal cells and cones. But in the salamander retina these interactions do little to enhance edges. Instead, a robust dynamic interaction between amacrine and bipolar cells appears to be responsible for a sharp edge enhancement. To demonstrate this we recorded extracellularly from a single ganglion cell and moved a flashed square, 300 micro(m) on a side, over a 1.5 x 1.0 mm2 grid at 25-micro(m) increments. Playing back all of these recordings simultaneously simulated the pattern of responses that would have been measured from an array of ganglion cells. The emerging pattern of ganglion cell activity first faithfully represented the flashed square, but after approximately 60 ms the center of the representation collapsed, leaving a representation of only the edges. We inferred that the feedback synapse from amacrine to bipolar cells at gamma-aminobutyric acid-C (GABAC) receptors mediated this effect: bicuculline and strychnine were ineffective in altering the response pattern, but in picrotoxin the center of the representation did not collapse. The GABAergic amacrine cells thought to mediate this effect have quite narrow spread of processes, so the existence of this edge-enhancing effect suggests a mechanism quite different from classical lateral inhibition, namely the delayed inhibition of a spatially expanding input pattern.