Impulse encoding mechanisms of ganglion cells in the tiger salamander retina

Theoretical prediction of broadband ambient light optogenetic vision restoration with ChRmine and its mutants

Vision restoration is one of the most promising applications of optogenetics. However, it is limited due to the poor-sensitivity, slow-kinetics and narrow band absorption spectra of opsins. Here, a detailed theoretical study of retinal ganglion neurons (RGNs) expressed with ChRmine, ReaChR, CoChR, CatCh and their mutants, with near monochromatic LEDs, and broadband sunlight, halogen lamp, RGB LED light, and pure white light sources has been presented. All the opsins exhibit improved light sensitivity and larger photocurrent on illuminating with broadband light sources compared to narrow band LEDs. ChRmine allows firing at ambient sunlight (1.5 nW/mm2) and pure white light (1.2 nW/mm2), which is lowest among the opsins considered. The broadband activation spectrum of ChRmine and its mutants is also useful to restore color sensitivity. Although ChRmine exhibits slower turn-off kinetics with broadband light, high-fidelity spikes can be evoked upto 50 Hz. This limit extends upto 80 Hz with the improved hsChRmine mutant although it requires double the irradiance compared to ChRmine. The present study shows that ChRmine and its mutants allow activation of RGNs with ambient light which is useful for goggle-free white light optogenetic retinal prostheses with improved quality of restored vision.

Nanoparticle-based optical interfaces for retinal neuromodulation: a review

Degeneration of photoreceptors in the retina is a leading cause of blindness, but commonly leaves the retinal ganglion cells (RGCs) and/or bipolar cells extant. Consequently, these cells are an attractive target for the invasive electrical implants colloquially known as "bionic eyes." However, after more than two decades of concerted effort, interfaces based on conventional electrical stimulation approaches have delivered limited efficacy, primarily due to the current spread in retinal tissue, which precludes high-acuity vision. The ideal prosthetic solution would be less invasive, provide single-cell resolution and an ability to differentiate between different cell types. Nanoparticle-mediated approaches can address some of these requirements, with particular attention being directed at light-sensitive nanoparticles that can be accessed via the intrinsic optics of the eye. Here we survey the available known nanoparticle-based optical transduction mechanisms that can be exploited for neuromodulation. We review the rapid progress in the field, together with outstanding challenges that must be addressed to translate these techniques to clinical practice. In particular, successful translation will likely require efficient delivery of nanoparticles to stable and precisely defined locations in the retinal tissues. Therefore, we also emphasize the current literature relating to the pharmacokinetics of nanoparticles in the eye. While considerable challenges remain to be overcome, progress to date shows great potential for nanoparticle-based interfaces to revolutionize the field of visual prostheses.

Spike desensitisation as a mechanism for high-contrast selectivity in retinal ganglion cells

In the vertebrate retina, several dozens of parallel channels relay information about the visual world to the brain. These channels are represented by the different types of retinal ganglion cells (RGCs), whose responses are rendered selective for distinct sets of visual features by various mechanisms. These mechanisms can be roughly grouped into synaptic interactions and cell-intrinsic mechanisms, with the latter including dendritic morphology as well as ion channel complement and distribution. Here, we investigate how strongly ion channel complement can shape RGC output by comparing two mouse RGC types, the well-described ON alpha cell and a little-studied ON cell that is EGFP-labelled in the Igfbp5 mouse line and displays an unusual selectivity for stimuli with high contrast. Using patch-clamp recordings and computational modelling, we show that a higher activation threshold and a pronounced slow inactivation of the voltage-gated Na+ channels contribute to the distinct contrast tuning and transient responses in ON Igfbp5 RGCs, respectively. In contrast, such a mechanism could not be observed in ON alpha cells. This study provides an example for the powerful role that the last stage of retinal processing can play in shaping RGC responses.

Retinal ganglion cells undergo cell type-specific functional changes in a computational model of cone-mediated retinal degeneration

Introduction

Understanding the retina in health and disease is a key issue for neuroscience and neuroengineering applications such as retinal prostheses. During degeneration, the retinal network undergoes complex and multi-stage neuroanatomical alterations, which drastically impact the retinal ganglion cell (RGC) response and are of clinical importance. Here we present a biophysically detailed in silico model of the cone pathway in the retina that simulates the network-level response to both light and electrical stimulation.

Methods

The model included 11, 138 cells belonging to nine different cell types (cone photoreceptors, horizontal cells, ON/OFF bipolar cells, ON/OFF amacrine cells, and ON/OFF ganglion cells) confined to a 300 × 300 × 210μm patch of the parafoveal retina. After verifying that the model reproduced seminal findings about the light response of retinal ganglion cells (RGCs), we systematically introduced anatomical and neurophysiological changes (e.g., reduced light sensitivity of photoreceptor, cell death, cell migration) to the network and studied their effect on network activity.

Results

The model was not only able to reproduce common findings about RGC activity in the degenerated retina, such as hyperactivity and increased electrical thresholds, but also offers testable predictions about the underlying neuroanatomical mechanisms.

Discussion

Overall, our findings demonstrate how biophysical changes typified by cone-mediated retinal degeneration may impact retinal responses to light and electrical stimulation. These insights may further our understanding of retinal processing and inform the design of retinal prostheses.

Modeling extracellular stimulation of retinal ganglion cells: theoretical and practical aspects

Objective.Retinal prostheses use electric current to activate inner retinal neurons, providing artificial vision for blind people. Epiretinal stimulation primarily targets retinal ganglion cells (RGCs), which can be modeled with cable equations. Computational models provide a tool to investigate the mechanisms of retinal activation, and improve stimulation paradigms. However, documentation of RGC model structure and parameters is limited, and model implementation can influence model predictions.Approach.We created a functional guide for building a mammalian RGC multi-compartment cable model and applying extracellular stimuli. Next, we investigated how the neuron's three-dimensional shape will influence model predictions. Finally, we tested several strategies to maximize computational efficiency.Main results.We conducted sensitivity analyses to examine how dendrite representation, axon trajectory, and axon diameter influence membrane dynamics and corresponding activation thresholds. We optimized the spatial and temporal discretization of our multi-compartment cable model. We also implemented several simplified threshold prediction theories based on activating function, but these did not match the prediction accuracy achieved by the cable equations.Significance.Through this work, we provide practical guidance for modeling the extracellular stimulation of RGCs to produce reliable and meaningful predictions. Robust computational models lay the groundwork for improving the performance of retinal prostheses.

Electrically-evoked responses for retinal prostheses are differentially altered depending on ganglion cell types in outer retinal neurodegeneration caused by Crb1 gene mutation

Background

Microelectronic prostheses for artificial vision stimulate neurons surviving outer retinal neurodegeneration such as retinitis pigmentosa (RP). Yet, the quality of prosthetic vision substantially varies across subjects, maybe due to different levels of retinal degeneration and/or distinct genotypes. Although the RP genotypes are remarkably diverse, prosthetic studies have primarily used retinal degeneration (rd) 1 and 10 mice, which both have Pde6b gene mutation. Here, we report the electric responses arising in retinal ganglion cells (RGCs) of the rd8 mouse model which has Crb1 mutation.

Methods

We first investigated age-dependent histological changes of wild-type (wt), rd8, and rd10 mice retinas by H&E staining. Then, we used cell-attached patch clamping to record spiking responses of ON, OFF and direction selective (DS) types of RGCs to a 4-ms-long electric pulse. The electric responses of rd8 RGCs were analyzed in comparison with those of wt RGCs in terms of individual RGC spiking patterns, populational characteristics, and spiking consistency across trials.

Results

In the histological examination, the rd8 mice showed partial retinal foldings, but the outer nuclear layer thicknesses remained comparable to those of the wt mice, indicating the early-stage of RP. Although spiking patterns of each RGC type seemed similar to those of the wt retinas, correlation levels between electric vs. light response features were different across the two mouse models. For example, in comparisons between light vs. electric response magnitudes, ON/OFF RGCs of the rd8 mice showed the same/opposite correlation polarity with those of wt mice, respectively. Also, the electric response spike counts of DS RGCs in the rd8 retinas showed a positive correlation with their direction selectivity indices (r = 0.40), while those of the wt retinas were negatively correlated (r = -0.90). Lastly, the spiking timing consistencies of late responses were largely decreased in both ON and OFF RGCs in the rd8 than the wt retinas, whereas no significant difference was found across DS RGCs of the two models.

Conclusion

Our results indicate the electric response features are altered depending on RGC types even from the early-stage RP caused by Crb1 mutation. Given the various degeneration patterns depending on mutation genes, our study suggests the importance of both genotype- and RGC type-dependent analyses for retinal prosthetic research.

Retinal ganglion cells undergo cell typeâ€"specific functional changes in a biophysically detailed model of retinal degeneration

Understanding the retina in health and disease is a key issue for neuroscience and neuroengineering applications such as retinal prostheses. During degeneration, the retinal network undergoes complex and multi-stage neuroanatomical alterations, which drastically impact the retinal ganglion cell (RGC) response and are of clinical importance. Here we present a biophysically detailed in silico model of retinal degeneration that simulates the network-level response to both light and electrical stimulation as a function of disease progression. The model is not only able to reproduce common findings about RGC activity in the degenerated retina, such as hyperactivity and increased electrical thresholds, but also offers testable predictions about the underlying neuroanatomical mechanisms. Overall, our findings demonstrate how biophysical changes associated with retinal degeneration affect retinal responses to both light and electrical stimulation, which may further our understanding of visual processing in the retina as well as inform the design and application of retinal prostheses.

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.

Short pulses of epiretinal prostheses evoke network-mediated responses in retinal ganglion cells by stimulating presynaptic neurons

OBJECTIVE

Microelectronic retinal implant aims to restore functional vision with electric stimulation. Short pulses are generally known to directly activate retinal ganglion cells (RGCs) with a notion of one or two spike(s) per pulse. In the present work, we systematically explore network-mediated responses that arise from various short pulses in both normal and degenerate retinas.

APPROACH

Cell-attached patch clamping was used to record spiking responses of RGCs in wild-type (C57BL/6J) and retinal degeneration (rd10) mice. Alpha RGCs of the mouse retinas were targeted by their large soma sizes and classified by their responses to spot flashes. Then, RGCs were electrically stimulated by various conditions such as duration (100-460 μs), count (1-10), amplitude (100-400 μA), and repeating frequency (10-40 Hz) of short pulses. Also, their responses were compared with each own response to a single 4-ms-long pulse which is known to evoke strong indirect responses.

MAIN RESULTS

Short pulses evoked strong network-mediated responses not only in both ON and OFF types of RGCs in the healthy retinas but also in RGCs of the severely degenerate retina. However, the spike timing consistency across repeats not decreased significantly in the rd10 RGCs compared to the healthy ON and OFF RGCs. Network-mediated responses of ON RGCs were highly dependent on the current amplitude of stimuli but much less on the pulse count and the repetition frequency. In contrast, responses of OFF RGCs were more influenced by the number of stimuli than the current amplitude.

SIGNIFICANCE

Our results demonstrate that short pulses also elicit indirect responses by activating presynaptic neurons. In the case of the commercial retinal prostheses using repeating short pulses, there is a possibility that the performance of clinical devices is highly related to the preserved retinal circuits. Therefore, examination of surviving retinal neurons in patients would be necessary to improve the efficacy of retinal prostheses.

Improving the spatial resolution of artificial vision using midget retinal ganglion cell populations modelled at the human fovea

OBJECTIVE

Retinal prostheses seek to create artificial vision by stimulating surviving retinal neurons of patients with profound vision impairment. Notwithstanding tremendous research efforts, the performance of all implants tested to date has remained rudimentary, incapable of overcoming the threshold for legal blindness. To maximize the perceptual efficacy of retinal prostheses, a device must be capable of controlling retinal neurons with greater spatiotemporal precision. Most studies of retinal stimulation were derived from either non-primate species or the peripheral primate retina. We investigated if artificial stimulation could leverage the high spatial resolution afforded by the neural substrates at the primate fovea and surrounding regions to achieve improved percept qualities.

APPROACH

We began by developing a new computational model capable of generating anatomically accurate retinal ganglion cell (RGC) populations within the human central retina. Next, multiple RGC populations across the central retina were stimulated in-silico to compare clinical and recently proposed neurostimulation configurations based on their ability to improve perceptual efficacy and reduce activation thresholds.

MAIN RESULTS

Our model uniquely upholds eccentricity-dependent characteristics such as RGC density and dendritic field diameter, whilst incorporating anatomically accurate features such as axon projection and three-dimensional RGC layering, features often forgone in favor of reduced computational complexity. Following epiretinal stimulation, the RGCs in our model produced response patterns in shapes akin to the complex percepts reported in clinical trials. Our results also demonstrated that even within the neuron-dense central retina, epiretinal stimulation using a multi-return hexapolar electrode arrangement could reliably achieve spatially focused RGC activation and could achieve single-cell excitation in 74% of all tested locations.

SIGNIFICANCE

This study establishes an anatomically accurate three-dimensional model of the human central retina and demonstrates the potential for an epiretinal hexapolar configuration to achieve consistent, spatially confined retinal responses, even within the neuron-dense foveal region. Our results promote the prospect and optimization of higher spatial resolution in future epiretinal implants.

A finite element method framework to model extracellular neural stimulation

OBJECTIVE

Increasing complexity in extracellular stimulation experiments and neural implant design also requires realistic computer simulations capable of modeling the neural activity of nerve cells under the influence of an electrical stimulus. Classical model approaches are often based on simplifications, are not able to correctly calculate the electric field generated by complex electrode designs, and do not consider electrical effects of the cell on its surrounding. A more accurate approach is the finite element method (FEM), which provides necessary techniques to solve the Poisson equation for complex geometries under consideration of electrical tissue properties. Especially in situations where neurons experience large and non-symmetric extracellular potential gradients, a FEM solution that implements the cell membrane model can improve the computer simulation results. To investigate the response of neurons in an electric field generated by complex electrode designs, a FEM framework for extracellular stimulation was developed in COMSOL.

APPROACH

Methods to implement morphologically- and biophysically-detailed neurons including active Hodgkin-Huxley (HH) cell membrane dynamics as well as the stimulation setup are described in detail. Covered methods are (i) development of cell and electrode geometries including meshing strategies, (ii) assignment of physics for the conducting spaces and the realization of active electrodes, (iii) implementation of the HH model, and (iv) coupling of the physics to get a fully described model.

MAIN RESULTS

Several implementation examples are briefly presented: (i) a full FEM implementation of a HH model cell stimulated with a honeycomb electrode, (ii) the electric field of a cochlear electrode placed inside the cochlea, and (iii) a proof of concept implementation of a detailed double-cable cell membrane model for myelinated nerve fibers.

SIGNIFICANCE

The presented concepts and methods provide basic and advanced techniques to realize a full FEM framework for innovative studies of neural excitation in response to extracellular stimulation.

Predicting Spike Features of Hodgkin-Huxley-Type Neurons With Simple Artificial Neural Network

Hodgkin-Huxley (HH)-type model is the most famous computational model for simulating neural activity. It shows the highest accuracy in capturing neuronal spikes, and its model parameters have definite physiological meanings. However, HH-type models are computationally expensive. To address this problem, a previous study proposed a spike prediction module (SPM) to predict whether a spike will take place 1 ms later based on three voltage values with intervals of 1 ms. Although SPM does well, it fails to evaluate the informative features of the spike. In this study, the feature prediction module (FPM) based on simple artificial neural network (ANN) was proposed to predict spike features including maximum voltage, minimum voltage, and dropping interval. Nine different HH-type models were adopted whose firing patterns cover most of the firing behaviors observed in the brain. Voltage and spike feature samples under constant external input current were collected for training and testing. Experiment results illustrated that the combination of SPM and FPM can accurately predict the spiking part of different HH-type models and can generalize to unseen types of input current. The combination of SPM and FPM may offer a possible way to simulate the action potentials of biological neurons with high accuracy and efficiency.

Mechanisms underlying activation of retinal bipolar cells through targeted electrical stimulation: a computational study

Objective. Retinal implants have been developed to electrically stimulate healthy retinal neurons in the progressively degenerated retina. Several stimulation approaches have been proposed to improve the visual percept induced in patients with retinal prostheses. We introduce a computational model capable of simulating the effects of electrical stimulation on retinal neurons. Leveraging this computational platform, we delve into the underlying mechanisms influencing the sensitivity of retinal neurons' response to various stimulus waveforms.Approach. We implemented a model of spiking bipolar cells (BCs) in the magnocellular pathway of the primate retina, diffuse BC subtypes (DB4), and utilized our multiscale admittance method (AM)-NEURON computational platform to characterize the response of BCs to epiretinal electrical stimulation with monophasic, symmetric, and asymmetric biphasic pulses.Main results. Our investigations yielded four notable results: (a) the latency of BCs increases as stimulation pulse duration lengthens; conversely, this latency decreases as the current amplitude increases. (b) Stimulation with a long anodic-first symmetric biphasic pulse (duration > 8 ms) results in a significant decrease in spiking threshold compared to stimulation with similar cathodic-first pulses (from 98.2 to 57.5µA). (c) The hyperpolarization-activated cyclic nucleotide-gated channel was a prominent contributor to the reduced threshold of BCs in response to long anodic-first stimulus pulses. (d) Finally, extending the study to asymmetric waveforms, our results predict a lower BCs threshold using asymmetric long anodic-first pulses compared to that of asymmetric short cathodic-first stimulation.Significance. This study predicts the effects of several stimulation parameters on spiking BCs response to electrical stimulation. Of importance, our findings shed light on mechanisms underlying the experimental observations from the literature, thus highlighting the capability of the methodology to predict and guide the development of electrical stimulation protocols to generate a desired biological response, thereby constituting an ideal testbed for the development of electroceutical devices.

Morphological Factors that Underlie Neural Sensitivity to Stimulation in the Retina

Retinal prostheses are a promising therapeutic intervention for patients afflicted by outer retinal degenerative diseases like retinitis pigmentosa and age-related macular degeneration. While significant advances in the development of retinal implants have been made, the quality of vision elicited by these devices remains largely sub-optimal. The variability in the responses produced by retinal devices is most likely due to the differences between the natural cell type-specific signaling that occur in the healthy retina vs. the non-specific activation of multiple cell types arising from artificial stimulation. In order to replicate these natural signaling patterns, stimulation strategies must be capable of preferentially activating specific RGC types. To design more selective stimulation strategies, a better understanding of the morphological factors that underlie the sensitivity to prosthetic stimulation must be developed. This review will focus on the role that different anatomical components play in driving the direct activation of RGCs by extracellular stimulation. Briefly, it will (1) characterize the variability in morphological properties of α-RGCs, (2) detail the influence of morphology on the direct activation of RGCs by electric stimulation, and (3) describe some of the potential biophysical mechanisms that could explain differences in activation thresholds and electrically evoked responses between RGC types.

Modeling ON Cone Bipolar Cells for Electrical Stimulation

Retinal prosthetic systems have been developed to help blind patients suffering from retinal degenerative diseases gain some useful form of vision. Various experimental and computational studies have been performed to test electrical stimulation strategies that can improve the performance of these devices. Detailed computational models of retinal neurons, such as retinal ganglion cells (RGCs) and bipolar cells (BCs), allow us to explore the mechanisms underlying the response of cells to electrical stimulation. While electrophysiological studies have shown the presence of voltage-gated ionic channels in different regions of BCs, many of the existing cone BCs models are assumed to be passive or only contain calcium channels at the synaptic terminals. We have utilized our Admittance Method (AM)-NEURON computational platform to implement a more realistic model of ON-BCs. Our model closely replicates the recent patch-clamp experiments directly measuring the response of ON-BCs to epiretinal electrical stimulation and thereby predicts the regional distributions of the ionic channels. Our computational results further indicate that outward potassium current strongly contributes to the depolarizing voltage transient of ON-BCs in response to electrical stimulation.

Theoretical analysis of optogenetic spiking with ChRmine, bReaChES and CsChrimson-expressing neurons for retinal prostheses

Objective.Optogenetics has emerged as a promising technique for neural prosthetics, especially retinal prostheses, with unprecedented spatiotemporal resolution. Newly discovered opsins with high light sensitivity and fast temporal kinetics can provide sufficient temporal resolution at safe light powers and overcome the limitations of presently used opsins. It is also important to formulate accurate mathematical models for optogenetic retinal prostheses, which can facilitate optimization of photostimulation factors to improve the performance.Approach.A detailed theoretical analysis of optogenetic excitation of model retinal ganglion neurons (RGNs) and hippocampal neurons expressed with already tested opsins for retinal prostheses, namely, ChR2, ReaChR and ChrimsonR, and also with recently discovered potent opsins CsChrimson, bReaChES and ChRmine, was carried out.Main results.Under continuous illumination, ChRmine-expressing RGNs begin to respond at very low irradiances ∼10^-4mW mm^-2, and evoke firing upto ∼280 Hz, highest among other opsin-expressing RGNs, at 10^-2mW mm^-2. Under pulsed illumination at randomized photon fluxes, ChRmine-expressing RGNs respond to changes in pulse to pulse irradiances upto four logs, although very bright pulses >10¹⁴photons mm^-2s^-1block firing in these neurons. The minimum irradiance threshold for ChRmine-expressing RGNs is lower by two orders of magnitude, whereas, the first spike latency in ChRmine-expressing RGNs is shorter by an order of magnitude, alongwith stable latency of subsequest spikes compared to others. Further, a good set of photostimulation parameters were determined to achieve high-frequency control with single spike resolution at minimal power. Although ChrimsonR enables spiking upto 100 Hz in RGNs, it requires very high irradiances. ChRmine provides control at light powers that are two orders of magnitude smaller than that required with experimentally studied opsins, while maintaining single spike temporal resolution upto 40 Hz.Significance.The present study highlights the importance of ChRmine as a potential opsin for optogenetic retinal prostheses.

M1-Type, but Not M4-Type, Melanopsin Ganglion Cells Are Physiologically Tuned to the Central Circadian Clock

Proper circadian photoentrainment is crucial for the survival of many organisms. In mammals, intrinsically photosensitive retinal ganglion cells (ipRGCs) can use the photopigment melanopsin to sense light independently from rod and cone photoreceptors and send this information to many brain nuclei such as the suprachiasmatic nucleus (SCN), the site of the central circadian pacemaker. Here, we measure ionic currents and develop mathematical models of the electrical activity of two types of ipRGCs: M1, which projects to the SCN, and M4, which does not. We illustrate how their ionic properties differ, mainly how ionic currents generate lower spike rates and depolarization block in M1 ipRGCs. Both M1 and M4 cells have large geometries and project to higher visual centers of the brain via the optic nerve. Using a partial differential equation model, we show how axons of M1 and M4 cells faithfully convey information from the soma to the synapse even when the signal at the soma is attenuated due to depolarization block. Finally, we consider an ionic model of circadian photoentrainment from ipRGCs synapsing on SCN neurons and show how the properties of M1 ipRGCs are tuned to create accurate transmission of visual signals from the retina to the central pacemaker, whereas M4 ipRGCs would not evoke nearly as efficient a postsynaptic response. This work shows how ipRGCs and SCN neurons' electrical activities are tuned to allow for accurate circadian photoentrainment.

The effect of axon trajectory on retinal ganglion cell activation with epiretinal stimulation

For epiretinal prostheses, disc electrodes stimulate retinal ganglion cells (RGCs) with electric current to create visual percepts. Prior studies have determined that the sodium channel band (SOCB), located on the RGC axon (30-50 μm from the soma) is the most sensitive site to extracellular stimulation because of its high sodium channel density. Biophysical cable models used to study RGC activation in silico often rely on simplified axon trajectories, disregarding the non-uniform paths that axons follow to the optic disc. However, since axonal activation is a critical mechanism in epiretinal stimulation, it is important to investigate variable RGC axon trajectories. In this study, we use a computational model to perform a sensitivity analysis examining how the morphology of an RGC axon affects predictions of retinal activation. We determine that RGC cable models are sensitive to changes in the ascending axon trajectory between the soma and nerve fiber layer. On the other hand, RGC cable models are relatively robust to trajectory deviations in the plane parallel to the disc electrode's surface. Overall, our results suggest that incorporating natural variations of soma depth and nerve fiber layer entry angle could result in a more realistic model of the retina's response to epiretinal stimulation and a better understanding of elicited visual percepts.

Color and cellular selectivity of retinal ganglion cell subtypes through frequency modulation of electrical stimulation

Epiretinal prostheses aim at electrically stimulating the inner most surviving retinal cells-retinal ganglion cells (RGCs)-to restore partial sight to the blind. Recent tests in patients with epiretinal implants have revealed that electrical stimulation of the retina results in the percept of color of the elicited phosphenes, which depends on the frequency of stimulation. This paper presents computational results that are predictive of this finding and further support our understanding of the mechanisms of color encoding in electrical stimulation of retina, which could prove pivotal for the design of advanced retinal prosthetics that elicit both percept and color. This provides, for the first time, a directly applicable "amplitude-frequency" stimulation strategy to "encode color" in future retinal prosthetics through a predictive computational tool to selectively target small bistratified cells, which have been shown to contribute to "blue-yellow" color opponency in the retinal circuitry. The presented results are validated with experimental data reported in the literature and correlated with findings in blind patients with a retinal prosthetic implant collected by our group.

Targeted Stimulation of Retinal Ganglion Cells in Epiretinal Prostheses: A Multiscale Computational Study

Retinal prostheses aim at restoring partial sight to patients that are blind due to retinal degenerative diseases by electrically stimulating the surviving healthy retinal neurons. Ideally, the electrical stimulation of the retina is intended to induce localized, focused, percepts only; however, some epiretinal implant subjects have reported seeing elongated phosphenes in a single electrode stimulation due to the axonal activation of retinal ganglion cells (RGCs). This issue can be addressed by properly devising stimulation waveforms so that the possibility of inducing axonal activation of RGCs is minimized. While strategies to devise electrical stimulation waveforms to achieve a focal RGCs response have been reported in literature, the underlying mechanisms are not well understood. This article intends to address this gap; we developed morphologically and biophysically realistic computational models of two classified RGCs: D1-bistratified and A2-monostratified. Computational results suggest that the sodium channel band (SOCB) is less sensitive to modulations in stimulation parameters than the distal axon (DA), and DA stimulus threshold is less sensitive to physiological differences among RGCs. Therefore, over a range of RGCs distal axon diameters, short-pulse symmetric biphasic waveforms can enhance the stimulation threshold difference between the SOCB and the DA. Appropriately designed waveforms can avoid axonal activation of RGCs, implying a consequential reduction of undesired strikes in the visual field.

Bayesian inference for biophysical neuron models enables stimulus optimization for retinal neuroprosthetics

While multicompartment models have long been used to study the biophysics of neurons, it is still challenging to infer the parameters of such models from data including uncertainty estimates. Here, we performed Bayesian inference for the parameters of detailed neuron models of a photoreceptor and an OFF- and an ON-cone bipolar cell from the mouse retina based on two-photon imaging data. We obtained multivariate posterior distributions specifying plausible parameter ranges consistent with the data and allowing to identify parameters poorly constrained by the data. To demonstrate the potential of such mechanistic data-driven neuron models, we created a simulation environment for external electrical stimulation of the retina and optimized stimulus waveforms to target OFF- and ON-cone bipolar cells, a current major problem of retinal neuroprosthetics.

Responsiveness of Retinal Ganglion Cells Through Frequency Modulation of Electrical Stimulation: A Computational Modeling Study

Electrical stimulation of surviving retinal neurons has proven effective in restoring sight to totally blind patients affected by retinal degenerative diseases. Morphological and biophysical differences among retinal ganglion cells (RGCs) are important factors affecting their response to epiretinal electrical stimulation. Although detailed models of ON and OFF RGCs have already been investigated, here we developed morphologically and biophysically realistic computational models of two classified RGCs, D1-bistratified and A2-monostratified, and analyzed their response to alternations in stimulation frequency (up to 200 Hz). Results show that the D1-bistratified cell is more responsive to high frequency stimulation compared to the A2-monostratified cell. This differential RGCs response suggests a potential avenue for selective activation, and in turn different encoded percept of RGCs.

Creation of virtual channels in the retina using synchronous and asynchronous stimulation - a modelling study

OBJECTIVE

Implantable retinal prostheses aim to provide artificial vision to those suffering from retinal degenerative diseases by electrically stimulating the remaining retinal neurons using a multi-electrode array. The spatial resolution of these devices can be improved by creation of so-called virtual channels (VCs) that are commonly achieved through synchronized stimulation of multiple electrodes. It is largely unclear though if VCs can be created using asynchronous stimulation, which was the primary aim of this study.

APPROACH

A computational model of multi-layered retina and epi-retinal dual-electrode stimulation was developed to simulate the neural activity of populations of retinal ganglion cells (RGCs) using the VC strategy under both synchronous and asynchronous stimulation conditions.

MAIN RESULTS

Our simulation suggests that VCs can be created using asynchronous stimulation. VC performance under both synchronous and asynchronous stimulation conditions can be improved by optimizing stimulation parameters such as current intensity, current ratio (α) between two electrodes, electrode spacing and the stimulation waveform. In particular, two VC performance measures; (1) linear displacement of the centroid of RGC activation, and (2) the RGC activation size consistency as a function of different current ratios α, have comparable performance under asynchronous and synchronous stimulation with appropriately selected stimulation parameters.

SIGNIFICANCE

Our findings support the possibility of creating VCs in the retina under both synchronous and asynchronous stimulation conditions. The results provide theoretical evidence for future retinal prosthesis designs with higher spatial resolution and power efficiency whilst reducing the number of current sources required to achieve these outcomes.

The effect of waveform asymmetry on perception with epiretinal prostheses

Objective

Retinal prosthetic implants have helped improve vision in patients blinded by photoreceptor degeneration. Retinal implant users report improvements in light perception and performing visual tasks, but their ability to perceive shapes and letters is limited due to the low precision of retinal activation, which is exacerbated by axonal stimulation and high perceptual thresholds. A previous in vitro study in our lab used calcium imaging to measure the spatial activity of mouse retinal ganglion cells (RGCs) in response to electrical stimulation. Based on this study, symmetric anodic-first (SA) stimulation effectively avoided axonal activation and asymmetric anodic-first stimulation (AA) with duration ratios (ratio of the anodic to cathodic phase) greater than 10 reduced RGC activation thresholds significantly. Applying these novel stimulation strategies in clinic may increase perception precision and improve the overall patient outcomes.

Approach

We combined human subject testing and computational modeling to further examine the effect of SA and AA stimuli on perception shapes and thresholds for epiretinal stimulation of RGCs.

Main results

Threshold measurement in three Argus II participants indicated that AA stimulation could increase perception probabilities compared to a standard symmetric cathodic-first (SC) pulse, and this effect can be intensified by addition of an interphae gap (IPG). Our in silico RGC model predicts lower thresholds with AA and asymmetric cathodic-first (AC) stimuli compared to a SC pulse. This effect was more pronounced at shorter pulse widths. The most effective pulse for threshold reduction with short pulse durations (≤0.12 ms) was AA stimulation with small duration ratios (≤5) and long IPGs (≥2 ms). For the 0.5 ms pulse duration, SC stimulation with IPGs longer than 0.5 ms, or asymmetric stimuli with large duration ratios (≥20) were most effective in threshold reduction. Phosphene shape analysis did not reveal a significant change in percept elongation with SA stimulation. However, there was a significant increase in percept size (P < 0.01) with AA stimulation compared to the standard pulse in one participant.

Significane

Including asymmetric waveform capability will provide more flexible options for optimization and personalized fitting of retinal implants.

Type-specific dendritic integration in mouse retinal ganglion cells

Neural computation relies on the integration of synaptic inputs across a neuron’s dendritic arbour. However, it is far from understood how different cell types tune this process to establish cell-type specific computations. Here, using two-photon imaging of dendritic Ca²⁺ signals, electrical recordings of somatic voltage and biophysical modelling, we demonstrate that four morphologically distinct types of mouse retinal ganglion cells with overlapping excitatory synaptic input (transient Off alpha, transient Off mini, sustained Off, and F-mini Off) exhibit type-specific dendritic integration profiles: in contrast to the other types, dendrites of transient Off alpha cells were spatially independent, with little receptive field overlap. The temporal correlation of dendritic signals varied also extensively, with the highest and lowest correlation in transient Off mini and transient Off alpha cells, respectively. We show that differences between cell types can likely be explained by differences in backpropagation efficiency, arising from the specific combinations of dendritic morphology and ion channel densities.

Neurons compute by integrating synaptic inputs across their dendritic arbor. Here, the authors show that distinct cell-types of mouse retinal ganglion cells that receive similar excitatory inputs have different biophysical mechanisms of input integration to generate their unique response tuning.

A Patient-Specific Computational Framework for the Argus II Implant

Goal

Retinal prosthesis performance is limited by the variability of elicited phosphenes. The stimulating electrode's position with respect to retinal ganglion cells (RGCs) affects both perceptual threshold and phosphene shape. We created a modeling framework incorporating patient-specific anatomy and electrode location to investigate RGC activation and predict inter-electrode differences for one Argus II user.

Methods

We used ocular imaging to build a three-dimensional finite element model characterizing retinal morphology and implant placement. To predict the neural response to stimulation, we coupled electric fields with multi-compartment cable models of RGCs. We evaluated our model predictions by comparing them to patient-reported perceptual threshold measurements.

Results

Our model was validated by the ability to replicate clinical impedance and threshold values, along with known neurophysiological trends. Inter-electrode threshold differences in silico correlated with in vivo results.

Conclusions

We developed a patient-specific retinal stimulation framework to quantitatively predict RGC activation and better explain phosphene variations.

Voltage- and calcium-gated ion channels of neurons in the vertebrate retina

In this review, we summarize studies investigating the types and distribution of voltage- and calcium-gated ion channels in the different classes of retinal neurons: rods, cones, horizontal cells, bipolar cells, amacrine cells, interplexiform cells, and ganglion cells. We discuss differences among cell subtypes within these major cell classes, as well as differences among species, and consider how different ion channels shape the responses of different neurons. For example, even though second-order bipolar and horizontal cells do not typically generate fast sodium-dependent action potentials, many of these cells nevertheless possess fast sodium currents that can enhance their kinetic response capabilities. Ca2+ channel activity can also shape response kinetics as well as regulating synaptic release. The L-type Ca2+ channel subtype, CaV1.4, expressed in photoreceptor cells exhibits specific properties matching the particular needs of these cells such as limited inactivation which allows sustained channel activity and maintained synaptic release in darkness. The particular properties of K+ and Cl- channels in different retinal neurons shape resting membrane potentials, response kinetics and spiking behavior. A remaining challenge is to characterize the specific distributions of ion channels in the more than 100 individual cell types that have been identified in the retina and to describe how these particular ion channels sculpt neuronal responses to assist in the processing of visual information by the retina.

Analysis of upper threshold mechanisms of spherical neurons during extracellular stimulation

Exceeding a certain stimulation strength can prevent the generation of somatic action potentials, as has been demonstrated in vitro with extracellularly stimulated dorsal root ganglion cells as well as retinal ganglion cells. This phenomenon, termed upper threshold, is currently thought to be a consequence of sodium current reversal in strongly depolarized regions. Here we analyze the contribution of membrane kinetics, using spherical model neurons that are stimulated externally with a microelectrode, in more detail. During extracellular pulse application, the electric field depolarizes one part and hyperpolarizes the other part of the cell. Strong transmembrane currents are generated only in the active depolarized region, changing the overall polarization level. The asymmetric membrane voltage distribution caused by the stimulus strongly influences the cell's behavior during and even after the stimulus. Effects on membrane voltage and transmembrane currents during and after the stimulus are shown and discussed in detail. Aside from the sodium current reversal, two more key mechanisms were identified in causing the upper threshold: strong potassium currents and inactivation of sodium channels. The contributions of the mechanisms involved strongly depend on cell properties, stimulus parameters, and other factors such as temperature. The conclusions presented here are based on several retinal ganglion cell models of the Fohlmeister group, a model with original Hodgkin-Huxley membrane, and a pyramidal cell model. NEW & NOTEWORTHY The upper threshold phenomenon in extracellular stimulation is analyzed in detail for spherical cells. Three main mechanisms were identified that prevent the generation of action potentials at high stimulation strengths: 1) strong potassium currents, 2) inactivating sodium ion channels, and 3) sodium current reversal. Ion channel kinetics in retinal ganglion cells, pyramidal cells, and the original Hodgkin-Huxley model were investigated under the influence of an extracellular stimulus.

Bistability in Hodgkin-Huxley-type equations

We study how initial conditions of the Hodgkin-Huxley model affect the dynamics of simulated neurons. We systematically vary the amplitudes of depolarization currents in order to bring neuron dynamics to stable equilibrium. Our results demonstrate that simulated neurons can have spontaneous spiking or a silent state, depending on the initial conditions. We propose the methodology to study the circumstances under which Purkinje cells transit between hyperpolarized quiescent state (down state) and a depolarized spiking state (up state). We show that results derived using the Hodgkin-Huxley methodology should be carefully analyzed before suggesting a direct relevance to neuroprosthetic implants.

Biophysical basis of the linear electrical receptive fields of retinal ganglion cells

Responses of retinal ganglion cells to direct electrical stimulation have been shown experimentally to be well described by linear-nonlinear models. These models rely on the simplifying assumption that retinal ganglion cell responses to stimulation with an array of electrodes are driven by a simple linear weighted sum of stimulus current amplitudes from each electrode, known as the 'electrical receptive field'.

OBJECTIVE

This paper aims to demonstrate the biophysical basis of the linear-nonlinear model and the electrical receptive field to facilitate the development of improved stimulation strategies for retinal implants.

APPROACH

We compare the linear-nonlinear model of subretinal electrical stimulation with a multi-layered, biophysical, volume conductor model of retinal stimulation.

MAIN RESULTS

Our results show that the linear electrical receptive field of the linear-nonlinear model matches the transmembrane currents induced by electrodes (the activating function) at the site of the high-density sodium channel band with only minor discrepancies. The discrepancies are mostly eliminated by including axial current flow originating from adjacent cell compartments. Furthermore, for cells where a single linear electrical receptive field is insufficient, we show that cell responses are likely driven by multiple sites of action potential initiation with multiple distinct receptive fields, each of which can be accurately described by the activating function.

SIGNIFICANCE

This result establishes that the biophysical basis of the electrical receptive field of the linear-nonlinear model is the superposition of transmembrane currents induced by different electrodes at and near the site of action potential initiation. Together with existing experimental support for linear-nonlinear models of electrical stimulation, this provides a firm basis for using this much simplified model to generate more optimal stimulation patterns for retinal implants.

Increasing Electrical Stimulation Efficacy in Degenerated Retina: Stimulus Waveform Design in a Multiscale Computational Model

A computational model of electrical stimulation of the retina is proposed for investigating current waveforms used in prosthetic devices for restoring partial vision lost to retinal degenerative diseases. The model framework combines a connectome-based neural network model characterized by accurate morphological and synaptic properties with an admittance method model of bulk tissue and prosthetic electronics. In this model, the retina was computationally "degenerated," considering cellular death and anatomical changes that occur early in disease, as well as altered neural behavior that develops throughout the neurodegeneration and is likely interfering with current attempts at restoring vision. A resulting analysis of stimulation range and threshold of ON ganglion cells within the retina that are either healthy or in beginning stages of degeneration is presented for currently used stimulation waveforms, and an asymmetric biphasic current stimulation for subduing spontaneous firing to allow increased control over ganglion cell firing patterns in degenerated retina is proposed. Results show that stimulation thresholds of retinal ganglion cells do not notably vary after beginning stages of retina degeneration. In addition, simulation of proposed asymmetric waveforms showed the ability to enhance the control of ganglion cell firing via electrical stimulation.

Formulation and Implementation of Nonlinear Integral Equations to Model Neural Dynamics Within the Vertebrate Retina

Existing computational models of the retina often compromise between the biophysical accuracy and a hardware-adaptable methodology of implementation. When compared to the current modes of vision restoration, algorithmic models often contain a greater correlation between stimuli and the affected neural network, but lack physical hardware practicality. Thus, if the present processing methods are adapted to complement very-large-scale circuit design techniques, it is anticipated that it will engender a more feasible approach to the physical construction of the artificial retina. The computational model presented in this research serves to provide a fast and accurate predictive model of the retina, a deeper understanding of neural responses to visual stimulation, and an architecture that can realistically be transformed into a hardware device. Traditionally, implicit (or semi-implicit) ordinary differential equations (OES) have been used for optimal speed and accuracy. We present a novel approach that requires the effective integration of different dynamical time scales within a unified framework of neural responses, where the rod, cone, amacrine, bipolar, and ganglion cells correspond to the implemented pathways. Furthermore, we show that adopting numerical integration can both accelerate retinal pathway simulations by more than 50% when compared with traditional ODE solvers in some cases, and prove to be a more realizable solution for the hardware implementation of predictive retinal models.

Upper stimulation threshold for retinal ganglion cell activation

OBJECTIVE

The existence of an upper threshold in electrically stimulated retinal ganglion cells (RGCs) is of interest because of its relevance to the development of visual prosthetic devices, which are designed to restore partial sight to blind patients. The upper threshold is defined as the stimulation level above which no action potentials (direct spikes) can be elicited in electrically stimulated retina.

APPROACH

We collected and analyzed in vitro recordings from rat RGCs in response to extracellular biphasic (anodic-cathodic) pulse stimulation of varying amplitudes and pulse durations. Such responses were also simulated using a multicompartment model.

MAIN RESULTS

We identified the individual cell variability in response to stimulation and the phenomenon known as upper threshold in all but one of the recorded cells (n  =  20/21). We found that the latencies of spike responses relative to stimulus amplitude had a characteristic U-shape. In silico, we showed that the upper threshold phenomenon was observed only in the soma. For all tested biphasic pulse durations, electrode positions, and pulse amplitudes above lower threshold, a propagating action potential was observed in the distal axon. For amplitudes above the somatic upper threshold, the axonal action potential back-propagated in the direction of the soma, but the soma's low level of hyperpolarization prevented action potential generation in the soma itself.

SIGNIFICANCE

An upper threshold observed in the soma does not prevent spike conductance in the axon.

Impact of Electrode Position on the Elicitation of Sodium Spikes in Retinal Bipolar Cells

Bipolar cells of the magnocellular pathway in the primate retina can generate action potentials because they have an axonal segment with high sodium channel density, comparable to the sodium channel band in retinal ganglion cells or pyramidal cells. The similarity between the non-human primate and the human retina is of interest for the research on retinal implants for the blind, and especially, the conditions to elicit sodium spikes in bipolar cells using extracellular stimulation. A comparison of excitation characteristics of three model neurons, a bipolar cell, a retinal ganglion cell, and a cortical pyramidal cell, demonstrates the similarities and differences regarding stimulation with microelectrodes. Moving a microelectrode parallel to the axon of a neuron commonly allows to generate spikes for every position - and this rule holds both for cathodic and anodic pulses. However, for the simulated bipolar cell anodic pulses cannot generate sodium spikes directly. Further, there is only a small region for electrode placing where extracellular cathodic stimulation causes direct spike initiation in the sodium channel band. For all other positions, a sodium spike can only be generated by antidromic current flow originating from strongly depolarized terminals.

High-amplitude electrical stimulation can reduce elicited neuronal activity in visual prosthesis

Retinal electrostimulation is promising a successful therapy to restore functional vision. However, a narrow stimulating current range exists between retinal neuron excitation and inhibition which may lead to misperformance of visual prostheses. As the conveyance of representation of complex visual scenes may require neighbouring electrodes to be activated simultaneously, electric field summation may contribute to reach this inhibitory threshold. This study used three approaches to assess the implications of relatively high stimulating conditions in visual prostheses: (1) in vivo, using a suprachoroidal prosthesis implanted in a feline model, (2) in vitro through electrostimulation of murine retinal preparations, and (3) in silico by computing the response of a population of retinal ganglion cells. Inhibitory stimulating conditions led to diminished cortical activity in the cat. Stimulus-response relationships showed non-monotonic profiles to increasing stimulating current. This was observed in vitro and in silico as the combined response of groups of neurons (close to the stimulating electrode) being inhibited at certain stimulating amplitudes, whilst other groups (far from the stimulating electrode) being recruited. These findings may explain the halo-like phosphene shapes reported in clinical trials and suggest that simultaneous stimulation in retinal prostheses is limited by the inhibitory threshold of the retinal ganglion cells.

Single-compartment models of retinal ganglion cells with different electrophysiologies

There are more than 15 different types of retinal ganglion cells (RGCs) in the mammalian retina. To model responses of RGCs to electrical stimulation, we use single-compartment Hodgkin-Huxley-type models and run simulations in the Neuron environment. We use our recently published in vitro data of different morphological cell types to constrain the model, and study the effects of electrophysiology on the cell responses separately from the effects of morphology. We find simple models that can match the spike patterns of different types of RGCs. These models, with different input-output properties, may be used in a network to study retinal network dynamics and interactions.

A Mammalian Retinal Ganglion Cell Implements a Neuronal Computation That Maximizes the SNR of Its Postsynaptic Currents

Neurons perform computations by integrating excitatory and inhibitory synaptic inputs. Yet, it is rarely understood what computation is being performed, or how much excitation or inhibition this computation requires. Here we present evidence for a neuronal computation that maximizes the signal-to-noise power ratio (SNR). We recorded from OFF delta retinal ganglion cells in the guinea pig retina and monitored synaptic currents that were evoked by visual stimulation (flashing dark spots). These synaptic currents were mediated by a decrease in an outward current from inhibitory synapses (disinhibition) combined with an increase in an inward current from excitatory synapses. We found that the SNR of combined excitatory and disinhibitory currents was voltage sensitive, peaking at membrane potentials near resting potential. At the membrane potential for maximal SNR, the amplitude of each current, either excitatory or disinhibitory, was proportional to its SNR. Such proportionate scaling is the theoretically best strategy for combining excitatory and disinhibitory currents to maximize the SNR of their combined current. Moreover, as spot size or contrast changed, the amplitudes of excitatory and disinhibitory currents also changed but remained in proportion to their SNRs, indicating a dynamic rebalancing of excitatory and inhibitory currents to maximize SNR.SIGNIFICANCE STATEMENT We present evidence that the balance of excitatory and disinhibitory inputs to a type of retinal ganglion cell maximizes the signal-to-noise ratio power ratio (SNR) of its postsynaptic currents. This is significant because chemical synapses on a retinal ganglion cell require the probabilistic release of transmitter. Consequently, when the same visual stimulus is presented repeatedly, postsynaptic currents vary in amplitude. Thus, maximizing SNR may be a strategy for producing the most reliable signal possible given the inherent unreliability of synaptic transmission.

Coding Properties of Three Intrinsically Distinct Retinal Ganglion Cells under Periodic Stimuli: A Computational Study

As the sole output neurons in the retina, ganglion cells play significant roles in transforming visual information into spike trains, and then transmitting them to the higher visual centers. However, coding strategies that retinal ganglion cells (RGCs) adopt to accomplish these processes are not completely clear yet. To clarify these issues, we investigate the coding properties of three types of RGCs (repetitive spiking, tonic firing, and phasic firing) by two different measures (spike-rate and spike-latency). Model results show that for periodic stimuli, repetitive spiking RGC and tonic RGC exhibit similar spike-rate patterns. Their spike- rates decrease gradually with increased stimulus frequency, moreover, variation of stimulus amplitude would change the two RGCs' spike-rate patterns. For phasic RGC, it activates strongly at medium levels of frequency when the stimulus amplitude is low. While if high stimulus amplitude is applied, phasic RGC switches to respond strongly at low frequencies. These results suggest that stimulus amplitude is a prominent factor in regulating RGCs in encoding periodic signals. Similar conclusions can be drawn when analyzes spike-latency patterns of the three RGCs. More importantly, the above phenomena can be accurately reproduced by Hodgkin's three classes of neurons, indicating that RGCs can perform the typical three classes of firing dynamics, depending on the distinctions of ion channel densities. Consequently, model results from the three RGCs may be not specific, but can also applicable to neurons in other brain regions which exhibit part(s) or all of the Hodgkin's three excitabilities.

A spectral element method with adaptive segmentation for accurately simulating extracellular electrical stimulation of neurons

The capacity to quickly and accurately simulate extracellular stimulation of neurons is essential to the design of next-generation neural prostheses. Existing platforms for simulating neurons are largely based on finite-difference techniques; due to the complex geometries involved, the more powerful spectral or differential quadrature techniques cannot be applied directly. This paper presents a mathematical basis for the application of a spectral element method to the problem of simulating the extracellular stimulation of retinal neurons, which is readily extensible to neural fibers of any kind. The activating function formalism is extended to arbitrary neuron geometries, and a segmentation method to guarantee an appropriate choice of collocation points is presented. Differential quadrature may then be applied to efficiently solve the resulting cable equations. The capacity for this model to simulate action potentials propagating through branching structures and to predict minimum extracellular stimulation thresholds for individual neurons is demonstrated. The presented model is validated against published values for extracellular stimulation threshold and conduction velocity for realistic physiological parameter values. This model suggests that convoluted axon geometries are more readily activated by extracellular stimulation than linear axon geometries, which may have ramifications for the design of neural prostheses.

Virtual electrode design for increasing spatial resolution in retinal prosthesis

Retinal prostheses systems are currently used to restore partial vision to patients blinded by degenerative diseases by electrically stimulating surviving retinal cells. To obtain likely maximum resolution, electrode size is minimised, allowing for a large quantity on an array and localised stimulation regions. Besides the small size leading to fabrication difficulties and higher electrochemical charge density, there are challenges associated with the number of drivers needed for a large electrode count as well as the strategies to deliver sufficient power to these drivers wirelessly. In hopes to increase electrode resolution while avoiding these issues, the authors propose a new 'virtual electrode' design to increase locations of likely stimulation. Passive metallisation strategically placed between disk electrodes, combined with alternating surrounding stimuli, channel current into a location between electrodes, producing a virtual stimulation site. A computational study was conducted to optimise the passive metal element geometry, quantify the expected current density output, and simulate retinal ganglion cell activity due to virtual electrode stimulation. Results show that this procedure leads to array geometry that focuses injected current and achieves retinal ganglion cell stimulation in a region beneath the 'virtual electrode,' creating an alternate stimulation site without additional drivers.

Electrical activity of ON and OFF retinal ganglion cells: a modelling study

OBJECTIVE

Retinal ganglion cells (RGCs) demonstrate a large range of variation in their ionic channel properties and morphologies. Cell-specific properties are responsible for the unique way RGCs process synaptic inputs, as well as artificial electrical signals such as that from a visual prosthesis. A cell-specific computational modelling approach allows us to examine the functional significance of regional membrane channel expression and cell morphology.

APPROACH

In this study, an existing RGC ionic model was extended by including a hyperpolarization activated non-selective cationic current as well as a T-type calcium current identified in recent experimental findings. Biophysically-defined model parameters were simultaneously optimized against multiple experimental recordings from ON and OFF RGCs.

MAIN RESULTS

With well-defined cell-specific model parameters and the incorporation of detailed cell morphologies, these models were able to closely reconstruct and predict ON and OFF RGC response properties recorded experimentally.

SIGNIFICANCE

The resulting models were used to study the contribution of different ion channel properties and spatial structure of neurons to RGC activation. The techniques of this study are generally applicable to other excitable cell models, increasing the utility of theoretical models in accurately predicting the response of real biological neurons.

A model of electrical stimulation of a retinal cell population using a multi-electrode array

A novel computational modelling approach is employed to investigate the response of a population of retinal ganglion cells (RGCs) to external electrical stimulation. Current is delivered via a multi-electrode array design that would be employed in a future retinal prosthesis device being developed by our group. The RGCs are morphologically realistic and allow examination of the biophysical responses of intracellular compartments to externally applied currents. A number of stimulation paradigms are simulated including the use of monopolar, hexapolar and quasi-monopolar return paths. The model provides a powerful simulation tool to test and optimize electrical stimulation strategies for future retinal prosthesis devices.

Modeling the Influence of Ion Channels on Neuron Dynamics in Drosophila

Voltage gated ion channels play a major role in determining a neuron's firing behavior, resulting in the specific processing of synaptic input patterns. Drosophila and other invertebrates provide valuable model systems for investigating ion channel kinetics and their impact on firing properties. Despite the increasing importance of Drosophila as a model system, few computational models of its ion channel kinetics have been developed. In this study, experimentally observed biophysical properties of voltage gated ion channels from the fruitfly Drosophila melanogaster are used to develop a minimal, conductance based neuron model. We investigate the impact of the densities of these channels on the excitability of the model neuron. Changing the channel densities reproduces different in situ observed firing patterns and induces a switch from integrator to resonator properties. Further, we analyze the preference to input frequency and how it depends on the channel densities and the resulting bifurcation type the system undergoes. An extension to a three dimensional model demonstrates that the inactivation kinetics of the sodium channels play an important role, allowing for firing patterns with a delayed first spike and subsequent high frequency firing as often observed in invertebrates, without altering the kinetics of the delayed rectifier current.

Selective activation of ON and OFF retinal ganglion cells to high-frequency electrical stimulation: a computational modeling study

In this study, ON and OFF retinal ganglion cell (RGC) models based on accurate biophysics and realistic representations of cell morphologies were used to understand how these cells selectively respond to high-frequency electrical stimulation (HFS). With optimized model parameters and the incorporation of detailed cell morphologies, these two models were able to closely replicate experimental ON and OFF RGC responses to epiretinal electrical stimulation. This modeling approach can be used to design electrical stimulus profiles capable of cell-specific activation, and is broadly applicable for the development of sophisticated stimulation strategies for visual prostheses.

Modeling intrinsic electrophysiology of AII amacrine cells: preliminary results

In patients who have lost their photoreceptors due to retinal degenerative diseases, it is possible to restore rudimentary vision by electrically stimulating surviving neurons. AII amacrine cells, which reside in the inner plexiform layer, split the signal from rod bipolar cells into ON and OFF cone pathways. As a result, it is of interest to develop a computational model to aid in the understanding of how these cells respond to the electrical stimulation delivered by a prosthetic implant. The aim of this work is to develop and constrain parameters in a single-compartment model of an AII amacrine cell using data from whole-cell patch clamp recordings. This model will be used to explore responses of AII amacrine cells to electrical stimulation. Single-compartment Hodgkin-Huxley-type neural models are simulated in the NEURON environment. Simulations showed successful reproduction of the potassium currentvoltage relationship and some of the spiking properties observed in vitro.

Influence of active dendrites on firing patterns in a retinal ganglion cell model

Active regional conductances and inhomogeneous distribution of membrane ionic channels in dendrites influence the integration of synaptic inputs in cortical neurons. How these properties shape the response properties of retinal ganglion cells (RGC) in the mammalian retina has remained largely unexplored. In this study, we used a morphologically-realistic RGC computational model to study how active dendritic properties contribute to neural behaviors. Our simulations suggest that the dendritic distribution of voltage-gated ionic channels strongly influences RGC firing patterns, indicating their important contribution to neuronal function.

Properties of a Glutamatergic Synapse Controlling Information Output from Retinal Bipolar Cells

One general categorization of retinal ganglion cells is to segregate them into tonically or phasically responding neurons, each conveying discrete aspects of the visual scene. Although best identified in the output signals of the retina, this distinction is initiated at the first synapse: between photoreceptors and the dendrites of bipolar cells. In this study we found that the output synapses of bipolar cells also contribute to separate these pathways. Both transient and sustained ganglion cells can produce maintained spike activity, but bipolar cell glutamate release exhibits a divergence that corresponds to the response characteristics of the ganglion cells. Comparing light intensity coding in the sustained and transient ON pathways revealed that they shared the intensity spectrum. The transient pathway had greater sensitivity but smaller dynamic range, and switched from intensity coding to event detection at light levels where sustained pathway sensitivity began to rise. The distinctive properties of the sustained pathway depended upon inhibition and shifted toward those of the transient pathway in the absence of inhibition. The transient system was comparatively unaffected by the loss of inhibition and this was due to the concomitant activation of perisynaptic NMDA receptors. Overall, the properties of bipolar cell dendritic and axon terminals both contribute to the formation of key aspects of the sustained/transient dichotomy normally associated with ganglion cells.

Voltage gating by molecular subunits of Na+ and K+ ion channels: higher-dimensional cubic kinetics, rate constants, and temperature

The structural similarity between the primary molecules of voltage-gated Na and K channels (alpha subunits) and activation gating in the Hodgkin-Huxley model is brought into full agreement by increasing the model's sodium kinetics to fourth order (m(3) → m(4)). Both structures then virtually imply activation gating by four independent subprocesses acting in parallel. The kinetics coalesce in four-dimensional (4D) cubic diagrams (16 states, 32 reversible transitions) that show the structure to be highly failure resistant against significant partial loss of gating function. Rate constants, as fitted in phase plot data of retinal ganglion cell excitation, reflect the molecular nature of the gating transitions. Additional dimensions (6D cubic diagrams) accommodate kinetically coupled sodium inactivation and gating processes associated with beta subunits. The gating transitions of coupled sodium inactivation appear to be thermodynamically irreversible; response to dielectric surface charges (capacitive displacement) provides a potential energy source for those transitions and yields highly energy-efficient excitation. A comparison of temperature responses of the squid giant axon (apparently Arrhenius) and mammalian channel gating yields kinetic Q10 = 2.2 for alpha unit gating, whose transitions are rate-limiting at mammalian temperatures; beta unit kinetic Q10 = 14 reproduces the observed non-Arrhenius deviation of mammalian gating at low temperatures; the Q10 of sodium inactivation gating matches the rate-limiting component of activation gating at all temperatures. The model kinetics reproduce the physiologically large frequency range for repetitive firing in ganglion cells and the physiologically observed strong temperature dependence of recovery from inactivation.

Feedback stimulation strategy: control of retinal ganglion cells activation

It is possible to cause a sensation of light in patients who have lost photoreceptors due to degenerative eye diseases by targeting surviving neurons with electrical stimulation by means of visual prosthetic devices. All stimulation strategies in currently used visual prostheses are open-loop, that is, the stimulation parameters do not depend on the level of activation of neurons surrounding stimulating electrodes. In this paper, we investigate a closed-loop stimulation strategy using computer simulations of previously constrained models of ON and OFF retinal ganglion cells. Using a proportional-integral-type controller we show that it is possible to control activation level of both types of retinal ganglion cells. We also demonstrate that the controller tuned for a particular combination of synaptic currents continues to work during retina degeneration when excitatory currents are reduced by 20%.