Influence of the sodium channel band on retinal ganglion cell excitation during electric stimulation--a modeling study

Auditory nerve fiber excitability for alternative electrode placement in the obstructed human cochlea: electrode insertion in scala vestibuli versus scala tympani

Objective. The cochlear implant (CI) belongs to the most successful neuro-prostheses. Traditionally, the stimulating electrode arrays are inserted into the scala tympani (ST), the lower cochlear cavity, which enables simple surgical access. However, often deep insertion is blocked, e.g. by ossification, and the auditory nerve fibers (ANFs) of lower frequency regions cannot be stimulated causing severe restrictions in speech understanding. As an alternative, the CI can be inserted into the scala vestibuli (SV), the other upper cochlear cavity.Approach. In this computational study, the excitability of 25 ANFs are compared for stimulation with ST and SV implants. We employed a 3-dimensional realistic human cochlear model with lateral wall electrodes based on aμ-CT dataset and manually traced fibers. A finite element approach in combination with a compartment model of a spiral ganglion cell was used to simulate monophasic stimulation with anodic (ANO) and cathodic (CAT) pulses of 50μs.Main results. ANO thresholds are lower in ST (mean/std =μ/σ= 189/55μA) stimulation compared to SV (μ/σ= 323/119μA) stimulation. Contrary, CAT thresholds are higher for the ST array (μ/σ= 165/42μA) compared to the SV array (μ/σ= 122/46μA). The threshold amplitude depends on the specific fiber-electrode spatial relationship, such as lateral distance from the cochlear axis, the angle between electrode and target ANF, and the curvature of the peripheral process. For CAT stimulation the SV electrodes show a higher selectivity leading to less cross-stimulation of additional fibers from different cochlear areas.Significance. We present a first simulation study with a human cochlear model that investigates an additional CI placement into the SV and its impact on the excitation behavior. Results predict comparable outcomes to ST electrodes which confirms that SV implantation might be an alternative for patients with a highly obstructed ST.

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.

High spatial resolution artificial vision inferred from the spiking output of retinal ganglion cells stimulated by optogenetic and electrical means

With vision impairment affecting millions of people world-wide, various strategies aiming at vision restoration are being undertaken. Thanks to decades of extensive research, electrical stimulation approaches to vision restoration began to undergo clinical trials. Quite recently, another technique employing optogenetic therapy emerged as a possible alternative. Both artificial vision restoration strategies reported poor spatial resolution so far. In this article, we compared the spatial resolution inferred ex vivo under ideal conditions using a computational model analysis of the retinal ganglion cell (RGC) spiking activity. The RGC spiking was stimulated in epiretinal configuration by either optogenetic or electrical means. RGCs activity was recorded from the ex vivo retina of transgenic late-stage photoreceptor-degenerated mice (rd10) using a high-density Complementary Metal Oxide Semiconductor (CMOS) based microelectrode array. The majority of retinal samples were stimulated by both, optogenetic and electrical stimuli using a spatial grating stimulus. A population-level analysis of the spiking activity of identified RGCs was performed and the spatial resolution achieved through electrical and optogenetic photo-stimulation was inferred using a support vector machine classifier. The best f1 score of the classifier for the electrical stimulation in epiretinal configuration was 86% for 32 micron wide gratings and increased to 100% for 128 microns. For optogenetically activated cells, we obtained high f1 scores of 82% for 10 microns grid width for a photo-stimulation frequency of 2.5 Hz and 73% for a photo-stimulation frequency of 10 Hz. A subsequent analysis, considering only the RGCs modulated in both electrical and optogenetic stimulation protocols revealed no significant difference in the prediction accuracy between the two stimulation modalities. The results presented here indicate that a high spatial resolution can be achieved for electrical or optogenetic artificial stimulation using the activated retinal ganglion cell output.

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.

Neuron matters: neuromodulation with electromagnetic stimulation must consider neurons as dynamic identities

Neuromodulation with electromagnetic stimulation is widely used for the control of abnormal neural activity, and has been proven to be a valuable alternative to pharmacological tools for the treatment of many neurological diseases. Tremendous efforts have been focused on the design of the stimulation apparatus (i.e., electrodes and magnetic coils) that delivers the electric current to the neural tissue, and the optimization of the stimulation parameters. Less attention has been given to the complicated, dynamic properties of the neurons, and their context-dependent impact on the stimulation effects. This review focuses on the neuronal factors that influence the outcomes of electromagnetic stimulation in neuromodulation. Evidence from multiple levels (tissue, cellular, and single ion channel) are reviewed. Properties of the neural elements and their dynamic changes play a significant role in the outcome of electromagnetic stimulation. This angle of understanding yields a comprehensive perspective of neural activity during electrical neuromodulation, and provides insights in the design and development of novel stimulation technology.

An in-silico analysis of retinal electric field distribution induced by different electrode design of trans-corneal electrical stimulation

OBJECTIVE

Trans-corneal electrical stimulation (TcES) produces therapeutic effects on many ophthalmic diseases non-invasively. Existing clinical TcES devices use largely variable design of electrode distribution and stimulation parameters. Better understanding of how electrode configuration paradigms and stimulation parameters influence the electric field distribution on the retina, will be beneficial to the design of next-generation TcES devices.

APPROACH

In this study, we constructed a realistic finite element human head model with fine eyeball structure. Commonly used DTL-Plus and ERG-Jet electrodes were simulated. We then conducted in silico investigations of retina observation surface (ROS) electric field distributions induced by different return electrode configuration paradigms and different stimulus intensities.

MAIN RESULTS

Our results suggested that the ROS electric field distribution could be modulated by re-designing TcES electrode settings and stimulus parameters. Under far return location (FRL) paradigms, either DTL-Plus or ERG-Jet approach could induce almost identical ROS electric field distribution regardless where the far return was located. However, compared with the ERG-Jet mode, DTL-Plus stimulation induced stronger nasal lateralization. In contrast, ERG-Jet stimulation induced relatively stronger temporal lateralization. The ROS lateralization can be further tweaked by changing the DTL-Plus electrode length.

SIGNIFICANCE

These results may contribute to the understanding of the characteristics of DTL-Plus and ERG-Jet electrodes based electric field distribution on the retina, providing practical implications for the therapeutic application of TcES.

Micro-magnetic stimulation of primary visual cortex induces focal and sustained activation of secondary visual cortex

Cortical visual prostheses that aim to restore sight to the blind require the ability to create neural activity in the visual cortex. Electric stimulation delivered via microelectrodes implanted in the primary visual cortex (V1) has been the most common approach, although conventional electrodes may not effectively confine activation to focal regions and thus the acuity they create may be limited. Magnetic stimulation from microcoils confines activation to single cortical columns of V1 and thus may prove to be more effective than conventional microelectrodes, but the ability of microcoils to drive synaptic connections has not been explored. Here, we show that magnetic stimulation of V1 using microcoils induces spatially confined activation in the secondary visual cortex (V2) in mouse brain slices. Single-loop microcoils were fabricated using platinum-iridium flat microwires, and their effectiveness was evaluated using calcium imaging and compared with that of monopolar and bipolar electrodes. Our results show that compared to the electrodes, the microcoils better confined activation to a small region in V1. In addition, they produced more precise and sustained activation in V2. The finding that microcoil-based stimulation propagates to higher visual centres raises the possibility that complex visual perception, e.g. that requiring sustained synaptic inputs, may be achievable. This article is part of the theme issue 'Advanced neurotechnologies: translating innovation for health and well-being'.

A simple model considering spiking probability during extracellular axon stimulation

The spiking probability of an electrically stimulated axon as a function of stimulus amplitude increases in a sigmoidal dependency from 0 to 1. However, most computer simulation studies for neuroprosthetic applications calculate thresholds for neural targets with a deterministic model and by reducing the sigmoid curve to a step function, they miss an important information about the control signal, namely how the spiking efficiency increases with stimulus intensity. Here, this spiking efficiency is taken into account in a compartment model of the Hodgkin Huxley type where a noise current is added in every compartment with an active membrane. A key parameter of the model is a common factor knoise which defines the ion current fluctuations across the cell membrane for every compartment by its maximum sodium ion conductance. In the standard model Gaussian signals are changed every 2.5 μs as a compromise of accuracy and computational costs. Additionally, a formula for other noise transmission times is presented and numerically tested. Spiking probability as a function of stimulus intensity can be approximated by the cumulative distribution function of the normal distribution with RS = σ/μ. Relative spread RS, introduced by Verveen, is a measure for the spread (normalized by the threshold intensity μ), that decreases inversely with axon diameter. Dynamic range, a related measure used in neuroprosthetic studies, defines the intensity range between 10% and 90% spiking probability. We show that (i) the dynamic range normalized by threshold is 2.56 times RS, (ii) RS increases with electrode—axon distance and (iii) we present knoise values for myelinated and unmyelinated axon models in agreement with recoded RS data. The presented method is applicable for other membrane models and can be extended to whole neurons that are described by multi-compartment models.

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.

Block Phenomena During Electric Micro-Stimulation of Pyramidal Cells and Retinal Ganglion Cells

Electric micro-stimulation of the nervous system is a means to restore various body functions. The stimulus amplitude necessary to generate action potentials, the lower threshold (LT), is well characterized for many neuronal populations. However, electric overstimulation above an upper threshold (UT) prevents action potential generation and therefore hinders optimal neuro-rehabilitation. Previous studies demonstrated the impact of the UT in micro-stimulation of retinal ganglion cells (RGCs). The observed phenomenon is mostly explained by (i) reversed sodium ion flow in the soma membrane, and (ii) anodal surround block that hinders spike conduction in strongly hyperpolarized regions of the axon at high stimulus intensities. However, up to now, no detailed study of the nature of these phenomena has been presented, particularly for different cell types. Here, we present computational analyses of LT and UT for layer 5 pyramidal cells (PCs) as well as alpha RGCs. Model neurons were stimulated in close vicinity to the cell body and LTs and UTs as well as the ratio UT/LT were compared. Aside from a simple point source electrode and monophasic stimuli also realistic electrode and pulse configurations were examined. The analysis showed: (i) in RGCs, the soma contributed to action potential initiation and block for small electrode distances, whereas in PCs the soma played no role in LTs or UTs. (ii) In both cell types, action potential always initiated within the axon initial segment at LT. (iii) In contrast to a complete block of spike conductance at UT that occurred in RGCs, an incomplete block of spiking appeared in PC axon collaterals. (iv) PC axon collateral arrangement influenced UTs but had small impact on LTs. (v) Population responses of RGCs change from circular regions of activation to ring-shaped patterns for increasing stimulus amplitude. A better understanding of the stimulation window that can reliably activate target neurons will benefit the future development of neuroprostheses.

Somatic inhibition by microscopic magnetic stimulation

Electric currents can produce quick, reversible control of neural activity. Externally applied electric currents have been used in inhibiting certain ganglion cells in clinical practices. Via electromagnetic induction, a miniature-sized magnetic coil could provide focal stimulation to the ganglion neurons. Here we report that high-frequency stimulation with the miniature coil could reversibly block ganglion cell activity in marine mollusk Aplysia californica, regardless the firing frequency of the neurons, or concentration of potassium ions around the ganglion neurons. Presence of the ganglion sheath has minimal impact on the inhibitory effects of the coil. The inhibitory effect was local to the soma, and was sufficient in blocking the neuron's functional output. Biophysical modeling confirmed that the miniature coil induced a sufficient electric field in the vicinity of the targeted soma. Using a multi-compartment model of Aplysia ganglion neuron, we found that the high-frequency magnetic stimuli altered the ion channel dynamics that were essential for the sustained firing of action potentials in the soma. Results from this study produces several critical insights to further developing the miniature coil technology for neural control by targeting ganglion cells. The miniature coil provides an interesting neural modulation strategy in clinical applications and laboratory research.

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.

Selective Activation of Cortical Columns Using Multichannel Magnetic Stimulation With a Bent Flat Microwire Array

OBJECTIVE

Cortical neural prostheses that aim to restore useful vision, hearing, and tactile sensations require the ability to selectively target different cortical regions simultaneously. Electrical stimulation via intracortical electrodes has been used to create spatial patterns of cortical activation. However, their efficacy remains limited due to the inability of conventional electrodes to confine activation to specific cortical regions around each electrode. Magnetic stimulation from single bent wires can selectively activate pyramidal neurons while avoiding passing axons, thereby confining activation to small cortical regions. This paper presents a novel bent flat microwire array and demonstrates its effectiveness for selective activation of cortical columns in mouse brain slices.

METHODS

A computational model was developed to compare the spatial resolution of magnetic stimulation from bent wire arrays with 280 and 530 μm tip spacings. The same array designs were fabricated for use in electrophysiological experiments, i.e., calcium imaging (GCaMP6s) of mouse brain slices.

RESULTS

All fabricated array designs reliably produced spatially discrete cortical activations at low stimulus amplitudes, but the 280-μm-spacing produced strong interference (constructive or destructive) at high stimulus amplitudes, thereby resulting in single strong activations or two asymmetric activations. 4-channel bent wire arrays with spacing of 340 μm avoided the interference and produced clearer spatial patterns of activation than electrodes.

CONCLUSION

Bent wire array designs can influence the strength or the spatial resolution of multichannel magnetic stimulation.

SIGNIFICANCE

These results suggest that bent microwire arrays can enhance the selectivity of multichannel stimulation of brain and therefore may help to develop reliable and effective cortical neural prostheses.

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.

Differential Responses to High-Frequency Electrical Stimulation in Brisk-Transient and Delta Retinal Ganglion Cells

Retinal microprostheses strive to evoke a sense of vision in individuals blinded by outer retinal degenerative diseases, by electrically stimulating the surviving retina. It is widely suspected that a stimulation strategy that can selectively activate different retinal ganglion cell types will improve the quality of evoked phosphenes. Previous efforts towards this goal demonstrated the potential for selective ON and OFF brisk-transient cell activation using high-rate (2000 pulses per second, PPS) stimulation. Here, we build upon this earlier work by testing an additional rate of stimulation and additional cell populations. We find considerable variability in responses both within and across individual cell types, but show that the sensitivity of a ganglion cell to repetitive stimulation is highly correlated to its single-pulse threshold. Consistent with this, we found thresholds for both stimuli to be correlated to soma size, and thus likely mediated by the properties of the axon initial segment. The ultimate efficacy of high-rate stimulation will likely depend on several factors, chief among which are (a) the residual ganglion types, and (b) the stimulation frequency.

The relationship between morphological properties and thresholds to extracellular electric stimulation in α RGCs

OBJECTIVE

Retinal prostheses strive to restore vison to patients that are blind from retinal degeneration by electrically stimulating surviving retinal ganglion cells (RGCs). The quality of elicited percepts remains limited however and it is desirable to develop improved stimulation strategies. Here, we examine how the anatomical and biophysical properties of RGCs influence activation thresholds, including the effects of variations found naturally.

APPROACH

Detailed reconstructions were made of a large number of mouse α RGCs and were used to create an array of model cells; the models were used to study the effects of individual anatomical features on activation threshold to electric stimulation. Stimulation was delivered epiretinally from a point-source or disk electrode and consisted of monophasic or biphasic rectangular pulses.

MAIN RESULTS

Modeling results show that the region of minimum threshold always is within the axon initial segment (AIS). The properties of this region as well as the absolute value of the minimum threshold are dependent on the length of the AIS as well as on the relative composition of sodium channels within the AIS. Other morphological features, including cell size, dendritic field size and the distance between the AIS and the soma had only a minimal influence on thresholds. Introducing even a small number of low-threshold Na_v1.6 channels into the AIS was sufficient to lower minimum thresholds substantially although further increases in Na_v1.6 had diminishing effects. The distance between the AIS and the electrode affects threshold levels while alignment of the electrode with the axon or dendritic parts of the RGC can result in lower thresholds, even if the distance to the cell remains the same.

SIGNIFICANCE

Intrinsic morphological features can influence activation thresholds with the AIS having the strongest influence. However, the combined influence remains limited and may not be large enough to allow for selective activation between different RGC types.

A Three-Dimensional Microelectrode Array to Generate Virtual Electrodes for Epiretinal Prosthesis Based on a Modeling Study

Despite many advances in the development of retinal prostheses, clinical reports show that current retinal prosthesis subjects can only perceive prosthetic vision with poor visual acuity. A possible approach for improving visual acuity is to produce virtual electrodes (VEs) through electric field modulation. Generating controllable and localized VEs is a crucial factor in effectively improving the perceptive resolution of the retinal prostheses. In this paper, we aimed to design a microelectrode array (MEA) that can produce converged and controllable VEs by current steering stimulation strategies. Through computational modeling, we designed a three-dimensional concentric ring–disc MEA and evaluated its performance with different stimulation strategies. Our simulation results showed that electrode–retina distance (ERD) and inter-electrode distance (IED) can dramatically affect the distribution of electric field. Also the converged VEs could be produced when the parameters of the three-dimensional MEA were appropriately set. VE sites can be controlled by manipulating the proportion of current on each adjacent electrode in a current steering group (CSG). In addition, spatial localization of electrical stimulation can be greatly improved under quasi-monopolar (QMP) stimulation. This study may provide support for future application of VEs in epiretinal prosthesis for potentially increasing the visual acuity of prosthetic vision.

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.

Scaling of the AIS and Somatodendritic Compartments in α S RGCs

The anatomical properties of the axon initial segment (AIS) are tailored in certain types of CNS neurons to help optimize different aspects of neuronal function. Here, we questioned whether the AISs of retinal ganglion cells (RGC) were similarly customized, and if so, whether they supported specific RGC functions. To explore this, we measured the AIS properties in alpha sustained RGCs (α S RGCs) of mouse; α S RGCs sizes vary systematically along the nasal temporal axis of the retina, making these cells an attractive population with which to study potential correlations between AIS properties and cell size. Measurements of AIS length as well as distance from the soma revealed that both were scaled to cell size, i.e., cells with large dendritic fields had long AISs that were relatively far from the soma. Within the AIS, the percentage of Na v 1.6 voltage-gated sodium channels remained highly consistent, regardless of cell size or other AIS properties. Although ON RGCs were slightly larger than OFF cells at any given location of the retina, the level of scaling and relative distribution of voltage-gated sodium channels were highly similar. Computational modeling revealed that AIS scaling influenced spiking thresholds, spike rate as well as the kinetics of individual action potentials, Interestingly, the effect of individual features of the AIS varied for different neuronal functions, e.g., AIS length had a larger effect on the efficacy by which the AIS initiated spike triggered the somatic spike than it did on repetitive spiking. The polarity of the effect varied for different properties, i.e., increases to soma size increased spike threshold while increases to AIS length decreased threshold. Thus, variations in the relative level of scaling for individual components could fine tune threshold or other neuronal functions. Light responses were highly consistent across the full range of cell sizes suggesting that scaling may post-synaptically shape response stability, e.g., in addition to several well-known pre-synaptic contributors.

Micro-Coil Design Influences the Spatial Extent of Responses to Intracortical Magnetic Stimulation

OBJECTIVE

Electrical stimulation via cortically implanted electrodes has been proposed to treat a wide range of neurological disorders. Effectiveness has been limited, however, in part due to the inability of conventional electrodes to activate specific types of neurons while avoiding other types. Recent demonstrations that magnetic stimulation from a micro-coil can selectively activate pyramidal neurons (PNs) while avoiding passing axons suggest the possibility that such an approach can overcome some this limitation and here we use computer simulations to explore how the micro-coil design influences the selectivity with which neurons are activated.

METHODS

A computational model was developed to compare the selectivity of magnetic stimulation induced by rectangular-, V-, and W-shaped coil designs. The more promising designs (V- and W-shapes) were fabricated for use in electrophysiological experiments including in vitro patch-clamp recording and calcium imaging (GCaMP6f) of mouse brain slices.

RESULTS

Both V- and W-shaped coils reliably activated layer 5 (L5) PNs but V-coils were more effective while W-coils were more selective. Activation thresholds with double-loop coils were approximately one-half those of single-loop coils. Calcium imaging revealed that both V- and W-coils better confine activation than electrodes.

CONCLUSION

Individual design features can influence both the strength as well as the selectivity of micro-coils and can be accurately predicted by computer simulations.

SIGNIFICANCE

Our results show that how coil design influences the response of cortical neurons to stimulation and are an important step toward the development of next-generation cortical prostheses.

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.

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.

High-Resolution Multi-Scale Computational Model for Non-Invasive Cervical Vagus Nerve Stimulation

OBJECTIVES

To develop the first high-resolution, multi-scale model of cervical non-invasive vagus nerve stimulation (nVNS) and to predict vagus fiber type activation, given clinically relevant rheobase thresholds.

METHODS

An MRI-derived Finite Element Method (FEM) model was developed to accurately simulate key macroscopic (e.g., skin, soft tissue, muscle) and mesoscopic (cervical enlargement, vertebral arch and foramen, cerebral spinal fluid [CSF], nerve sheath) tissue components to predict extracellular potential, electric field (E-Field), and activating function along the vagus nerve. Microscopic scale biophysical models of axons were developed to compare axons of varying size (Aα-, Aβ- and Aδ-, B-, and C-fibers). Rheobase threshold estimates were based on a step function waveform.

RESULTS

Macro-scale accuracy was found to determine E-Field magnitudes around the vagus nerve, while meso-scale precision determined E-field changes (activating function). Mesoscopic anatomical details that capture vagus nerve passage through a changing tissue environment (e.g., bone to soft tissue) profoundly enhanced predicted axon sensitivity while encapsulation in homogenous tissue (e.g., nerve sheath) dulled axon sensitivity to nVNS.

CONCLUSIONS

These findings indicate that realistic and precise modeling at both macroscopic and mesoscopic scales are needed for quantitative predictions of vagus nerve activation. Based on this approach, we predict conventional cervical nVNS protocols can activate A- and B- but not C-fibers. Our state-of-the-art implementation across scales is equally valuable for models of spinal cord stimulation, cortex/deep brain stimulation, and other peripheral/cranial nerve models.

Minimizing activation of overlying axons with epiretinal stimulation: The role of fiber orientation and electrode configuration

Currently, a challenge in electrical stimulation of the retina with a visual prosthesis (bionic eye) is to excite only the cells lying directly under the electrode in the ganglion cell layer, while avoiding excitation of axon bundles that pass over the surface of the retina in the nerve fiber layer. Stimulation of overlying axons results in irregular visual percepts, limiting perceptual efficacy. This research explores how differences in fiber orientation between the nerve fiber layer and ganglion cell layer leads to differences in the electrical activation of the axon initial segment and axons of passage. Approach. Axons of passage of retinal ganglion cells in the nerve fiber layer are characterized by a narrow distribution of fiber orientations, causing highly anisotropic spread of applied current. In contrast, proximal axons in the ganglion cell layer have a wider distribution of orientations. A four-layer computational model of epiretinal extracellular stimulation that captures the effect of neurite orientation in anisotropic tissue has been developed using a volume conductor model known as the cellular composite model. Simulations are conducted to investigate the interaction of neural tissue orientation, stimulating electrode configuration, and stimulation pulse duration and amplitude. Main results. Our model shows that simultaneous stimulation with multiple electrodes aligned with the nerve fiber layer can be used to achieve selective activation of axon initial segments rather than passing fibers. This result can be achieved while reducing required stimulus charge density and with only modest increases in the spread of activation in the ganglion cell layer, and is shown to extend to the general case of arbitrary electrode array positioning and arbitrary target volume. Significance. These results elucidate a strategy for more targeted stimulation of retinal ganglion cells with experimentally-relevant multi-electrode geometries and achievable stimulation requirements.

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.

A computational model of orientation-dependent activation of retinal ganglion cells

Currently, a challenge in electrical stimulation for epiretinal prostheses is the avoidance of stimulation of axons of passage in the nerve fiber layer that originate from distant regions of the ganglion cell layer. A computational model of extracellular stimulation that captures the effect of neurite orientation in anisotropic tissue is developed using a modified version of the standard volume conductor model, known as the cellular composite model, embedded in a four layer model of the retina. Simulations are conducted to investigate the interaction of neural tissue orientation, electrode placement, and stimulation pulse duration and amplitude. Using appropriate multiple electrode configurations and higher frequency stimulation, preferential activation of the axon initial segment is shown to be possible for a range of realistic electrode-retina separation distances. These results establish a quantitative relationship between the time-course of stimulation and physical properties of the tissue, such as fiber orientation.

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.