Finite element bidomain model of epiretinal stimulation

A multi-scale simulation of retinal physiology

We present a detailed physiological model of the (human) retina that includes the biochemistry and electrophysiology of phototransduction, neuronal electrical coupling, and the spherical geometry of the eye. The model is a parabolic-elliptic system of partial differential equations based on the mathematical framework of the bi-domain equations, which we have generalized to account for multiple cell-types. We discretize in space with non-uniform finite differences and step through time with a custom adaptive time-stepper that employs a backward differentiation formula and an inexact Newton method. A refinement study confirms the accuracy and efficiency of our numerical method. Numerical simulations using the model compare favorably with experimental findings, such as desensitization to light stimuli and calcium buffering in photoreceptors. Other numerical simulations suggest an interplay between photoreceptor gap junctions and inner segment, but not outer segment, calcium concentration. Applications of this model and simulation include analysis of retinal calcium imaging experiments, the design of electroretinograms, the design of visual prosthetics, and studies of ephaptic coupling within the retina.

Efficacy of the hexpolar configuration in localizing the activation of retinal ganglion cells under electrical stimulation

Retinal visual prostheses provide hope of restoring sight to patients suffering from retinal degeneration such as retinitis pigmentosa and age-related macular degeneration. Retinal prostheses are used to electrically stimulate residual neurons that are spared in these diseases, namely the retinal ganglion cells (RGCs), eliciting percepts of light termed 'phosphenes'. The elicitation of multiple phosphenes via an electrode array allows patterns to be produced, resulting in a rudimentary form of vision. For such patterns to be produced effectively, the prosthesis must generate well-defined phosphenes. To this end, the hexpolar configuration has been proposed as an alternative to the traditional monopolar or bipolar configurations. It utilizes six electrodes surrounding the stimulating electrode to serve as a combined return, or 'hex guard', purportedly localizing the activation to cells located within them. In this study, the efficacy of the hexpolar configuration in localizing activity was investigated by using patch-clamp electrophysiology to measure the activation thresholds of RGCs to electrical stimulation in isolated rabbit retina. Cells located outside the hex guard were found to have significantly higher relative hexpolar thresholds (>2 fold) as compared to cells located within the hex guard. This confirms the efficacy of the hexpolar configuration in localizing activity to within the hex guard. Furthermore, the effect of using cathodic-first versus anodic-first stimulation on hexpolar threshold and localization was investigated. No significant difference was observed between the two groups, in terms of lowering thresholds or improving localization.

Discrete cortical responses from multi-site supra-choroidal electrical stimulation in the feline retina

Exploration into electrical stimulation of the retina has thus far focussed primarily upon the development of prostheses targeted at one of two sites of intervention - the epi- and sub-retinal surfaces. These two approaches have sound, logical merit owing to their proximity to retinal neurons and their potential to deliver stimuli via the surviving retinal neural networks respectively. There is increasing evidence, however, that electric field effects, electrode engineering limitations, and electrode-tissue interactions limit the spatial resolution that once was hoped could be elicited from electrical stimulation at epi- and sub-retinal sites. An alternative approach has been proposed that places a stimulating electrode array within the supra-choroidal space - that is, between the sclera and the choroid. Here we investigate whether discrete, cortical activity patterns can be elicited via electrical stimulation of a feline retina using a custom, 14 channel, silicone rubber and Pt electrode array arranged in two hexagons comprising seven electrodes each. Cortical responses from Areas 17/18 were acquired using a silicon-based, multi-channel, penetrating probe developed at IMTEK, University of Freiburg, within the European research project NeuroProbes. Multi-unit spike activity was recorded in synchrony with the presentation of electrical stimuli. Results show that distinct cortical response patterns could be elicited from each hexagon separated by 1.8 mm (center-to-center) with a center-to-center electrode spacing within each hexagon of 0.55 mm. This lends support that higher spatial resolution may also be discerned.