Fig 1.
Unwanted stimulation of retinal ganglion cell axons of passage.
Retinal ganglion cell somas and axon initial segments represent the target regions for epiretinal stimulation (region shaded blue). Activation of passing axons in the nerve fiber layer (gray shaded region) results in long, arc-shaped visual percepts and degradation of the quality of artificial vision. Retinal ganglion cell axon bundles in the nerve fiber layer that pass close to stimulating electrodes may be stimulated preferentially to target locations in the ganglion cell layer. Activated retinal ganglion cells are colored red. Simulations presented in this research use epiretinal multi-electrode arrays (100 μm diameter, 200 μm pitch). Note that the orientation of initial axonal segments is much more varied in reality than shown in this schematic.
Fig 2.
Fiber orientation distributions along the length of the axon.
Fiber orientation is calculated relative to the axon initial segment, and determined from all available mammalian retinal ganglion cell reconstructions on NeuroMorpho.org. The distribution of orientations at axonal locations of 100 μm (blue), 300 μm (red), and 500 μm (green) from the soma are shown. (a) Azimuthal (i.e., x-y) change in orientation between the axon initial segment and more distal axonal locations. (b) Exponential fits to the distributions in (a) with 95% confidence intervals. Statistical analysis of these fits is discussed in the main text. (c) Altitudinal (i.e., z) change in orientation between the axon initial segment and more distal axonal locations, with all following an exponential distribution. Insets illustrate planes in which orientations are compared. All orientations are calculated relative to the orientation of the axon initial segment. Due to variation in the length of axon reconstructions, each trace is calculated using a different subset of cells (100 μm—all 749 cells, 300 μm—158 cells, 500 μm—44 cells).
Fig 3.
Geometry of the four-layer model of the retina.
Modeled layers are the insulator, vitreous, nerve fiber layer, and ganglion cell layer. The insulator is assumed to have zero conductivity and is modeled using a zero flux boundary condition. The GCL is assumed to have infinite extent in the z-direction. The distance from electrodes to the retinal surface and the thickness of the NFL are denoted by dER and dN, respectively.
Table 1.
Conductivity and thickness of modeled layers.
Fig 4.
Simulation of experiments from Fried et al. [23].
The current waveforms used for stimulation and the maximum simulated membrane potential responses are shown. The maximum simulated membrane potential for each simulation corresponds to the membrane threshold, Vth, for that location in the axon.
Table 2.
Model parameter values, unless stated otherwise.
Fig 5.
Normalized spread of extracellular potential with distance from a stimulating electrode.
Spread is shown in (a) the y-z plane, parallel to the orientation of AOPs, and in (b) the x-z plane, perpendicular to the orientation of AOPs. The simulated extracellular potential at each z-slice is normalized to the range [0, 1] by subtracting the minimum and scaling the maximum per slice to 1. This is done for illustrative purposes due to the rapid fall-off of extracellular potential with increasing distance from the electrode. Contour lines indicate the full-width at half-maximum potential. Stimulation is with a single electrode located 100 μm above the retinal surface at the origin in the x-y plane. Dashed lines indicate layer boundaries.
Fig 6.
Geometry and simulated membrane potentials for axons of passage and axon initial segments at a variety of x-y orientations.
(a) Four-layer model geometry showing the electrode array, an example of a parallel axon of passage (orange), and the neurite orientations considered in the ganglion cell layer (green-brown). Membrane potential at the end of the cathodic phase is shown along the axes of the neurites being simulated for configurations of (b) one, (c) two, and (d) four electrodes aligned with the axon of passage. Dotted lines represent membrane thresholds for axons of passage (orange) and axon initial segments (black). Stimulus currents have been chosen such that they drive the axon of passage precisely to its threshold level. Colors in (b)-(d) indicate corresponding neurites in (a).
Fig 7.
Proportion of axon initial segment orientations preferentially activated for different electrode-retina separations (dER) and pulse durations.
Heat maps indicate the proportion of axon initial segments activated at a lower stimulus current than any fibers in the nerve fiber layer for (a) one-, (b) two- and (c) four-electrode configurations (aligned with the axon of passage). Regions of low (<10%), medium (10-40%), and high (>40%) stimulation selectivity are separated by dotted contours. White markers indicate the parameters used in Fig 6, and black markers indicate the parameters used for subplots (d), (e) and (f), which show examples of simulated membrane potentials for axons of passage and axon initial segments. Colors in (d)-(f) correspond to those in Fig 6(a).
Fig 8.
Performance of different electrode configurations with respect to GCL activation level, required stimulus charge density per phase, and radius of activation.
(a) The proportion of AIS orientations activated vs. stimulus charge density for various electrode configurations and electrode-retina separation distances, dER. (b) The radius of the activated region vs. stimulus charge density per phase. (c) The relationship between activation radius and activation level. Stimulation strategies analyzed in (a)-(c) include one-, two-, and four-electrode configurations, as well as separation distances of 100 μm (filled square, ■) and 300 μm (unfilled triangle, Δ). Solid and dashed regions in (a)-(c) represent configurations that result in preferential activation of AISs and preferential activation of AOPs, respectively. Labeled points in (a)-(c) correspond to the examples plotted in (d)-(f), which show the spread of GCL activation in the x-y plane when stimulus charge is set to acheive maximum GCL activation of 50%. Dashed blue lines in (d)-(f) correspond to one-dimensional insets. All simulations used a pulse phase duration of 200 μs, with amplitudes indicated in terms charge density per phase.
Fig 9.
Preferential stimulation for two non-ideal electrode array placements.
(a)-(b) Membrane potential along neurite axes for axons of passage and axon initial segments, with stimulus current chosen to maximally activate initial segments without activating any passing axons. Colors correspond to those in Fig 6(a), with green parallel to axons of passage and brown perpendicular. Insets describe the geometry of each simulation, indicating target region (red), electrodes used (black), and the orientation of axons of passage (orange). (c)-(d) Ganglion cell layer activation level vs. activation radius for non-ideal and ideal (as in Fig 8(f)) geometries. Transitions from solid to dashed lines represent the transitions from axon initial segment to axon of passage preferential activation. (e)-(f) The spread of ganglion cell layer activation in the x-y plane. The dashed blue line corresponds to the one-dimensional inset. Colors are mapped according to the color bar in Fig 8. All simulations used a pulse phase duration of 200 μs and electrode-retina separation of 100 μm.