shape of the elicited spike waveform). Studies outside the retina suggest that either the initial segment or the nodes of Ranvier can be the target of stimulation [56].

To determine the site of lowest threshold, Fried et al. [10] measured threshold as a function of the position of the stimulating electrode. Measurements were made in a dense spatial grid around the soma, proximal axon and distal axon of directionally selective (DS) ganglion cells (one of the rabbit ganglion cell types). They found that thresholds were lowest in a region that was centered approximately 40 mm from the soma (Fig. 12.4a). Immunochemical staining revealed that a dense band of voltage-gated sodium channels in the proximal axon was centered at the same approximate location (Fig. 12.4c). Overlay of the two images reveals that the band of sodium channels was centered within the region of low threshold (Fig. 12.4b) suggesting that the band may be the source of low thresholds and possibly the site of spike initiation. Threshold maps were found to be qualitatively, but not quantitatively similar in other cell types.

Additional unpublished measurements from Fried et al. revealed that threshold levels in the distal axon were comparable to (and sometimes lower) than those of the proximal axon (Fig. 12.4d). These results are consistent with the Jensen et al. [23] physiological study as well as with the modeling studies mentioned earlier [13, 47]; all of which found that axonal thresholds were only slightly higher than the lowest thresholds (found in other portions of the cell).

The low activation thresholds associated with RGC axons suggests that focal percepts may be difficult to obtain via stimulation schemes that target RGCs. This further suggests that stimulation methods that avoid activation of axons are needed in order to create spatially relevant patterns of retinal activity.

12.2.1.3  Threshold vs. Stimulating Electrode Diameter

The size of the electrode used to elicit activity will ultimately determine the ­maximum electrode density within the array. Therefore, small diameter electrodes presumably offer the highest possible spatial resolution. To explore the effects of electrode size, Sekirnjak et al. [49] measured threshold as a function of stimulating electrode diameter and found that both the current and the charge needed to elicit activity was reduced as the stimulating electrode diameter was decreased (Fig. 12.5a, b). However, they also found that both current and charge densities increased as the stimulating electrode diameter decreased (Fig. 12.5c, d). This trade-off arises because the reduction­ of charge associated with a smaller electrode is less than the corresponding reduction in electrode surface area.

The findings from Sekirnjak et al. are supported by an earlier study from Jensen et al. [25], in which a 125 mm diameter electrode exhibited a reduction in threshold when compared to a 500 mm diameter electrode. The electrodes used by Jensen et al. are larger than those used by Sekirnjak et al. but support the notion that smaller diameter electrodes are associated with lower thresholds (charge and current). Whereas the above studies compare thresholds for direct activation, Ahuja et al. [1] found that 10 mm electrodes had higher thresholds than 200 mm electrodes when

Fig. 12.5  Threshold vs. electrode size. Thresholds in response to 0.1-ms pulses (filled circles) and 0.05-ms pulses (open circles) were plotted as a function of electrode diameter for rodent RGCs. (a) Current, (b) charge, (c) current density, (d) charge density. Each is plotted for the same set of data. All responses were long-latency spikes. Reprinted from [49], Fig. 10, with permission

indirectly activating RGCs (via activation of presynaptic neurons). Ahuja et al. suggest that this may arise because the electric fields of large electrodes extend deeper into the retina and therefore can more easily activate presynaptic neurons. Further research is needed to confirm this hypothesis and also to determine whether other mechanisms are at work.

Sekirnjak et al. also compared the effects of varying the pulse duration and found that threshold increased as the pulse duration decreased from 0.1 to 0.05 ms. This finding is in agreement with an earlier study by Jensen et al. [25] which found that thresholds increased consistently as pulse duration was reduced from 50 to 0.1 ms. These studies suggest that the smallest diameter electrode that could be safely used is also a function of pulse duration and therefore, short duration pulses, which exclusively activate RGCs, may require large-diameter electrodes.

12.2.1.4  Spatial Extent of Activation

Another consideration for creating focal percepts is the spatial extent of activation arising from a single stimulating electrode. Ideally, activation should be limited to the immediate vicinity of the electrode. However, the relationship between the strength of the electric field and the extent of activation is not well known. Several studies, employing a variety of methods, have begun to explore this question.

Jensen et al. [23] measured threshold as a function of the distance between a very small stimulating electrode and the targeted cell body (Fig. 12.6a). They found that threshold was lowest when the stimulating electrode was at (or near) the soma (0.5 mA or 0.31 mC/cm2). Threshold increased as the stimulating electrode was moved away from the soma increasing by a factor of 20–30 at a distance of 100 mm. Sekirnjak et al. and Ahuja et al. [1] found similar increases in mouse and salamander RGCs respectively; Ahuja et al. showed that threshold increased with increasing distance regardless of the pulse duration (durations ranged from 60 to 1,000 ms).

Further support comes from a study by Schanze et al. [46] who found that moving the epiretinal electrode off the retina by 50 mm resulted in a 50% decrease in the cortical response. These results are similar to studies that found the cortical signal decreased when the distance between the stimulating electrode and the retina increased [44–46, 48].

The results in the retina are consistent with a large number of previous non-retinal stimulation studies (see [56] for a review). In general, thresholds increase with the square of the distance (between stimulating electrode and targeted neuron). The equation I = K · ´ · r2 can be used to describe the increase – where I is the threshold current, r is the distance between electrode and neuron and K is the excitability constant. In non-retinal neurons, the experimentally determined excitability constant was found to be small for large, myelinated neurons and large for small, unmyelinated neurons.

Jensen et al. [23] determined that the threshold for activating brisk-transient rabbit RGCs increased approximately with the square of the distance between stimulating electrode and targeted neuron (the actual threshold increase was in proportion to the distance raised to the 1.8 power). Jensen et al. also found that the rate of threshold increase was lower when the stimulating electrode was within 50 mm of the soma and higher for distances greater than 50 mm. While the reason for the different rates of increase is not known, it is possible that they arise from the long sodium channel bands described by Fried et al. (Fig. 12.4c). Thresholds are lowest when the stimulating electrode is centered directly above the sodium channel band and increase slowly as the electrode moves away from the center of the band but remains above a portion of the band. Once the stimulating electrode moves beyond the edges of the sodium channel band, threshold increases rapidly with increasing distance. Further studies are needed to confirm whether this is in fact the case.

To get a practical sense of how the increase in threshold with distance affected the activation of RGCs, Sekirnjak et al. [49] used a multielectrode array that was capable of stimulating and recording from many closely spaced electrodes. They found that threshold was always lowest when the same electrode that was used to record also delivered the stimulus pulse; if an adjacent electrode (60 mm spacing) was used to stimulate, threshold increased by a factor of three. This suggested that the use of low amplitude pulses would activate only those cells that were close to the electrode.

To confirm that low amplitude stimulation from each electrode operated independently, Sekirnjak et al. independently delivered stimulus pulses from each of seven nearby electrodes; seven distinct responses were recorded (Fig. 12.7a, spacing between neighboring electrodes: 60 mm). They then activated all seven electrodes simultaneously and measured the response in each electrode (Fig. 12.7b). They found that the response elicited by activation from all seven electrodes was nearly identical to the response elicited by activation from a single electrode. This suggests that the activation from one electrode did not interfere with that of neighboring electrodes. This is an encouraging result as it suggests that nearby electrodes can independently create activity in focal regions. At stronger stimulation levels however, Sekirnjak et al. found that stimulation from one electrode activated RGCs in the vicinity of neighboring electrodes. In some cases, activity could be detected 150 mm

Fig. 12.7  Multiple site stimulation. Rat retina was stimulated by 7 electrodes simultaneously (0.8 mA cathodal pulses). (a) Overlay of several trials is shown for each electrode (1–7) and evoked long-latency spikes marked with an asterisk.

Inset (top right): location of active electrodes on the array. Latencies ranged from 5 to 18 ms. (b) Traces from neighboring electrodes 1 (left) and 2 (right). For comparison, spikes are shown for individual stimulation at only that electrode (single) as well as when all 7 electrodes were active (all). Evoked spikes showed no difference. Arrowhead indicates that the large spikes seen on electrode 2 were visible on electrode 1 as small deflections. Reprinted from [49], Fig. 9, with permission