Title: 3D Electrode Array for Single-cell selectivity in Visual Prosthesis

Background : Visual prostheses electrically stimulate nearby neurons to generate artificial vision in patients blinded by retinal degenerative diseases. Current prosthetic devices offer limited spatial resolution that results in unselective stimulation of retinal ganglion cells (RGCs). This can be understood as a falling short of visual prosthesis to generate a complete visual scene with detail perception. In this report, the 3D linear electrode carrier is introduced. Our analysis develops a proof of principle to identify the usefulness of the 3D array to activate selectively single RGCs using small electrode size at the highest-density cell. Methods : A simulation framework was built by locating the 3D linear electrode carrier with the highest-density cell. Stimulation of the 3D carrier is implemented at horizontal meridian in the superior retina within the region of 1 mm away from the fovea centralis. Stimulation in that space is needed for critical functions such as object recognition, reading, and driving. The simulation framework obeyed the RGC density and distribution, ganglionic layer thickness, vertical distribution and cell diameter at the fovea. To verify RGC electrical stimulation, the relevant retinal interface elements and dynamics of the voltage-gated ionic channels were integrated into a 3D computational model in COMSOL Multiphysics. Results : the distribution of stimulus from a single active electrode to ground generates a volume of stimulation equivalent to the volume contained by a single RGC at the highest-density cell. Sensitive retinal tissue is safeguarded from electrochemical reactions caused by excessive charge density, the formation of corrosion and neural tissue heating since the advanced technology of the 3D array injects low thresholds for effective stimulation. Conclusions : The 3D electrode array can provide a safe stimulus to enhance visual resolution that can be delivered by +1000 electrodes. This is required in humans for activities where visual detail is of primary importance and thus relevant for high-resolution vision. The 3D electrode array reveals small proximities of electrodes to cells for activation. This is of an advantage for cells located near and very-deep in the ganglion layer because low thresholds are injected to the electrodes producing a well-defined localization of stimulus, an independent activation that targets single RGCs and a safe stimulus. Computer simulations of RGC activation (see Fig. 3) illustrate the volume enclosed by the threshold average boundary-peak stimulus of 3.1 A/m 2 that was straightforwardly attained from COMSOL Multiphysics using the surface/contour feature. The white line in the plots represents the zone for penetration depth for stimulation across the geometry. Stimulus from the electrode required an average peak current value in the region of 36.9 A/m 2 to produce the stimulation cube. This is equivalent to deliver an average threshold peak stimulus of 1.63 nA from the electrode. This reflects the fact that the 3D carrier can accommodate individual electrodes very close to the cells for precise selective activation. Stimulation cube is assembled by equal lengths 𝑙 # of a value of 10.75 µm assuming a volumetric cell density of 8.05e5 mm -3 . As illustrated, groups of planes ( zx , xy , yz ) show dimensions comparable to the stimulation cube. This indicates that the 3D linear carrier could theoretically present an approach to enhance selective activation of targeting cells using visual prostheses.


Background
Visual prostheses are designed to restore some vision to patients blinded by photoreceptor degenerative diseases, such as retinitis pigmentosa and age-related macular degeneration [Humayun et al., 1996]. The upgrade of visual prosthetic devices has been a followed subject since current status on clinical trials has not exhibited an array of independent phosphenes. Visual prosthesis would ideally generate an array of circularshaped percepts with narrow dimensions that would represent a building block for the pattern of visual perception. Three of the major problems with current visual prostheses are the 1) use of large electrodes that misdirect the stimulus and create phosphenes with shapes other than a small spot of light, 2) incapability to adapt electrode stimulation at locations with high RGC density and 3) atypical patterns of retinal activity are induced by stimulation [Stingl et al., 2013;Humayun et al., 2018]. This presumably may be the cause that patients do not obtain a complete visual scene composed of simultaneously presented percepts using current retinal implant devices. Current prosthetic devices developed by [Mahadevappa et al., 2005 Visual and spatial perception of retinal prosthesis demands small electrode usage to independently activate ganglion cells and replicate natural patterns of activity in the retina [Jepson, 2013;Fried et al., 2006]. Smallelectrode size can allow the excitation of small groups of cells. However, the sensitive retinal tissue is exposed because of the required charge density activation by small electrode dimensions [Lujan et al. (b), 2017]. Safe charge density limit is currently a major concern [Lujan (a), 2016; Lujan (b), 2016; Horsager et al., 2011]. For detail recognition, the resolution of implants must be improved. This can be achieved by increasing both the number and density of electrodes [Weiland et al., 2014]. There is plenty of evidence that a high number of electrodes ranging from 625 [Cha et al., 1992] to 1000+ [Chader et al., 2009] can enhance visual resolution originated by electrical stimulation. This insight is well-correlated to upgrade mobility, independent living and walking in crowded environments [Cha et al., 1992], face recognition [Thompson et al., 2003], reading large-sized letters [Bagnoud et al., 2001;Dagnelie et al., 2006;Chai et al., 2007].
The proximity of cells to the electrodes plays a major role to activate nearby cells [Lujan et al. (b), 2017]. Close proximity reduces threshold current and charge density, producing a well-defined localization of stimulus. Despite that safe stimulus can be delivered from the electrodes by approaching them to the retina surface, however, surgical challenges are present to maintain the proximity as close as possible. Distant proximity contributes to the varying current spread from electrodes causing an increment in the volume of stimulation [Lujan et al. (b), 2017] and compromising visual resolution . The proximity between the implant and the retina also increases the possibility of thermal damage caused by the dissipated heat from the implant [Zrenner, 2002]. Large electrode diameter can safeguard sensitive retinal tissue against irreversible reactions at the electrode interface. This technique is frequently used in current visual devices [Mahadevappa et al., 2005;Eger et al., 2006;Humayun et al., 2012;Klauke et al., 2011]. However, bundles of cells are activated by a single electrode leading a low visual resolution. Therefore, a trade-off is exhibited between reaching better quality of visual resolution and safety.
Electrode array topology influences the shape and breadth of the phosphenes while the retina is electrically stimulated [Lujan et al. (b), 2017]. That is, by applying a given value of peak stimulus amplitude, the current spread varies according to the topology of the electrode array and the position of the active and ground electrodes. This could lead to changes in the area of stimulation, thereby causing the generation of phosphenes with shapes other than a small spot of light. Thus, electrode topology is fundamental to restrict the stimulus to the space required for producing round dot-like percepts. Experiments performed with different electrode topologies revealed dissimilar shapes of phosphenes e.g. elongated shapes [Brindley et al., 1968;, triangles [Veraart et al., 1998], lines/bars Wilke et al., 2011], doughnut-shaped , complicated patterns [Veraart et al., 1998] and round spots of light Mahadevappa et al., 2005;. Table 1 lists the visual prostheses currently implanted in humans or isolated primate retinas with their quantity information of electrode number, diameter, and spacing.
Currently, visual prostheses transmit the stimulus from a flat 2D surface electrode array expecting to stimulate selectivity a single RGC [Jepson et al., 2013[Jepson et al., & 2014. Photomicrographs of the retina of healthy human [Kolb et al., 1995;Ross et al., 2003], monkey [Boycott et al., 1969] and mice [Ong et al., 2001] showed that the peak volumetric density of RGCs along the vertical section leans towards the middle of the ganglionic layer, leaving few RGCs neighboring the boundary with the vitreous medium. These findings suggest that considering the stimulation of nearby RGC to the electrode array as the sole assumption for high visual resolution may result in a clear misdirection and a misrepresentation of the natural spatiotemporal patterns of activity in RGCs of a different type. To achieve a near-normal vision, the diameter and density of stimulation electrodes must approach the size and density of the cells designed to stimulate [Sekirnjak et al., 2008]. Truthful restoration of natural RGC activity is likely to require independent activation of different cells. More specifically, a clear exhibition of independence would be selective stimulation of a single cell without activating simultaneously neighboring cells of any type [Jepson et al., 2013]. Previous work on the isolated retina [Jepson et al., 2013;Hottowy et al., 2012] indicated that single-cell selectivity is possible for some RGCs using electrode arrays with much higher density and smaller electrodes than clinical prostheses. Jepson showed in principle the possibility to activate safely single RGCs in the high-resolution visual pathways (highest-density cell) at their native spatial and temporal resolution. These results revealed direct stimulation of ON and OFF midget, ON and OFF parasol, and small bistratified RGCs using 15 µm electrode diameter and small current pulses that provide safe charge density range. [Fried et al., 2006] supported the use of small electrodes to activate small groups of cells, leading to rich resolution patterns of artificial-induced activity at the retina. Decreasing electrode dimensions generate higher resolution patterns of prosthetic-elicited activity that are closer to light elicited patterns. However, single-cell selectivity of RGCs will require higher-density electrode arrays, novel electrode geometries, and more sophisticated stimulation patterns [Grumet et al., 1999;Rattay et al., 2004].
As for the technology of advance electrode carriers, [Rodger et al., 2008] designed, fabricated and implanted in animals a biomimetic retinal parylene C-based electrode array with 60 of 1024 75 µm-diameter electrodes connected through dual-layer process. The biomimetic retinal array was able to stimulate tissue, elicit a response similar to the response generated from a light pulse and confirm excellent biostability. Although that the biomimetic retinal array retained the spherical curvature of the retina and produced a complex biomimetic pattern that closely mirrored the area density distribution of RGCs in the human retina [Curcio et al., 1990], the reasoning of how the biomimetic pattern is generated is incomplete. RGCs found in the human ganglion cell layer [Curcio et al., 1990] are not distributed along the border between the ganglion layer and the vitreous chamber but along the three-dimensional space of the ganglion layer that makes the volumetric density of cells. Peak volumetric density is not in contact with the border between the ganglion layer and the vitreous chamber but leans toward the boundary between the ganglion layer and the inner nuclear layer [Kolb et al., 1995;Ross et al., 2003;Boycott et al., 1969;Ong et al., 2001]. These findings suggest that considering the area cell density as the only assumption could result in a clear misdirection of electrode stimulus to empty regions of cells, a misuse of electrodes and a misrepresentation of the nature of cell distribution. [Lohmann et al., 2019] designed the star-shaped very large electrode array for retinal stimulation or VLARSdesign. The implantation surgery was established in cadaveric porcine eyes. To analyze biocompatibility, ten rabbits were implanted with the device. Any movement after implantation had to be done with great caution since the epiretinal VLARS was not fixated with a retinal tack. On the electrode array design, the proximity between active electrodes varies on their position, i.e. approximately 520 µm on the wings versus 300 µm in the center). The VLARS-design supports 250 individual electrodes, each having a diameter of 100 µm except to the solely larger return electrode located at the base of the connecting lead of the array with a diameter of 1mm [Waschkowski et al., 2014]. Although the VLARS results on a complete array diameter of 12 mm that covers approximately 110 mm 2 , and a visual angle of 37.6° (corresponding to a visual field of 18.8°), the geometric mathematical reasoning of the electrode array design was misdirected to target single-cell selectivity. That is, the analogy between the volume covered by the current density distribution per electrode and the volume per RGC was neglected.
Argus I and II epi-retinal prostheses (Second Sight Medical Products, Inc, Sylmar, CA) implanted in patients reported streak-like visual percepts rather than a natural more commonly reported punctate-shaped phosphenes, suggesting a direct stimulation of axonal bundles [Humayun et al., 2012]. This is to be expected considering that the study used large electrodes of 200 µm of diameter and located far from the ganglionic layer (~180µm), necessitating over large amplitudes of current to reach RGC stimulation thresholds. As for experimental testimonies, both Argus II and Alpha IMS (Retina Implant AG in Germany) patients cannot perceive uncomplicated forms and letters instantly; rather they scan their head over objects to judge what they are seeing [Weiland, 2014]. In previous clinical trials of both sub-and epiretinal approaches demonstrate that patients do not experience such flawless pixelized sight as shown in many publications. An idea that each electrode produces a similar spot of light as compared with its neighbor is not completely the case. Argus II clinical trial demonstrated that 55% of single electrodes were capable to produce a spot of light within the safe boundaries  Weiland et al., 2014]. Our simulation framework places the 3D electrode array 1 mm away from the fovea at the peak density of RGC. This is a requisite in visual prostheses because actions that require visual detail are processed within ±15° of eccentricity. We consider a three-dimensional reconstruction of the ganglion layer with realistic a) density distribution of RGCs along the retina, b) distribution of RGCs in the vertical section, c) diameter of RGC and d) ganglionic layer depth as a function of the eccentricity along the retina. Depth accuracy stimulation is examined at the peak volumetric density of RGCs along the vertical section at the ganglionic layer. To provide functional vision, we investigated safe stimulation of an existing ASIC design that can provide 1024 electrodes with low power consumption [Meza-Cuevas et al., 2014]. Electrochemical reactions of neural tissue heating from the retina implant, watervoltage window, and charge density injection limits were included in our study.

Linear Carrier Element
3D linear carrier element (LCE) as shown in Fig. 1(a) is connected to an electrode connecting point and carrying a plurality of the electrodes. The electrodes carried by a linear carrier element are arranged along a substantially straight line to penetrate into or through the surface of the ganglionic layer. Due to the close proximity to RGC, the electrodes can stimulate straightforwardly a single RGC with low injected current. In any event, the 3D linear carrier element can facilitate the desired placement of the electrodes within the respective retinal layer. For implantation, the dimensions and mechanical properties of the 3D linear carrier element may be selected such that its placement within the retinal tissue would not cause substantial damage to the nerve cells. Single, monophasic linear decrease pulse shape of uniform current is injected from active to the ground electrode to drive cell activation. This externally applied current density is distributed to the retinal tissue and the participating channel types found in this particular RGC membrane. In this present study, we implemented in COMSOL Multiphysics the membrane model developed by [Fohlmeister et al., 1990]. The basic mathematical structure for voltage-gated ion channels was based on the equations developed by [Hodgkin & Huxley, 1952]. Four conductances associated with voltage-gated channels were considered: calcium gCa channel; sodium gNa channel; non-activating K+ (delayed rectifier) gK; inactivating K+ (A-type) gaK; calcium-activated K+ gkCa channel was gated by calcium Ca2+ and modeled on that basis.  [Fohlmeister et al., 1990]. We assumed that the peak boundary current density in the RGC membrane serves as an input parameter in the RGC circuit modeling. Hence, the peak boundary current density across the RGC membrane computed in Comsol Multiphysics is assumed to be equal to the extracellular current density of the circuit modeling. Threshold injected current required for RGC activation by means of extracellular stimulation must generate a voltage shift of around +30 mV in the RGC membrane. Retinal network cells (i.e. bipolar, horizontal and amacrine cells, ON-and OFF networks) are excluded because the severe rod and cone photoreceptor impairment cannot drive visual phototransduction process started light photocurrent input. [Raza et al., 2015] measured the ganglion layer thicknesses for 43 eyes of 36 human healthy controls. In this study, the data found by Raza was used in the reconstruction of the ganglion layer. In this present work, the distribution of RGC diameter found by [Ryskamp et al., 2011] and [Rossi et al., 2017] is used in the reconstruction of the ganglion layer.

Vertical Distribution of Retinal Ganglion Cells
Photomicrographs of the retina of healthy humans [Kolb et al., 1995;Ross et al., 2003], monkey [Boycott, 1969] and mice [Ong et al., 2001] were considered in the estimation of the RGC distribution along the vertical section. The ganglionic layer was divided in horizontal segments of equal thickness and cell nuclei were counted for each segment. Then, the results were averaged, normalized and plotted in red with circular markers against the thickness of the ganglionic layer, see Fig. 1(c). The normalized results of each reference are shown in black using four different line styles. The curve shape of the averaged and normalized data was fitted to a 3 rd order polynomial and plotted in red with a solid line. The curve peak amplitude, not included in Fig. 1(c), was built such that the integral of the polynomial over the RGC thickness yields the same realistic amount of cells per mm 2 measured by [Curcio et al., 1990]. Thus, the polynomial where t is the RGC thickness. # is the area cell density. Here we assumed that the cell distribution along the vertical section behaves the same for all four meridians.

Investigation of Electrode Stimulation
The present work focuses on meridian maps of area cell density along the horizontal meridians (nasal and temporal) in the superior direction. This is mainly because 1) the highest ganglion cell densities are found in the horizontal meridian and 2) in peripheral retina densities in superior retina exceed those at the corresponding eccentricities in the inferior retina by 60% [Curcio et al., 1990]. Following the findings by Curcio, the peak cell density is found about 1 mm from the foveal center. At greater eccentricities within the central retina, ganglion cell density falls off with eccentricity more rapidly along the vertical meridian than along the horizontal meridian. Let us then obey the RGC density and distribution [Curcio et al., 1990], ganglionic layer thickness [44], where peak cell density is located. This boundary includes the region until 10° (2.7 mm) needed for critical functions such as object recognition, reading, and driving [Nelson et al., 2003].

Mathematical Approach for Single-cell Selectivity
Let us consider place the 3D linear electrode carrier at the location of 1 mm away from the foveal center, in the horizontal meridian (nasal and temporal) in the superior direction. This is equal to have a RGC density of 31,300 mm -2 , the ganglionic layer thickness of 60µm, RGC diameter of 10µm and a vertical distribution as seen in Fig.  1(c). RGCs located in the ganglion layer have their peak nearly in the center of their vertical distribution. Thus, the stimulating electrode array is placed about the middle of the ganglionic layer, see Fig. 1(b). The stimulating electrode array consists of one active and one ground electrodes. Single, monophasic linear decrease pulse shape of 100µs is used. The mathematical approach for single-cell selectivity states that the current density distribution to the ground electrode generates the volume of stimulation that must be equal to the volume contained by a single RGC, and calculated as $ is the volumetric cell density in µm -3 . The volumetric cell density at the vertical distribution can be computed as explained in (Eq. 1). The result of (Eq. 2) is called the stimulation cube. It is defined as a tridimensional space on the retina where the distribution of the stimulus initiated at the active electrode in effect triggers a response of a single cell. The criterion of the stimulation states that if stimulation of an electrode is achieved inside its volume, the cell is activated. Otherwise, the cell is not activated. Let us adopt that the cell distribution per volume is uniform in a manner that the volume can be represented as a cube with equal lengths calculated as the cube root of the cube volume The proximity of neighboring face-to-face electrodes is equal to # .

Threshold of RGC Stimulation
The procedure for obtaining the threshold current density of a single RGC and the stimulation threshold for the cube is explained as follows. Single excitation of a RGC follows the placement of a cell inside the ganglionic layer, exactly between the linear carrier elements where the electrodes are located, see Fig. 1(b). This is arranged such that there is an equivalent distance from the RGC and the active and ground electrodes. Single RGC stimulation was investigated by increasing the peak stimulation current with an interval of 0.1 nano amperes until the action potential is generated. The stimulation threshold for the cube is as follows. A single cell is placed in several points of the cube, see Fig. 2(a), and peak stimulation current was increased with an interval of 0.1 nano amperes until the action potential is generated. Threshold values for each case are stored. To ensure an effective threshold value, this procedure was repeated six times to include all possible point alternatives. Afterward, the stimulation threshold for the cube was determined as the average of all threshold values. For both procedures are used a single pair of stimulating electrodes consisting of one active electrode and one ground.

Average Power Density and Neural Tissue Heating
The main objective of retinal stimulation, using either epi-or subretinal technique, is to provide a functional vision that comes from at least 1024 image pixels with at least 20 images per second. To achieve this request, the viability of using at least 1024 electrodes is studied by attaching 16

Stimulation Safety
Safety in terms of electrical performance is mainly related to three factors: charge density injection level, neural tissue heating due to the power dissipation by the device, and the water-voltage window. Electrolysis of water may occur as well as a result when the maximum cathodic and anodic potential across the electrodes surpass the "water window" boundary [Merrill et al., 2005]. The water window is a potential range that is defined by the reduction of water, forming hydrogen gas, in the negative direction, and the oxidation of water, forming oxygen, in a positive direction which may cause corrosion. High charge density is required by small electrode usage that can cause a breakdown of the electrode, adverse tissue reactions and gas bubbling evolution, which damage the soft retinal tissue layers [Brummer et al., 1977]. The neural interface devices must be shown not to cause significant temperature increases in the implanted tissue. As regards to visual prosthesis, the liquid environment of the vitreous humor acts as a heat sink that is capable of dissipating a significant amount of power. An electronic chip positioned away from the retina can run at considerably higher powers than a chip positioned on the retinal surface [Piyathaisere et al., 2003]. It is reported that maximum permissible temperature increase in the cortex is about 1°C or maximum power density is 80 mW/cm 2 of exposed tissue area [Seese et al., 1998]. [Rose & Robblee, 1990] applied platinum electrodes and brief pulses while measured a conservative charge density limit of 0.1-0.15 mC/cm 2 (cathodal-first biphasic) or 0.05-0.1 mC/cm 2 (anodal-first biphasic). Charge density limit of 0.1 mC/cm 2 is comparatively conservative. [Brummer & Turner, 1977] suggested that charge densities of up to 0.30-0.35 mC/cm 2 are safe for longer pulses to generate adverse electrochemical reactions at the surface of platinum electrodes. [Ray et al., 2011] in a recent study of high-frequency stimulation in rat retina found no significant histological changes to the retina up to 0.68mC/cm 2 with platinum electrodes. Argus II and Alpha IMS used platinum gray and titanium nitride respectively. Typical electrode material in neurostimulation is bulk platinum. The charge injection capacity for such material is 0.1-0.35 mC/cm 2 . Platinum gray can inject up to 1mC/cm 2 , and titanium nitride until 0.9mC/cm 2 , which represents an important step for implantable bioelectronics. In this study, electrochemical safety is examined in terms of charge density injection level, electrode voltage (or water-voltage window) and neural tissue heating due to the power dissipation by the device. Voltage window limit of 1.5 V assuming a PEDOT-NaPSS coat for invasive electrodes [Boretius et al., 2010]. Neural tissueheating limit is 1°C based on circular electrode areas fell within the limits previously stated. Because the pulse shape used in this study was a monophasic linear decrease, we compared our activation thresholds to the midpoint of these safe charge density values of 0.1 mC/cm 2 for gas-free and erosion-free operation. For computing the average power density and the neural tissue heating, we extracted from Comsol Multiphysics the average peak stimulus density from the electrode and voltage across the electrodes. The charge density injected to the electrodes is calculated as is the radius of the electrode, is the peak threshold current injected along an initial and final time of stimulation 7 and 8 , respectively. A Matlab script organized the extracted data and performed several tasks to obtain the heat dissipated by the device and charge density on the electrode. Peak threshold current density applied at the electrode is calculated by dividing the peak threshold current applied at electrode over the crosssection area of the electrode. Electrode potential is calculated internally in COMSOL Multiphysics.

RGC Activation
The simplest stimulus is a single, monophasic linear decrease pulse shape. On top-left a zoomed-in view specifies the waveform until the final time of 100 µs, see Fig. 2(b). Action potential is triggered with a threshold peak stimulus of 0.5 nA that results in an average peak stimulus density of 11.31 A/m 2 from the electrode. Single RGC located between the active and ground electrodes obtains an average boundary-peak stimulus density of 3.1 A/m 2 for effective stimulation.
For the stimulation cube, a single RGC was located in six different points of the cube, see Fig. 2(a) and peak stimulation current is increased until membrane activation. The action potential is generated with an average threshold peak stimulus of 1.63 nA that results in an average peak stimulus density of 36.9 A/m 2 from the electrode, see Fig. 2(c) and Table 3. Effective membrane activation required different values of electrode peak stimulus as the RGC shifted its position along with the cube. Points (1), (2), (4) and (5) required peak amplitudes ranging between 43 to 45.3 A/m 2 applied to the RGC. Points (3) and (6) required small stimulus amplitudes varying between 22 to 23 A/m 2 . This twofold increase of the electrode peak stimulus is mainly because of the close proximity of the RGC to the electrode. Single RGC located at six different points of the cube obtains an average boundary-peak stimulus density of 3.7 A/m 2 for effective stimulation using an interval of 0.1 nano amperes of peak electrode stimulus see Fig. 2(d).

Stimulation Safety
Natural RGC visual perception is attained by activating small areas of the retina [Jepson, 2013]. As a result, small electrodes are the topmost requirement because small groups of cells can be activated. Despite visual reception is improved; however, the exposure of sensitive retinal tissue must be safeguarded because of the charge density required by small electrode dimensions. The formation of corrosion [Fried et al., 2006 RGC stimulation by the 3D electrode array can inject safe stimulus below the limits of electrochemical reactions to produce the stimulation cube (see Table 3). Average power density was calculated using a monophasic linear decrease pulse duration of 100 µs, a total number of electrodes of 1024, a total chip surface area of 0. RGC proximity to the electrode using the 3D electrode array is beneficial to minimize electrode peak stimulus for effective stimulation. This is advantageous to avoid irreversible reactions such as gas-bubbling formation caused by high injected charge densities, neural tissue heating produced by high power dissipation by the device, and the water-voltage window triggered by high electrode voltage. Small proximity of electrodes to RGC, as a result, allows electrodes to activate more likely a single cell. RGCs of different types can be independently stimulated without simultaneous activation of neighboring cells of any type. Accordingly, a truthful restoration of natural RGC activity that likely requires independent activation of different cells [Jepson, 2013] may be achievable using the 3D electrode array.
To date, electrode array requires major improvement for safe stimuli and visual acuity. Safe activation of RGCs requires high charge density threshold coming from small electrodes. Reason is that injected charge densities would increase the likelihood to produce gas-bubbling formation while electrode diameter is reduced. Small electrode dimensions can produce greater resolution patterns of artificial-elicited activity that are closer to lightelicited patterns [Cai et al., 2011]. RGC activation by the 3D array can reduce the threshold peak stimulus to the electrode and as a result, can reduce electrode size. Small electrode diameter can be applied, allowing selective excitation of small groups of ganglion cells.
Pulses shorter than 150 µs of duration which can replicate light-elicited spiking patterns; trigger solely a single spike with precise temporal pattern and send a more physiological signal to the brain [Fried et al., 2006]. [Jensen & Rizzo III, 2005] addressed this issue. In short, short-current pulses of 100µs or less showed significant preference because passing retinal ganglion cell axons can be avoided while stimulation. Choosing that pulse duration, the amount of current needed to generate the response of a cell is much lower than that required to generate an axonal response. [Greenberg et al., 1999] supported these observations by reporting that axonal threshold was 20% higher than that of the retinal ganglion cell. Experimental findings by [Jepson et al., 2014] exhibited single spike responses with sub-millisecond latency, which is a characteristic of direct ganglion cell activation. In this study, short pulse durations of 100 µs and small electrodes of 7.5 µm of diameter were used.

Stimulation Cube Volume for Single-cell Selectivity
Volumetric cell density along the vertical section of the ganglionic layer is described by the solution of the third-order polynomial, see (Eq. 1). Current density distribution to the ground electrode specifies the generation of the stimulation cube volume, which is equivalent to the volume contained by a single RGC. The criterion of the stimulation states that if stimulation of an electrode is achieved inside its volume, the cell is activated. Otherwise, the cell is not activated. Stimulation cube volume computed as the reciprocal of the volumetric cell density applies a uniform cell distribution. This simplifies the representation of the cube with equal lengths computed as the cube root of the cube volume see Fig. 2(a).
Vertical volumetric RGC density in µm -3 is calculated as a function of the ganglionic thickness at the location of 1 mm away from the foveal center, in the horizontal meridian (nasal and temporal) at the superior direction. Through these results, the stimulation cube volume and length corresponding to the cube volume contained by a single RGC are computed. As previously stated, active and ground electrodes are located face-to-face in Figure 2(a) Six different points of the cube to investigate the threshold current from the electrode. Note that all points are repeated based on the coordinate of interest. Fig. 2(b) threshold current density for exiting a single RGC. The cell is placed inside the ganglionic layer exactly between the linear carrier elements where the electrodes are located. Action potential is triggered with an average peak stimulus density of 11.31 A/m 2 from the electrode. Single RGC located between active and ground electrodes obtains an average boundary-peak stimulus density of 3.1 A/m 2 for stimulation. Fig. 2(c) threshold current density for generating the stimulation cube. Single RGC was placed in six different points to investigate membrane activation. Action potential is generated with an average peak stimulus density of 36.9 A/m 2 from the electrode. Effective membrane stimulation required different values of electrode peak stimulus as the RGC shifted its position along the cube. Fig. 2(d) average boundary-peak stimulus density for effective stimulation of a single RGC located at six different points of the cube. different linear carrier elements around the middle of the ganglionic layer. Reason is that peak volumetric density is located close to the center of the ganglion layer. Peak volumetric cell density obtains 8.05e5 mm -3 or 8.05e-4 µm -3 . Cube volume dimensions at the peak of the volumetric density obtain 1.24e3 µm 3 and an equal cube length of 10.75 µm. RGC diameter of 10µm is applied in the reconstruction of the ganglion layer. Stimulation cube volume and RGC sphere volume ratio of 2.4 represents the viability to locate the 3D electrode array without damaging the cells.
Current density penetration depth described by the time-dependent electrical current simulation of electrical current distribution in conductive and capacitive media was applied in our study. Stimulus from the electrode required an average peak-current value in the region of 36.9 A/m 2 to produce the stimulation cube for effective stimulation, see Fig. 2(c). Since 3.1 A/m 2 is sufficient to generate an action potential, the volume enclosed by that threshold average boundary-peak stimulus was directly obtained from (COMSOL Multiphysics, Version 5.3) using the surface/contour feature (see Fig. 3). The white line in the plots represents the zone of current penetration depth for stimulation across the geometry. Dashed-line squares represent accurately the dimensions of the stimulation cube. Groups of planes (zx, xy, yz) illustrate the electrical current distribution in conductive and capacitive media at a time of 10 µs. Collectively, each group corresponds to seven sub-planes located at a distance of (± # /2, ±4e-6, ±2e-6) µm away from the center sub-plane. As a reminder, # represents the lengths of the cube calculated as the cube root of the cube volume √ ! . Stimulation cube is assembled by equal lengths # of a value of 10.75 µm assuming a volumetric cell density of 8.05e5 mm -3 .

Discussion
In this study, the 3D electrode carrier is introduced. RGC localized stimulation is examined as the 3D carrier is placed at horizontal meridians (nasal and temporal) at the superior direction with the highest volume density of RGCs. In brief, our results indicate that electrode stimulus utilizing the 3D carrier generates a volume of stimulation equivalent to the volume contained by a single RGC. Excitation of a small volume of the retina allows a more natural visual perception and replicates truthful spatiotemporal patterns of activity in the retina. The exposure of sensitive retinal tissue caused by electrochemical reactions is safeguarded as a result of injecting low thresholds for effective stimulation.

Precise stimulation of very-near and deep ganglion cells
Ganglion cell types can be differentiated from one another based on morphological and physiological criteria [Cook, 1997;Rowe el al. 1977;Dacey, 1999]  Computer simulations of RGC activation (see Fig. 3) illustrate the volume enclosed by the threshold average boundary-peak stimulus of 3.1 A/m 2 that was straightforwardly attained from COMSOL Multiphysics using the surface/contour feature. The white line in the plots represents the zone for penetration depth for stimulation across the geometry. Stimulus from the electrode required an average peak current value in the region of 36.9 A/m 2 to produce the stimulation cube. This is equivalent to deliver an average threshold peak stimulus of 1.63 nA from the electrode. This reflects the fact that the 3D carrier can accommodate individual electrodes very close to the cells for precise selective activation. Stimulation cube is assembled by equal lengths # of a value of 10.75 µm assuming a volumetric cell density of 8.05e5 mm -3 . As illustrated, groups of planes (zx, xy, yz) show dimensions comparable to the stimulation cube. This indicates that the 3D linear carrier could theoretically present an approach to enhance selective activation of targeting cells using visual prostheses.
Healthy human [Kolb et al., 1995;Ross et al., 2003], monkey [Boycott, 1969] and mice [Ong et al., 2001] photomicrographs of the retina indicates that RGC peak volumetric density leans towards the middle of the vertical section of the ganglionic layer, leaving few RGCs neighboring the surface of the electrodes, see Fig.  1(c). Typical 2D surface electrode array delivers radially the current density in the retinal tissues expecting to stimulate selectivity a single RGC. If achievable, accurate selective activation would stimulate RGC close to the carrier, see Fig. 4(a). However, cells located deeply in the vertical segment of the ganglionic layer would leave inactive. As a result, visual prostheses may induce responses that constitute of irregular patterns far from being natural patterns of prosthetic-elicited activity of the retina. This suggests that considering the stimulation of nearby RGC to the electrode array as the sole assumption for high visual resolution may result in a clear misrepresentation of the natural spatiotemporal patterns of activity in RGCs of a different type. Reason is that RGC types can be differentiated from one another based on morphological and physiological criteria [Cook et al., 1997;Rowe el al. 1977;Dacey et al., 1999]. Studies in the cat retina suggest there may be as many as 20 such RGC types [Enroth-Cugell et al., 1966;Boycott et al., 1974]. In a healthy retina, the brain collects different features of the visual scene by temporal patterns of activity in around 20 different RGC types that are spatially intermixed [Dacey et al., 1999]. Accordingly, RGCs that are near one another often transmit very different spatiotemporal signals. A suggestion to stimulate selectively RGCs by a flat 2D surface carrier may disregard significant contributions of bundles of cells and may reproduce inaccurately natural spatiotemporal patterns of activity of the retina. That is, accurate selective activation of RGC by 2D surface electrodes clearly provides complete negligence of cells placed deeply in the vertical segment of the ganglionic layer. This presumably may be the cause that patients do not obtain a complete visual scene composed of simultaneously presented percepts using current visual prosthetic devices.
As opposed to the 2D carrier, precise stimulation of very-near and deep RGCs can be realized with the advanced technology of the 3D electrode carrier, see Fig. 4(b). Reason is that 3D carrier technology can distribute the stimulus in a small volume equivalent to the volume contained by a single cell, generating the stimulation cube (for more information see Mathematical Approach for Single-cell Selectivity). Any cell positioned randomly in the vertical segment of the ganglionic layer can accurately be activated by low threshold stimulus, preventing the generation of electrochemical reactions. Natural RGC visual perception can be realized by activating small areas of the retina [Jepson, 2013]. As a result, small electrodes are the topmost requirement because small groups of cells can be activated. As an advantage, the 3D electrode array can minimize the peak threshold stimulus that allows the reduction of the electrode size to a degree that produces safe stimulation.

Electrode Carrier Dimensions and Total Chip Surface Area
The electrode carrier width can be calculated by applying the length of the stimulation cube as # ( 9 − 1) + : 9 , where 9 is the number of rows of linear carrier elements and : represents the depth of the individual linear carrier. The electrode carrier length is computed as # ; , where ; is the number of columns of linear carrier elements. For a 16x16 array of linear carrier elements that collectively accommodate 1024 electrodes (four electrodes per linear carrier), the total electrode carrier width and length is 193 x 172 µm respectively, assuming a linear carrier element thickness of 2 µm. Since the cube volume dimensions at the peak of the volumetric density obtain 1240 µm 3 and an equal cube length of 10.75 µm, the individual linear carrier can accommodate as far as five electrodes in a 60 µm vertical thickness in the ganglionic layer. This would be equal to house 1280 electrodes. Our simulations suggested that that amount of electrodes can deliver safe stimulus by injecting low thresholds and generating volume of stimulation equivalent to the volume contained by a single RGC.
Advance carrier technology should not add substantial size to the electronics since the total implant dimensions require a small-sized device to safely fit in the eye and ideally fit inside the orbit. Epiretinal implant size is limited because of the small incisions that can be safely made in the eyewall [Weiland, 2014]. The total chip surface area can be assembled using attachments of layers to minimize the total area. As a result, the total width . Volume enclosed by the threshold average boundary-peak stimulus for generating the stimulation cube. This volume was obtained from the surface/contour feature in COMSOL Multiphysics. The white line in the plots represents the zone for penetration depth for stimulation across the geometry. Dashed-line squares represent accurately the dimensions of the stimulation cube. Groups of planes (zx, xy, yz) illustrate the electrical current distribution in conductive and capacitive media. Together, each group corresponds of seven sub-planes located at a distance of (± ! /2, ±4e-6, ±2e-6) µm away from the center sub-plane (csp). ! represents the cube length.

Planes xy
of one layer is computed as 9 , and the total length of one layer is computed as ; . Where 9 and ; are the number of columns and rows of single ASICs. To accommodate the electronics that control 1024 electrodes, 16 ASICs of 64 electrodes each is required [Meza-Cuevas et al., 2014]. We selected a two-layer arrangement of 2x4 each to minimize the total area of their attachment. The width and length of one layer are 15.7 and 8.4mm, respectively. The total area of a single layer is 1.32cm 2 . The height between the layers is can be fixed to 1 mm.

3D Electrode Carrier´s Key Features
Visual prostheses would ideally reproduce accurately natural spatiotemporal patterns of activity in RGCs. This requires the capacity of each electrode to reach single-cell selectively. In other words, RGCs are tightly-packed in the ganglionic layer, mainly at the fovea. Unique characteristics of the visual space are sent to the brain via temporal patterns of activity in RGC types that are spatially mixed. RGCs that are close to each other frequently transmit very different signals.
It's not a secret that despite the challenges to overcome functional vision, fundamental research stipulated around 1000+ electrodes per single array are needed to upgrade basic issues such as mobility, independent living and navigating on the interior and exterior environments. Currently, a small number of companies such as Second Sight Medical Products (SS), Retina Implant GmbH (RI) and Intelligent Medical Implants GmbH (IMI) have developed a complete visual prosthesis device. Electrode diameters of IMI, RI, and SS are 100 and 360, 70 and 200 µm, respectively. Retinal implant devices previously stated likely activate hundreds of ganglion cells simultaneously over a particular region due to the size of the electrode used. Beyond just this coarse stimulation of cells restricts spatial resolution, the activity generated by stimulation remains dissimilar from a healthy retina too. Thus, those vision progresses need a significant enhancement to restore functional vision. [Mahadevappa, 2005] found that the threshold current to activate ganglion cells was found to increase with time of surgery. The main reason is most likely the lifting off of the array from the underlying tissue. Simulationbased studies have been underscored the importance of controlling the distance between the array and the retina surface ]. Despite that safe stimulus is delivered by approaching the electrode carrier to the surface of the retina, however, surgical challenges are thus delivered to maintain the proximity as close as possible. Close proximity of RGC to the electrodes reduces threshold stimulus allowing small electrodes to generate phosphenes within safe heat limits [Fried et al., 2006].
As described in this report, the novel advance technology of 3D electrode array provides key features that successfully address major concerns of current visual prosthetic devices: 1) increase number of electrodes up to +1000 for high-resolution vision, 2) electrode size reduction for one-to-one electrode-ganglion cell stimulation, 3) proximity of cell to electrode reduction for lowering threshold stimulus (safe stimulus below electrochemical limits) and targeting single cells during stimulation, 4) reinforce vertical-thickness depth accuracy stimulation.

Considerations for practical applications
The advance carrier technology of the 3D electrode array could potentially provide a strategy to improve cell selectivity on epi-retinal stimulation in visual implants. This reflects the fact that active electrodes inject low stimulus causing small volumes of stimulation corresponding to the volume enclosed by a single cell. Connected with the fact that current distribution could create electrochemical reactions, however, RGC stimulation using the 3D electrode carrier can supply stimuli below the limits of electrochemical reactions. As an advantage, the electrode carrier dimension is highly dependent on the volumetric cell density at the ganglionic layer, which in turn generates the stimulation cube as = $ %& . For any three-dimensional topography of RGCs, the response of this formulation can be accurate by outputting the volume required for potentially stimulate single cells. The inputs of the simulation framework include veridical vertical spatial distribution of RGCs in a perspective threedimensional view, ganglionic layer thickness, realistic volumetric cell density and RGC diameter at 1 mm away from the foveal center. [Santos et al., 1997] demonstrated the feasibility to implant a retinal device by indicating that 25% to 30% of ganglion cells are preserved in the inner retinal region in patients suffering critical Retinitis pigmentosa (RP) or Age-related macular degeneration (AMD). As a result, these experimental-based findings demonstrate that visually impaired patients suffering from RP or AMD can restore their sight using a visual prosthesis. Although courageously, though, a suitable visual prosthesis should be developed such that visual and detail perception yield natural spatiotemporal activity of cells. The applicability of the 3D carrier can accommodate the electrodes towards the generation of precise regions of stimulation.

Conclusion
In this report, the 3D electrode carrier is introduced. RGC localized stimulation is examined as the 3D carrier is placed at horizontal meridians (nasal and temporal) at the superior direction with the highest volume density of RGCs. This is required for a truthful restoration of natural RGC activity that likely requires independent activation of different cells. The simulation-based model obeyed the RGC density and distribution, ganglionic layer thickness, vertical distribution and the cell diameter at the location of 1 mm away from the fovea center.
Our results indicate that electrode activation employing the 3D electrode carrier generates a volume of stimulation equivalent to the volume contained by a single RGC. Stimulation of small volume of the retina allows a more natural visual perception and replicates truthful spatiotemporal patterns of activity in the retina. The exposure of sensitive retinal tissue caused by electrochemical reactions is safeguarded as a result of the advanced technology of the 3D array that injects low thresholds for effective stimulation.