Avoidance of axonal stimulation with sinusoidal epiretinal stimulation

Objective. Neuromodulation, particularly electrical stimulation, necessitates high spatial resolution to achieve artificial vision with high acuity. In epiretinal implants, this is hindered by the undesired activation of distal axons. Here, we investigate focal and axonal activation of retinal ganglion cells (RGCs) in epiretinal configuration for different sinusoidal stimulation frequencies. Approach. RGC responses to epiretinal sinusoidal stimulation at frequencies between 40 and 100 Hz were tested in ex-vivo photoreceptor degenerated (rd10) isolated retinae. Experiments were conducted using a high-density CMOS-based microelectrode array, which allows to localize RGC cell bodies and axons at high spatial resolution. Main results. We report current and charge density thresholds for focal and distal axon activation at stimulation frequencies of 40, 60, 80, and 100 Hz for an electrode size with an effective area of 0.01 mm2. Activation of distal axons is avoided up to a stimulation amplitude of 0.23 µA (corresponding to 17.3 µC cm−2) at 40 Hz and up to a stimulation amplitude of 0.28 µA (14.8 µC cm−2) at 60 Hz. The threshold ratio between focal and axonal activation increases from 1.1 for 100 Hz up to 1.6 for 60 Hz, while at 40 Hz stimulation frequency, almost no axonal responses were detected in the tested intensity range. With the use of synaptic blockers, we demonstrate the underlying direct activation mechanism of the ganglion cells. Finally, using high-resolution electrical imaging and label-free electrophysiological axon tracking, we demonstrate the extent of activation in axon bundles. Significance. Our results can be exploited to define a spatially selective stimulation strategy avoiding axonal activation in future retinal implants, thereby solving one of the major limitations of artificial vision. The results may be extended to other fields of neuroprosthetics to achieve selective focal electrical stimulation.


Introduction
Neural interfaces and neuroprosthetics exploit neuromodulation to restore lost motor or sensory functions by stimulating neural networks.Successful neuroprosthetic or neuromodulation applications include stimulation of deep brain nuclei (Limousin et al 1998, Deuschl et al 2006, Krauss et al 2021), of the spinal cord (Lorach et al 2023), of the cochlea (Clark 2003, Wilson andDorman 2008) as well as peripheral nerves (Plachta et al 2014).A type of neuroprostheses with mixed outcomes is retinal implants used for the treatment of retinitis pigmentosa or agerelated macular degeneration.Although some promising examples of clinical outcomes in implanted patients have been reported (Humayun et al 2012, Muqit et al 2019, Cehajic Kapetanovic et al 2020), retinal implants have faced setbacks due to unsuccessful designs leading to two companies discontinuing their CE approved devices (Ayton et al 2020).New implants are, however, in clinical trials or under testing (Lorach et al 2015, Ayton et al 2020, Vagni et al 2022).
Among the difficulties to restore some visual percepts using retinal prosthetics is the lack of optimal stimulation waveforms.This problem is most obvious in epiretinal configuration, where the unmyelinated axons from peripheral retinal ganglion cells (RGCs) travel towards the optic nerve, thereby crossing the stimulation electrodes.Activation of axons of passage prevents the possibility to stimulate RGCs with high spatial resolution, thus limiting the visual acuity perceived by the patient.In the absence of selective stimulation, axons of passage are activated, creating misleading elongated percepts in the patients (Nanduri et al 2012, Beyeler et al 2019).The problem of activation of passing axons may be tackled via closed-loop stimulus optimization algorithms (Grosberg et al 2017, Madugula et al 2022, Gogliettino et al 2023).However, the simplest way to avoid axonal stimulation would be a stimulation waveform capable of activating only the soma or the axon initial segment (AIS) of a target cell, here defined as focal stimulation, without activating nearby distal axons of passage and without requiring prior knowledge of RGC location.In this work, we used sinusoidal waveforms to investigate focal stimulation of RGCs and identified the amplitude and frequency window for such selective activation.
To date, commercial retinal implants apply square pulses in the millisecond range that are likely to activate axons (Ayton et al 2020).On the other hand, lowfrequency waveforms and especially sinusoidal stimulation, despite showing promising preliminary results, received little attention.In a remarkable study, Weitz et al (2015) reported low frequency stimuli to be able to avoid the activation of passing axons and thereby circumvent elongated percepts in one patient.In-vitro experiments corroborated this finding, however, without providing information about the resolution that could be achieved.Single-cell based studies of sinusoidal stimulation had been conducted over the years by the Fried.Through the combination of epiretinal micro-electrode stimulation and simultaneous patch-clamp recordings they identified a window of selective activation up to 25 Hz in the rabbit retina group (Freeman et al 2010, Twyford andFried 2016).
Notably, low-frequency (<200 Hz) sinusoidal waveforms are being utilized in various neuroprostheses, such as spinal cord subperception neuromodulation (Gilbert et al 2022), cochlear implants operating with analog waveforms (Stupak et al 2018), and specific cases of deep brain stimulation (Xie et al 2015).However, none of these applications deals with the delicate and close neighborhood between targeted cell bodies and axons of passage such as in the retina.A first indication for focal epiretinal ganglion cell stimulation in a blind retina was reported recently by our lab (Corna et al 2021).There, however, the stimulation was fixed to one frequency (40 Hz) and only a few stimulation amplitudes.Spatially localized stimulation was also reported for epiretinal stimulation using elongated 'grating-like' electrodes at the same frequency (40 Hz) and one single amplitude (Cojocaru et al 2022).Here, we therefore sought to investigate the effect of sinusoidal frequencies up to 100 Hz in epiretinal configuration by electrically imaging (Zeck et al 2017) RGCs in the ex-vivo photoreceptor-degenerated mouse retina.The approach presented here identifies a window of opportunity at frequencies between 40 and 60 Hz, in which focal activation is achieved at lower amplitudes compared to axonal stimulation.As a result, we propose an optimal stimulation strategy that can be implemented to enhance spatial resolution and visual acuity in future retinal implants.The implications of our results extend beyond retinal implants, as they could have valuable applications in various neuroprosthetics scenarios.

Extracellular electrophysiology of the ex vivo retina
Ex-vivo retinae from rd10 (retinal degeneration 10; B6.CXB1-Pde6brd10/J) and rd10-ChR2 (rd10 expressing ChR2-EYFP, Channelrhodopsin-2-Enhanced Yellow Fluorescent Protein in a subset of RGCs) of age 35-121 d of both genders were used in this study.In addition a single retina sample from a wild type (C57BL/6) expressing ChR2-EYFP was used for the epifluorescence image (figure 5).Dissection of the retina was conducted following previously established protocols (Corna et al 2018(Corna et al , 2021)).In short, after the removal of the cornea, the lens is extracted exposing the retina.After cutting the eye in two parts the retina is isolated and the vitreous removed.Finally, a portion of the retina (ca.3-4 mm 2 ) is placed on the microelectrode array (MEA) with the RGCs facing downward contacting the sensors (figure 1(A)).Occasionally, gentle pressure with a membrane was applied for a few seconds after the placing to completely flatten the isolated retina on the MEA.Before placing, the MEA was cleaned with 5% Tickopur R36 (Stamm/Berlin), plasma cleaned (Diener electronic) and coated with poly-L-lysine (200 µl, 1 mg ml −1 , P1399, MW 150-300 kDa, Sigma-Aldrich) to improve adhesion.Retina samples were kept in darkness or dim red light throughout the duration of the recording, and recordings were conducted following 30-45 min of dark adaptation.The explants were continuously perfused with carbogenated Ames medium (A1420, Sigma-Aldrich) at a flow rate of 2-4 ml min −1 at temperatures ranging from 34 • C to 36 • C. The MEA is connected to the preamplifier mounted on a motorized stage (CONEX CC, Newport) under an upright microscope (BX 50 W, Olympus) with a light source (Cool LED/µMatrix, Rapp OptoElectronic) for light stimulation.The experimental procedures for preparation of the ex-vivo retina were approved by the Center for Biomedical Research, Medical University Vienna, Austria.
Recordings were conducted at a sampling rate of 20 kHz except for data from figure 2 which were recorded at a sampling rate of 10 kHz.To eliminate electrical stimulation artifacts, the recorded signals were band-pass filtered in the range of 1-3.5 kHz.In some cases, a wider frequency band was used (figure 2).Spike sorting was performed with the provided software (CMOS-MEA-Tools software, MultiChannel Systems MCS GmbH) based on an ICA-based algorithm to improve cell detection in the presence of stimulation artifacts (Leibig et al 2016).To recover axon positions we performed spike triggered averaging (STA) of the extracellular voltages starting from the spike times output of the spike sorter.The STA algorithm calculates the average voltage signal of a spike across the electrode array by averaging multiple spikes of a single neuron aligned by the spike timing.The result is a voltage trace with reduced noise allowing the detection and tracking of the axonal signal (Zeck et al 2011).

Electrical stimulation
Sinusoidal stimulation at frequencies of 40, 60, 80 and 100 Hz were tested.Two different electrode configurations were used in this work: (a) in figure 2(A) two rectangular shaped stimulation electrodes (0.023 mm 2 ) were alternatively activated for 100 ms and a break of 100 ms (30 repetitions).The stimulation electrode is a combination of 4 by 9 single stimulation sites.The electrode area was calculated using the effective electrode surface.(b) The data used to calculate the threshold curves (figures 3 and 4) were obtained using a smaller electrode configuration (equivalent area: 0.01 mm 2 , 4 by 4 single stimulation sites), stimulating for 200 ms with a 200 ms break (50 repetitions).
The stimulation electrodes of the CMOS-MEA work via capacitive stimulation across the dielectric top layer of the chip.The stimulation current density is proportional to the derivative of the applied voltage (i stim = C × dV/dt).To maximize the capacitance (C) the chips used in this study relied on the native oxide of the top titanium nitride electrode without a deposited dielectric layer.The amplitude and waveform of the stimulation current, was measured as voltage drop across a 10 Ω resistor in series to the Ag/AgCl reference electrode (E201ML, Science Products) of the CMOS MEA, using a commercial voltage amplifier (DLPVA, Femto Messtechnik GmbH, Berlin, Germany, (figure 1(B))).

Pharmacological blocking of synaptic transmission
In order to assess the impact of network activity on the evoked responses, we conducted two experiments in which presynaptic inputs to RGCs were blocked pharmacologically (figure 4(D)).In the first experiment we used 100 µM DNQX disodium salt (Tocris Cat.no.2312) in conjunction with the standard Ames medium to inhibit ionotropic glutamatergic synaptic inputs to RGCs.A second, unspecific synaptic blocker (100 µM CdCl 2 ) was applied in a separate series of experiments (Twyford and Fried 2016).Recordings were conducted following a continuous perfusion period of 30 min to ensure thorough drug application.A 1 Hz green full field Flicker stimuli was used to elicit photoreceptor-mediated visual responses (supplementary figure) to test light responsiveness after the addition of synaptic blockers.

Data analysis
In order to classify RGCs as focally or axonally activated (figures 3 and 4), we selected a radius of 96 µm from the stimulating electrode center.This distance is based on the geometrical dimension of the stimulating electrode, in order to count all cells up to the corner of the electrode.All the RGCs stimuli located inside this radius were marked as focally activated, if they increased the firing rate to stimulation.
Firing rate (FR) was calculated using the average number of spikes during multiple stimulus repetitions (see electrical stimulation section for details).The average response is calculated as the average firing rate between all the RGCs considered in the analysis.RGCs were included in the analyzed dataset if their firing rate at the highest stimulation intensity was at least double the firing rate at the lowest stimulation intensity.Additionally, we required the firing rate at the highest intensity to be at least 50% of the stimulation frequency (i.e. on average the RGC should be activated in 50% of the stimulus repetitions).We excluded 3 ms at the beginning and at the end of the stimulus repetition to avoid spikes miscounts due to the stimulation artifact.The normalized firing rate (figure 4) was calculated as [FR − min(FR)]/max[FR − min(FR)] and the corresponding error as standard error of the mean divided by the max(FR).Threshold was defined as the amplitude when firing rate reached 50% of the normalized firing rate.Comparisons of means (figure 3) were conducted using a t-test (figure 3).

Selective activation of RGCs, somatic and axonal responses
The aim of this work is to define a stimulation strategy able to focally activate RGGs while avoiding the stimulation of nearby axons of passage.As a proof of concept of focal activation, we first stimulated a single RGC (figure 2(A)).The cell position was identified by the spike sorting algorithm while the axon trajectory was revealed by spike-triggered-averaging (see methods for details).We selected two rectangular stimulation electrodes each 0.023 mm 2 in size (from a rectangular combination of 4 by 9 single stimulation sites) separated by 128 µm (figure 2(A)).The cell body of the identified RGC was located over one of two electrodes (pink markers) and the axon traversed over the second (blue markers).The stimulation protocol consisted of different intensity levels at three frequencies (40, 60 and 80 Hz).In figure 2(B)  on the left, the filtered voltage of the recording electrode under the soma during one repetition of 100 ms of continuous stimulation is shown.For the 60 Hz low amplitude stimulation (0.4 µA/8.73 µC cm −2 ), the cell responded reliably if the stimulation electrode was located under the soma (pink).The firing rate increased during the stimulation compared to the spontaneous activity and the cell fired in phase with the cathodic phase of the stimulation current.When instead the electrode under the axon (blue) was activated there was no noticeable response.The same results were obtained for 40 Hz stimulation at high intensity (0.43 µA/13.5 µC cm −2 ).We define this type of stimulation as selective stimulation.In contrast, for stimulation at 80 Hz and at 60 Hz for higher stimulus intensity (0.85 µA/14.1 µC cm −2 and 0.64 µA/13.9µC cm −2 ), the RGC was activated by stimulation with either one of the two electrodes.If the cell is activated by the distant electrode, an action potential is elicited in the axon, backpropagating to the soma (orthodromic) but also in the direction of the optic nerve (antidromic).Such phenomenon is further referred to as non-selective or axonal activation.All stimulation protocols were presented alternating between the two electrodes for a total of 30 repetitions to qualitatively observe the reliability of activation without fading (figure 2(C)).Although quite illustrative, the stimulation protocol used here employed relatively large electrodes, potentially activating a large part of the presynaptic network and being spatially unspecific.Therefore, in the following experiments we employ smaller, square-shaped electrodes of 0.01 mm 2 to obtain a clearer answer regarding spatial selectivity.

Sinusoidal stimulation allows for selective focal activation of RGCs
Six intensity levels were tested for stimulation with a square shape electrode (area of 0.01 mm 2 ) and the evoked ganglion cell spiking was evaluated as firing rate (FR) during the stimulation (figures 3(A) and (B)).Cells are marked as focally activated or axonally activated based on the relative position to the stimulation electrode.Cells with the soma located in a radius of 96 µm from the electrode center were marked as focally activated.Only activated RGCs, i.e. cells showing an increase in firing rate were considered in the following analysis (see Methods for details).At a stimulation frequency of 40 Hz the firing rate increased linearly up to 40 Hz (i.e. about 1 spike/sinusoidal waveform) for the maximal stimulus intensity of 0.23 µA (17.3 µC cm −2 ).The positions of all activated RGCs with respect to the electrode center are shown in figure 3(C), with the change in firing rate being color-coded.The qualitative raster plot suggests that the RGC soma or the nearby AIS might be the site of preferred activation.The linear increase in firing rate was observed exclusively for focal activation (n = 16 RGCs), with one exception where the distal axon of one RGC could be stimulated increasing the spontaneous firing rate from ∼10 to 20 Hz.A similar linear increase of the firing rate was detected for focal activation during 60, 80 and 100 Hz stimulation; the firing rate increased with increasing stimulus strength and reached about 1 spike/sinusoidal waveform at an amplitude of 0.36, 0.46 and 0.56 µA, respectively (17.9, 17.7 and 17.5 µC cm −2 ).For these stimulation frequencies axonal activation was detected, however with a different property.The axonal activation curves have a steeper increase, i.e. a smaller dynamic range, with the rising onset at higher intensity compared to the focal activation (figure 3(D)).The difference between focal and axonal activation onset decreases with increasing frequency, for example at 60 Hz a large gap is detected between axonal and focal activation curves.This window of opportunity narrows for 80 Hz and closes at 100 Hz, where the two activation curves overlap for most amplitudes.To identify the window of selective activation we performed a t-test between the focal and axonal response distribution at each stimulation intensity.The activation curves are an average of multiple cells (40/60/80/100 Hz: focal: 16/17/15/7; axons: 1/22/69/62).For 60, 80 and 100 Hz, we identified a window of selective activation up to 0.28, 0.3 and 0.29 µA (14.8, 11.6 and 8.8 µC cm −2 ).

Strength-duration relationship and stimulation mechanism
To better compare the results at different frequencies we investigated the activation curves as normalized firing rate versus the peak stimulation current and versus the charge density calculated within half of the sine wave (figures 4(A) and (B)).Using the normalized firing rate allows to exclude the spontaneous activity from the threshold calculation.Qualitative inspection of the activation curves leads to two results.First, there is a separation between the focal and axonal activation curve, and this difference shrinks when increasing the stimulation frequency.Secondly, the peak current necessary for focal activation of RGCs increased linearly with frequency (red curves in figure 4(A)), which is equivalent to a constant charge needed to achieve a certain activation level, independent of the tested frequency (red curves in figure 4(B)).For axonal activation however this behavior was not observed (blue curves in figure 4(B)).
In order to quantify these two results, we calculated the stimulation threshold as the peak current or charge necessary to reach 50% of the normalized maximal firing rate (see methods for details).Considering that only one cell responded to axonal stimulation for 40 Hz, we excluded it from this part of the analysis.The thresholds for focal activation at 40, 60, 80 and 100 Hz were 0.14, 0.19, 0.28 and 0.33 µA, respectively (10.6, 9.5, 10.6 and 10 µC cm −2 ).Thresholds for activation of distal axons at 60, 80 and 100 Hz were 0.29, 0.35 and 0.36, respectively (15.3, 13.6, 11.2 µC cm −2 ).When we analyzed activation threshold versus peak current, both the focal and axonal threshold increased with stimulation frequency (figure 4(C), upper panel).However, the slope for focal threshold increase is steeper with the threshold doubling when doubling the stimulation frequency, similarly to previous results (Freeman et al 2010).For the axonal curves instead, the thresholds for 80 and 100 Hz were very similar (0.353 and 0.358 µA).On the other hand, if the normalized firing rate was plotted versus the stimulation charge the focal threshold was constant across frequencies at ∼10 µC cm −2 (figure 4(C), bottom panel) or in other words, the focal activation happened always at the same charge level.The threshold for axonal activation instead linearly decreased from ∼15 µC cm −2 (60 Hz) to ∼10 µC cm −2 (100 Hz).These results suggest that the focal response, potentially via the AIS, and the distal axon response, originates from differences in the strength-duration curve of the two cell elements.This difference results in the window of opportunity for selective stimulation.The relation between focal and axonal threshold at different stimulation frequencies is shown by the change in charge threshold ratios (figure 4(C), bottom panel).The threshold ratio increased from 1.1 to 1.3 and 1.6 reducing the stimulation frequency from 100 to 80 and 60 Hz, respectively.An even higher threshold ratio is expected for 40 Hz, however the maximum stimulation amplitude was limited by the CMOS electronics which allowed us to infer a conservative maximum threshold ratio of 1.64.
The question arises, however, if the hypothesized 'focal activation' is actually driven by presynaptic cells, as suggested in the rabbit retina for lowfrequency stimulation (Freeman et al 2010, Twyford andFried 2016).Activation of one single spike per sinusoidal waveform, however, suggests direct activation of the RGC without implication of the presynaptic network.To confirm or reject this hypothesis we performed two additional experiments using different synaptic blockers to inhibit the network input to RGCs by either using 100 µM DNQX or 100 µM CdCl 2 (figure 4(D)) (Cohen andMiller 1999, Freeman et al 2010).The experiments were conducted in two different retina samples from a young rd10 mouse.At the early stage of degeneration, rd10 mice show photosensitivity that was used to prove the efficacy of the drug by confirming the disappearance of light response after drug application (supplementary figure 1).In figure 4(D) the focal activation curves under control condition, i.e. prior to the drug application, and after drug application are shown.For both blockers there is no significant change among the activation curves indicating that the focal stimulation happens via direct stimulation and not via the network.

Axon bundles and radius of activation
Despite axonal stimulation being a well-known phenomenon in epiretinal stimulation, the extent of the activation radius and the number of activated RGCs has not been fully clarified.Weitz et al (2015) showed thresholds as a function of displacement from electrode center and the extent of the radius of activation via calcium imaging.However, they reported stimulation thresholds one order of magnitude higher compared to the thresholds found in this study, possibly due to the imaging technique.Here we report the radius of activation via electrical imaging with a planar HD MEA that provides a higher sensitivity and temporal resolution up to single spike resolution.
Axons in the retina often form bundles, therefore stimulation electrodes are in the proximity to multiple axons inside a bundle (figure 5(A)).Axonal activation presents a narrow dynamic range, i.e. a steep activation curve (figure 4(A)).This aggravates the problems related to axonal stimulation.As soon as the activation intensity for axons is reached the majority of cells with the axon passing over the stimulation electrode are activated.In figures 5(B)-(E) the firing rate in response to sinusoidal 100 Hz stimulation is shown for 4 different intensity levels (0.29, 0.37, 0.46, 0.56 µA).With an increase of the stimulation intensity from 0.29 to 0.56 µA the majority of the RGCs detected in the 1 mm 2 sensor area with the axon passing over the stimulation electrode are activated and possibly the activation could extend to RGCs located outside the sensor area.The color coded representations in figures 5(B)-(E) underestimate the real number of activated RGCs as with extracellular electrophysiological recording only a subpopulation of all RGCs in the interface retina is being recorded.Interestingly, due to axon trajectories in the retina the distance of the RGC to the stimulation electrode does not affect the response (figures 3(C) and 5(C)-(E)).

Discussion
Here, we report on the selectivity window of electrical stimulation using low-frequency sinusoidal (40-100 Hz) waveforms as a technique to improve the outcome in retinal implants.Our experiments demonstrate that sinusoidal stimulation, within the range of 40-60 Hz selectively activates RGCs while avoiding the distal axons of passage.All results were obtained in epiretinal configuration in photoreceptor degenerated ex-vivo retinas (rd10) to mimic implantation conditions in vitro.Our findings support the possibility of sinusoidal stimulation as a promising approach for future retinal implants.

Spatially selective activation of RGCs in epiretinal configuration
In this work we demonstrate that sinusoidal waveforms can selectively target the soma or AIS of RGCs (focal activation) while avoiding the activation of distal axons passing over the stimulation electrode.Our findings demonstrate, for the first time, a significant difference in the activation threshold between soma/AIS and distal axon at frequencies of 40 and 60 Hz.Focal selective stimulation at lower frequencies, up to 25 Hz, was previously shown by Weitz et al (2015) who demonstrated that axonal stimulation can be reduced by 16 ms square pulses or completely avoided by 25 ms square pulses or 25 Hz sinusoidal stimulation.Freeman et al (2010) also reported similar findings with 10 and 25 Hz sinusoidal waveforms for RGCs recorded by the patch-clamp technique.They also presented a similar relation as shown in this work between stimulation threshold and stimulation frequency; however at higher stimulation currents and partially involving the retinal network.
Compared to other approaches such as square pulse stimulation sinusoidal stimulation displays a higher degree of selectivity.It has been shown that optimization of the square pulse parameters, i.e. duration and asymmetry, or the stimulus orientation can increase square pulse selectivity (Esler et al 2018, Chang et al 2019, Paknahad et al 2020).However, the stimulus current used in those studies was orders of magnitude higher to the results presented here.A possible explanation could be the recording technique, with calcium imaging requiring the generation of multiple spikes for reaching detection threshold.Other studies, using MEA recordings, with stimulation currents in the range of the one applied here do not show any difference between axonal and focal threshold, or even a bias towards axonal stimulation (Madugula et al 2022, Gogliettino et al 2023).In case of non-selective stimulation, focal activation could be achieved with the use of small electrodes on bidirectional implants (Shah and Chichilnisky 2020).By recording spontaneous RGCs activity it is possible to infer the stimulus sensitivity of specific RGCs and use the information to target single cells via the soma or the axon (Madugula et al 2022, Gogliettino et al 2023).However, questions arise regarding the percentage of cells that can be a single target over the total population with this approach.
It must be considered that all state-of-the-art MEAs, like the one used here, only allow for the recording of a subset of the total RGC population.The generalization of the results from the cells presented in figure 3 to a broader statement about axonal avoidance may be clarified in future work involving alternative recording methods.

Considerations regarding sinusoidal stimulation in epiretinal implants
Before discussing the feasibility of sinusoidal stimulation in an epiretinal implant we would like to clarify that the CMOS-based capacitive device presented here served only as a bidirectional tool for experimental purposes.We do not expect such device to be implanted for several reasons, including stiffness of the CMOS chip, low stimulation charge achievable by the capacitive electrodes and power requirements.
Given the challenge of powering a portable device implanted inside a moving organ like the eye, retinal implants require low power consumption.This becomes even more critical given the recent transition of the device from wired to wireless photovoltaic control (Boinagrov et al 2013, Corna et al 2018, Ayton et al 2020).In the context of stimulation from the epiretinal side, we were able to achieve focal activation with a peak current of 0.23 µA for 40 Hz (corresponding to a charge density of 10.6 µC cm −2 ) and 0.36 µA (9.5 µC cm −2 ) for 60 Hz, respectively.These values are slightly smaller compared to the reported values for epiretinal square pulses (∼1 µA) (Madugula et al 2022, Gogliettino et al 2023).A bias towards lower thresholds for sinusoidal stimulation has been also reported by other studies, using calcium imaging, when comparing 20 Hz pulses to 20 Hz sinusoidal pulses (Weitz et al 2015).Our results also show that focal activation occurs within the first cycle of the sinusoidal stimulus (figure 2(B)), without the need for continuous stimulation.An important consideration beyond the results presented here, relates to the feasibility of sinusoidal stimulation in a retinal implant.Recent work suggests implementation of the sinusoidal signal generator either at a remote location from the stimulation electrode itself (Schütz et al 2020) or as a system-on-chip (Löhler et al 2023) at the cost of spatial resolution.
When comparing in vitro thresholds to clinical data from patients with an epiretinal implant (Chris et al 2006, de Balthasar et al 2008) we note a difference by about two orders of magnitude.In clinical settings the threshold charge density for short pulses (∼1 ms) ranged between ∼50 up to 500 µC cm −2 .The increased thresholds are mainly caused by a relatively large distance between the stimulating electrode and the retina.A tight contact in vivo may be achieved by conformal (Lohmann et al 2019, Zhou et al 2023), flexible (Ferlauto et al 2018) or 3D (Steins et al 2022) electrode arrays.If tight interfacing fails, the change of preferential activation with vertical displacement needs to be considered.Modeling work (Schiefer andGrill 2006, Mueller andGrill 2013) demonstrated that for short pulses preferential, focal activation of RGCs does not deteriorate for short anodic or cathodic current pulses up to vertical displacements of 150 µm.A conceptually similar modeling is required for sinusoidal stimuli, guided by our experimental results and those of others (Freeman et al 2010, Twyford andFried 2016).Modeling should also consider RGC density and the stacked RGC layers in the human retina close to the fovea.
Avoidance of axonal stimulation aims to improve spatial resolution.However, the spatial resolution achievable with sinusoidal waveforms needs to be tested, since RGCs surrounding the stimulation electrode may be activated.Previous work using small object stimulation demonstrated discrimination of 32 µm spatial jitter for 40 Hz stimulation, which translates to 1 • of visual angle (Corna et al 2021).In the same work a radius of activation proportional to the electrode size was reported, potentially superior to the one shown for 25 ms pulses (Weitz et al 2015).Similar results were found using grating stimulation, closely matching the spatial resolution achieved by optogenetic stimulation (Cojocaru et al 2022).These in vitro findings need to be validated in clinical settings.A challenge may constitute the spread of the electric field above the stimulation electrodes, which ideally should penetrate the retina perpendicular to the electrode surface (Spencer et al 2016).
Lastly, a strategy for encoding visual stimuli needs to be developed.One key consideration is whether low frequency sine waves can provide the necessary stimulation frequency for rate coding.Weitz et al demonstrated that 25 Hz pseudo-sinusoidal stimulation was able to evoke percept in patients, suggesting promising results for this approach (2015).Here we demonstrate that even higher stimulation frequency, in the range of human flicker fusion and potentially providing continuous percepts to patients (Mankowska et al 2021), can retain selectivity.
Nonetheless, several open questions remain regarding the required spike rate and frequency for effective visual information encoding.A second important aspect is contrast encoding.Previous work suggested encoding contrast by changing the stimulation frequency but not the stimulation amplitude (Nanduri et al 2012).Indeed, such strategy would circumvent increased percepts by a radially spreading increasing electric field.However, our results (figure 4) indicate that with such strategy the spatial selectivity is lost above 60 Hz and therefore only a restricted contrast range may be achievable.We have shown previously under laboratory conditions that contrast encoding with sinusoidal stimulation can be achieved (Corna et al 2021); however, under ideal experimental conditions involving a reference electrode in the subretinal space.

The mechanism underlying focal activation with sinusoidal stimulation
To fully understand the mechanism of RGC activation during sinusoidal stimulation, we investigated the activation curves versus the applied peak current and the charge within one half sinusoidal phase.RGCs respond in the cathodic phase of the sinus in line with previous reports in epiretinal configuration (Eickenscheidt et al 2012, Boinagrov et al 2014, Twyford and Fried 2016).Previous studies indicated that low frequency stimulation in the healthy retina operates via network-mediated activation (Freeman et al 2010, Twyford andFried 2016).Our results, in photoreceptor-degenerated retinae, show that sinusoidal stimulation, for the frequencies tested, acts via direct stimulation.Once the network component is ruled out, focal activation may occur via the stimulation of the AIS, of the soma or of the dendritic tree.We therefore use the general term 'focal activation' in this work.The AIS represents the section of RGCs with the highest sodium channel density and therefore the lowest local stimulation threshold (Fried et al 2009, Werginz et al 2020, Kish et al 2023, Radivojevic et al 2016).Therefore, the most natural conclusion is that the focal activation reported here happens with the AIS in close proximity to the stimulation electrodes and the two different cellular compartments AIS and distal axon, have different strength-duration relationships.Indeed, compartmental modeling for short (<1 ms) square pulses and the concept of the activating function (Rattay et al 2012) may explain the constant charge threshold (figure 4(C)) we report here for focal activation.Future modeling work and a wider stimulation range are needed to clarify if threshold charge density remains constant for sinusoidal stimulation at low frequencies.
Interestingly, sinusoidal selective stimulation has been reported both here with the use of planar MEA, where a high resistivity cleft is formed between the electrodes and the RGCs (Zeitler et al 2011) and with single stimulating electrodes ∼20 µm above the RGC layer (Freeman et al 2010).The tight interface between RGCs and the electrodes in our configuration partially explains the low threshold values.A second contribution likely comes from the so-called activating function (Rattay 1988) at the electrode edge of extended electrodes (Eickenscheidt andZeck 2014, Paknahad et al 2020).
A final consideration needs to be done regarding cell type specificity.The retina does not operate as a simple light detector but occupies a crucial role in the first steps of visual processing.RGCs are classified in cell types based on many different parameters, such as their receptive field or morphology (Baden et al 2016, Goetz et al 2022).Despite several different and complex cell types have been already identified, in the field of retinal implants, generally a simplified separation in two major RGC classes, ON and OFF, cells is used.Achieving cell type specificity will represent a turning point, significantly improving the performance of artificial vision.Unfortunately, cell type specific stimulation still remains elusive.The stimulation reported here due to a direct mechanism should target equally ON and OFF RGCs.Some work has been done to identify cell-specific stimuli (Freeman et al 2010, Twyford and Fried 2016, Oesterle et al 2020) but a definitive conclusion is missing.

Importance for future retinal implants
Up to date, artificial vision approaches due to the constraint of electrical neuromodulation have been limited as a tradeoff between spatial and temporal resolution and visual field size.Currently, subretinal implants offer superior spatial resolution and subsequent visual acuity and reported the best clinical results (Cehajic Kapetanovic et al 2020).However, their visual field is restricted due to the requirement of subretinal implantation (Lorach et al 2015).On the other hand, there is a growing emphasis on the significance of a large visual field, which can only be achieved in epiretinal configuration (Ghezzi 2023).Nevertheless, epiretinal implants so far faced challenges in spatial resolution especially due to axonal stimulation.In this work we demonstrated that sinusoidal stimulation can provide a potential solution to the problem via spatially selective activation.

Conclusion
Here, we present our findings investigating the efficacy of sinusoidal stimulation of the ex vivo retina.Experiments were conducted in epiretinal configuration using a HD MEA that provided a high resolution bidirectional interface with photoreceptor degeneration mouse models (rd10) explanted retina.Through our experiments, we have demonstrated, for the first time, that sinusoidal stimulation, within the range of 40-60 Hz, exhibits selective focal stimulation at low charge density via direct activation.Collectively, these findings provide strong support for the efficacy of sinusoidal stimulation in epiretinal stimulation, potentially leading to advancements in future visual prosthetics.

Figure 1 .
Figure 1.Experimental setup and stimulation parameters.(A) Image of a retina sample placed on top of the HD MEA.The dashed black square indicates the 1 mm 2 area comprising the sensor and the stimulation arrays.Upper inset: arrangement of stimulation and recording sites on the CMOS MEA.The equivalent circle diameter of a single stimulation site (yellow) is 28.3 µm.Lower inset: schematic of the retina HD MEA interface.The retina sample is placed in epiretinal configuration with RGCs in close contact to the array.(B) Measured stimulation peak currents (black symbols) and calculated charge and charge density (red symbols) upon stimulation with sinusoidal waveforms (x-axis showing the peak-to-peak voltage).Stimulation is performed with an electrode area of 0.01 mm 2 (equivalent circular electrode of radius of 54 µm) by selecting multiple stimulation sites.Inset: representative current traces are shown.The areas indicated in red are used to calculate the average charge density within the anodal sinusoidal half-waves.

Figure 2 .
Figure 2. Exemplary stimulated spiking activity of one RGC to focal and to axonal stimulation.(A) Schematic of the selected cell with the identified soma (black circle) and axon (black line) based on spike-triggered-averaging. The RGC was stimulated by two rectangular stimulating areas (red and blue) of equal size (area: 0.023 mm 2 ).Each pink or blue marker (small squares) indicates a single stimulating site as shown in figure 1(A).Additional identified RGCs are shown in gray, but not evaluated any further.(B) Stimulated spiking activity recorded underneath the RGC highlighted in (A).Each trace shows a 300 ms recording of the extracellular voltage (after artifact removal and filtering).The 100 ms sinusoidal stimulation period is highlighted in pink if stimulation was performed at the soma (pink electrode) and highlighted in blue if stimulation was performed at the distal axon (blue electrode).Recordings for three stimulation frequencies (40/60/80 Hz) and two different stimulus intensity levels are shown.(C) Raster plots of the detected spikes after spike sorting of the recordings shown in (B).Thirty repetitions of each stimulation parameter set are presented.Selective stimulation conditions are marked with rectangular contours based on qualitative criteria, i.e. reliable activation.

Figure 3 .
Figure 3. Selective activation window: (A)-(B) RGC responses to 60 Hz stimulation with the firing rate color-coded between 0 (blue) and 60 Hz (red) for two different stimulation intensities (A) 14.8 µC cm −2 , (B) 17.9 µC cm −2 .The colored cells are the ones considered in the analysis, i.e. activated by the stimuli (see methods for details), while all the other RGCs (dashed circles) detected during the recording were not activated.Scale bars in (A)-(B) 100 µm, RGC soma are not to scale.(C) Two dimensional representation of RGCs response versus distance to the stimulation electrode center at different frequencies and charge densities.Each dot represents a single RGC included in the analysis, color coded by the cell firing rate between 0 Hz (blue) and the stimulation frequency (red).Each row along the y-axis comprises all cells stimulated at one stimulus strength and frequency indicated on the y-axis.Rows are separated by a dotted line.Dots representing RGCs are randomly jittered inside a row in the y-direction to avoid overlap.The length of the gray background in the x-direction indicates the RGC distance from the center of the stimulation electrode considered as focal activation (i.e.96 µm).(D) Focal (black) and axonal (green) activation curves for the 4 different stimulation frequencies (40, 60, 80 and 100 Hz).For all RGCs the firing rate during stimulation is plotted versus the average stimulation charge measured during one sinusoidal phase.Gray and green shadings indicate the standard error of the mean.The y-axis scaling varies for each stimulation frequency, with the firing rate matching the stimulation frequency at high intensity.Significance levels are indicated as follows: * = p < 0.05, * * = p < 0.01, * * * = p < 0.001.

Figure 4 .
Figure 4. Stimulation thresholds and demonstration of direct activation: (A), (B).Focal and axonal activation curves are shown by plotting normalized firing rate versus peak current (A) and charge density (B) for the four tested frequencies (40, 60, 80 and 100 Hz).(C) Focal (red) and axonal (blue) peak current (top) and charge (bottom) thresholds are plotted versus the stimulation frequency.Additionally, threshold ratios are shown for charge threshold.The dashed line represents the linear fit for each condition.(D) Focal activation curves for 60 Hz sinusoidal stimulation before (control, black) and after (green and red) the application of two different synaptic blockers.Either the ionotropic glutamate receptor blocker DNQX or the unspecific synaptic blocker, CdCl2 was added to the bath.

Figure 5 .
Figure 5. Axon bundle stimulation extends the radius of activation: (A) Fluorescence image of somas and axons in a subset of RGCs expressing ChR2-EYFP.The gre + ay squares (top right) indicate the size of the stimulation area used to obtain the results shown in figures 3 and 4 and the subplots (B)-(E) of this figure.(B)-(E).Axonal bundle activation.RGC responses to 100 Hz stimulation and four increasing intensity levels.RGC somas (circle size does not correspond to real soma size) and axons are localized via electrical imaging.The firing rate is color-coded from 0 (blue) to 100 Hz (red).