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We present a finite element based simulation and analysis method to describe the spatial extent of stimulation and the effects of electrode-tissue interactions in subretinal prostheses. In particular, we estimate the threshold stimulation current needed to depolarise and evoke action potentials in the ganglion cells to be stimulated at a particular distance from the electrode. This is achieved through the application of a threshold electric field to a passive point neuron model of a ganglion cell under consideration. Threshold stimulation currents and the lateral extent of the stimulation zone were computed for microelectrode stimulation in subretinal mode. Recent evidence indicates a decrease in threshold charge with time following subretinal implantation. Consequently, to explain the variation in threshold stimulation currents, we propose a hypothesis based on an electrode-tissue gap. Threshold stimulation currents and impedances for different electrode-tissue gaps were computed. We validate the hypothesis with our simulation results that the changes in impedance observed with time in vivo can be mainly attributed to the varying distance of the ganglion cells from electrodes due to changes in electrode-tissue gap. Our simulation framework proposes a convenient and practical method applicable for studying different electrode geometries used for retinal stimulation.
Keywords: Biomedical microdevices, electrical subretinal stimulation, electrode-tissue interface, finite element method, implant resolution, retinal implant, visual prosthesis
Electronic retinal prostheses aimed at restoring sight by stimulating inner retinal neurons in human subjects suffering from retinitis pigmentosa (RP) and age-related macular degeneration (AMD) is a major focus of biomedical research . When the outer retina is significantly degenerated, the inner layers undergo anatomical reorganisation . A detailed study of patients with RP and AMD , as well as of animal models of degenerative retinal diseases have demonstrated that substantial number of inner retinal cells can survive and that ganglion cells remain functional even at the late stages of degeneration. This has motivated many research groups to investigate efficacy of extracellular electrical stimulation as a means to restore some visual function by epiretinal , or subretinal microelectrode array approaches. Most prostheses designed to interface with the retina rely on the hypothesis that a direct stimulation applied either to the outer layers of the retina or to the ganglion cell layer could restore sight to the patients.
Ganglion cells form the innermost retinal cell layer, relaying the transformed visual input to the brain, implying that they are the targets in either subretinal or epiretinal stimulation schemes. They can be excited either by direct or indirect electric stimulation applied through the intermediate retinal network. Indirect stimulation of ganglion cells is experimentally observed through activation of bipolar and amacrine cells and also predicted theoretically by modelling bipolar cell stimulation . Based on the result that "short stimulation pulses are preferable for safety and efficacy considerations in subretinal prostheses and that direct activation of ganglion cells will be necessary for reliable activation during high-frequency stimulation" ; in this study, we are modelling direct activation of ganglion cells by extracellular stimulation. A simple passive model of extracellular stimulation of the soma of a ganglion cell has been considered before for analytical studies . We consider a ganglion cell as a point neuron and hypothesise its activation by assigning a cross-membrane depolarisation condition.
Patch clamp and extracellular multi-electrode recordings have been used to measure the threshold currents required to activate ganglion cells in both subretinal and epiretinal approaches. The threshold stimulation current applied on electrodes is one of the key elements in determining the performance of a retinal prosthesis. Palanker and co-workers approximated a threshold electric field of 3000V/m to perform analytical calculations and draw predictions on various parameters affected during stimulation. In the present study, we define a typical threshold as the minimum stimulation current required to obtain an electric field of 3000V/m at a certain distance between the stimulating electrode and the retinal ganglion cell.
A recent psychophysical study in blind human volunteers demonstrated a strong decrease in threshold charge delivered by the electrodes as a function of time after implantation . We hypothesize that this decrease is linked to the discharge pattern of the current above the electrode as a result of changing measured impedance. Impedance variations may occur owing to changes in electrode impedances due to various factors like physical and chemical changes in electrodes, mechanical alterations, retinal tissue remodelling in the process of degeneration, etc. Under ideal implantation conditions and assuming that electrode corrosion does not occur , the impedance variation can be explained by two main theories:
Gliosis theory - a proliferation of glial cells at the site of a tissue injury or neuronal loss caused by surgical intervention and insertion of the implant.
Gap theory - soon after implantation, the retina may not be in intimate contact with the electrodes giving rise to a gap. This gap is predicted to be very small in the order of a few microns. It is likely that a close contact between the retina and electrodes is recovered within a few days. Similar post-implantation effect of an electrode-tissue gap is also observed between the target tissue and the stimulation electrodes immediately after a deep brain implantation .
In the case of a glial reaction, new cells surround the electrode surface resulting in retinal ganglion cells moving farther away from the electrode. The highly resistive glial cells increase the impedance and consequently raise the threshold stimulation currents. On the contrary, when the retinal cells move closer to the electrode and fill the electrode-retina gap, it has the same effect of increasing the impedance due to the higher resistivity of the retinal cells and eventually reducing the threshold of stimulation currents.
Numbers of studies related to the experimental determination of threshold stimulation currents in subretinal stimulation on various species in vitro have been reported . Despite the extent of literature on the stimulation parameters and methods, there is still a lack of understanding on the relationship between the electrical properties of the retinal tissue and the microelectrode specifications.
The electrical properties of the retinal tissue influence the electric field generated at different depths in the retina from the surface of the stimulating electrode. The retina is a multi-layered structure composed of different cell types and densities. As a consequence, the electrical conductivity in the retina is inhomogeneous . This inhomogeneity in the electrical conductivity within the retina is represented primarily by the high resistivity of the retinal pigment epithelium (or photoreceptor layer) and the decreased resistivity at the ganglion cell layer. Considering the direct activation of a ganglion cell, this irregularity has a considerable impact on retinal stimulation in both epiretinal and subretinal stimulation schemes. This effect can be demonstrated by comparing the electric field distributions in a homogeneous and layered model of a retina.
A simple model to characterise the electrical properties of tissue is useful for simulating electric fields in the retinal tissue. Considering the inhomogeneous nature of the retina and the convenience offered by computational tools, it is more accurate to use a multi-layer instead of the homogeneous single layer model to calculate electric field distributions in the retina. An electric model of the human retina derived from extrapolating resistivity measurements on an intact macaque retina is assumed for our simulations. This model represents the retina by layers of different electrical resistivities. Earlier numerical modelling studies instead consider the retina as a homogeneous medium bearing an electrical resistivity of â‰¤1Î©m.
Finite element method (FEM) is one of the numerous strategies available to analyse electric field magnitudes in the region surrounding microelectrodes during stimulation. It has been used previously in the field of retinal prostheses for basic electrostatic potential distribution calculations , applied to neuron models, three-dimensional distribution of electric field of a planar electrode array and electrostatic interactions between two electrodes in various stimulation configurations .
The aim of this work is to predict the threshold currents for subretinal stimulation of the retina by using a layered resistivity model of the retinal tissue. The stimulation of the retina is based on the direct activation of ganglion cells neglecting the contribution of the inner layers within the retina. We assume a passive point neuron model of a ganglion cell with an electric field stimulation criterion of 3000V/m. A lateral extent of the stimulation zone is estimated at the ganglion cell layer depth in the retina for a given value of stimulation current. Finally, the effect of an electrode-tissue gap on the threshold currents and impedance is analysed. We demonstrate a simple finite element simulation framework aimed at predicting the activation
electrode (left) and when a layer of PF is present between the retina and the electrode (right).
The gap is assumed to be filled with PF whose electrical conductivity is assigned a value of 2Î©m.
Impedance is computed as the ratio between the applied stimulation voltage and the resulting current seen at the electrode accounting for the retina with or without an electrode-tissue gap. In all simulations, the electric field lines originating from the stimulation electrode were computed assuming a return (ground) electrode in far field.
The impedance can be modelled as contributions from the electrode-electrolyte interface and the series complex tissue impedance .
Animal model and impedance spectroscopy
Impedance recordings were performed on P23H line 1 rats at least 3 months old which were implanted with custom made polyimide-based implants under a well defined surgical intervention protocol . As described previously , the implants consisted of a 1 mm circular head and a 40mm long shaft. The thickness was 22mm. There were four stimulating 50¼m disc electrodes on each implant, surrounded by a large return electrode. The electrode geometry used in this modelling study is based on the electrode design used in these implants.
The impedance spectra were acquired using an Agilent 4284A impedance analyser, controlled by proprietary Java software. Electrodes were connected to the impedance analyser via a 150mm 5 pole-cable and a DIP-switch (Grayhill 90HBW05) mounted on a printed circuit board, to which the impedance analyser was connected. Measurements were carried out using a voltage of 50 to 1000mV RMS with each frequency spectrum taken between 100Hz-1MHz, with the sweep starting at the highest frequency. The measurements were made between one of the four 50Î¼m electrodes and the surrounding return electrode. The commercial software ZViewTM was used to analyse the impedance data. The individual electric elements modelling the electrode-tissue measurement setup were extracted using a complex non-linear least square fitting algorithm (CNLs) built into ZViewTM.
Stimulation amplitude of 50mV was selected for the subsequent impedance measurements to minimise the risk of tissue and electrode damage by excessive current densities. Smaller amplitudes however contributed to noisy measurements. The tissue impedance extracted from the electrical equivalent model was calculated at 10kHz due to two main reasons:
Relevant as the applied stimulation pulse width is around 0.1ms in high frequency stimulation.
This frequency appeared as a compromise for the different sample frequency spectra studied, i.e. the largest change in impedance occurred around 100kHz right after implantation, whereas it occurred closer to 1kHz after a few weeks.
In the FEM simulations presented in this work, we have used a monopolar stimulation scheme for which the ground electrode is located far away from the stimulation electrode. The stimulation electrode is placed 10mm away from the encircled 100Î¼m-wide ground electrode on the same plane. An external bounding box of 18´12mm drawn from the axis of the stimulation electrode and confining the implant is used to limit the computation space. The retinal resistivity model presented before is placed in close contact with the electrodes except during the case studies on electrode-tissue gap.
Simulations were performed with the Comsol Multiphysics® finite element modelling environment. An axisymmetric finite element model of the stimulation and the ground electrodes were created with a mesh resolution of 480805 nodes. By default, the Delaunay meshing algorithm was utilised in Comsol for meshing the simulation volume. Meshing was chosen to be progressive, with the finest elements measuring 40nm close to the stimulation electrode. The data extracted from the simulations were post-processed in Matlab to generate the required plots.
The time-varying bio-electric fields, currents and voltages in a biological medium can be examined in the conventional quasistatic limit . Under these circumstances, the electric scalar potential, V in the biological medium is defined by solving the Laplace's equation:
where, Ïƒ and Îµr are the conductivity and relative permittivity of the matter respectively. The angular frequency of the driving stimulus is Ï‰=2Ï€f, Îµ0 is the permittivity of vacuum, and i is the imaginary unit. The current density on the electrode, J is related to V given by Ohm's law:
We computed the threshold current and the impedance using both harmonic and DC modes of representing the biological medium.
In the harmonic mode, frequencies of 1kHz and 10kHz were used based on the time scale of commonly applied pulses for stimulation. The biological medium was represented by conductivity and permittivity values taking into account the dispersive (frequency-dependent) properties of the tissue. The electrode-electrolyte interface impedance was also implemented into this mode in the form of a thin-layer approximation as described by Cantrell et al. . Simulations indicated that above certain electrode potential, the potential drop seen across the electrode, also known as overpotential, is negligible compared to the potential drop across the tissue impedance. Furthermore, an estimate of the capacitive component of the tissue impedance at the given frequency is more than an order of magnitude higher than the resistive component for both the frequencies. These observations suggest that the simulation problem could be reduced to a simple and computationally less expensive DC model.
Consequently, a frequency independent DC model considering the biological medium as purely resistive along with the neglected electrode interface impedance was modelled. Simulations were performed under electrostatic conditions with an applied DC voltage between the stimulation and ground electrodes. The FEM was solved using a direct linear solver known as PARDISO. Appropriate Dirichlet, von Neumann and continuity boundary conditions were used to define the electrode-retina interfaces, the insulating material-retina interfaces and the boundaries of the simulation bounding box. Material properties, in this case, electrical resistivities of Platinum (Pt) electrode and insulator (assumed as Polyimide) were adjusted parameters. The current delivered by the electrode was computed by a boundary integration of the euclidean norm of the current density over the ground electrode.
Spatial extent of the threshold current
For a given depth in the retina, the threshold current is increased for the cells located away from the axis of the electrode. In subretinal implants, the spatial extent of the stimulation represented in a cross section of the retina just above an electrode is shown in . The different curves show the area that is stimulated by the electrode with the 3000V/m criteria at different stimulation currents. For instance, the plot corresponding to the stimulation current of 3.5Î¼A applied on the electrode is the locus of electric field strength criterion. The threshold current value on the electrode axis is 39mA for GL. In this case, theoretically, just one cell is stimulated right above the electrode at the height measured subretinally. Higher values of stimulating current correspondingly stimulate cells over a wider space above the electrode. This can be seen from the curve corresponding to the locus of 59mA stimulation current, where the lateral stimulation zone extends to about 190¼m off-axis from the electrode for GL layer. The simulations show that the excitable cells in the GL region can be stimulated with threshold currents above 39¼A using our subretinal electrodes. It is also seen that the ganglion cells can no longer be stimulated at a lower value than the threshold current.
Figure : Spatial extent of threshold stimulation criterion met for different electrode currents in a subretinal scheme. The points along the horizontal line at GL (175Î¼m) represent the lateral extent of stimulated cells with two different currents. The thick black horizontal bar represents the location of the electrode.
shows the evolution of the threshold currents with the lateral distance from the axis of the stimulation electrode. The off-axis threshold currents increase almost in a quadratic manner with lateral distance from the electrode axis implying that larger currents are required to stimulate wider area of cells away from the axis of the electrode.
Figure : Evolution of the threshold currents (3000V/m criterion) in the GL vs. the lateral distance from the electrode axis. The thick black horizontal bar represents the location of the electrode. A 10% increase in stimulation current from minimum stimulation current results in a lateral extent of 70-75Î¼m in the GL.
A maximal admissible current during stimulation is based on the hypothesis of an electrochemical limit. For an electrode current ~69Î¼A applied for 0.1ms on a 50Î¼m diameter disc electrode, the electrochemical limit of ~0.35mC/cm2 for Platinum is reached. It is seen that the computed minimum threshold stimulation current of ~39Î¼A required for stimulating the GL is approximately a factor two below the electrode current at the electrochemical limit.
Effect of a gap between the electrode and the retinal tissue
The electrode-tissue gap plays an important role in the electric potential distribution above the stimulation electrode and consequently the strength of the threshold currents originating from the electrode. There is also a significant impact on the impedance due to the space between the electrode and the retinal tissue being gradually replaced by a fluid more conductive than the retina itself. We will now study both these effects of a gap between the electrode and the tissue by varying the gap between the retina and implant surface in the FEM model.
Effect on threshold currents
shows the dependence of the on-axis stimulation current required to reach the 3000V/m criterion in the GL as a function of the gap between the stimulation electrode and the bottom surface of the retina. It is seen that the threshold current increases rapidly in GL as the gap between the electrode and the tissue increases. As a result, the electrode electrochemical limit is reached when the gap exceeds 5Î¼m for GL stimulation.
Figure : Dependence of the on-axis threshold current with the electrode-tissue gap at GL in the retina.
Effect on impedance
Knowledge of impedance can be used as an indirect measurement of the electrode-tissue gap. It is also well known that Advanced Optical Coherence Tomography (OCT) imaging technique can be used to determine the distance between an electrode and tissue in in vivo post-implantation .
Our simulation framework can predict the gap between an electrode and tissue by relating computed values with actual measurements of impedance. shows the computed impedance as a function of the gap between the retina and the stimulation electrode. The impedance decreases with increasing gap values. A gap of 50Î¼m is sufficient to decrease the impedance by a factor of 10 and almost attain a resistivity equivalent to that of the PF. The line at 36kW corresponds to the computed impedance of the PF as seen by the stimulating electrode with respect to the ground.
In vivo impedance measurements () demonstrate that the impedance measured just after subretinal implantation in rats is appreciably lower than the expected value obtained when there is a close contact between the electrode and retina. This corresponds to the hypothesis of an electrode-tissue gap. Typically, after 20 days, the electrode impedance increases to a high value. It is observed from additional measurements after two months that the attained high value remains stable. This situation corresponds to a small electrode-tissue gap in our model.
Figure : Variation of impedance with changes in electrode-tissue gap.
Figure Evolution of the in vivo electrical impedance of retinal tissue measured at 10 kHz in rats during a two-month period. The impedance measurements were performed with implanted rats that exhibited low fibrous reaction.
Using FEM simulations, this report investigated the estimation of spatial extent of the threshold currents and the evolution of threshold currents with lateral distance in the GL for subretinal stimulation. The effect of electrode-tissue gap on the threshold current and impedance was also studied.
Stimulation experiments conducted by independent research groups indicate that the thresholds for activating the ganglion cells vary depending on the manner of activation - direct or indirect, pulse type, time-course, polarity and many other unknown parameters. Based on our assumptions, the computed thresholds for direct activation were expressed as charge densities. The value is in the order of 0.2mC/cm2 in the GL for a balanced, cathodic-first, rectangular stimulus with a pulse duration of 0.1ms. These compare with the threshold charge density values obtained from in vitro subretinal stimulation trials by Tsai et al. . They experimentally determined that short balanced biphasic pulses of the order of 0.1ms/phase directly activated retinal ganglion cells with a threshold charge density ranging between 0.06mC/cm2 and 0.12mC/cm2.
Considering the limitations of our passive model, the computed thresholds were close to the values obtained by Tsai et al. Based on the comparison with their measurements, we predict a higher limit for the threshold currents.
Spatial extent of stimulation
The spatial resolution of a local electrical stimulation triggered by a monopolar electrode is related to the spatial extent of the elicited retinal response. The retinal response is directly related to the activation of spatially distributed ganglion cells in the GL. We computed a near-quadratic variation of threshold current with increasing lateral distances from the electrode centre for the geometry presented. During actual experiments, to ensure stimulation, there is a tendency to use stimulation currents 10-20% above the pre-determined minimum threshold current. For a 10% excess on the minimum threshold current, it is observed from that a spatial region of 70-75Î¼m is in the zone of stimulation at GL. Eckhorn et al. quote in their paper concerning in vitro experiments performed by Stett et al. in normal and degenerated rat retinas that the spatial resolution at retinal level, subretinally stimulated by multi-electrode arrays, is at least 70Î¼m. This limiting value is a good starting point to associate with the spatial resolution computed at the GL in our FEM model. Our FEM framework predicts a realistic spatial resolution for the simulated geometry and retina model presented. Consequently, these values can be used as a guideline for determining density of stimulation electrodes needed to attain reasonable resolution using current and futuristic retinal implants.
Effect of electrode size
In this study, effects of an inhomogeneous retina and the electrode-retina gap on subretinal stimulation using a 50Î¼m diameter disc electrode were computed. Increasing electrode size has proven to increase thresholds in epiretinal stimulation . It also has the effect of reducing the spatial resolution for epiretinal stimulation. In contrary to these results, we performed simulations in subretinal mode to predict the direct ganglion cell stimulation thresholds and the lateral extents. The lateral extends for smaller electrodes (up to 5Î¼m) were only slightly lesser than with the 50Î¼m discs. For larger sizes (up to 200Î¼m), both the stimulation threshold and the lateral extents increase marginally.
displays the computed values for each of the electrode sizes simulated with the simulation framework.
Computed thresholds of stimulation and lateral extents for different electrode sizes
Electrode size (Î¼m)
Stimulation threshold (Î¼A)
Lateral extent (Î¼m)
We also deduced that in smaller electrodes up to 50Î¼m, similar values of threshold currents imply large current densities eventually giving rise to electrochemical problems during stimulation. Additionally, reducing sizes signify larger impedance that causes higher voltages on the electrode surface. This has an impact on the voltage delivering capabilities of the power source used for firing up the electrodes.
Effect of electrode-tissue gap
In chronic retinal implantations, there have been no observations of a fibrotic or gliotic capsule surrounding the implant area . A mention on the stimulation electrodes unaffected by corrosion also indicates that they are mostly electrochemically stable. To our best knowledge, explicit record of impedance measurements over a period in time after subretinal implantation is not available. But, the recent results on post-implantation threshold voltage measurements with time along with computed threshold charge suggest a time variation of impedance in conformance with our hypothesis. This may imply that the change in impedance is mainly due to the gap between the tissue and the electrode. Our FEM computations on the effect of an electrode-tissue gap on the impedance anticipate that it is the gap between the electrode and the retina which contributes mainly to the increase of impedance and not the resistivity of the encapsulating tissue surrounding the implanted electrode in retinal implantations.
From the simulation results it can be concluded that the impedance measured immediately after subretinal implantation may correspond to the electrode-tissue gap filled with PF. The value of the impedance reached post-implantation after a certain settling period corresponds to the impedance measured at a petite electrode-tissue distance. This hypothesis is supported substantially by the impedance variation over time measured in vivo as demonstrated in . Consequently, the low impedance measured immediately after implantation corresponds to a leakage of current resulting from the gap present between the electrodes and the tissue. The increase of impedance is a sign of the achievement of an intimacy between them.
Figure Relationship between the threshold current and the corresponding impedance for increasing electrode-tissue gap values. No gap (0mm) corresponds to an impedance of 320k© as shown in . Higher values of gap result in lower impedance and higher thresholds.
Interestingly, we can deduce a relationship between variations in threshold current with changes in impedance. The association between them is presented in which is essentially a combination of and . Similar behaviour has been observed in measurements with epiretinal implants on human subjects . We postulate that monitoring impedance is not only an effective and simple method to check the integrity of the implant; but with an appropriate electrical model of the retina it can predict a realistic stimulation current.
Understanding electrode-tissue interactions is a key to efficient and successful stimulation by a retinal prosthesis. Through the current study, we have shown that it is possible to study subretinal stimulation applying an electric resistivity model of the retina in a finite element simulation framework. The following conclusions can be drawn based on our simulation study:
A layered electrical model of a retina is more realistic and accurate in comparison to a homogeneous model.
Employing the 3000V/m criterion on a passive point neuron model of a ganglion cell results in predicting the maximum limits of threshold current and lateral extent of stimulation to which in vivo experiments conducted by various researchers can be benchmarked.
The effect of an electrode-tissue gap is to increase the threshold currents and a corresponding decrease in the impedance. The increasing impedance related to a closer proximity of retina to the electrodes in our model is well supported by in vivo tissue impedance measurements. Therefore, the impedance can be a tool to monitor electrode-tissue gap and predict stimulation current simultaneously.
We conclude that the importance of performing impedance measurements after implanting stimulation devices, ensuring the close contact of target neural tissue with the stimulation electrodes, is instrumental in successful neural stimulation. With further refinement and validation, it may be possible to use our method to design and simulate different electrode geometries that optimise stimulation efficiency of the retina, and the techniques used in this method can be expanded to electrodes used in other neural stimulation devices.
Conflict of Interest Statement
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.