Zhijie Charles Chen

A bstract: Retinal resistivity is a key parameter for modeling both the electric field in tissue and the resulting neural response - a crucial step in designing retinal prostheses, especially since both depend on resistivity nonlinearly. Previous studies using penetrating microelectrodes reported vastly different values, varying by as much as two orders of magnitude, likely due to parasitic capacitance in microelectrodes, compression of tissue, and its rupture by the inserted probe, allowing the conductive medium to seep in and alter the measurement. To measure retinal resistivity without compression or rupture, we applied electrical resistance tomography using a planar multielectrode array with a 30 µm pitch. Voltage waveforms generated in response to current injected from one electrode were measured on other electrodes in the array, at distances ranging from 30 to 600 µm. Data from wild-type and degenerated rat retinas were analyzed using two methods: a commercial inversion software, Res2DInv, and a custom machine learning-based decoder, with healthy retina approximated as a 4-layer structure and degenerated retina - as a 3-layer one. In healthy retina, average resistivity was 2.7 kΩ·cm for the combined ganglion cell-nerve fiber layer, 1.6 kΩ·cm for the inner plexiform layer, 2.3 kΩ·cm for the outer and inner nuclear layers, and 1.0 kΩ·cm for the photoreceptor inner and outer segments; a single-layer approximation yielded 1.7 kΩ·cm. In degenerated retina, average resistivity was 3.4 kΩ·cm for the ganglion cell-nerve fiber layer, 1.1 kΩ·cm for the inner plexiform layer, and 4 kΩ·cm for the inner nuclear layer, with a single-layer approximation of 2 kΩ·cm. S ignificance: Designing retinal prostheses to restore vision after loss of photoreceptors requires accurate modeling of electric field in tissue, but published resistivity values vary by two orders of magnitude due to inconsistencies with penetrating microelectrode-based measurements. We adapted electrical resistance tomography, a non-destructive technique from geophysics based on inverse problem solving, and developed a machine learning-based decoder to map resistivity in rat retinas using a planar microelectrode array. Our analysis yields quantitative, layer-specific resistivities for healthy and degenerated retina. Beyond retinal prostheses, this approach offers a general, deformation-free strategy for measuring electrical properties of biological tissues.

Modeling of Multi-Electrode Arrays used in neural stimulation can be computationally challenging since it may involve incredibly dense circuits with millions of interconnected resistors, representing current pathways in an electrolyte (resistance matrix), coupled to nonlinear circuits of the stimulating pixels themselves. Here, we present a method for accelerating the modeling of such circuits with minimal error by using a sparse plus low-rank approximation of the resistance matrix. We prove that thresholding of the resistance matrix elements enables its sparsification with minimized error. This is accomplished with a sorting algorithm, implying efficient O (N log (N)) complexity. The eigenvalue-based low-rank compensation then helps achieve greater accuracy without significantly increasing the problem size. Utilizing these matrix techniques, we reduced the computation time of the simulation of multi-electrode arrays by about 10-fold, while maintaining an average error of less than 0.3% in the current injected from each electrode. We also show a case where acceleration reaches at least 133 times with additional error in the range of 4%, demonstrating the ability of this algorithm to perform under extreme conditions. Critical improvements in the efficiency of simulations of the electric field generated by multi-electrode arrays presented here enable the computational modeling of high-fidelity neural implants with thousands of pixels, previously impossible. Computational acceleration techniques described in this manuscript were developed for simulation of high-resolution photovoltaic retinal prostheses, but they are also immediately applicable to any circuits involving dense connections between nodes, and, with modifications, more generally to any systems involving non-sparse matrices.

Objective: Modeling of Multi-Electrode Arrays used in neural stimulation can be computationally challenging since it may involve incredibly dense circuits with millions of intercon-nected resistors, representing current pathways in an electrolyte (resistance matrix), coupled to nonlinear circuits of the stimulating pixels themselves. Here, we present a method for accelerating the modeling of such circuits with minimal error by using a sparse plus low-rank approximation of the resistance matrix. Methods: We prove that thresholding of the resistance matrix elements enables its sparsification with minimized error. This is accomplished with a sorting algorithm, implying efficient O (N log (N)) complexity. The eigenvalue-based low-rank compensation then helps achieve greater accuracy without significantly increasing the problem size. Results: Utilizing these matrix techniques, we reduced the computation time of the simulation of multi-electrode arrays by about 10-fold, while maintaining an average error of less than 0.3% in the current injected from each electrode. We also show a case where acceleration reaches at least 133 times with additional error in the range of 4%, demonstrating the ability of this algorithm to perform under extreme conditions. Conclusion: Critical improvements in the efficiency of simulations of the electric field generated by multi-electrode arrays presented here enable the computational modeling of high-fidelity neural implants with thousands of pixels, previously impossible. Significance: Computational acceleration techniques described in this manuscript were developed for simulation of high-resolution photovoltaic retinal prostheses, but they are also immediately applicable to any circuits involving dense connections between nodes, and, with modifications, more generally to any systems involving non-sparse matrices.

Objective. Retinal prosthetics offer partial restoration of sight to patients blinded by retinal degenerative diseases through electrical stimulation of the remaining neurons. Decreasing the pixel size enables increasing prosthetic visual acuity, as demonstrated in animal models of retinal degeneration. However, scaling down the size of planar pixels is limited by the reduced penetration depth of the electric field in tissue. We investigated 3-dimensional (3d) structures on top of photovoltaic arrays for enhanced penetration of the electric field, permitting higher resolution implants. Approach. 3D COMSOL models of subretinal photovoltaic arrays were developed to accurately quantify the electrodynamics during stimulation and verified through comparison to flat photovoltaic arrays. Models were applied to optimize the design of 3D electrode structures (pillars and honeycombs). Return electrodes on honeycomb walls vertically align the electric field with bipolar cells for optimal stimulation. Pillars elevate the active electrode, thus improving proximity to target neurons. The optimized 3D structures were electroplated onto existing flat subretinal prostheses. Main results. Simulations demonstrate that despite exposed conductive sidewalls, charge mostly flows via high-capacitance sputtered iridium oxide films topping the 3D structures. The 24 μm height of honeycomb structures was optimized for integration with the inner nuclear layer cells in the rat retina, whilst 35 μm tall pillars were optimized for penetrating the debris layer in human patients. Implantation of released 3D arrays demonstrates mechanical robustness, with histology demonstrating successful integration of 3D structures with the rat retina in-vivo. Significance. Electroplated 3D honeycomb structures produce vertically oriented electric fields, providing low stimulation thresholds, high spatial resolution, and high contrast for pixel sizes down to 20 μm. Pillar electrodes offer an alternative for extending past the debris layer. Electroplating of 3D structures is compatible with the fabrication process of flat photovoltaic arrays, enabling much more efficient retinal stimulation.

Objective High-resolution retinal prosthetics offer partial restoration of sight to patients blinded by retinal degenerative diseases through electrical stimulation of the remaining neurons. Decreasing the pixel size enables an increase in prosthetic visual acuity, as demonstrated in animal models of retinal degeneration. However, scaling down the size of planar pixels is limited by the reduced penetration depth of the electric field in tissue. We investigate 3-dimensional structures on top of the photovoltaic arrays for enhanced penetration of electric field to permit higher-resolution implants. Approach We developed 3D COMSOL models of subretinal photovoltaic arrays that accurately quantify the device electrodynamics during stimulation and verified it experimentally through comparison with the standard (flat) photovoltaic arrays. The models were then applied to optimise the design of 3D electrode structures (pillars and honeycombs) to efficiently stimulate the inner retinal neurons. The return electrodes elevated on top of the honeycomb walls surrounding each pixel orient the electric field inside the cavities vertically, aligning it with bipolar cells for optimal stimulation. Alternatively, pillars elevate the active electrode into the inner nuclear layer, improving proximity to the target neurons. Modelling results informed a microfabrication process of electroplating the 3D electrode structures on top of the existing flat subretinal prosthesis. Main results Simulations demonstrate that despite the conductive sidewalls of the 3D electrodes being exposed to electrolyte, most of the charge flows via the high-capacitance sputtered Iridium Oxide film that caps the top of the 3D structures. The 24 µm height of the electroplated honeycomb structures was optimised for integration with the inner nuclear layer cells in rat retina, while 35 µm height of the pillars was optimized for penetrating the debris layer in human patients. Release from the wafer and implantation of the 3D arrays demonstrated that they are mechanically robust to withstand the associated forces. Histology demonstrated successful integration of the 3D structures with the rat retina in-vivo. Significance Electroplated 3D honeycomb structures produce a vertically oriented electric field that offers low stimulation threshold, high spatial resolution and high contrast for the retinal implants with pixel sizes down to 20µm in width. Pillar electrodes offer an alternative configuration for extending the stimulation past the debris layers. Electroplating of the 3D structures is compatible with the fabrication process of the flat photovoltaic arrays, thereby enabling much more efficient stimulation than in their original flat configuration.

Retinal implants have been developed and implanted to restore vision from outer retinal degeneration, but their performance is still limited due to the poor spatial resolution. To improve the localization of stimulation, microelectrodes in various three-dimensional (3D) shapes have been investigated. In particular, computational simulation is crucial for optimizing the performance of a novel microelectrode design before actual fabrication. However, most previous studies have assumed a uniform conductivity for the entire retina without testing the effect of electrodes placement in different layers. In this study, we used the finite element method to simulate electric fields created by 3D microelectrodes of three different designs in a retina model with a stratified conductivity profile. The three electrode designs included two conventional shapes - a conical electrode (CE) and a pillar electrode (PE); we also proposed a novel structure of pillar electrode with an insulating wall (PEIW). A quantitative comparison of these designs shows the PEIW generates a stronger and more confined electric field with the same current injection, which is preferred for high-resolution retinal prostheses. Moreover, our results demonstrate both the magnitude and the shape of potential distribution generated by a penetrating electrode depend not only on the geometry, but also substantially on the insertion depth of the electrode. Although epiretinal insertions are mainly discussed, we also compared results for subretinal insertions. The results provide valuable insights for improving the spatial resolution of retinal implants using 3D penetrating microelectrodes and highlight the importance of considering the heterogeneity of conductivities in the retina.

In patients blinded by geographic atrophy, subretinal photovoltaic implant with 100µm pixels provided visual acuity closely matching the pixel pitch. However, such flat bipolar pixels cannot be scaled below 75µm, limiting the attainable visual acuity. This limitation can be overcome by shaping the electric field with 3-dimensional electrodes. In particular, elevating the return electrode on top of honeycomb-shaped vertical walls surrounding each pixel extends the electric field vertically and decouples its penetration into tissue from the pixel width. This approach relies on migration of the retinal cells into the honeycomb wells. Here, we demonstrate that the majority of the inner retinal neurons migrate into 25µm deep wells, leaving the third-order neurons, such as amacrine and ganglion cells, outside. This is important for selective stimulation of the second-order neurons to preserve the retinal signal processing in prosthetic vision. Comparable glial response to that with flat implants suggests that migration and separation of the retinal cells by the walls does not cause additional stress. Furthermore, retinal migration into the honeycombs does not negatively affect its electrical excitability.

Localized stimulation of the inner retinal neurons for high-acuity prosthetic vision requires small pixels and minimal crosstalk from the neighboring electrodes. Local return electrodes within each pixel limit the crosstalk, but they over-constrain the electric field, thus precluding the efficient stimulation with subretinal pixels smaller than 55 μm. Here we demonstrate a high-resolution prosthetic vision based on a novel design of a photovoltaic array, where field confinement is achieved dynamically, leveraging the adjustable conductivity of the diodes under forward bias to turn the designated pixels into transient returns. We validated the computational modeling of the field confinement in such an optically-controlled circuit by in-vitro and in-vivo measurements. Most importantly, using this strategy, we demonstrated that the grating acuity with 40 μm pixels matches the pixel pitch, while with 20 μm pixels, it reaches the 28 μm limit of the natural visual resolution in rats. This method enables customized field shaping based on individual retinal thickness and distance from the implant, paving the way to higher acuity of prosthetic vision in atrophic macular degeneration.

Objective. PRIMA, the photovoltaic subretinal prosthesis, restores central vision in patients blinded by atrophic age-related macular degeneration (AMD), with a resolution closely matching the 100 µ m pixel size of the implant. Improvement in resolution requires smaller pixels, but the resultant electric field may not provide sufficient stimulation strength in the inner nuclear layer (INL) or may lead to excessive crosstalk between neighboring electrodes, resulting in low contrast stimulation patterns. We study the approaches to electric field shaping in the retina for prosthetic vision with higher resolution and improved contrast. Approach. We present a new computational framework, Retinal Prosthesis Simulator (RPSim), that efficiently computes the electric field in the retina generated by a photovoltaic implant with thousands of electrodes. Leveraging the PRIMA clinical results as a benchmark, we use RPSim to predict the stimulus strength and contrast of the electric field in the retina with various pixel designs and stimulation patterns. Main results. We demonstrate that by utilizing monopolar pixels as both anodes and cathodes to suppress crosstalk, most patients may achieve resolution no worse than 48 µ m. Closer proximity between the electrodes and the INL, achieved with pillar electrodes, enhances the stimulus strength and contrast and may enable 24 µ m resolution with 20 µ m pixels, at least in some patients. Significance. A resolution of 24 µ m on the retina corresponds to a visual acuity of 20/100, which is over 4 times higher than the current best prosthetic acuity of 20/438, promising a significant improvement of central vision for many AMD patients.

Objective. Retinal prostheses aim at restoring sight in patients with retinal degeneration by electrically stimulating the inner retinal neurons. Clinical trials with patients blinded by atrophic age-related macular degeneration using the PRIMA subretinal implant, a 2 × 2 mm array of 100 µ m-wide photovoltaic pixels, have demonstrated a prosthetic visual acuity closely matching the pixel size. Further improvement in resolution requires smaller pixels, which, with the current bipolar design, necessitates more intense stimulation. Approach. We examine the lower limit of the pixel size for PRIMA implants by modeling the electric field, leveraging the clinical benchmarks, and using animal data to assess the stimulation strength and contrast of various patterns. Visually evoked potentials measured in Royal College of Surgeons rats with photovoltaic implants composed of 100 µ m and 75 µ m pixels were compared to clinical thresholds with 100 µ m pixels. Electrical stimulation model calibrated by the clinical and rodent data was used to predict the performance of the implant with smaller pixels. Main results. PRIMA implants with 75 µ m bipolar pixels under the maximum safe near-infrared (880 nm) illumination of 8 mW mm ⁻² with 30% duty cycle (10 ms pulses at 30 Hz) should provide a similar perceptual brightness as with 100 µ m pixels under 3 mW mm ⁻² irradiance, used in the current clinical trials. Contrast of the Landolt C pattern scaled down to 75 µ m pixels is also similar under such illumination to that with 100 µ m pixels, increasing the maximum acuity from 20/420 to 20/315. Significance. Computational modeling defines the minimum pixel size of the PRIMA implants as 75 µ m. Increasing the implant width from 2 to 3 mm and reducing the pixel size from 100 to 75 µ m will nearly quadrupole the number of pixels, which should be very beneficial for patients. Smaller pixels of the same bipolar flat geometry would require excessively intense illumination, and therefore a different pixel design should be considered for further improvement in resolution.