Accelerated Simulation of Multi-Electrode Arrays Using Sparse and Low-Rank Matrix Techniques.

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 while minimizing the error of a simplified simulation by using a sparse plus low-rank approximation of the resistance matrix. Specifically, 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 adding significantly to the problem size. Utilizing these matrix techniques, we accelerated the simulation of multi-electrode arrays by an order of magnitude, reducing the computation time 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. Although the techniques presented here are used for simulations of photovoltaic retinal prostheses, they are also immediately applicable to any circuit involving dense connections between nodes, and, with modifications, more generally to any systems involving non-sparse matrices. This approach promises significant improvements in the efficiency of modeling the next-generation retinal implants having thousands of pixels, enabling iterative design with broad applicability.

Pixel size limit of the PRIMA implants: from humans to rodents and back.

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 100µm-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 100µm and 75µm pixels were compared to clinical thresholds with 100µm 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 75µm bipolar pixels under the maximum safe near-infrared (880 nm) illumination of 8 mW mm-2with 30% duty cycle (10 ms pulses at 30 Hz) should provide a similar perceptual brightness as with 100µm pixels under 3 mW mm-2irradiance, used in the current clinical trials. Contrast of the Landolt C pattern scaled down to 75µm pixels is also similar under such illumination to that with 100µm pixels, increasing the maximum acuity from 20/420 to 20/315.Significance.Computational modeling defines the minimum pixel size of the PRIMA implants as 75µm. Increasing the implant width from 2 to 3 mm and reducing the pixel size from 100 to 75µm 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.

Photovoltaic implant simulator reveals resolution limits in subretinal prosthesis.

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 100µm 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 48µm. Closer proximity between the electrodes and the INL, achieved with pillar electrodes, enhances the stimulus strength and contrast and may enable 24µm resolution with 20µm pixels, at least in some patients.Significance.A resolution of 24µm 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.