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

Abstract

ObjectiveModeling 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. MethodsWe 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. ConclusionCritical 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.