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

Objective: 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. 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(Nlog(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.