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.