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

Area of Science:

• Computational neuroscience
• Biomedical engineering
• Electrical engineering

Background:

• Modeling neural stimulation with multi-electrode arrays involves complex, dense circuits.
• Simulating these circuits, including resistance matrices and nonlinear pixel circuits, is computationally intensive.

Purpose of the Study:

• To develop a method for accelerating the computational modeling of multi-electrode arrays used in neural stimulation.
• To reduce simulation time with minimal error by approximating the resistance matrix.

Main Methods:

• Utilized a sparse plus low-rank approximation of the resistance matrix.
• Employed thresholding for matrix sparsification with minimized error, achieving O(N log N) complexity.
• Applied eigenvalue-based low-rank compensation for enhanced accuracy without significant problem size increase.

Main Results:

• Reduced computation time for multi-electrode array simulations by approximately 10-fold.
• Maintained an average error of less than 0.3% in injected current per electrode.
• Demonstrated acceleration up to 133 times with ~4% error under extreme conditions.

Conclusions:

• The developed computational acceleration techniques enable high-fidelity modeling of neural implants with thousands of pixels.
• These methods are applicable to circuits with dense connections and systems involving non-sparse matrices, including photovoltaic retinal prostheses.