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

Nathan Jensen¹, Zhijie Charles Chen¹, Anna Kochnev Goldstein¹

¹Department of Electrical Engineering, Stanford University, Stanford, CA 94305 USA.

Biorxiv : the Preprint Server for Biology

|August 12, 2024

Summary

This study introduces a sparse plus low-rank approximation to accelerate neural stimulation modeling. The new method significantly reduces computation time for multi-electrode arrays while maintaining high accuracy.

Keywords:

Circuit simulator Low-Rank Multi-Electrode arrays Neural prostheses Optimization Retinal prosthesis

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Area of Science:

Computational neuroscience
Electrical engineering
Applied mathematics

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 an efficient method for accelerating the modeling of multi-electrode array circuits.
To reduce computational challenges in neural stimulation simulations with minimal error.

Main Methods:

Utilized a sparse plus low-rank approximation of the resistance matrix.
Employed thresholding for matrix sparsification with minimized error, achieving O(Nlog(N)) complexity.
Applied eigenvalue-based low-rank compensation for enhanced accuracy.

Main Results:

Achieved a ~10-fold reduction in simulation time for multi-electrode arrays with <0.3% average error.
Demonstrated acceleration up to 133 times with ~4% error in extreme cases.
Enabled high-fidelity computational modeling of neural implants with thousands of pixels.

Conclusions:

The developed matrix techniques significantly improve the efficiency of simulating electric fields generated by multi-electrode arrays.
These computational acceleration methods are applicable to various dense circuits and systems with non-sparse matrices, including retinal prostheses.