Comprehensive optimization of the tripolar concentric ring electrode with respect to the accuracy of Laplacian estimation based on the finite dimensions model of the electrode

Optimization performed in this study is based on the finite dimensions model of the concentric ring electrode as opposed to the negligible dimensions model widely used in the past. This makes the optimization problem comprehensive since all of the electrode parameters, including, for the first time, the radius of the central disc and individual widths of concentric rings, are optimized simultaneously. The optimization criterion used is maximizing the accuracy of the surface Laplacian estimation since the ability to estimate the Laplacian at each electrode constitutes the primary biomedical significance of concentric ring electrodes. Even though the obtained results and derived principles defining optimal electrode configurations are illustrated on tripolar (two concentric rings) electrodes, they were also confirmed for quadripolar (three rings) and pentapolar (four rings) electrodes and are likely to continue to hold for any higher number of concentric rings. For tripolar concentric ring electrodes, the optimal configuration was compared to previously proposed, linearly increasing inter-ring distances and constant inter-ring distances in configurations of the same size and based on the same finite dimensions model of the electrode. The obtained results suggest that previously proposed configurations correspond to almost two-fold and more than three-fold increases in Laplacian estimation error, respectively, compared to the optimal configuration proposed in this study.