Solving the inter-ring distances optimization problem for pentapolar and sextopolar concentric ring electrodes based on the negligible dimensions model of the electrode

Concentric ring electrodes are noninvasive and wearable sensors for electrophysiological measurement capable of estimating the surface Laplacian (second spatial derivative of surface potential) at each electrode. Recently, progress has been made toward optimization of inter-ring distances (distances between the recording surfaces of a concentric ring electrode), maximizing the accuracy of the surface Laplacian estimate based on the negligible dimensions model of the electrode. However, this progress was limited to tripolar (number of concentric rings n equal to 2) and quadripolar (n = 3) electrode configurations only. In this study, inter-ring distances optimization problem is solved for pentapolar (n = 4) and sextopolar (n = 5) concentric ring electrode configurations using a wide range of truncation error percentiles ranging from 1^st to 25^th. For example, for the 5^th percentile threshold, the optimal range of values of α, β and γ for the pentapolar concentric ring electrode configuration with middle rings radii equal to αr, βr and γr and outer ring radius of r such that 0 < α < β < γ < 1 was determined to be αβγ ≤ 0.213. Respective optimal range of values of α, β, γ and δ for the sextopolar concentric ring electrode configuration with an additional middle ring of radius δr such that 0 < α < β < γ < δ < 1 was determined to be αβγδ ≤ 0.204. Obtained results also suggest consistency between the optimal ranges for all the considered concentric ring electrode configurations corresponding to n ranging from 2 to 5 that may allow estimation of optimal ranges for electrode configurations with n ≥ 6. Therefore, this study may inform future concentric ring electrode design for n ≥ 4 which is important since the accuracy of surface Laplacian estimation has been previously shown to increase with an increase in n.