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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. Previously, progress was 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, the 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 1st to 25th. Obtained results also suggest consistency between all the considered concentric ring electrode configurations corresponding to n ranging from 2 to 5 that may allow estimation of optimal ranges of inter-ring distances 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 shown to increase with an increase in n.