Solving the general inter-ring distances optimization problem for concentric ring electrodes to improve Laplacian estimation

摘要

Superiority of noninvasive tripolar concentric ring electrodes over conventional disc electrodes in accuracy of surface Laplacian estimation has been demonstrated in a range of electrophysiological measurement applications. Recently, a general approach to Laplacian estimation for an (n?+?1)-polar electrode with n rings using the (4n?+?1)-point method has been proposed and used to introduce novel multipolar and variable inter-ring distances electrode configurations. While only linearly increasing and linearly decreasing inter-ring distances have been considered previously, this paper defines and solves the general inter-ring distances optimization problem for the (4n?+?1)-point method. General inter-ring distances optimization problem is solved for tripolar (n?=?2) and quadripolar (n?=?3) concentric ring electrode configurations through minimizing the truncation error of Laplacian estimation. For tripolar configuration with middle ring radius αr and outer ring radius r the optimal range of values for α was determined to be 0?