Finite element method modeling to assess Laplacian estimates via novel variable inter-ring distances concentric ring electrodes.

Noninvasive concentric ring electrodes are a promising alternative to conventional disc electrodes. Currently, superiority of tripolar concentric ring electrodes over disc electrodes, in particular, in accuracy of Laplacian estimation has been demonstrated in a range of applications. In our recent work we have shown that accuracy of Laplacian estimation can be improved with multipolar concentric ring electrodes using a general approach to estimation of the Laplacian for an (n + 1)-polar electrode with n rings using the (4n + 1)-point method for n ≥ 2. This paper takes the next step toward further improving the Laplacian estimate by proposing novel variable inter-ring distances concentric ring electrodes. Derived using a modified (4n + 1)-point method, linearly increasing and decreasing inter-ring distances tripolar (n = 2) and quadripolar (n = 3) electrode configurations are compared to their constant inter-ring distances counterparts using finite element method modeling. Obtained results suggest that increasing inter-ring distances electrode configurations may decrease the estimation error resulting in more accurate Laplacian estimates compared to respective constant inter-ring distances configurations. For currently used tripolar electrode configuration the estimation error may be decreased more than two-fold while for the quadripolar configuration more than six-fold decrease is expected.