Toward improving the Laplacian estimation with novel multipolar concentric ring electrodes.

Conventional electroencephalography with disc electrodes has major drawbacks including poor spatial resolution, selectivity and low signal-to-noise ratio that are critically limiting its use. Concentric ring electrodes are a promising alternative with potential to improve all of the aforementioned aspects significantly. In our previous work, the tripolar concentric ring electrode was successfully used in a wide range of applications demonstrating its superiority to conventional disc electrode, in particular, in accuracy of Laplacian estimation. This paper takes the first fundamental step toward further improving the Laplacian estimation of the novel multipolar concentric ring electrodes by proposing 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 that allows cancellation of all the truncation terms up to the order of 2n. Examples of using the proposed approach to estimate the Laplacian for the cases of tripolar and, for the first time, quadripolar concentric ring electrode are presented.