title: Improving the accuracy of Laplacian estimation with novel multipolar concentric ring electrodes.
abstract: 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, consisting of several elements including the central disc and a number of concentric rings, 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 next step toward further improving the Laplacian estimation with novel multipolar concentric ring electrodes by completing and validating a general approach to estimation of the Laplacian for an (n+ 1)-polar electrode withnrings using the (4n+ 1)-point method forn≥ 2 that allows cancellation of all the truncation terms up to the order of 2n. An explicit formula based on inversion of a square Vandermonde matrix is derived to make computation of multipolar Laplacian more efficient. To confirm the analytic result of the accuracy of Laplacian estimate increasing with the increase ofnand to assess the significance of this gain in accuracy for practical applications finite element method model analysis has been performed. Multipolar concentric ring electrode configurations withnranging from 1 ring (bipolar electrode configuration) to 6 rings (septapolar electrode configuration) were directly compared and obtained results suggest the significance of the increase in Laplacian accuracy caused by increase ofn.
authors.affiliation: Department of Mathematics, Diné College, 1 Circle Dr., Tsaile, AZ 86556, USA.
authors.forename: Oleksandr
authors.initials: O
authors.lastname: Makeyev
authors.affiliation: Department of Physiological Nursing, University of California San Francisco, 2 Koret Way, San Francisco, CA 94131, USA.
authors.forename: Quan
authors.initials: Q
authors.lastname: Ding
authors.affiliation: Department of Electrical, Computer, and Biomedical Engineering, University of Rhode Island, 4 East Alumni Ave., Kingston, RI 02881, USA.
authors.forename: Walter G
authors.initials: WG
authors.lastname: Besio
keywords: Electroencephalography; Laplacian; finite element method; modeling; multipolar concentric ring electrodes