Makeyev Oleksandr, Besio Walter G
Annu Int Conf IEEE Eng Med Biol Soc. 2016 Aug;2016:2058-2062. doi: 10.1109/EMBC.2016.7591132.
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 inter-ring distances tripolar (n = 2) and quadripolar (n = 3) electrode configurations are analytically compared to their constant inter-ring distances counterparts using coefficients of the Taylor series truncation terms. Obtained results suggest that increasing inter-ring distances electrode configurations may decrease the truncation error of the Laplacian estimation resulting in more accurate Laplacian estimates compared to respective constant inter-ring distances configurations. For currently used tripolar electrode configuration the truncation error may be decreased more than two-fold while for the quadripolar more than seven-fold decrease is expected.
无创同心环电极是传统圆盘电极的一种有前景的替代方案。目前，在一系列应用中已证明三极同心环电极相对于圆盘电极具有优越性，尤其是在拉普拉斯估计的准确性方面。在我们最近的工作中，我们表明，对于n≥2的具有n个环的（n + 1）极电极，使用（4n + 1）点法估计拉普拉斯算子的通用方法，多极同心环电极可以提高拉普拉斯估计的准确性。本文通过提出新型可变环间距同心环电极，朝着进一步改进拉普拉斯估计迈出了下一步。使用改进的（4n + 1）点法推导得出，将线性增加环间距的三极（n = 2）和四极（n = 3）电极配置与其恒定环间距对应配置，利用泰勒级数截断项的系数进行分析比较。所得结果表明，与各自的恒定环间距配置相比，增加环间距的电极配置可能会降低拉普拉斯估计的截断误差，从而得到更准确的拉普拉斯估计。对于目前使用的三极电极配置，截断误差可能会降低两倍以上，而对于四极配置，预计截断误差会降低七倍以上。
