Department of Mathematics, Diné College, 1 Circle Dr, Tsaile, AZ, 86556, USA.
Biomed Eng Online. 2018 Aug 30;17(1):117. doi: 10.1186/s12938-018-0549-6.
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 < α ≤ 0.22 while for quadripolar configuration with an additional middle ring with radius βr the optimal range of values for α and β was determined by inequalities 0 < α < β < 1 and αβ ≤ 0.21. Finite element method modeling and full factorial analysis of variance were used to confirm statistical significance of Laplacian estimation accuracy improvement due to optimization of inter-ring distances (p < 0.0001).
Obtained results suggest the potential of using optimization of inter-ring distances to improve the accuracy of surface Laplacian estimation via concentric ring electrodes. Identical approach can be applied to solving corresponding inter-ring distances optimization problems for electrode configurations with higher numbers of concentric rings. Solutions of the proposed inter-ring distances optimization problem define the class of the optimized inter-ring distances electrode designs. These designs may result in improved noninvasive sensors for measurement systems that use concentric ring electrodes to acquire electrical signals such as from the brain, intestines, heart or uterus for diagnostic purposes.
在一系列电生理测量应用中，已经证明非侵入式三极同心环电极在表面拉普拉斯估计的准确性方面优于传统的盘状电极。最近，提出了一种使用（4n+1）点法对具有 n 个环的（n+1）极电极进行拉普拉斯估计的通用方法，并用于引入新型的多极和可变的环间距离电极配置。虽然之前只考虑了线性增加和线性减少的环间距离，但本文定义并解决了（4n+1）点法的一般环间距离优化问题。
通过最小化拉普拉斯估计的截断误差，解决了三极（n=2）和四极（n=3）同心环电极配置的一般环间距离优化问题。对于中间环半径αr和外环半径 r 的三极配置，确定了α的最优值范围为 0<α≤0.22，而对于具有半径βr 的附加中间环的四极配置，通过不等式 0<α<β<1 和αβ≤0.21 确定了α和β的最优值范围。有限元法建模和完全方差分析用于确认由于环间距离优化导致的拉普拉斯估计准确性提高的统计学意义（p<0.0001）。
研究结果表明，通过同心环电极优化环间距离有潜力提高表面拉普拉斯估计的准确性。相同的方法可以应用于解决具有更高同心环数量的电极配置的相应环间距离优化问题。所提出的环间距离优化问题的解决方案定义了优化的环间距离电极设计的类。这些设计可能会改进用于以诊断为目的从大脑、肠道、心脏或子宫获取电信号的测量系统的非侵入式传感器。
