Solving the general inter-ring distances optimization problem for concentric ring electrodes to improve Laplacian estimation.
Solving the general inter-ring distances optimization problem for concentric ring electrodes to improve Laplacian estimation.
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DOI：
10.1186/s12938-018-0549-6
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发表时间：
2018-08-30
影响因子：
3.9
通讯作者：
Makeyev O
中科院分区：
文献类型：
--
作者：
Makeyev O
在一系列电生理测量应用中，已经证明了非侵入性三极同心环电极在表面拉普拉斯估计准确性方面优于传统圆盘电极。最近，提出了一种使用（4n + 1）点方法对具有n个环的（n + 1）极电极进行拉普拉斯估计的通用方法，并用于引入新颖的多极和可变环间距离电极配置。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。对于中环半径为 αr 和外环半径为 r 的三极配置，α 值的最佳范围确定为 0 < α ≤ 0.22，而对于具有半径为 βr 的附加中环的四极配置，α 和 β 值的最佳范围由不等式 0 < α < β < 1 和αβ ≤ 0.21。使用有限元方法建模和全因子方差分析来确认由于环间距离优化而导致的拉普拉斯估计精度提高的统计显着性（p<<0.0001）。获得的结果表明，通过同心环电极优化环间距离可以提高表面拉普拉斯估计的准确性。对于具有更多同心环的电极配置，可以应用相同的方法来解决相应的环间距离优化问题。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别。这些设计可能会改进用于测量系统的无创传感器，这些传感器使用同心环电极来获取来自大脑、肠道、心脏或子宫的电信号以用于诊断目的。
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.
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