Comprehensive Optimization of the Tripolar Concentric Ring Electrode Based on Its Finite Dimensions Model and Confirmed by Finite Element Method Modeling

Abstract

The optimization performed in this study is based on the finite dimensions model of the concentric ring electrode as opposed to the negligible dimensions model used in the past. This makes the optimization problem comprehensive, as all of the electrode parameters including, for the first time, the radius of the central disc and individual widths of concentric rings, are optimized simultaneously. The optimization criterion used is maximizing the accuracy of the surface Laplacian estimation, as the ability to estimate the Laplacian at each electrode constitutes primary biomedical significance of concentric ring electrodes. For tripolar concentric ring electrodes, the optimal configuration was compared to previously proposed linearly increasing inter-ring distances and constant inter-ring distances configurations of the same size and based on the same finite dimensions model. The obtained analytic results suggest that previously proposed configurations correspond to almost two-fold and more than three-fold increases in the Laplacian estimation error compared with the optimal configuration proposed in this study, respectively. These analytic results are confirmed using finite element method modeling, which was adapted to the finite dimensions model of the concentric ring electrode for the first time. Moreover, the finite element method modeling results suggest that optimal electrode configuration may also offer improved sensitivity and spatial resolution.

Looking for optimal concentric ring electrodes: influence of design aspects on their performance

“…Our results show that the larger the electrode the better in terms of the signal amplitude (and associated signal-to-noise ratio). This agrees with previous analytical and simulation results [29] as well as with experimental results from cardiac and uterine electromyographic signal recordings with a polymer BCRE, where larger electrodes, keeping the CD and pole widths constant, provided signals of larger amplitude and signal-to-noise ratio [22,23]. Nonetheless, our results also show that larger electrodes entail larger Laplacian estimation errors and worse SS.…”

“…- For BCRE, definitions would be equivalent but with only one ring (R) Similar to previous works [28,29], the dimensions of the CRE in the finite dimensional model vary in a discrete fashion. Specifically, the maximum outer diameter of the CRE (Dmax) is subdivided into nine evenly spaced intervals.…”

“…Specifically, the maximum outer diameter of the CRE (Dmax) is subdivided into nine evenly spaced intervals. This yields more precise models than when using six intervals, which were also used in previous works [28,29], and is considered a good balance between the number of different CRE configurations that can be assessed (146 for TCRE, 84 for BCRE) and the complexity of the computation and analysis. In this context, the following notation for a given configuration of a TCRE with Dmax will be used: 'Trip CD interval(s), MR interval(s), OR interval(s)'; e.g.…”

“…Normalized maximum error (NME): This is the NME of the Laplacian estimate of the CRE over the whole mesh surface. It is a common parameter to assess the accuracy of the Laplacian potential estimation [29]. The smaller the NME value, the more accurate the estimation:…”

“…These optimal candidates are also compared to previous approaches to CRE optimization as well as to commercial CREs. In [34] and [29], we proposed optimal versions of BCRE and TCRE, respectively, with one criterion of minimizing the Laplacian estimation error and with the constraint that the outer diameter of the CRE should be Dmax. The optimal candidates were Bip1,3-9 and Trip1,3,5-9.…”