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Concentric ring electrodes (CREs) allow improved spatial resolution, reduced crosstalk and interference, and increased bandwidth in the sensing of bioelectrical activity. A wide variety of designs have been used, but their selection is rarely well-founded. The aim of this work is to assess the implications of aspects of CRE design such as the distance between poles, their width and their maximum diameter on aspects such as the signal amplitude (and, therefore, quality), Laplacian estimation error and spatial selectivity (SS). For this purpose, a finite dimensional model of the CRE was used, and its response to the activity of an electric dipole of variable depth was simulated via finite element method modeling. Our results show that increasing the electrode size increases the error to a greater extent than the signal amplitude increases. Pole widths should be as small as possible. The middle ring of the tripolar CRE should be as far away as possible from the central disc. Tripolar CREs typically outperform bipolar CREs of the same outer diameter, significantly reducing the Laplacian estimation error and improving the SS at the cost of a small decrease in signal amplitude. Our results also show that the design of current commercial versions of CREs can be optimized. Furthermore, we propose a methodology that facilitates the selection of an adequate CRE configuration based on the specifications for CRE performance and practical aspects, such as the depth of activity sources to be recorded from and/or the maximum size of electrodes to be used. The monitoring and analysis of bioelectrical signals in a wide range of applications can benefit from the enhanced electrode design and methodology proposed in this work. 

Concentric ring electrodes are showing promise in noninvasive electrophysiological measurement but electrode design criteria are rarely detailed and justified. Toward that goal, the use of realistic finite dimensions model of concentric ring electrode in this study was two-fold. First, it was used to optimize the surface Laplacian estimate coefficients for tripolar electrode configuration with dimensions approximating the commercially available t-Lead electrodes manufactured by CREmedical. Two differential signals representing differences between potentials on the middle ring and on the central disc as well as on the outer ring and on the central disc are combined linearly into the Laplacian estimate with aforementioned coefficients representing the weights of differential signals. Second, it was used to directly compare said tripolar configuration to the optimal tripolar concentric ring electrode configuration of the same size via finite element method modeling based computation of relative and normalized maximum errors of Laplacian estimation. Obtained results suggest the optimal coefficients for Laplacian estimate based on the approximation of the t-Lead dimensions to be (6, -1) as opposed to (16, -1) widely used with this electrode in the past. Moreover, compared to the optimal tripolar concentric ring electrode configuration, commercially available tripolar electrode of the same size leads to a median increase in Laplacian estimation errors of over 4 times. These results are consistent with previously obtained results based on both negligible and finite dimensions models but further investigation on real life phantom and human data via physical concentric ring electrode prototypes is needed for conclusive proof. 

Concentric ring electrodes are noninvasive and wearable sensors for electrophysiological measurement capable of estimating the surface Laplacian (second spatial derivative of surface potential) at each electrode. Significant progress has been made toward optimization of inter-ring distances (distances between the recording surfaces of the electrode), maximizing the accuracy of the surface Laplacian estimate based on the negligible dimensions model of the electrode. However, novel finite dimensions model offers comprehensive optimization including all of the electrode parameters simultaneously by including the radius of the central disc and the widths of the concentric rings into the model. Recently, such comprehensive optimization problem has been solved analytically for the tripolar electrode configuration. This study, for the first time, introduces a finite dimensions model based finite element method model (as opposed to the negligible dimensions model based one used in the past) to confirm the analytic results. Specifically, finite element method modeling results confirmed that previously proposed linearly increasing inter-ring distances and constant inter-ring distances configurations of tripolar concentric ring electrodes correspond to an almost two-fold and more than three-fold increases in relative and normalized maximum errors of Laplacian estimation when directly compared to the optimal tripolar concentric ring electrode configuration of the same size. 

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.