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1. Finite element method modeling to confirm the results of comprehensive optimization of the tripolar concentric ring electrode based on its finite dimensions model

   https://doi.org/10.1109/EMBC46164.2021.9629784  

   Makeyev, Oleksandr; Ye-Lin, Yiyao; Prats-Boluda, Gema; Garcia-Casado, Javier (November 2021, 2021 43rd Annual International Conference of the IEEE Engineering in Medicine & Biology Society (EMBC))

   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. 

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2. Validating the Comparison Framework for the Finite Dimensions Model of Concentric Ring Electrodes Using Human Electrocardiogram Data

   https://doi.org/10.3390/app9204279  

   Makeyev, Oleksandr; Musngi, Mark; Moore, Larry; Ye-Lin, Yiyao; Prats-Boluda, Gema; Garcia-Casado, Javier (October 2019, Applied Sciences)

   While progress has been made in design optimization of concentric ring electrodes maximizing the accuracy of the surface Laplacian estimation, it was based exclusively on the negligible dimensions model of the electrode. Recent proof of concept of the new finite dimensions model that adds the radius of the central disc and the widths of concentric rings to the previously included number of rings and inter-ring distances provides an opportunity for more comprehensive design optimization. In this study, the aforementioned proof of concept was developed into a framework allowing direct comparison of any two concentric ring electrodes of the same size and with the same number of rings. The proposed framework is illustrated on constant and linearly increasing inter-ring distances tripolar concentric ring electrode configurations and validated on electrocardiograms from 20 human volunteers. In particular, ratios of truncation term coefficients between the two electrode configurations were used to demonstrate the similarity between the negligible and the finite dimension models analytically (p = 0.077). Laplacian estimates based on the two models were calculated on electrocardiogram data for emulation of linearly increasing inter-ring distances tripolar concentric ring electrode. The difference between the estimates was not statistically significant (p >> 0.05) which is consistent with the analytic result. 

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3. Optimizing Laplacian estimation for the finite dimensions model of a commercial tripolar concentric ring electrode and comparing it to the optimal electrode configuration via finite element method modeling

   Makeyev, Oleksandr; Ye-Lin, Yiyao; Prats-Boluda, Gema; Garcia-Casado, Javier (November 2022, 9th International Electronic Conference on Sensors and Applications session Applications)

   Falcone, Francisco (Ed.)

   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. 

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4. Solving the Inter-Ring Distances Optimization Problem for Pentapolar and Sextopolar Concentric Ring Electrodes Based on the Negligible Dimensions Model of the Electrode

   https://doi.org/10.3390/ecsa-8-11280  

   Makeyev, Oleksandr; Lee, Alana; Begay, Ashton (November 2021, Engineering Proceedings)

   Vallan, Alberto (Ed.)

   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. Previously, progress was made toward optimization of inter-ring distances (distances between the recording surfaces of a concentric ring electrode), maximizing the accuracy of the surface Laplacian estimate based on the negligible dimensions model of the electrode. However, this progress was limited to tripolar (number of concentric rings n equal to 2) and quadripolar (n = 3) electrode configurations only. In this study, the inter-ring distances optimization problem is solved for pentapolar (n = 4) and sextopolar (n = 5) concentric ring electrode configurations using a wide range of truncation error percentiles ranging from 1st to 25th. Obtained results also suggest consistency between all the considered concentric ring electrode configurations corresponding to n ranging from 2 to 5 that may allow estimation of optimal ranges of inter-ring distances for electrode configurations with n ≥ 6. Therefore, this study may inform future concentric ring electrode design for n ≥ 4 which is important since the accuracy of surface Laplacian estimation has been shown to increase with an increase in n. 

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

   https://doi.org/10.1088/1361-6501/ad0f0e  

   Garcia-Casado, Javier; Ye-Lin, Yiyao; Prats-Boluda, Gema; Makeyev, Oleksandr (December 2023, Measurement Science and Technology)

   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. 

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