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. 2016 Jun 10;16(6):858.
doi: 10.3390/s16060858.

Improving the Accuracy of Laplacian Estimation with Novel Variable Inter-Ring Distances Concentric Ring Electrodes

Oleksandr Makeyev  1 , Walter G Besio  2
Affiliations

Improving the Accuracy of Laplacian Estimation with Novel Variable Inter-Ring Distances Concentric Ring Electrodes

Oleksandr Makeyev et al. Sensors (Basel). .

Abstract

Noninvasive concentric ring electrodes are a promising alternative to conventional disc electrodes. Currently, the superiority of tripolar concentric ring electrodes over disc electrodes, in particular, in accuracy of Laplacian estimation, has been demonstrated in a range of applications. In our recent work, we have shown that accuracy of Laplacian estimation can be improved with multipolar concentric ring electrodes using a general approach to estimation of the Laplacian for an (n + 1)-polar electrode with n rings using the (4n + 1)-point method for n ≥ 2. This paper takes the next step toward further improving the Laplacian estimate by proposing novel variable inter-ring distances concentric ring electrodes. Derived using a modified (4n + 1)-point method, linearly increasing and decreasing inter-ring distances tripolar (n = 2) and quadripolar (n = 3) electrode configurations are compared to their constant inter-ring distances counterparts. Finite element method modeling and analytic results are consistent and suggest that increasing inter-ring distances electrode configurations may decrease the truncation error resulting in more accurate Laplacian estimates compared to respective constant inter-ring distances configurations. For currently used tripolar electrode configuration, the truncation error may be decreased more than two-fold, while for the quadripolar configuration more than a six-fold decrease is expected.

Keywords: Laplacian; concentric ring electrodes; electroencephalography; electrophysiology; finite element method; modeling; multipolar; noninvasive; sensors.

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Figures

Figure 1
Figure 1
Conventional disc electrode (A) and tripolar concentric ring electrode (B).
Figure 2
Figure 2
Regular plane square grid with inter-point distances equal to r.
Figure 3
Figure 3
Linearly increasing and linearly decreasing inter-ring distances TCREs.
Figure 4
Figure 4
Schematic of the FEM model with an evenly spaced square mesh size of 600 × 600 used to assess and compare the accuracy of Laplacian estimates for constant and variable inter-ring distances CRE configurations.
Figure 5
Figure 5
Relative locations of rings, with respect to the central disc, for constant inter-ring distances (A), increasing inter-ring distances (B), and decreasing inter-ring distances (C) TCRE and QCRE configurations.
Figure 6
Figure 6
Relative (Top) and Maximum (Bottom) Errors of seven Laplacian estimates corresponding to bipolar, TCRE, and QCRE configurations.
Figure 7
Figure 7
Ratios of constant inter-ring distances to increasing inter-ring distances truncation term coefficients as functions of the truncation term order for TCRE and QCRE configurations.
Figure 8
Figure 8
Ratios of decreasing inter-ring distances to constant inter-ring distances truncation term coefficients as functions of the truncation term order for TCRE and QCRE configurations.
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References

    1. Desmedt J.E., Chalklin V., Tomberg C. Emulation of somatosensory evoked potential (SEP) components with the 3-shell head model and the problem of “ghost potential fields” when using an average reference in brain mapping. Electroencephalogr. Clin. Neurophysiol. Potentials Sect. 1990;77:243–258. doi: 10.1016/0168-5597(90)90063-J. - DOI - PubMed
    1. Nunez P.L., Silberstein R.B., Cadusch P.J., Wijesinghe R.S., Westdorp A.F., Srinivasan R. A theoretical and experimental study of high resolution EEG based on surface Laplacians and cortical imaging. Electroencephalogr. Clin. Neurophysiol. 1994;90:40–57. doi: 10.1016/0013-4694(94)90112-0. - DOI - PubMed
    1. Lantz G., Grave de Peralta R., Spinelli L., Seeck M., Michel C.M. Epileptic source localization with high density EEG: How many electrodes are needed? Clin. Neurophysiol. 2003;114:63–69. doi: 10.1016/S1388-2457(02)00337-1. - DOI - PubMed
    1. He B. Brain electric source imaging: Scalp Laplacian mapping and cortical imaging. Crit. Rev. Biomed. Eng. 1998;27:149–188. - PubMed
    1. Srinivasan R. Methods to Improve the Spatial Resolution of EEG. Int. J. Bioelectromagn. 1999;1:102–111.