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

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          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 (4 n + 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 (4 n + 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.

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          Most cited references 39

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          Scalp current density mapping: value and estimation from potential data.

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            Epileptic source localization with high density EEG: how many electrodes are needed?

            Electroencephalography (EEG) source reconstruction is becoming recognized as a useful technique to non-invasively localize the epileptic focus. Whereas, large array magnetoencephalography (MEG) systems are available since quite some time, application difficulties have previously prevented multichannel EEG recordings. Recently, however, EEG systems which allow for quick (10-20min) application of, and recording from, up to 125 electrodes have become available. The purpose of the current investigation was to systematically compare the accuracy of epileptic source localization with high electrode density to that obtained with sparser electrode setups. Interictal epileptiform activity was recorded with 123 electrodes in 14 epileptic patients undergoing presurgical evaluation. Each single epileptiform potential was down sampled to 63 and 31 electrodes, and a distributed source model (EPIFOCUS) was used to reconstruct the sources with the 3 different electrode configurations. The localization accuracy with the 3 electrode setups was then assessed, by determining the distance from the inverse solution, maximum of each single spike to the epileptogenic lesion. In 9/14 patients, the distance from the EEG source to the lesion was significantly smaller with 63 than with 31 electrodes, and increasing the number of electrodes to 123 increased this number of patients from 9 to 11. Simulations confirmed the relation between the number of electrodes and localization accuracy. The results illustrate the necessity of multichannel EEG recordings for high source location accuracy in epileptic patients.
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              Spline Laplacian estimate of EEG potentials over a realistic magnetic resonance-constructed scalp surface model.

              This paper presents a realistic Laplacian (RL) estimator based on a tensorial formulation of the surface Laplacian (SL) that uses the 2-D thin plate spline function to obtain a mathematical description of a realistic scalp surface. Because of this tensorial formulation, the RL does not need an orthogonal reference frame placed on the realistic scalp surface. In simulation experiments the RL was estimated with an increasing number of "electrodes" (up to 256) on a mathematical scalp model, the analytic Laplacian being used as a reference. Second and third order spherical spline Laplacian estimates were examined for comparison. Noise of increasing magnitude and spatial frequency was added to the simulated potential distributions. Movement-related potentials and somatosensory evoked potentials sampled with 128 electrodes were used to estimate the RL on a realistically shaped, MR-constructed model of the subject's scalp surface. The RL was also estimated on a mathematical spherical scalp model computed from the real scalp surface. Simulation experiments showed that the performances of the RL estimator were similar to those of the second and third order spherical spline Laplacians. Furthermore, the information content of scalp-recorded potentials was clearly better when the RL estimator computed the SL of the potential on an MR-constructed scalp surface model.
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                Author and article information

                Contributors
                Role: Academic Editor
                Role: Academic Editor
                Journal
                Sensors (Basel)
                Sensors (Basel)
                sensors
                Sensors (Basel, Switzerland)
                MDPI
                1424-8220
                10 June 2016
                June 2016
                : 16
                : 6
                Affiliations
                [1 ]Department of Mathematics, Diné College, Tsaile, AZ 86556, USA
                [2 ]Department of Electrical, Computer, and Biomedical Engineering, University of Rhode Island, Kingston, RI 02881, USA; besio@ 123456uri.edu
                Author notes
                [* ]Correspondence: omakeyev@ 123456dinecollege.edu ; Tel.: +1-928-724-6960
                Article
                sensors-16-00858
                10.3390/s16060858
                4934284
                27294933
                © 2016 by the authors; licensee MDPI, Basel, Switzerland.

                This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license ( http://creativecommons.org/licenses/by/4.0/).

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