Brain activity generates electrical potentials that are spatio-temporal in nature. Electroencephalography (EEG) is the least costly and most widely used noninvasive technique for diagnosing many brain problems. It has high temporal resolution, but lacks high spatial resolution. In an attempt to increase the spatial selectivity, researchers introduced a bipolar electrode configuration utilizing a five-point finite difference method (FPM) and others applied a quasi-bipolar (tri-polar with two elements shorted) concentric electrode configuration. To further increase the spatial resolution, the authors report on a tri-polar concentric electrode configuration for approximating the analytical Laplacian based on a nine-point finite difference method (NPM). For direct comparison, the FPM, quasi-bipolar method (a hybrid NPM), and NPM were calculated over a 400 x 400 mesh with 1/400 spacing using a computer model. A closed-form analytical computer model was also developed to evaluate and compare the properties of concentric bipolar, quasi-bipolar, and tri-polar electrode configurations, and the results were verified with tank experiments. The tri-polar configuration and the NPM were found to have significantly improved accuracy in Laplacian estimation and localization. Movement-related potential (MRP) signals were recorded from the left prefrontal lobes on the scalp of human subjects while they performed fast repetitive movements. Disc, bipolar, quasi-bipolar, and tri-polar electrodes were used. MRP signals were plotted for all four electrode configurations. The signal-to-noise ratio and spatial selectivity of the MRP signals acquired with the tri-polar electrode configuration were significantly better than the other configurations.

Potentials recorded on the body surface from the heart are of a spatial and temporal function. The 12-lead electrocardiogram (ECG) provides a useful means of global temporal assessment; however, it yields limited spatial information due to the smoothing effect caused by the volume conductor. In an attempt to circumvent the smoothing problem, researchers have used the five-point method (FPM) to numerically estimate the analytical solution of the Laplacian with an array of monopolar electrodes. Researchers have also developed a bipolar concentric ring electrode system to estimate the analytical Laplacian, and others have used a quasi-bipolar electrode configuration. In a search to find an electrode configuration with a close approximation to the analytical Laplacian, development of a tri-polar concentric ring electrode based on the nine-point method (NPM) was conducted. A comparison of the NPM, FPM, and discrete form of the quasi-bipolar configuration was performed over a 400 x 400 mesh with 1/400 spacing by computer modeling. Different properties of bipolar, quasi-bipolar and tri-polar concentric ring electrodes were evaluated and compared, and verified with tank experiments. One-way analysis of variance (ANOVA) with post hoc t-test and Bonferroni corrections were performed to compare the performance of the various methods and electrode configurations. It was found that the tri-polar electrode has significantly improved accuracy and local sensitivity. This paper also discusses the development of an active sensor using the tri-polar electrode configuration. A 1-cm active Laplacian tri-polar sensor based on the NPM was tested and deemed feasible for acquiring Laplacian cardiac surface potentials.

Potentials on the body surface from the heart are of a spatial and temporal function. The 12-lead electrocardiogram (ECG) provides useful global temporal assessment, but it yields limited spatial information due to the smoothing effect caused by the volume conductor. The smoothing complicates identification of multiple simultaneous bioelectrical events. In an attempt to circumvent the smoothing problem, some researchers used a five-point method (FPM) to numerically estimate the analytical solution of the Laplacian with an array of monopolar electrodes. The FPM is generalized to develop a bi-polar concentric ring electrode system. We have developed a new Laplacian ECG sensor, a trielectrode sensor, based on a nine-point method (NPM) numerical approximation of the analytical Laplacian. For a comparison, the NPM, FPM and compact NPM were calculated over a 400 x 400 mesh with 1/400 spacing. Tri and bi-electrode sensors were also simulated and their Laplacian estimates were compared against the analytical Laplacian. We found that tri-electrode sensors have a much-improved accuracy with significantly less relative and maximum errors in estimating the Laplacian operator. Apart from the higher accuracy, our new electrode configuration will allow better localization of the electrical activity of the heart than bi-electrode configurations.

No abstract