Time and Frequency Domain Synchrony of Current and Optimal Laplacian Estimates via T-Lead Electrodes on Human Electroencephalogram Data

Lead is a commercial tripolar concentric ring electrode designed for noninvasive electrophysiological measurement applications. Utilizing the unique ability of concentric ring electrodes to estimate the second spatial derivative (surface Laplacian) at each individual electrode by combining differential voltages recorded between the central disc and the rings with specific coefficients makes them of significant importance in biomedicine. Our recent research showed that optimal coefficients (6, -1) for the electrodes with dimensions similar to the t- Lead that maximize the accuracy of Laplacian estimation are different from the currently used coefficients (16, - 1). This study applies time and frequency domain (cross-correlation and coherence respectively) signal synchrony measures to resting electroencephalogram data from six healthy humans to assess the difference due to current and optimal coefficients. This task is important since diagnostic value may be impacted by the differences in the estimated Laplacian signal. Two bipolar Laplacian estimates (each ring minus the central disc) were also added to the analysis resulting in six pairwise comparisons including all combinations of optimal and suboptimal tripolar as well as larger and smaller bipolar Laplacian estimates. Three of the comparisons resulted in very high average cross-correlation and coherence (0.9 to 1.0) while remaining three (all including larger bipolar estimate) did not. High signal synchrony between tripolar Laplacian estimates could indicate that the difference due to optimal and suboptimal coefficients may not be significant though further investigation is required going beyond synchrony measures. Results for larger bipolar Laplacian estimate are consistent with prior results of Laplacian estimation accuracy increasing with increase in the number of concentric rings and with decrease in the electrode size.