Local spatial analysis of EEG signals using the Laplacian montage

Objectives. One pressing problem when recording brain activity signals by electroencephalography (EEG) is the need to reduce the effect of interference (artifacts). This study presents a method for resolving this problem using the Laplace differential operator. The aim is to determine the number of electrodes included in the Laplacian montage, as well as to clarify the requirements for the geometric shape of their placement, in order to ensure the best quality of EEG signal processing.Methods. The Laplacian montage method is based on the use of individual electrodes to determine the second derivative of the signal, proportional to the electric current at the corresponding point on the surface of the head. This approach allows the potential of neural activity of the source located in a small area limited by the electrode complex to be evaluated. By using a small number of equidistant electrodes placed around the target electrode, the Laplacian montage can produce a significantly higher quality signal from the area under the electrode complex.Results. Among all the methods for constructing the Laplacian montage discussed in the article, a complex consisting of 16 + 1 electrodes was shown to be preferable. The choice of the 16 + 1 scheme was determined by the best compromise between the quality of EEG signal processing and the complexity of manufacturing the electrode complex with given geometric parameters. The quality assessment was carried out by simulating the interference signal which allowed the correctness of the choice of installation design to be evaluated.Conclusions. The use of the Laplacian montage method can significantly reduce the effect of artifacts. The proposed montage scheme ensures a good suppression of interference signals, the sources of which are located far beyond the projection of the electrode complex. However, not all interference arising from sources deep inside the brain, can be effectively suppressed using the Laplacian montage scheme alone.