Issues and considerations for using the scalp surface Laplacian in EEG/ERP research: A tutorial review

Despite the recognition that the surface Laplacian may counteract adverse effects of volume conduction and recording reference for surface potential data, electrophysiology as a discipline has been reluctant to embrace this approach for data analysis. The reasons for such hesitation are manifold but often involve unfamiliarity with the nature of the underlying transformation, as well as intimidation by a perceived mathematical complexity, and concerns of signal loss, dense electrode array requirements, or susceptibility to noise. We revisit the pitfalls arising from volume conduction and the mandated arbitrary choice of EEG reference, describe the basic principle of the surface Laplacian transform in an intuitive fashion, and exemplify the differences between common reference schemes (nose, linked mastoids, average) and the surface Laplacian for frequently-measured EEG spectra (theta, alpha) and standard event-related potential (ERP) components, such as N1 or P3. We specifically review common reservations against the universal use of the surface Laplacian, which can be effectively addressed by employing spherical spline interpolations with an appropriate selection of the spline flexibility parameter and regularization constant. We argue from a pragmatic perspective that not only are these reservations unfounded but that the continued predominant use of surface potentials poses a considerable impediment on the progress of EEG and ERP research.