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Chunk #16 — 1. Introduction — 1.2. What is a surface Laplacian transform?

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Issues and considerations for using the scalp surface Laplacian in EEG/ERP research: A tutorial review.
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The biophysical principle of volume conduction relates current sources generated within the brain to the macroscopic potentials observable at scalp according to Poisson’s equation (e.g., Carvalhaes and de Barros, 2015; Nunez and Srinivasan, 2006; Tenke and Kayser, 2012). A surface Laplacian (often also termed Laplacian, scalp current density [SCD], current source density [CSD]), is a mathematical simplification of this equation as a vector form of Ohm’s law, relating current generators within an (isotropic) electrical conductor to the (negative) second spatial derivative of the field potential at each electrode.3 To help understanding what this means, let us consider a series of values at discrete locations labeled A-I, with locations spreading in a single direction and separated by an equal amount of distance (Fig. 4). In this scenario, we may conceive this data series as a numerical function, which can be characterized by its instantaneous change in amplitude that is equal to the slope of a tangent line at each data point (first derivative = differences between neighboring points = gradient). Repeating this operation on the resulting data series (second derivative =