Generator localization by current source density (CSD): Implications of volume conduction and field closure at intracranial and scalp resolutions

Abstract

The topographic ambiguity and reference-dependency that has plagued EEG/ERP research throughout its history are largely attributable to volume conduction, which may be concisely described by a vector form of Ohm’s Law. This biophysical relationship is common to popular algorithms that infer neuronal generators via inverse solutions. It may be further simplified as Poisson’s source equation, which identifies underlying current generators from estimates of the second spatial derivative of the field potential (Laplacian transformation). Intracranial current source density (CSD) studies have dissected the “cortical dipole” into intracortical sources and sinks, corresponding to physiologically-meaningful patterns of neuronal activity at a sublaminar resolution, much of which is locally cancelled (i.e., closed field). By virtue of the macroscopic scale of the scalp-recorded EEG, a surface Laplacian reflects the radial projections of these underlying currents, representing a unique, unambiguous measure of neuronal activity at scalp. Although the surface Laplacian requires minimal assumptions compared to complex, model-sensitive inverses, the resulting waveform topographies faithfully summarize and simplify essential constraints that must be placed on putative generators of a scalp potential topography, even if they arise from deep or partially-closed fields. CSD methods thereby provide a global empirical and biophysical context for generator localization, spanning scales from intracortical to scalp recordings.

Enhancement of brain event-related potentials to speech sounds is associated with compensated reading skills in dyslexic children with familial risk for dyslexia

“…CSD transformation was employed to sharpen the broad ERP voltage topographies caused by volume conduction throughout physiological tissues (Law et al, 1993;Nunez, 1981;Nunez & Srinivasan, 2006). It acts as a valuable, although not necessary, preprocessing step for temporal principal component analysis by giving a rough estimate of inner surface (dura) potential by filtering off the volume conduction (tPCA; Kayser & Tenke, 2006;Kayser & Tenke, 2015a;Tenke & Kayser, 2012). However, the use of the CSD in Studies II and III was not possible, because while applying longitudinal data, it was reasonable to use similar methods as in the previous publications of the same data.…”

The surface Laplacian technique in EEG: Theory and methods

“…Our goal here is to introduce some concepts from the physics of EEG that are often unfamiliar to the EEG researcher, and that have direct relevance to the surface Laplacian technique. We do not attempt to reproduce the main arguments about the relationship between the surface Laplacian and the dura-surface potential, nor with the Current Source Density (CSD), which are found, for example, in Nunez and Srinivasan (2006) and Tenke and Kayser (2012). Instead we focus on the more fundamental aspects that are often overlooked.…”

“…The literature dedicated to provide theoretical explanations about the surface Laplacian technique is scarce, but it contains substantial and valuable information (see Nunez and Srinivasan, 2006;Tenke and Kayser, 2012). Nevertheless, there are still some gaps that, if filled, can help comprehension and permit a more intuitive view of the technique.…”

Sending mixed signals: worry is associated with enhanced initial error processing but reduced call for subsequent cognitive control

“…The RID-Rihaczek distribution computes a complex TFD with uniform timefrequency resolution, avoiding the trade-off between time and frequency resolution inherent to wavelet analysis. To avoid spurious phase synchrony between scalp electrodes due to volume conduction (Srinivasan et al, 2007), all EEG epochs were first converted to current source density (CSD) using published methods (Tenke and Kayser, 2012). In these analyses, we computed the phase differences between pairs of electrodes across trials.…”