A generalized theory for current-source density analysis in brain tissue

The current-source density analysis is a widely used method in brain electrophysiology, but this method rests on a series of assumptions, namely that current sources are exclusively made by dipoles, and that the surrounding medium is resistive and uniform. Because of these assumptions, this standard model cannot be used to estimate the contributions of monopolar sources or of non-resistive aspects of the extracellular medium. We propose here a general framework to model electric fields and potentials resulting from current source densities, without relying on such assumptions. We develop a mean-field formalism which is a generalization of the standard model, and which can directly incorporate non-resistive (non-ohmic) properties of the extracellular medium, such as ionic diffusion effects. This formalism recovers the classic results of the standard model such as the current-source density (CSD) analysis, but in addition, we provide expressions to generalize the CSD approach to situations with non-resistive media and arbitrarily complex multipolar configurations of current sources. We found that the power spectrum of the signal contains the signature of the nature of current sources and medium, which provides a direct way to estimate those properties from experimental data, and in particular, estimate the possible contribution of electric monopoles.