J Comput Neurosci (2008) 24:291–313 DOI 10.1007/s10827-007-0056-4 Estimation of population firing rates and current source densities from laminar electrode recordings Klas H. Pettersen · Espen Hagen · Gaute T. Einevoll Received: 26 May 2007 / Revised: 9 August 2007 / Accepted: 17 September 2007 / Published online: 10 October 2007 © Springer Science + Business Media, LLC 2007 Abstract This model study investigates the validity of methods used to interpret linear (laminar) mul- tielectrode recordings. In computer experiments ex- tracellular potentials from a synaptically activated population of about 1,000 pyramidal neurons are calcu- lated using biologically realistic compartmental neuron models combined with electrostatic forward modeling. The somas of the pyramidal neurons are located in a 0.4 mm high and wide columnar cylinder, mimicking a stimulus-evoked layer-5 population in a neocortical column. Current-source density (CSD) analysis of the low-frequency part (<500 Hz) of the calculated poten- tials (local field potentials, LFP) based on the ‘inverse’ CSD method is, in contrast to the ‘standard’ CSD method, seen to give excellent estimates of the true underlying CSD. The high-frequency part (>750 Hz) of the potentials (multi-unit activity, MUA) is found to scale approximately as the population firing rate to the power 3/4 and to give excellent estimates of the underlying population firing rate for trial-averaged Action Editor: Alain Destexhe K. H. Pettersen · E. Hagen · G. T. Einevoll (B ) Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, Ås, Norway e-mail: Gaute.Einevoll@umb.no K. H. Pettersen · E. Hagen · G. T. Einevoll Center for Integrative Genetics, Norwegian University of Life Sciences, Ås, Norway K. H. Pettersen e-mail: Klas.Pettersen@umb.no E. Hagen e-mail: espenhgn@gmail.com data. The MUA signal is found to decay much more sharply outside the columnar populations than the LFP. Keywords Local field potential · LFP · Multi-unit activity · MUA · Current source density · Population firing rate 1 Introduction Recordings of extracellular potentials with laminar electrodes, i.e., linear multielectrodes, have for the last few decades become a standard method for study- ing population activity in cortical tissue, see, e.g., Rappelsberger et al. (1981), Mitzdorf (1985), Barth and Di (1991), Schroeder et al. (2001), Ulbert et al. (2001), Buzsáki (2004), Einevoll et al. (2007). The laminar elec- trodes have typically been placed perpendicular to the cortical surface, and the common analysis method has been to evaluate the depth-distribution of the current- source density (CSD) based on the low-frequency part, the local field potential (LFP), of the recorded poten- tials. The standard CSD estimation method assumes homogeneous cortical in-plane activity, constant ex- tracellular electrical conductivity and equidistant elec- trode contacts, and under these conditions the CSD can be estimated from a discrete double spatial derivative of the recorded LFP (Nicholson and Freeman 1975). Recently, we developed a new CSD estimation method where effects of spatially confined cortical ac- tivity and spatially varying extracellular conductivity can be incorporated (Pettersen et al. 2006). The calcu- lation of the electrical potential from a given CSD dis- tribution is in principle straightforward, and the inverse