The Bernstein Center for Computational Neuroscience Freiburg
Announcement for the next
Gaute Einevoll, PhD
Klaas Pettersen, PhD
Department of Mathematical Sciences and Technology
Norwegian University of Life Sciences
Mathematical modelling of extracellular potentials
Wednesday, May 31st, 2006
|Lecture Hall (ground floor)
Gaute T. Einevoll1: I. Laminar population modelling in rat barrel cortex
Klas H. Pettersen2: II. iCSD method for current source-density estimation
III. High-frequency attenuation of action-potential signatures
Single-unit extracellular recordings have for decades given an experimental window into physiological properties of single neurons. The high-frequency part of local field potentials has provided a reliable means of recording action potentials, but the low-frequency part has proved difficult to interpret. The technology for large-scale electrical recordings using various types of multi-electrodes is rapidly improving, and there is a need for new methods for extraction of relevant information from electrical potential recordings. In these talks we present results from several projects aimed at this.
I. We first present a new method to extract information about the cortical microcircuit from laminar-electrode recordings of cortical activity. In such recordings the extracellular potential is measured at about 20 different cortical depths with a typical spacing of 0.1 mm. The high-frequency part (multi-unit activity; MUA) of such data reflects firing of action potentials in cortical populations, while the low-frequency part (local field potential; LFP) are thought to be dominated by dendritic processing of synaptic inputs. In our laminar population modelling (LPM) the MUA and LFP data are jointly used to (i) identify laminar cortical populations, (ii) estimate the temporal firing rates of these populations, and (iii) estimate the functional connection patterns between the populations. Example results from applying LPM on stimulus-averaged laminar-electrode data from anesthesised rat whisker cortex following single-flick whisker stimulation, will be shown. Further, preliminary results from estimating a population firing-rate model from the estimated temporal firing rates are given.
II. The standard way to interpret LFP data from laminar electrodes has been to estimate the current source density (CSD), i.e., the laminar distribution of currents crossing the neuronal membranes into the extracellular volume. The standard CSD estimation procedure assumes infinite planes of homogeneous CSD as well as homogeneous extracellular conductivity. The infinite-activity assumption is clearly questionable in, f.ex., the rat barrel cortex where stimulation of a single whisker evokes its main response in a barrel column with a diameter of less than 0.5 mm. Here our new inverse CSD (iCSD) method is presented. This method is based on the explicit inversion of the electrostatic forward solution and various choices of source geometries and spatially varying conductivities can be directly incorporated. An easy-to-use MATLAB program will be used to compare CSD estimates from iCSD with results from the standard CSD method. This program (and example data) can be downloaded from http://arken.umb.no/compneuro/iCSD_download.html.
III. Extracellular potentials in cortex are widespread in terms of frequency with substantial power from one hertz up to several kilohertz. High frequencies appear to be more attenuated with distance from the neural source, and inhomogeneities in the extracellular conductivity have been suggested as the explanation. However, current conservation requires that the net current leaving a neuron must be zero at each instant in time, i.e., the monopole source term is zero. The morphology of the neuronal source will thus always strongly affect the resulting extracellular potential. Here we study the extracellular signature of action potentials for various dendritic morphologies. The extracellular potential is calculated as a weighted sum over transmembrane currents from the entire neuronal surface. Our models all exhibit high-frequency attenuation even with a homogeneous extracellular conductivity, and we argue that this is the most natural explanation for the observed high-frequency attenuation.
1 Comput. Neurosci.Unit, IMT, Norwegian University of Life Sciences, Ås (Gaute.Einevoll@umb.no)
2 Comput. Neurosci.Unit, IMT, Norwegian University of Life Sciences, Ås (Klas.Pettersen@umb.no)
The talk is open to the public. Guests are cordially invited!www.bccn.uni-freiburg.de