Frequency scaling in local field potentials: A neuron population forward modelling study

• ¹ Norwegian University of Life Sciences, Norway

Extracellular field potentials are commonly used as a measure of activity in neuronal tissue. The signal is usually filtered into two distinctive frequency bands, one low-pass band below 500 Hz, referred to as the local field potential (LFP) and a high-pass band with frequencies above approximately 750 Hz, referred to as multi-unit activity (MUA). Whereas the MUA is believed to mostly represent spiking activity of neurons located near the electrode, the LFP is commonly assumed to reflect synaptic input to the neuronal population. The relation between the synaptic activity and the spectral content of LFP is however far from understood.

It has been reported that the power of cortical LFP signals follow a 1/fα-scaling law, which is also evident in EEG recordings [1] . Bedárd et al. have shown that when the input to a neuronal population is Poissonian spike trains and synaptic filtering is taken into account, there is still a factor 1/f missing to account for the frequency attenuation seen in experimental LFP data [2] . They suggested that filtering effects in the extracellular medium may explain this frequency-dependent attenuation. However, in a more recent experimental study, no such frequency attenuation in the extracellular medium could be found [3] . Here we propose as an alternative explanation that the filtering effects arise in the neurons themselves due to a frequency-dependence in the typical separation between the synaptic input currents and the transmembrane return currents following synaptic activation. As a consequence, the current dipole length will shorten with increasing frequency and the contribution to the LFP will be correspondingly reduced.

We have studied this filtering effect in detail by simulating synaptically activated populations of morphologically reconstructed neurons. The resulting transmembrane currents are then used to calculate the extracellular potential in a foward-modelling electrostatic scheme. We consider only passive membranes and current synapses so that the system is linear and can thus estimate the filtering properties in the frequency-domain by injecting sinusoidal synaptic model currents with different frequencies. We indeed find that for low input frequencies the separation between outward and inwards currents will be larger than for higher frequencies, effectively leading to a low-pass filtering of the LFP. To elucidate this effect we also consider a simplified dendritic stick model where analytic results allow for a more detailed qualitative understanding, in analogy with a previous study of low-pass filtering of extracellular action potential signatures [4].