Modeling Local Field Potentials

LFP is a common measure of neuronal activity, but it is still not completely clear how the LFP is related to single neuron variables like synaptic or ionic currents, and membrane potentials. Computational models sometimes use as a description of the LFP the average membrane potential of the neurons of the network [75] (link), even though it seems definitely more likely that the LFP is rather more directly related to the synaptic activity [29] (link). The spectrum of the average membrane potential in our model has a faster decay at high frequencies than the measured LFP, and therefore does not reproduce it well (Figure S4). However, the information content of the average membrane potential turns out to be similar to the one of the recorded LFPs (Table 4).
On the opposite side, LFPs have been computed using compartmental neuron models [32] ,[51] (link). The model used in [51] (link) adopted the neuronal structure described in [76] (link): dendritic branches were divided into cilindrical compartments of 50 µm length. Each compartment contained many synapses, whose characteristics depended on the branch (apical, basal etc). The LFP was computed for every point in the space surrounding the neuron as the total extracellular potential originated by the trasmembrane currents of the hundreds of different compartments. In [32] the procedure was similar but the neuronal structure was reduced to a total of 15 compartments. In both models, LFPs were originated by synaptic currents on pyramidal neurons dendrites.
Here, we resorted to a similar but simpler approach, which takes into account that our model makes no attempt to replicate the spatial organization of cortical neurons, and thus the sum in space of currents has to be abstracted and simplified, as follows. To capture in a simple way the fact that pyramidal cells contribute the most to LFP generation because their apical dendrites are arranged in an approximate open field configuration, we assumed that the LFP is generated by the dipole-like dendrites of pyramidal cells, in which currents flow in the cell through apical excitatory synaptic contacts while they flow out through basal inhibitory contacts [77] . This suggests to model LFPs as the sum of the absolute values of AMPA and GABA currents (|I_A|+|I_G|) on pyramidal cells, which was the model we adopted in this work, and that was able to reproduce correctly both the power spectrum of recorded LFPs and its information content (Table 4, Figure 7B, and Figure S4). Taking the LFP to be a different linear combination of AMPA and GABA currents give rise to qualitatively similar results (Table 4 and Figure S4). LFP signals are high-passed at 1 Hz with a 4th order Butterworth filter to reproduce experimental recording procedures of [14] (link).