A kernel-based method to calculate local field potentials from networks of spiking neurons

The local field potential (LFP) is usually calculated from current sources arising from transmembrane currents, in particular in asymmetric cellular morphologies such as pyramidal neurons. Here, we adopt a different point of view and relate the spiking of neurons to the LFP through efferent synaptic connections and provide a method to calculate LFPs. We show that the so-called unitary LFPs (uLFP) provide the key to such a calculation. We show experimental measurements and simulations of uLFPs in neocortex and hippocampus, for both excitatory and inhibitory neurons. We fit a "kernel" function to measurements of uLFPs, and we estimate its spatial and temporal spread by using simulations of morphologically detailed reconstructions of hippocampal pyramidal neurons. Assuming that LFPs are the sum of uLFPs generated by every neuron in the network, the LFP generated by excitatory and inhibitory neurons can be calculated by convolving the trains of action potentials with the kernels estimated from uLFPs. This provides a method to calculate the LFP from networks of spiking neurons, even for point neurons for which the LFP is not easily defined. We show examples of LFPs calculated from networks of point neurons.