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The relation between neural mass signals, like local field potentials (LFP) or electro-encephalograms (EEG), and the spiking activity of neurons in a network is still poorly understood. Recently, linear temporal filters have been used to map multi-unit activity (MUA) to LFP signals recorded at the same electrode [1]. Similar kernels have been previously identified relating simulated network activity to the human EEG [2]. However, currently there are no theoretical/computational models to explain the form of these filters that map MUA to LFP or EEG.  Here we studied the relation between MUA and LFP in a minimal network model of the neocortex. Using simplified statistical models of neurons [3,4], the firing rate response of neuronal populations to time-dependent inputs can be characterized as that of a high pass filter. At the same time, the LFP recorded in the neocortex can be interpreted as a measure of the summated synaptic input to the population of nearby neurons [5], filtered by the neuronal membranes and the recurrent network [6]. Combining these various filter operations, we arrive at the forward model (LFP to MUA) of a band-pass filter, which can be inverted to predict the LFP from the MUA. Our results explain the form of the experimentally obtained kernels [1] and provide insight into the encoding of a stimulus by local neuronal populations. Furthermore, our theory explains characteristic properties of the neocortical LFP, solely based on effective neuronal refractoriness, membrane filtering and recurrent connectivity.

Linking neural mass signals and spike train statistics through point process and linear systems theory