Physical model of coherent potentials measured with different electrode recording site sizes

A question that still complicates interpretation of local field potentials (LFPs) is how electrode properties like impedance, size, and shape affect recorded LFPs. In addition, how any such effects should be considered when comparing LFP, electroencephalogram (EEG), or electrocorticogram (ECoG) data has not been clearly described. A generally accepted concrete physical model describes that an electrode records the spatial average of the voltage across its uninsulated tip, yet the effects of this spatial averaging on recorded coherence have never been modeled. Using simulations based on this physical model, we show here that for any effects to occur, a spatial voltage gradient on a scale smaller than an electrode's recording site must exist over the site's surface. When this occurs, larger electrodes on average report higher coherence between locations, with the effect continuously increasing as the voltage profile over the extent of the recording site is increasingly nonuniform. We quantitatively compared published coherence estimates of LFP, ECoG, and EEG data across a range of studies and found a possible modest effect of electrode size in published ECoG data only. We used the model to quantify the expected coherence for any electrode size in relation to any given spatial frequency of a voltage profile. From this and existing estimates of the spread of voltages underlying each of these data types, our simulations quantitatively agree with the published data and importantly suggest that LFP coherence will be independent of recording site size within the range of microelectrodes typically used for extracellular recordings.