Spatiotemporal spike-centered averaging reveals symmetry of temporal and spatial components of the spike-LFP relationship during human focal seizures

The electrographic manifestation of neural activity can reflect the relationship between the faster action potentials of individual neurons and the slower fluctuations of the local field potential (LFP). This relationship is typically examined in the temporal domain using the spike-triggered average. In this study, we add a spatial component to this relationship. Here we first derive a theoretical model of the spike-LFP relationship across a macroelectrode. This mathematical derivation showed a special symmetry in the spike-LFP relationship wherein a sinc function in the temporal domain predicts a sinc function in the spatial domain. We show that this theoretical result is observed in a real-world system by characterizing the spike-LFP relationship using microelectrode array (MEA) recordings of human focal seizures. To do this, we present a approach, termed the spatiotemporal spike-centered average (st-SCA), that allows for visualization of the spike-LFP relationship in both the temporal and spatial domains. We applied this method to 25 MEA recordings obtained from seven patients with pharmacoresistant focal epilepsy. Of the five patients with MEAs implanted in recruited territory, three exhibited spatiotemporal patterns consistent with a sinc function, and two exhibited spatiotemporal patterns resembling deep wells of excitation. These results suggest that in some cases characterization of the spike-LFP relationship in the temporal domain is sufficient to predict the underlying spatial pattern. Finally, we discuss the biological interpretation of these findings and propose that the sinc function may reflect the role of mid-range excitatory connections during seizure activity.