Hierarchical interaction structure of neural activities in cortical slice cultures.

Recent advances in the analysis of neuronal activities suggest that the instantaneous activity patterns can be mostly explained by considering only first-order and pairwise interactions between recorded elements, i.e., action potentials or local field potentials (LFP), and do not require higher-than-pairwise-order interactions. If generally applicable, this pairwise approach greatly simplifies the description of network interactions. However, an important question remains: are the recorded elements the units of interaction that best describe neuronal activity patterns? To explore this, we recorded spontaneous LFP peak activities in cortical organotypic cultures using planar, integrated 60-microelectrode arrays. We compared predictions obtained using a pairwise approach with those using a hierarchical approach that uses two different spatial units for describing the activity interactions: single electrodes and electrode clusters. In this hierarchical model, short-range interactions within each cluster were modeled by pairwise interactions of electrode activities and long-range interactions were modeled by pairwise interactions of cluster activities. Despite the relatively low number of parameters used, the hierarchical model provided a more accurate description of the activity patterns than the pairwise model when applied to ensembles of 10 electrodes. Furthermore, the hierarchical model was successfully applied to a larger-scale data of approximately 60 electrodes. Electrode activities within clusters were highly correlated and spatially contiguous. In contrast, long-range interactions were diffuse, suggesting the presence of higher-than-pairwise-order interactions involved in the LFP peak activities. Thus, the identification of appropriate units of interaction may allow for the successful characterization of neuronal activities in large-scale networks.