Unraveling Neuronal Cluster Dynamics in Basal Ganglia Using Hierarchical Drift-Diffusion Modeling

The Basal Ganglia (BG) plays a pivotal role in movement-related decision-making. In Parkinson's disease (PD) like scenario, neuronal properties and network connectivity get altered. This leads to aberrant neuronal spiking characteristics affecting the overall oscillatory dynamics of the network. Classically, the rate of change (drift) in the membrane potential and the variation (diffusion) of the same across multiple spikes are modelled using drift-diffusion framework. During active state of a subject, the movement due to behavioral responses are a result of sustained spiking of multiple neurons within a nucleus. The diversity within a nucleus leads to formation of groups of neurons having similar dynamics. However, relation between the diversity in the neuronal responses and the movement behavior are not well studied. In this paper, we proposed a novel framework to cluster neurons based on the Hierarchical Drift Diffusion Model (HDDM). Considering the sustained nature of neuronal spiking, we distinguished between active and resting states which inherently reflected the broader network states responsible for behavioral responses. We used Density-Based Spatial Clustering of Applications with Noise (DBSCAN) to group neurons based on HDDM latent variables like drift rate. Our findings revealed discrete clusters in regions like the globus pallidus externa (GPe), globus pallidus interna (GPi), and subthalamic nucleus (STN) in the BG. Results demonstrated the well formed clusters using the latent information of HDDM which were not revealed using direct observables such as Revised Local Variation (LvR) and Instantaneous Firing Rate (IFR).