Frequency and function in the basal ganglia: the origins of beta and gamma band activity

Abstract

Neural oscillations in the basal ganglia (BG) are well studied yet remain poorly understood. Behavioural correlates of spectral activity are well described, yet a quantitative hypothesis linking time domain dynamics and spectral properties to BG function has been lacking. We show, for the first time, that a unified description is possible by interpreting previously ignored structure in data describing globus pallidus interna responses to cortical stimulation. These data were used to expose a pair of distinctive neuronal responses to the stimulation. This observation formed the basis for a new mathematical model of the BG, quantitatively fitted to the data, which describes the dynamics in the data, and is validated against other stimulus protocol experiments. A key new result is that when the model is run using inputs hypothesised to occur during the performance of a motor task, beta and gamma frequency oscillations emerge naturally during static-force and movement, respectively, consistent with experimental local field potentials. This new model predicts that the pallido-striatum connection has a key role in the generation of beta band activity, and that the gamma band activity associated with motor task performance has its origins in the pallido-subthalamic feedback loop. The network's functionality as a selection mechanism also occurs as an emergent property, and closer fits to the data gave better selection properties. The model provides a coherent framework for the study of spectral, temporal and functional analyses of the BG and therefore lays the foundation for an integrated approach to study BG pathologies such as Parkinson's disease in silico.

Roles for globus pallidus externa revealed in a computational model of action selection in the basal ganglia

“…We used the model by Gurney Prescott and Redgrave (Gurney et al, 2001a,b) -henceforth referred to as the GPR model -as the basis for the extended architecture of connectivity modelled in this study. The architecture for the GPR model was based on the connectivity shown in Fig 1A. It included all the major pathways known at the time of its construction (for related review see Prescott et al 2002, see also Humphries and Gurney 2002;Gurney et al 2004;Humphries et al 2006;Stewart et al 2012;Chersi et al 2013;Blenkinsop et al 2017) and provides a firm base for our model building. The assumption in the GPR model was that the brain processes a large number of sensory and cognitive streams or channels acting in parallel, each of them representing and requiring an action to be performed.…”

“…These models also cover a range of levels of biological description -from abstract system-level to detailed multicompartmental neuronal models, as well as simulations of ensembles of neurons. Addressing computations at the level of the subnuclei of the basal ganglia, there have been several models of the striatal microcircuitry (Humphries et al, 2009b,a;Damodaran et al, 2015), the subthalamic nuclei (STN, Frank 2006), as well as examinations of the oscillations associated within the STN-GPe network (Blenkinsop et al, 2017;Corbit et al, 2016).…”

“…We aimed to incorporate the arkypallidal neurons into a well-tested model architecture of the basal ganglia (Gurney, Prescott, Redgrave, Gurney et al 2001a,b). The architecture has been validated at several levels of description: at the systems level using rate coded neural populations constrained by anatomical and physiological data (see Gurney et al 2004;Humphries and Gurney 2002;Blenkinsop et al 2017); spiking neuron models challenged with physiological data (Humphries et al, 2006;Stewart et al, 2012;Chersi et al, 2013); and at the behavioural level in embodied (robotic) models (Prescott et al, 2006). Most recently, it has been used to link a raft of neurobehavioural phenomena to neuronal mechanisms observed in vitro 2 (Gurney et al, 2015).…”

Model and Analysis for the Onset of Parkinsonian Firing Patterns in a Simplified Basal Ganglia

“…This external input does seem to indicate a larger loop, such as the entire CBGTC, is necessary to generate this oscillations, agreeing with our model. Blenkinsop et al 57 show that their second-order DDE model showcasing two interconnected channels of the basal ganglia is capable of investigating oscillation generation with varying levels of cortical input and dopamine in addition to finding oscillation sources. Though this is an interesting endeavor, it relies on several delays that make it a strong predictor of results but gives little insight to what is changing during the disease.…”

“…54 for review). These models can also come in different forms such as damped wave equations for cortical activity [55][56][57] and models that use stochastic optimization approaches. 27 We will focus our efforts of the firing rate method as been done in several recent papers.…”