The role of coupling connections in a model of the cortico-basal ganglia-thalamocortical neural loop for the generation of beta oscillations

Highlights

• A two oscillator model is built to explore the Parkinsonian beta oscillations.

• Intra- and inter-coupling have different roles in inducing the beta oscillations.

• Cortical oscillator may also be the origin of the lower beta oscillations.

Abstract

Excessive neural synchronization in the cortico-basal ganglia-thalamocortical circuits in the beta ($\beta$) frequency range (12–35 Hz) is closely associated with dopamine depletion in Parkinson’s disease (PD) and correlated with movement impairments, but the neural basis remains unclear. In this work, we establish a double-oscillator neural mass model for the cortico-basal ganglia-thalamocortical closed-loop system and explore the impacts of dopamine depletion induced changes in coupling connections within or between the two oscillators on neural activities within the loop. Spectral analysis of the neural mass activities revealed that the power and frequency of their principal components are greatly dependent on the coupling strengths between nuclei. We found that the increased intra-coupling in the basal ganglia-thalamic (BG-Th) oscillator contributes to increased oscillations in the lower $\beta$ frequency band (12–25 Hz), while increased intra-coupling in the cortical oscillator mainly contributes to increased oscillations in the upper $\beta$ frequency band (26–35 Hz). Interestingly, pathological upper $\beta$ oscillations in the cortical oscillator may be another origin of the lower $\beta$ oscillations in the BG-Th oscillator, in addition to increased intra-coupling strength within the BG-Th network. Lower $\beta$ oscillations in the BG-Th oscillator can also change the dominant oscillation frequency of a cortical nucleus from the upper to the lower $\beta$ band. Thus, this work may pave the way towards revealing a possible neural basis underlying the Parkinsonian state.

Introduction

Rhythmic activity is one of the most widely studied phenomena in the brain (Fountas & Shanahan, 2017). Excessive rhythms within the beta ($\beta$) frequency band (12–35 Hz) that occur in the basal ganglia (BG) and related cortico-basal ganglia-thalamocortical loops are believed to be associated with Parkinsonian symptoms, especially with rigidity and bradykinesia (Beck et al., 2016, Degos et al., 2009, Hammond et al., 2007, Mallet et al., 2008, Stein and Bar-Gad, 2013, Uhlhaas and Singer, 2006). In Parkinson’s disease (PD), it is generally accepted that degeneration of the dopaminergic neurons is the dominant cause of the neuronal abnormality, which is also supported by the fact that the dopamine replacement therapies such as L-DOPA and D2 dopamine receptor agonist can effectively suppress the abnormal $\beta$ rhythms, followed by improvements of movement disorder symptoms (Bronte-Stewart et al., 2009, Canessa et al., 2016, Doyle Gaynor et al., 2008, Giannicola et al., 2010, Kühn et al., 2009, Wingeier et al., 2006). Moreover, previous studies have shown that electrical stimulation, especially deep brain stimulation (DBS), plays a positive role in suppressing the abnormal neural rhythmic activities. However, the neural dynamics mechanism underlying PD is still unknown, and there are different arguments about the source of the abnormal rhythms associated with PD that contributes to the development of DBS and the other therapies (Bevan et al., 2002, Brittain and Brown, 2014, Corbit et al., 2016, Gillies et al., 2002, Gradinaru et al., 2009, Holgado et al., 2010, Humphries et al., 2006, Jahanshahi et al., 2010, Jenkinson and Brown, 2011, Kumar et al., 2011, Litvak et al., 2011, Liu et al., 2017, Magill et al., 2001, McCarthy et al., 2011, Moran et al., 2011, Nevado-Holgado et al., 2014, Park and Rubchinsky, 2012, Plenz and Kital, 1999, Terman et al., 2002).

Four predominating theories exist to explore the origin of the enhanced Parkinsonian $\beta$ rhythms. The first hypothesis is that the subthalamic nucleus (STN)-external globus pallidus (GPe) reciprocal network is responsible for the excessive $\beta$ rhythms (i.e. STN-GPe pacemaker hypothesis) (Bevan et al., 2002, Gillies et al., 2002, Holgado et al., 2010, Humphries et al., 2006, Nevado-Holgado et al., 2014, Park and Rubchinsky, 2012, Plenz and Kital, 1999, Terman et al., 2002). The STN-GPe network has been shown to induce oscillatory activities when it is isolated from two of its major afferents (the cortex and the striatum) in in vitro experiments. The frequency of the oscillations can be modulated by striatal inhibition of GPe neurons (Plenz & Kital, 1999). There are computational model studies supporting this theory, and a simple set of necessary conditions to guarantee the pathological $\beta$ rhythms has been identified (Holgado et al., 2010).

The second main theory about the pathological $\beta$ rhythms associated with the Parkinsonian state is the cortical originhypothesis (Gradinaru et al., 2009, Hammond et al., 2007, Jenkinson and Brown, 2011, Litvak et al., 2011), where rhythmic cortical inputs transfer the $\beta$ rhythms to the cortico-basal ganglia-thalamocortical neural loop. As supporting evidence, dopamine release attenuates the propagation of cortical beta activity (Magill et al., 2001), and a deficit of dopamine allows the propagation of the $\beta$ oscillations around the cortico-basal ganglia-thalamocortical circuit (Jahanshahi et al., 2010). Considering that $\beta$ rhythmic activities do not proliferate throughout the cortico-basal ganglia-thalamocortical loop in a uniform fashion, butrather in two distinct frequency bands, i.e. lower $\beta$ (12–25 Hz) and upper $\beta$ (26–35 Hz) (Brittain & Brown, 2014), we recently explored the different origins of the lower and upper $\beta$ oscillations in a STN-GPe network (Liu et al., 2017). A combined $\beta$ oscillation origin hypothesis is proposed in our previous work, where we used colored filtered signals to model the rhythmic cortical activities (Liu et al., 2017). We found that the pathological oscillations in the upper $\beta$ frequency band in the BG were driven by the high-frequency $\beta$ cortical rhythms, while the emergence of exaggerated oscillations in the lower $\beta$ frequency band within the BG depended greatly on the enhanced excitation of the STN-GPe network. Also it was shown that the increased self-inhibition within the GPe contributed to an increase in upper $\beta$ oscillations driven by the cortical rhythm, while the decrease in the self-inhibition within the GPe facilitated an enhancement of the lower $\beta$ oscillations induced by the increased excitability of the BG (Liu et al., 2017).

A third theory is based on a striatum-origin viewpoint. Specifically, this theory suggested that the enhanced $\beta$ rhythms emerge from the increased inhibitory interactions between striatal neurons (Corbit et al., 2016, McCarthy et al., 2011).

The fourth theory predicts that the excessive $\beta$ rhythms result from a comprehensive effect of the alterations of brain connectivity in the cortico-basal ganglia-thalamocortical neural loop and the intrinsic properties of the neurons within the loop (Moran et al., 2011). Moran et al. found that chronic dopamine depletion reorganized the cortico-basal ganglia-thalamocortical circuit, with increased effective connectivity in the pathway from cortex to STN and decreased connectivity from STN to GPe (Moran et al., 2011). Based on the neural mass model of the cortico-basal ganglia-thalamocortical neural loop, they estimated the alterations in brain connectivity underlying the $\beta$ rhythms in Parkinsonism. However, their conclusion seems to be contrary to other similar work (Rubin, McIntyre, Turner, & Wichmann, 2012). Increased connectivity from STN to GPe and decreased connectivity in the pathway from cortex to the STN are more biologically realistic (Rubin et al., 2012, van Albada et al., 2009), which is contrary with the conclusion of Moran et al. (2011). Thus, considering that the upper and lower $\beta$ oscillations are both observed in the Parkinsonian basal ganglia-thalamic (BG-Th) network and upper $\beta$ oscillations are observed in the Parkinsonian cortex (Brittain & Brown, 2014), a double-oscillator system containing the BG-Th network and cortex is presented here, so as to explore the impacts of changes in connectivity of the cortico-basal ganglia-thalamocortical neural loop on the pathological $\beta$ rhythms. Based on dopamine-depletion-induced changes in couplings of the BG-Th network (Davidson, de Paor, Cagnan, & Lowery, 2016), we propose a hypothesis that the increased couplings between the nuclei in the BG-Th network in the Parkinsonian state may facilitate the excessive $\beta$ rhythms in the lower $\beta$ range. Additionally, given the repeated results of coherence and directionality analysis between motor cortical areas and BG confirming a predominant cortical drive to the BG in the upper $\beta$ range (Hirschmann et al., 2011, Litvak et al., 2011), we also hypothesize that an abnormal upper $\beta$ rhythm originates from the excessive coupling between the nuclei within the cortex. Based on the proposed double-oscillator system model, we discuss the roles of the coupling between the two oscillators (i.e. the BG-Th network and cortex) and determine how it differs when the intrinsic properties of each oscillator are changed. The intrinsic properties of each oscillator constitute the state of the oscillator being normal or pathological, which is determined by the coupling strength within each oscillator as hypothesized above.