Bidirectional Hopf bifurcation control of narrowband gamma oscillations in Parkinson's disease by the corticothalamic system via non-canonical pathways.

Gamma oscillation ([Formula: see text]) is an important neuronal rhythmic activity closely related to various brain functions, such as Parkinson's disease (PD). By identifying several direct glutamatergic projections from the cortical-thalamic system (CTS) to the subthalamic nucleus (STN)-external globus pallidus (GPe) circuit, we have established a novel cortical-basal ganglia-thalamus (CBGT) model. Within the CBGT model, we systematically investigate the dynamical mechanisms underlying the origin and control of [Formula: see text]. We find that significant narrowband [Formula: see text] in the 30-100 Hz range can emerge in the BG by adjusting the coupling weights and delays within the BG. Supercritical and subcritical Hopf bifurcations (SPHB and SBHB) can be used to explain the mechanisms underlying the origin of [Formula: see text]. We observe that all four direct glutamatergic projections from the CTS to the STN-GPe circuit can effectively inhibit [Formula: see text]. Interestingly, adjusting the activation levels of the thalamus and cortex can exert significant bidirectional Hopf bifurcation control over [Formula: see text] in the BG, through interaction among these four projections. This bidirectional Hopf bifurcation regulatory phenomenon exhibits good robustness with respect to parameters in the CBGT model, and parameters in the BG have a significant impact on the control patterns. Furthermore, we find that all pathways in the CTS actively participate in controlling [Formula: see text] in the BG, by adjusting the activation levels of cortical and thalamic nuclei. We observe the existence of significant high and low critical mean discharge rates (CMDR) in BG nuclei, as well as complex triggered mean discharge rates (TMDR) in cortical and thalamic nuclei, at the critical boundaries between [Formula: see text] and the stable state. These key dynamical indicators might provide testable foundations for experimental research. Notably, our computational findings suggest that cortical and thalamic nuclei could theoretically serve as potential targets for regulating oscillatory activity in the BG, providing a hypothesis for future experimental investigation into supplementary therapeutic approaches for PD.