The theoretical mechanism of Parkinson's oscillation frequency bands: a computational model study

The neuronal and synaptic dynamics underlying post-inhibitory rebound burst related to major depressive disorder in the lateral habenula neuron model

A burst behavior observed in the lateral habenula (LHb) neuron related to major depressive disorder has attracted much attention. The burst is induced from silence by the excitatory N-methyl-D-aspartate (NMDA) synapse or by the inhibitory stimulation, i.e., a post-inhibitory rebound (PIR) burst, which has not been explained clearly. In the present paper, the neuronal and synaptic dynamics for the PIR burst are acquired in a theoretical neuron model. At first, dynamic cooperations between the fast rise of inhibitory γ-aminobutyric acid (GABA) synapse, slow rise of NMDA synapse, and T-type calcium current to evoke the PIR burst are obtained. Similar to the inhibitory pulse stimulation, fast rising GABA current can reduce the membrane potential to a level low enough to de-inactivate the low threshold T-type calcium current to evoke a PIR spike, which can enhance the slow rising NMDA current activated at a time before or after the PIR spike. The NMDA current following the PIR spike exhibits slow decay to induce multiple spikes to form the PIR burst. Such results present a theoretical explanation and a candidate for the PIR burst in real LHb neurons. Then, the dynamical mechanism for the PIR spike mediated by the T-type calcium channel is obtained. At large conductance of T-type calcium channel, the resting state corresponds to a stable focus near Hopf bifurcation and exhibits an "uncommon" threshold curve with membrane potential much lower than the resting membrane potential. Inhibitory modulation induces membrane potential decreased to run across the threshold curve to evoke the PIR spike. At small conductance of the T-type calcium channel, a stable node appears and manifests a common threshold curve with higher membrane potential, resulting in non-PIR phenomenon. The results present the dynamic cooperations between neuronal dynamics and fast/slow dynamics of different synapses for the PIR burst observed in the LHb neuron, which is helpful for the modulations to major depressive disorder.

Closed-loop modulation of model parkinsonian beta oscillations based on CAR-fuzzy control algorithm

Closed-loop deep brain stimulation (DBS) can apply on-demand stimulation based on the feedback signal (e.g. beta band oscillation), which is deemed to lower side effects of clinically used open-loop DBS. To facilitate the application of model-based closed-loop DBS in clinical, studies must consider state variations, e.g., variation of desired signal with different movement conditions and variation of model parameters with time. This paper proposes to use the controlled autoregressive (CAR)-fuzzy control algorithm to modulate the pathological beta band (13-35 Hz) oscillation of a basal ganglia-cortex-thalamus model. The CAR model is used to identify the relationship between DBS frequency parameter and beta oscillation power. Then the error between the one-step-ahead predicted beta power of CAR model and the desired value is innovatively used as the input of fuzzy controller to calculate the next step stimulation frequency. Compared with 130 Hz open-loop DBS, the proposed closed-loop DBS method could lower the mean stimulation frequency to 74.04 Hz with similar beta oscillation suppression performance. The Mamdani fuzzy controller is selected because which could establish fuzzy controller rules according to human operation experience. Adding prediction module to closed-loop control improves the accuracy of fuzzy control, compared with proportional-integral control and fuzzy control, the proposed CAR-fuzzy control algorithm has higher tracking reliability, response speed and robustness.

A model description of beta oscillations in the external globus pallidus

The external globus pallidus (GPe), a subcortical nucleus located in the indirect pathway of the basal ganglia, is widely considered to have tight associations with abnormal beta oscillations (13-30 Hz) observed in Parkinson's disease (PD). Despite that many mechanisms have been put forward to explain the emergence of these beta oscillations, however, it is still unclear the functional contributions of the GPe, especially, whether the GPe itself can generate beta oscillations. To investigate the role played by the GPe in producing beta oscillations, we employ a well described firing rate model of the GPe neural population. Through extensive simulations, we find that the transmission delay within the GPe-GPe pathway contributes significantly to inducing beta oscillations, and the impacts of the time constant and connection strength of the GPe-GPe pathway on generating beta oscillations are non-negligible. Moreover, the GPe firing patterns can be significantly modulated by the time constant and connection strength of the GPe-GPe pathway, as well as the transmission delay within the GPe-GPe pathway. Interestingly, both increasing and decreasing the transmission delay can push the GPe firing pattern from beta oscillations to other firing patterns, including oscillation and non-oscillation firing patterns. These findings suggest that if the transmission delays within the GPe are at least 9.8 ms, beta oscillations can be produced originally in the GPe neural population, which also may be the origin of PD-related beta oscillations and should be regarded as a promising target for treatments for PD.