Mathematical derivation and mechanism analysis of beta oscillations in a cortex-pallidum model.

In this paper, we develop a new cortex-pallidum model to study the origin mechanism of Parkinson's oscillations in the cortex. In contrast to many previous models, the globus pallidus internal (GPi) and externa (GPe) both exert direct inhibitory feedback to the cortex. Using Hopf bifurcation analysis, two new critical conditions for oscillations, which can include the self-feedback projection of GPe, are obtained.

The mechanism of Parkinson oscillation in the cortex: Possible evidence in a feedback model projecting from the globus pallidus to the cortex.

The origin, location and cause of Parkinson's oscillation are not clear at present. In this paper, we establish a new cortex-basal ganglia model to study the origin mechanism of Parkinson beta oscillation. Unlike many previous models, this model includes two direct inhibitory projections from the globus pallidus external (GPe) segment to the cortex.

The adjustment mechanism of the spike and wave discharges in thalamic neurons: a simulation analysis.

Different from many previous theoretical studies, this paper explores the regulatory mechanism of the spike and wave discharges (SWDs) in the reticular thalamic nucleus (TRN) by a dynamic computational model. We observe that the SWDs appears in the TRN by changing the coupling weights and delays in the thalamocortical circuit. The abundant poly-spikes wave discharges is also induced when the delay increases to large enough.

Existence of solutions of an impulsive integro-differential equation with a general boundary value condition.

In this paper, we discuss the existence of solutions for a first-order nonlinear impulsive integro-differential equation with a general boundary value condition. New comparison principles are developed, and existence results for extremal solutions are obtained using the established principles and the monotone iterative technique. The results are more general than those of the periodic boundary problems, which may be widely applied in this field.

The inhibition mechanism of epilepsy disease in a computational model.

Background: The mechanism of prevention and treatment of epilepsy is a hot issue in theoretical research.

Objective: In this paper, we studied the control mechanism of the generalized spike-and-wave discharges (GSWD) by different types of external electrical stimulation acting on the subthalamic nucleus (STN) in a computational model.

Methods: Firstly, we analyzed the pathological mechanism of seizures, which were induced by different parameters in the thalamocortical (TC) circuit.

A bidirectional Hopf bifurcation analysis of Parkinson's oscillation in a simplified basal ganglia model.

In this paper, we study the parkinson oscillation mechanism in a computational model by bifurcation analysis and numerical simulation. Oscillatory activities can be induced by abnormal coupling weights and delays. The bidirectional Hopf bifurcation phenomena are found in simulations, which can uniformly explain the oscillation mechanism in this model.

Quasilinearization method for an impulsive integro-differential system with delay.

In this paper, we obtain solution sequences converging uniformly and quadratically to extremal solutions of an impulsive integro-differential system with delay. The main tools are the method of quasilinearization and the monotone iterative. The results obtained are more general and applicable than previous studies, especially the quadratic convergence of the solution for a class of integro-differential equations, which have been involved little by now.

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

Excessive synchronous oscillation activities appear in the brain is a key pathological feature of Parkinson's disease, the mechanism of which is still unclear. Although some previous studies indicated that oscillation (13-30 Hz) may directly originate in the network composed of the subthalamic nucleus (STN) and external globus pallidus (GPe) neurons, specific onset mechanisms of which are unclear, especially theoretical evidences in numerical simulation are still little. In this paper, we employ a STN-GPe mean-field model to explore the onset mechanism of Parkinson's oscillation.

The therapeutic mechanism of epilepsy seizures in different target areas: Research on a theoretical model.

Background: The selection of optimal target areas in the surgical treatment of epilepsy is always a difficult problem in medicine.

Objective: We employed a theoretical calculation model to explore the control mechanism of seizures by an external voltage stimulus acting in different nerve nuclei.

Methods: Theoretical analysis and numerical simulation were combined.