Oscillations in the basal ganglia are an active area of research and have been shown to relate to the hypokinetic motor symptoms of Parkinson's disease. We study oscillations in a multi-channel mean field model, where each channel consists of an interconnected pair of subthalamic nucleus and globus pallidus sub-populations.To study how the channels interact, we perform two-dimensional bifurcation analysis of a model of an individual channel, which reveals the critical boundaries in parameter space that separate different dynamical modes; these modes include steady-state, oscillatory, and bi-stable behaviour. Without self-excitation in the subthalamic nucleus a single channel cannot generate oscillations, yet there is little experimental evidence for such self-excitation. Our results show that the interactive channel model with coupling via pallidal sub-populations demonstrates robust oscillatory behaviour without subthalamic self-excitation, provided the coupling is sufficiently strong. We study the model under healthy and Parkinsonian conditions and demonstrate that it exhibits oscillations for a much wider range of parameters in the Parkinsonian case. In the discussion, we show how our results compare with experimental findings and discuss their possible physiological interpretation. For example, experiments have found that increased lateral coupling in the rat basal ganglia is correlated with oscillations under Parkinsonian conditions.

中文翻译：

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基底神经节的交互式通道模型：健康和帕金森病条件下的分叉分析。

基底神经节的振荡是一个活跃的研究领域，并且已被证明与帕金森病的运动功能减退症状有关。我们研究多通道平均场模型中的振荡，其中每个通道由一对相互连接的丘脑底核和苍白球亚群组成。为了研究通道如何相互作用，我们对个体模型进行二维分叉分析通道，它揭示了参数空间中分隔不同动态模式的临界边界；这些模式包括稳态、振荡和双稳态行为。如果下丘脑核没有自激，单个通道就不能产生振荡，但这种自激的实验证据很少。我们的结果表明，如果耦合足够强，则通过苍白球亚群耦合的交互式通道模型在没有丘脑底自激的情况下表现出强大的振荡行为。我们研究了健康和帕金森病条件下的模型，并证明它在帕金森病病例中对更广泛的参数范围表现出振荡。在讨论中，我们展示了我们的结果如何与实验结果进行比较，并讨论了它们可能的生理解释。例如，实验发现大鼠基底神经节中增加的横向耦合与帕金森病条件下的振荡相关。我们研究了健康和帕金森病条件下的模型，并证明它在帕金森病病例中对更广泛的参数范围表现出振荡。在讨论中，我们展示了我们的结果如何与实验结果进行比较，并讨论了它们可能的生理解释。例如，实验发现大鼠基底神经节中增加的横向耦合与帕金森病条件下的振荡相关。我们研究了健康和帕金森病条件下的模型，并证明它在帕金森病病例中对更广泛的参数范围表现出振荡。在讨论中，我们展示了我们的结果如何与实验结果进行比较，并讨论了它们可能的生理解释。例如，实验发现大鼠基底神经节中增加的横向耦合与帕金森病条件下的振荡相关。