It is well-known that 10-Hz alpha oscillations in humans observed by electroencephalogram (EEG) are enhanced when the eyes are closed. Toward explaining this, a previous experimental study using manipulation by transcranial magnetic stimulation (TMS) revealed more global propagation of phase resetting in the eyes-open condition than in the eyes-closed condition in the alpha band. Those results indicate a significant increase of directed information flow across brain networks from the stimulated area to the rest of the brain when the eyes are open, suggesting that sensitivity to environmental changes and external stimuli is adaptively controlled by changing the dynamics of the alpha rhythm. However, the mathematical mechanism mediating the changes in the sensitivity has not been well elucidated. In this study, we propose a qualitative mathematical model that describes the characteristic behavior of the EEG phase dynamics. Numerically, we find that the propagation properties of the phase resetting qualitatively depend on whether the population of oscillators at the stimulated area are synchronized. These results support the hypothesis that the dynamics of the alpha oscillations controls sensitivity to external stimuli.

中文翻译：

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人脑α节律状态依赖相位重置特性的数学机制

众所周知，通过脑电图 (EEG) 观察到的人类 10 Hz α 振荡在闭眼时会增强。为了解释这一点，先前使用经颅磁刺激 (TMS) 操纵的实验研究显示，在 α 波段中，睁眼条件下的相位重置比闭眼条件下的全局传播更多。这些结果表明，当眼睛睁开时，从受刺激区域到大脑其他部分的大脑网络中的定向信息流显着增加，这表明对环境变化和外部刺激的敏感性是通过改变 alpha 节律的动态来自适应地控制的。然而，调节灵敏度变化的数学机制尚未得到很好的阐明。在这项研究中，我们提出了一个定性数学模型来描述 EEG 相位动力学的特征行为。在数值上，我们发现相位重置的传播特性定性地取决于受激区域的振荡器数量是否同步。这些结果支持阿尔法振荡的动力学控制对外部刺激的敏感性的假设。