Deriving theoretical phase locking values of a coupled cortico-thalamic neural mass model using center manifold reduction
Deriving theoretical phase locking values of a coupled cortico-thalamic neural mass model using center manifold reduction
复制标题
使用中心流形约简推导耦合皮质丘脑神经质量模型的理论锁相值
DOI：
10.1007/s10827-017-0638-8
复制
发表时间：
2017
影响因子：
1.2
通讯作者：
Y. Jimbo
中科院分区：
文献类型：
--
作者：
Y. Ogawa;I. Yamaguchi;K. Kotani;Y. Jimbo
诸如感觉处理和记忆过程的认知功能导致脑电图中的相位同步或不同脑区域之间的局部场电位。有很多计算研究推导锁相值（PLV），这是一个指标的相位同步强度，从神经模型。然而，这些研究通过数值推导出PLV。据我们所知，还没有关于理论PLV推导的报告。在这项研究中，我们提出了一种分析方法，推导出理论PLVs从皮质丘脑神经质量模型所描述的延迟微分方程。首先，用于产生神经信号的模型被转换成一个正常的形式的霍普夫分岔使用中心流形减少。其次，规范形式被转换成一个相位模型，这是适合于分析同步现象。第三，推导了相位模型的Fokker-Planck方程，得到了相位差分布。最后，从相位差的平稳分布计算PLV。通过数值仿真验证了该方法的有效性。此外，我们将所提出的方法应用于工作记忆过程，并讨论了相位同步现象背后的神经生理基础。结果表明，在工作记忆过程中，降低独立噪声的强度是非常重要的。所提出的方法将是非常有用的各种实验研究和模拟相关的相位同步，因为它使神经生理变化对PLV的影响进行分析，从数学的角度来看。
Cognitive functions such as sensory processing and memory processes lead to phase synchronization in the electroencephalogram or local field potential between different brain regions. There are a lot of computational researches deriving phase locking values (PLVs), which are an index of phase synchronization intensity, from neural models. However, these researches derive PLVs numerically. To the best of our knowledge, there have been no reports on the derivation of a theoretical PLV. In this study, we propose an analytical method for deriving theoretical PLVs from a cortico-thalamic neural mass model described by a delay differential equation. First, the model for generating neural signals is transformed into a normal form of the Hopf bifurcation using center manifold reduction. Second, the normal form is transformed into a phase model that is suitable for analyzing synchronization phenomena. Third, the Fokker–Planck equation of the phase model is derived and the phase difference distribution is obtained. Finally, the PLVs are calculated from the stationary distribution of the phase difference. The validity of the proposed method is confirmed via numerical simulations. Furthermore, we apply the proposed method to a working memory process, and discuss the neurophysiological basis behind the phase synchronization phenomenon. The results demonstrate the importance of decreasing the intensity of independent noise during the working memory process. The proposed method will be of great use in various experimental studies and simulations relevant to phase synchronization, because it enables the effect of neurophysiological changes on PLVs to be analyzed from a mathematical perspective.