The brain is intrinsically organized into large-scale networks that constantly re-organize on multiple timescales, even when the brain is at rest. The timing of these dynamics is crucial for sensation, perception, cognition, and ultimately consciousness, but the underlying dynamics governing the constant reorganization and switching between networks are not yet well understood. Electroencephalogram (EEG) microstates are brief periods of stable scalp topography that have been identified as the electrophysiological correlate of functional magnetic resonance imaging defined resting-state networks. Spatiotemporal microstate sequences maintain high temporal resolution and have been shown to be scale-free with long-range temporal correlations. Previous attempts to model EEG microstate sequences have failed to capture this crucial property and so cannot fully capture the dynamics; this paper answers the call for more sophisticated modeling approaches. We present a dynamical model that exhibits a noisy network attractor between nodes that represent the microstates. Using an excitable network between four nodes, we can reproduce the transition probabilities between microstates but not the heavy tailed residence time distributions. We present two extensions to this model: first, an additional hidden node at each state; second, an additional layer that controls the switching frequency in the original network. Introducing either extension to the network gives the flexibility to capture these heavy tails. We compare the model generated sequences to microstate sequences from EEG data collected from healthy subjects at rest. For the first extension, we show that the hidden nodes ‘trap’ the trajectories allowing the control of residence times at each node. For the second extension, we show that two nodes in the controlling layer are sufficient to model the long residence times. Finally, we show that in addition to capturing the residence time distributions and transition probabilities of the sequences, these two models capture additional properties of the sequences including having interspersed long and short residence times and long range temporal correlations in line with the data as measured by the Hurst exponent.

中文翻译：

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用于脑电微状态之间转换的嘈杂网络吸引子模型

大脑本质上是组织成大规模网络的，即使在大脑静止时，它们也会在多个时间尺度上不断地重新组织。这些动态的时机对于感觉，知觉，认知和最终意识至关重要，但是控制网络不断重组和在网络之间切换的基本动态尚未得到很好的理解。脑电图（EEG）微状态是稳定的头皮地形的短暂时期，已被确定为功能磁共振成像定义的静止状态网络的电生理相关性。时空微状态序列保持较高的时间分辨率，并已证明是无标度的，具有长期的时间相关性。先前尝试对EEG微状态序列进行建模的尝试未能捕获此关键属性，因此无法完全捕获动态。本文回答了对更复杂的建模方法的呼吁。我们提出了一个动力学模型，该动力学模型在代表微状态的节点之间展现出一个嘈杂的网络吸引子。使用四个节点之间的可激励网络，我们可以重现微状态之间的转移概率，而不是重尾滞留时间分布。我们对该模型进行了两个扩展：首先，在每个状态下添加一个隐藏节点；第二层是控制原始网络中开关频率的附加层。在网络中引入任一扩展都可以灵活地捕获这些沉重的尾巴。我们将模型生成的序列与从静止健康受试者收集的EEG数据的微状态序列进行比较。对于第一个扩展，我们显示隐藏节点“捕获”轨迹，从而可以控制每个节点的停留时间。对于第二个扩展，我们表明控制层中的两个节点足以对长停留时间进行建模。最后，我们表明，除了捕获序列的停留时间分布和转移概率外，这两个模型还捕获了序列的其他属性，包括散布的长和短停留时间以及与时间序列相关的长期时间相关性，如赫斯特指数。我们显示隐藏节点“捕获”轨迹，从而控制每个节点的停留时间。对于第二个扩展，我们显示了控制层中的两个节点足以模拟较长的停留时间。最后，我们表明，除了捕获序列的停留时间分布和转移概率外，这两个模型还捕获了序列的其他属性，包括散布的长和短停留时间以及与时间序列相关的长期时间相关性，如赫斯特指数。我们显示隐藏节点“捕捉”轨迹，从而控制每个节点的停留时间。对于第二个扩展，我们显示了控制层中的两个节点足以模拟较长的停留时间。最后，我们表明，除了捕获序列的停留时间分布和转移概率外，这两个模型还捕获了序列的其他属性，包括散布的长和短停留时间以及与时间序列相关的长期时间相关性，如赫斯特指数。