标准化连接体通过其第二大特征值显示出随年龄增加的同步性
Normalized Connectomes Show Increased Synchronizability with Age Through Their Second Largest Eigenvalue
摘要：
在正常和病理条件下，如癫痫，不同脑区的同步被广泛观察到。然而，这些大脑区域的动态之间的关系，它们之间的连接，以及同步的能力仍然是一个悬而未决的问题。我们研究了具有稳态可塑性的Wilson-Cowan/Neural field方程网络中的区域间同步问题，每个方程都可以作为一个孤立的大脑区域的模型。我们考虑了任意连接配置文件，只有一个约束：连接矩阵的行都是相同的归一化。我们发现，这些系统往往同步到从一个单一的，自耦合的神经区域获得的解决方案。我们分析了这个解决方案的稳定性，通过一个简单的修改的主稳定性函数（MSF）的方法，并发现同步解决方案失去稳定性的连接矩阵时，第二大正特征值是足够大的，为值的全球耦合参数，是不是太大。这一结果在环系统和晶格中得到了数值证实，并且对于每个节点中的稳态设定点中的少量异质性也是鲁棒的。最后，我们测试了这一结果的连接体从196个主题在广泛的年龄范围（4-85岁）从人类连接体项目。我们发现，第二大特征值往往随着年龄的增长而减少，这表明同步性的增加可能与老年癫痫患病率的增加有关。
英文摘要：
The synchronization of different brain regions is widely observed under both normal and pathological conditions such as epilepsy. However, the relationship between the dynamics of these brain regions, the connectivity between them, and the ability to synchronize remains an open question. We investigated the problem of inter-region synchronization in networks of Wilson-Cowan/Neural field equations with homeostatic plasticity, each of which acts as a model for an isolated brain region. We considered arbitrary connection profiles with only one constraint: the rows of the connection matrices are all identically normalized. We found that these systems often synchronize to the solution obtained from a single, self-coupled neural region. We analyze the stability of this solution through a straightforward modification of the Master Stability Function (MSF) approach and found that synchronized solutions lose stability for connectivity matrices when the second largest positive eigenvalue is sufficiently large, for values of the global coupling parameter that are not too large. This result was numerically confirmed for ring systems and lattices and was also robust to small amounts of heterogeneity in the homeostatic set points in each node. Finally, we tested this result on connectomes obtained from 196 subjects over a broad age range (4-85 years) from the Human Connectome Project. We found that the second largest eigenvalue tended to decrease with age, indicating an increase in synchronizability that may be related to the increased prevalence of epilepsy with old age.
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