Metastability in human brain networks: a computational exploration with the Kuramoto model

This thesis delves into metastability in brain networks, a concept that has received a lot of attention in neuroscience due to its capacity to capture the adaptive and flexible dynamics of the brain. The research comprises four main studies and combines methodologies from graph theoretical analysis and dynamics on networks to offer new insights into metastability. The foundation is laid with the introduction of a novel approach for selecting a representative structural group brain network from a set of individuals, the dynamics-based consensus. We posit that the notion of representativeness should extend to dynamics, instead of solely to structure, and we introduce a metric to quantify dynamical representativeness. Shifting focus to structural aspects, we utilise machine learning to predict metastability based on structural metrics. Feature importance helps us narrow down crucial structural features, corroborating findings in the literature about the impact of global measures like modularity, but also shedding light on the capacity of nodal features such as betweenness centrality to predict metastability. We follow with an investigation that utilises a systematic and convergent series of null network models, to dissect out the structural features that are most determinant of the metastable dynamics of the network. It is shown that retaining the degree distribution, degree correlations and clustering are sufficient to capture metastable behaviour. Finally, we investigate the functional implications of differences in metastability with a perturbational study that explores the link between metastability and the critical transition. By perturbing the dynamics-based consensus, it is revealed that metastability can predict the magnitude of the response to perturbations, and the metastability peak coincides with the maximum perturbation response. This work shows that the maximum of metastability indeed marks the critical transition, and highlights a functional implication of network metastability (namely, its predictive capacity for perturbation sensitivity). Future studies could validate these findings in weighted networks or models tuned to empirical data.本论文聚焦于脑网络中的亚稳态（metastability）这一概念，该概念因能够刻画大脑的适应性与柔性动态特性，在神经科学领域受到广泛关注。本研究包含四项核心内容，融合了图论分析（graph theoretical analysis）与网络动力学（dynamics on networks）的研究方法，为亚稳态的相关研究提供了全新视角。研究首先提出了一种从个体脑网络集合中筛选具有代表性的结构化群体脑网络的全新方法——基于动力学的一致性网络（dynamics-based consensus），并据此奠定了研究基础。我们提出，代表性的定义不应仅局限于结构层面，还应延伸至动力学维度，并引入了一种量化动力学代表性的指标。随后将研究重心转向结构层面，我们利用机器学习方法，基于结构指标对亚稳态进行预测。通过特征重要性分析，我们筛选出了关键的结构特征：一方面验证了现有文献中关于模块化（modularity）等全局指标对亚稳态的影响的结论，另一方面也揭示了介数中心性（betweenness centrality）这类节点特征在预测亚稳态方面的潜力。接下来，我们采用一系列系统性且一致性的空网络模型（null network models）展开研究，以剖析对网络亚稳态动力学起决定性作用的结构特征。研究结果表明，仅保留度分布、度相关性与聚类系数（clustering）即可复现亚稳态行为。最后，我们通过一项探究亚稳态与临界转变（critical transition）之间关联的扰动研究（perturbational study），分析了亚稳态差异所带来的功能层面的影响。通过对基于动力学的一致性网络施加扰动，我们发现亚稳态能够预测扰动响应的幅度，且亚稳态峰值与最大扰动响应相吻合。本研究证实，亚稳态的峰值确实对应临界转变，并揭示了网络亚稳态的一项功能意义：即其对扰动敏感性的预测能力。未来的研究可在加权网络或针对实证数据校准的模型中验证本研究的结论。