通过构建简单复合物评估人类癫痫脑网络

IF 5.3 1区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Chaos Solitons & Fractals Pub Date : 2024-11-01 DOI:10.1016/j.chaos.2024.115699
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引用次数: 0

摘要

作为一个强大的框架,高阶网络在模拟复杂系统的非成对相互作用方面受到了广泛关注。其中,简单复合物是一种重要的数学工具,可用于描述高阶相互作用。然而,以往关于简单复数的研究主要集中在合成数据上。在本文中,我们提出了一种基于多变量相位同步的方法,利用癫痫患者记录的多通道立体脑电图(SEEG)数据构建简单复合物。此外,我们还研究了该方法描述高阶大脑网络的全局和局部特征的能力。具体来说,我们首先引入霍奇拉普拉斯来描述高阶相互作用的特征,并利用欧拉特征数来确定网络同步性,这是一个重要的全局特征。然后,我们定义了一种改进的基于引力的中心性方法,以简约复数识别高阶网络中的重要节点。此外,我们还采用了基于不同节点间高阶距离的网络效率来评估该方法在区分重要节点方面的有效性。我们特别发现海马回和镰状回可能会促进癫痫脑网络的同步化。总之,我们认为我们的方法为研究具有高阶交互作用的大脑网络铺平了道路,有助于识别癫痫网络中的枢纽,并在癫痫治疗中具有潜在的应用价值。
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Evaluation of human epileptic brain networks by constructing simplicial complexes
As a powerful framework, higher-order networks have gained significant attention to model the non-pairwise interactions of complex systems. Particularly, simplicial complex is an important mathematical tool which can be used to depict higher-order interactions. However, previous works on simplicial complexes have mainly focused on synthetic data. In this paper, we propose a method based on multivariate phase synchronization to construct simplicial complexes using multichannel stereo-electroencephalography (SEEG) data recorded from epilepsy patients. Furthermore, we examine its ability to describe both global and local characteristics of the higher-order brain network. Specifically, we first introduce the Hodge Laplacian to characterize higher-order interactions and employ the Euler characteristic number to determine the network synchronizability which is a significant global characteristic. Afterwards, we define an improved gravity-based centrality method to identify vital nodes in the higher-order network with simplicial complexes. Additionally, network efficiency based on the higher-order distance between different nodes is adopted to evaluate the effectiveness of this method in distinguishing the important nodes. In particular, we find that the Hippocampus and Fusiform gyrus may promote the synchronization of the epileptic brain network. All in all, we believe that our method paves the way to investigate brain networks with higher-order interactions, which contributes to identifying hubs in the epileptic network and has potential applications in epileptic treatment.
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来源期刊
Chaos Solitons & Fractals
Chaos Solitons & Fractals 物理-数学跨学科应用
CiteScore
13.20
自引率
10.30%
发文量
1087
审稿时长
9 months
期刊介绍: Chaos, Solitons & Fractals strives to establish itself as a premier journal in the interdisciplinary realm of Nonlinear Science, Non-equilibrium, and Complex Phenomena. It welcomes submissions covering a broad spectrum of topics within this field, including dynamics, non-equilibrium processes in physics, chemistry, and geophysics, complex matter and networks, mathematical models, computational biology, applications to quantum and mesoscopic phenomena, fluctuations and random processes, self-organization, and social phenomena.
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