We present a unified statistical framework for characterizing community
structure of brain functional networks that captures variation across
individuals and evolution over time. Existing methods for community detection
focus only on single-subject analysis of dynamic networks; while recent
extensions to multiple-subjects analysis are limited to static networks. To
overcome these limitations, we propose a multi-subject, Markov-switching
stochastic block model (MSS-SBM) to identify state-related changes in brain
community organization over a group of individuals. We first formulate a
multilayer extension of SBM to describe the time-dependent, multi-subject brain
networks. We develop a novel procedure for fitting the multilayer SBM that
builds on multislice modularity maximization which can uncover a common
community partition of all layers (subjects) simultaneously. By augmenting with
a dynamic Markov switching process, our proposed method is able to capture a
set of distinct, recurring temporal states with respect to inter-community
interactions over subjects and the change points between them. Simulation shows
accurate community recovery and tracking of dynamic community regimes over
multilayer networks by the MSS-SBM. Application to task fMRI reveals meaningful
non-assortative brain community motifs, e.g., core-periphery structure at the
group level, that are associated with language comprehension and motor
functions suggesting their putative role in complex information integration.
Our approach detected dynamic reconfiguration of modular connectivity elicited
by varying task demands and identified unique profiles of intra and
inter-community connectivity across different task conditions. The proposed
multilayer network representation provides a principled way of detecting
synchronous, dynamic modularity in brain networks across subjects.

使用统一的统计框架，提出了 MSS-SBM 方法，可以跨个体并能捕捉时间上的演化，用于大量 multi-subject 的人脑功能网络的群体分析，应用于任务 fMRI 的分析中，探测了动态重构特征和不同任务条件下的 community connectivity 独特性。

跨个体检测功能性脑网络的动态社群结构：一种多层方法

Detecting Dynamic Community Structure in Functional Brain Networks  Across Individuals: A Multilayer Approach

In recent years, longitudinal neuroimaging study has become increasingly
popular in neuroscience research to investigate disease-related changes in
brain functions. In current neuroscience literature, one of the most commonly
used tools to extract and characterize brain functional networks is independent
component analysis (ICA). However, existing ICA methods are not suited for
modelling repeatedly measured imaging data. In this paper, we propose a novel
longitudinal independent component model (L-ICA) which provides a formal
modeling framework for extending ICA to longitudinal studies. By incorporating
subject-specific random effects and visit-specific covariate effects, L-ICA is
able to provide more accurate estimates of changes in brain functional networks
on both the population- and individual-level, borrow information across
repeated scans within the same subject to increase statistical power in
detecting covariate effects on the networks, and allow for model-based
prediction for brain networks changes caused by disease progression, treatment
or neurodevelopment. We develop a fully traceable exact EM algorithm to obtain
maximum likelihood estimates of L-ICA. We further develop a subspace-based
approximate EM algorithm which greatly reduce the computation time while still
retaining high accuracy. Moreover, we present a statistical testing procedure
for examining covariate effects on brain network changes. Simulation results
demonstrate the advantages of our proposed methods. We apply L-ICA to ADNI2
study to investigate changes in brain functional networks in Alzheimer disease.
Results from the L-ICA provide biologically insightful findings which are not
revealed using existing methods.

本文提出了一种新的长期独立成分模型 (L-ICA)，可以更准确地估计个体和总体层面上脑功能网络的变化，并通过包含随机和访问特定的协变量效应来提高重复测量成像数据处理的统计功效。通过将 L-ICA 应用于 ADNI2 研究，提出了在失智症时脑功能网络变化的生物学见解。

一种用于纵向神经影像研究的分层独立成分分析模型

A hierarchical independent component analysis model for longitudinal  Neuroimaging studies

The idea that complex systems have a hierarchical modular organization
originates in the early 1960s and has recently attracted fresh support from
quantitative studies of large scale, real-life networks. Here we investigate
the hierarchical modular (or "modules-within-modules") decomposition of human
brain functional networks, measured using functional magnetic resonance imaging
(fMRI) in 18 healthy volunteers under no-task or resting conditions. We used a
customized template to extract networks with more than 1800 regional nodes, and
we applied a fast algorithm to identify nested modular structure at several
hierarchical levels. We used mutual information, 0 < I < 1, to estimate the
similarity of community structure of networks in different subjects, and to
identify the individual network that is most representative of the group.
Results show that human brain functional networks have a hierarchical modular
organization with a fair degree of similarity between subjects, I=0.63. The
largest 5 modules at the highest level of the hierarchy were medial occipital,
lateral occipital, central, parieto-frontal and fronto-temporal systems;
occipital modules demonstrated less sub-modular organization than modules
comprising regions of multimodal association cortex. Connector nodes and hubs,
with a key role in inter-modular connectivity, were also concentrated in
association cortical areas. We conclude that methods are available for
hierarchical modular decomposition of large numbers of high resolution brain
functional networks using computationally expedient algorithms. This could
enable future investigations of Simon's original hypothesis that hierarchy or
near-decomposability of physical symbol systems is a critical design feature
for their fast adaptivity to changing environmental conditions.

通过使用计算方法提出一种层次化模块分解大量高分辨率脑功能网络的方法，探讨人类大脑功能网络的层次化模块组织及模块内模块结构，揭示了模块间连接的关键作用，为研究大脑的适应性提供了基础。