Brain functional connectivity (FC), the temporal synchrony between brain networks, is essential to understand the functional organization in the brain and to identify changes due to neurological disorders, development, treatment, and other phenomena. Independent component analysis (ICA) is a matrix decomposition method used extensively for simultaneous estimation of functional brain topography and connectivity. However, estimation of FC via ICA is often sub-optimal due to the use of ad-hoc estimation methods or temporal dimension reduction prior to ICA. Bayesian ICA methods can avoid dimension reduction, produce more accurate estimates of latent variables and model parameters, and facilitate inference via posterior distributions. In this paper, we develop a novel, computationally feasible Bayesian ICA method with population-derived priors on both the spatial ICs and their temporal correlation. For the latter we consider two priors: the inverse-Wishart, which is designed for covariance matrices and has limitations for modeling correlation matrices; and a novel informative prior for correlation matrices. For both choices of prior, we derive a variational Bayes algorithm to estimate the model variables and obtain posterior variances or distributions of quantities of interest. Through extensive realistic simulation studies, we evaluate the performance of the proposed methods and compare them with existing approaches. Finally, we analyze fMRI data from over 400 healthy adults in the Human Connectome Project. We find that our Bayesian ICA algorithms produce highly accurate measures of functional connectivity and spatial brain features. Our informative prior for correlation matrices outperforms the inverse-Wishart, but comes with a higher computational burden. The proposed framework is applicable to single-subject analysis, making it potentially clinically viable.

翻译：脑功能连接（FC）作为脑网络间的时间同步性，对于理解大脑功能组织以及识别由神经系统疾病、发育过程、治疗干预及其他现象引起的变化至关重要。独立成分分析（ICA）作为一种矩阵分解方法，被广泛用于同时估计脑功能拓扑结构与连接性。然而，由于采用临时性估计方法或在ICA前进行时间维度降维，通过ICA估计FC往往难以达到最优。贝叶斯ICA方法能够避免维度降维，更精确地估计潜变量和模型参数，并通过后验分布促进统计推断。本文提出了一种计算可行的新型贝叶斯ICA方法，该方法在空间独立成分及其时间相关性上均采用基于群体信息的先验分布。针对时间相关性，我们考虑两种先验：适用于协方差矩阵但对相关矩阵建模存在局限性的逆Wishart分布，以及一种针对相关矩阵的新型信息先验分布。针对两种先验选择，我们推导了变分贝叶斯算法以估计模型变量，并获得关注量的后验方差或分布。通过大量真实场景的模拟研究，我们评估了所提方法的性能并与现有方法进行比较。最后，我们分析了人类连接组计划中400多名健康成人的功能磁共振成像数据。研究发现，我们的贝叶斯ICA算法能够产生高精度的功能连接度量与脑空间特征。针对相关矩阵的信息先验在性能上优于逆Wishart先验，但需要更高的计算成本。所提出的框架适用于单被试分析，使其具备临床应用的潜在可行性。