Infinite von Mises-Fisher Mixture Modeling of Whole Brain fMRI Data

Cluster analysis of functional magnetic resonance imaging (fMRI) data is often performed using gaussian mixture models, but when the time series are standardized such that the data reside on a hypersphere, this modeling assumption is questionable. The consequences of ignoring the underlying spherical manifold are rarely analyzed, in part due to the computational challenges imposed by directional statistics. In this letter, we discuss a Bayesian von Mises–Fisher (vMF) mixture model for data on the unit hypersphere and present an efficient inference procedure based on collapsed Markov chain Monte Carlo sampling. Comparing the vMF and gaussian mixture models on synthetic data, we demonstrate that the vMF model has a slight advantage inferring the true underlying clustering when compared to gaussian-based models on data generated from both a mixture of vMFs and a mixture of gaussians subsequently normalized. Thus, when performing model selection, the two models are not in agreement. Analyzing multisubject whole brain resting-state fMRI data from healthy adult subjects, we find that the vMF mixture model is considerably more reliable than the gaussian mixture model when comparing solutions across models trained on different groups of subjects, and again we find that the two models disagree on the optimal number of components. The analysis indicates that the fMRI data support more than a thousand clusters, and we confirm this is not a result of overfitting by demonstrating better prediction on data from held-out subjects. Our results highlight the utility of using directional statistics to model standardized fMRI data and demonstrate that whole brain segmentation of fMRI data requires a very large number of functional units in order to adequately account for the discernible statistical patterns in the data. </jats:p

Inferring individual-level variations in the functional parcellation of the cerebral cortex

Objective: Functional parcellation of the cerebral cortex is variable across different subjects or between cognitive states. Ignoring individual - or state - dependent variations in the functional parcellation may lead to inaccurate representations of individual functional connectivity, limiting the precision of interpretations of differences in individual connectivity profiles. However, it is difficult to infer the individual-level variations due to the relatively low robustness of methods for parcellation of individual subjects. Methods: We propose a method called “joint K-means” to robustly parcellate the cerebral cortex using fMRI data for contrasts between two states or subjects that intended to characterize variance in individual functional parcellations. The key idea of the proposed method is to jointly infer parcellations in contrasted datasets by iterative descent, while constraining the similarity of the two pathways in searches for local minima to reduce spurious variations. Results: Parcellations of resting-state fMRI datasets from the Human Connectome Project show that the similarity of parcellations for an individual subject studied on two sessions is greater than that between different subjects. Differences in parcellations between subjects are non-uniformly distributed across the cerebral cortex, with clusters of higher variance in the prefrontal, lateral temporal and occipito-parietal cortices. This pattern is reproducible across sessions, between groups and using different numbers of parcels. Conclusion: The individual-level variations inferred by the proposed method are plausible and consistent with the previously reported functional connectivity variability. Significance: The proposed method is a promising tool for investigating relationships between the cerebral functional organization and behavioral differences

Improving Reliability of Subject-Level Resting-State fMRI Parcellation with Shrinkage Estimators

A recent interest in resting state functional magnetic resonance imaging (rsfMRI) lies in subdividing the human brain into anatomically and functionally distinct regions of interest. For example, brain parcellation is often used for defining the network nodes in connectivity studies. While inference has traditionally been performed on group-level data, there is a growing interest in parcellating single subject data. However, this is difficult due to the low signal-to-noise ratio of rsfMRI data, combined with typically short scan lengths. A large number of brain parcellation approaches employ clustering, which begins with a measure of similarity or distance between voxels. The goal of this work is to improve the reproducibility of single-subject parcellation using shrinkage estimators of such measures, allowing the noisy subject-specific estimator to "borrow strength" in a principled manner from a larger population of subjects. We present several empirical Bayes shrinkage estimators and outline methods for shrinkage when multiple scans are not available for each subject. We perform shrinkage on raw intervoxel correlation estimates and use both raw and shrinkage estimates to produce parcellations by performing clustering on the voxels. Our proposed method is agnostic to the choice of clustering method and can be used as a pre-processing step for any clustering algorithm. Using two datasets---a simulated dataset where the true parcellation is known and is subject-specific and a test-retest dataset consisting of two 7-minute rsfMRI scans from 20 subjects---we show that parcellations produced from shrinkage correlation estimates have higher reliability and validity than those produced from raw estimates. Application to test-retest data shows that using shrinkage estimators increases the reproducibility of subject-specific parcellations of the motor cortex by up to 30%.Comment: body 21 pages, 11 figure