A parcellation scheme based on von Mises-Fisher distributions and Markov random fields for segmenting brain regions using resting-state fMRI

Understanding the organization of the human brain requires identification of its functional subdivisions. Clustering schemes based on resting-state functional magnetic resonance imaging (fMRI) data are rapidly emerging as non-invasive alternatives to cytoarchitectonic mapping in postmortem brains. Here, we propose a novel spatio-temporal probabilistic parcellation scheme that overcomes major weaknesses of existing approaches by (i) modeling the fMRI time series of a voxel as a von Mises-Fisher distribution, which is widely used for clustering high dimensional data; (ii) modeling the latent cluster labels as a Markov random field, which provides spatial regularization on the cluster labels by penalizing neighboring voxels having different cluster labels; and (iii) introducing a prior on the number of labels, which helps in uncovering the number of clusters automatically from the data. Cluster labels and model parameters are estimated by an iterative expectation maximization procedure wherein, given the data and current estimates of model parameters, the latent cluster labels, are computed using α-expansion, a state of the art graph cut, method. In turn, given the current estimates of cluster labels, model parameters are estimated by maximizing the pseudo log-likelihood. The performance of the proposed method is validated using extensive computer simulations. Using novel stability analysis we examine the sensitivity of our methods to parameter initialization and demonstrate that the method is robust to a wide range of initial parameter values. We demonstrate the application of our methods by parcellating spatially contiguous as well as non-contiguous brain regions at both the individual participant and group levels. Notably, our analyses yield new data on the posterior boundaries of the supplementary motor area and provide new insights into functional organization of the insular cortex. Taken together, our findings suggest that our method is a powerful tool for investigating functional subdivisions in the human brain.