| Description |
Functional magnetic resonance imaging (fMRI) measures the change of oxygen consumption level in the blood vessels of the human brain, hence indirectly detecting the neuronal activity. Resting-state fMRI (rs-fMRI) is used to identify the intrinsic functional patterns of the brain when there is no external stimulus. Accurate estimation of intrinsic activity is important for understanding the functional organization and dynamics of the brain, as well as differences in the functional networks of patients with mental disorders. This dissertation aims to robustly estimate the functional connectivities and networks of the human brain using rs-fMRI data of multiple subjects. We use Markov random field (MRF), an undirected graphical model to represent the statistical dependency among the functional network variables. Graphical models describe multivariate probability distributions that can be factorized and represented by a graph. By defining the nodes and the edges along with their weights according to our assumptions, we build soft constraints into the graph structure as prior information. We explore various approximate optimization methods including variational Bayesian, graph cuts, and Markov chain Monte Carlo sampling (MCMC). We develop the random field models to solve three related problems. In the first problem, the goal is to detect the pairwise connectivity between gray matter voxels in a rs-fMRI dataset of the single subject. We define a six-dimensional graph to represent our prior information that two voxels are more likely to be connected if their spatial neighbors are connected. The posterior mean of the connectivity variables are estimated by variational inference, also known as mean field theory in statistical physics. The proposed method proves to outperform the standard spatial smoothing and is able to detect finer patterns of brain activity. Our second work aims to identify multiple functional systems. We define a Potts model, a special case of MRF, on the network label variables, and define von Mises-Fisher distribution on the normalized fMRI signal. The inference is significantly more difficult than the binary classification in the previous problem. We use MCMC to draw samples from the posterior distribution of network labels. In the third application, we extend the graphical model to the multiple subject scenario. By building a graph including the network labels of both a group map and the subject label maps, we define a hierarchical model that has richer structure than the flat single-subject model, and captures the shared patterns as well as the variation among the subjects. All three solutions are data-driven Bayesian methods, which estimate model parameters from the data. The experiments show that by the regularization of MRF, the functional network maps we estimate are more accurate and more consistent across multiple sessions. |
