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Bayesian Inference of Task-Based Functional Brain Connectivity Using Markov Chain Monte Carlo Methods
The study of functional networks in the brain is essential in order to gain a better insight into its diverse set of operations and to characterise the associated normal and abnormal behaviours. Present methods of analysing fMRI data to obtain functional connectivity are largely limited to approaches such as correlation, regression and independent component analysis, which give simple point estimates. By contrast, we propose a stochastic linear model in a Bayesian setting and employ Markov Chain Monte Carlo methods to approximate posterior distributions of full connectivity and covariance matrices. Through the use of a Bayesian probabilistic framework, distributional estimates of the linkage strengths are obtained as opposed to point estimates, and the uncertainty of the existence of such links is accounted for. We decompose the connectivity matrix as the Hadamard product of binary indicators and real-valued variables, and formulate an efficient joint-sampling scheme to infer them. The well-characterised somato-motor network is examined in a self-paced, right-handed finger opposition task based experiment, while nodes from the visual network are used for contrast during the same experiment. Unlike for the visual network, significant changes in connectivity are found in the motor network during the task. Our work provides a distributional metric for functional connectivity along with causality information, and contributes to the collection of network level descriptors of brain functions.Engineering and Physical Sciences Research Council Grant ID: EP/K020153/1; Yousef Jameel Scholarship Programm
Nonparametric Modeling of Dynamic Functional Connectivity in fMRI Data
Dynamic functional connectivity (FC) has in recent years become a topic of
interest in the neuroimaging community. Several models and methods exist for
both functional magnetic resonance imaging (fMRI) and electroencephalography
(EEG), and the results point towards the conclusion that FC exhibits dynamic
changes. The existing approaches modeling dynamic connectivity have primarily
been based on time-windowing the data and k-means clustering. We propose a
non-parametric generative model for dynamic FC in fMRI that does not rely on
specifying window lengths and number of dynamic states. Rooted in Bayesian
statistical modeling we use the predictive likelihood to investigate if the
model can discriminate between a motor task and rest both within and across
subjects. We further investigate what drives dynamic states using the model on
the entire data collated across subjects and task/rest. We find that the number
of states extracted are driven by subject variability and preprocessing
differences while the individual states are almost purely defined by either
task or rest. This questions how we in general interpret dynamic FC and points
to the need for more research on what drives dynamic FC.Comment: 8 pages, 1 figure. Presented at the Machine Learning and
Interpretation in Neuroimaging Workshop (MLINI-2015), 2015 (arXiv:1605.04435
Inverse Modeling for MEG/EEG data
We provide an overview of the state-of-the-art for mathematical methods that
are used to reconstruct brain activity from neurophysiological data. After a
brief introduction on the mathematics of the forward problem, we discuss
standard and recently proposed regularization methods, as well as Monte Carlo
techniques for Bayesian inference. We classify the inverse methods based on the
underlying source model, and discuss advantages and disadvantages. Finally we
describe an application to the pre-surgical evaluation of epileptic patients.Comment: 15 pages, 1 figur
Doctor of Philosophy
dissertationFunctional 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
Network Inference from Co-Occurrences
The recovery of network structure from experimental data is a basic and
fundamental problem. Unfortunately, experimental data often do not directly
reveal structure due to inherent limitations such as imprecision in timing or
other observation mechanisms. We consider the problem of inferring network
structure in the form of a directed graph from co-occurrence observations. Each
observation arises from a transmission made over the network and indicates
which vertices carry the transmission without explicitly conveying their order
in the path. Without order information, there are an exponential number of
feasible graphs which agree with the observed data equally well. Yet, the basic
physical principles underlying most networks strongly suggest that all feasible
graphs are not equally likely. In particular, vertices that co-occur in many
observations are probably closely connected. Previous approaches to this
problem are based on ad hoc heuristics. We model the experimental observations
as independent realizations of a random walk on the underlying graph, subjected
to a random permutation which accounts for the lack of order information.
Treating the permutations as missing data, we derive an exact
expectation-maximization (EM) algorithm for estimating the random walk
parameters. For long transmission paths the exact E-step may be computationally
intractable, so we also describe an efficient Monte Carlo EM (MCEM) algorithm
and derive conditions which ensure convergence of the MCEM algorithm with high
probability. Simulations and experiments with Internet measurements demonstrate
the promise of this approach.Comment: Submitted to IEEE Transactions on Information Theory. An extended
version is available as University of Wisconsin Technical Report ECE-06-
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