@MASTERSTHESIS\{IMM2015-06988,
    author       = "S. F. V. Nielsen",
    title        = "Modelling Dynamic Functional Brain Connectivity",
    year         = "2015",
    school       = "Technical University of Denmark, Department of Applied Mathematics and Computer Science",
    address      = "Richard Petersens Plads, Building 324, {DK-}2800 Kgs. Lyngby, Denmark, compute@compute.dtu.dk",
    type         = "",
    note         = "Supervisors: Morten M{\o}rup, {DTU} Compute. Mikkel N. Schmidt, {DTU} Compute. Rasmus R{\o}ge, {DTU} Compute. Kristoffer H. Madsen, Danish Research Centre for Magnetic Resonance",
    url          = "http://www.compute.dtu.dk/English.aspx",
    abstract     = "Functional brain connectivity, the statistical dependence between activity in segregated brain regions, has been studied extensively over the last two decades. Most models that describe functional connectivity have parameters in the model that do not change over time, implicitly assuming that functional connectivity is temporally static. Recent research shows that a wealth of information can be gained by modeling functional connectivity in a dynamic setting, i.e. that the brain can be in different states throughout an experiment. 

We investigated two different non-parametric Bayesian models of dynamic functional connectivity, one simple model with relatively few parameters, and another more complex model with relatively many parameters. Both were based on the infinite hidden Markov model to model transitions between brain states. We investigated how model complexity can affect the number of states extracted from data, and how that affects our interpretation of dynamic functional connectivity. We first conducted several synthetic experiments, generating data from the two models considered and afterwards ran inference by Markov chain Monte Carlo on the same data. The aim of this was to study the behaviour of the models in a setting where there was a clear model mismatch. Furthermore, we investigated whether the models were able to characterize task and resting state functional magnetic resonance imaging (fMRI) data from the Danish Research Center for Magnetic Resonance (DRCMR) and from the Human Connectome Project (HCP). On synthetic data we showed that the simple model found many states on data generated from the complex model, but that the complex model was able to find the true number of states in data from the simple model. We found that the more complex model with only one state could characterize real-world data better than the simple model that found evidence for multiple states. The fact that the complex model only found one state in real-world data contradicts our intuition that multiple brain states should be present, but this could be explained by the dimensionality reduction carried out in this project. 

The results of this thesis indicate that one must always interpret dynamics in functional connectivity in terms of the model used and especially its limitations. We suspect that preprocessing and dimensionality reduction has a huge impact on the conclusions that can be drawn. This should be investigated further."
}