Stochastic Techniques for Modelling Brain Connectivity in Neuroimaging

A fundamental question in neuroscience is how different brain areas communicate with each other. Dynamic causal modelling (DCM) is a generic formalism to study effective brain connectivity based on neuroimaging data, particularly functional magnetic resonance imaging (fMRI). The interactions between neuronal activity at different brain areas areas are modelled as a first-order differential equation which also incorporates a generative model of how the neuronal activity is transformed into the measured haemodynamic fMRI response the haemodynamic response function (HRF). The problem of discriminating between different structures of connectivity can be solved by state-of-the-art Bayesian methods, whereby parameter estimation is followed by model selection. These methods are computationally expensive and may converge to parameter values that are valid only for a particular dataset. In this thesis, the well-known multiple-model kalman filter (MMKF) is applied in a number of different ways to perform model selection in an efficient manner, upon simulated data from models with different connectivity structures. The problem of estimating the haemodynamic response function (HRF) is first addressed and the methodology is then extended to the full problem of estimating the DCM. The results show that the MMKF seems to be very accurate at choosing the correct connectivity structure between two parametrized models, even taking into account the output non-linearity (the HRF). In conclusion, this work provides the first demonstration of the applicability of MMKF approaches to the problem of estimating effective brain connectivity based on DCM for fMRI.