Solving large-scale MEG/EEG source localisation and functional connectivity problems simultaneously using state-space models

State-space models are widely employed across various research disciplines to study unobserved dynamics. Conventional estimation techniques, such as Kalman filtering and expectation maximisation, offer valuable insights but incur high computational costs in large-scale analyses. Sparse inverse covariance estimators can mitigate these costs, but at the expense of a trade-off between enforced sparsity and increased estimation bias, necessitating careful assessment in low signal-to-noise ratio (SNR) situations. To address these challenges, we propose a three-fold solution: (1) Introducing multiple penalised state-space (MPSS) models that leverage data-driven regularisation; (2) Developing novel algorithms derived from backpropagation, gradient descent, and alternating least squares to solve MPSS models; (3) Presenting a K-fold cross-validation extension for evaluating regularisation parameters. We validate this MPSS regularisation framework through lower and more complex simulations under varying SNR conditions, including a large-scale synthetic magneto- and electro-encephalography (MEG/EEG) data analysis. In addition, we apply MPSS models to concurrently solve brain source localisation and functional connectivity problems for real event-related MEG/EEG data, encompassing thousands of sources on the cortical surface. The proposed methodology overcomes the limitations of existing approaches, such as constraints to small-scale and region-of-interest analyses. Thus, it may enable a more accurate and detailed exploration of cognitive brain functions

The development and application of structural priors for diffuse optical imaging in infants from newborn to two years of age

This thesis describes the development and application of age-appropriate structural priors to improve the localisation accuracy of diffuse optical tomography (DOT) approaches in infants aged from birth to two years of age. Knowledge of the target cranial anatomy, known as a structural prior, is required to produce three-dimensional images localising concentration changes to the cortex. A structural prior would ideally be subject-specific, i.e. derived from structural magnetic resonance imaging (MRI) data from each specific subject. Requiring a structural scan from every infant participant, however, is not feasible and undermines many of the benefits of DOT. A review was conducted to catalogue available infant structural MRI data, and selected data was then used to produce structural priors for infants aged 1- to 24-months. Conventional analyses using functional near-infrared spectroscopy (fNIRS) implicitly assume that head size and array position are constant across infants. Using DOT, the validity of assuming these parameters constant in a longitudinal infant cohort was investigated. The results show that this assumption is reasonable at the group-level in infants aged 5- to 12-months but becomes less valid for smaller group sizes. A DOT approach was determined to illicit more subtle effects of activation, particularly for smaller group sizes and expected responses. Using state-of-the-art MRI data from the Developing Human Connectome Project, a database of structural priors of the neonatal head was produced for infants aged pre-term to term-equivalent age. A leave-one-out approach was used to determine how best to find a match between a given infant and a model from the database, and how best to spatially register the model to minimise the anatomical and localisation errors relative to subject-specific anatomy. Model selection based on the 10/20 scalp positions was determined to be the best method (of those based on external features of the head) to minimise these errors