Critique of linear connectivity methods in functional magnetic resonance imaging

Functional magnetic resonance imaging (fMRI) garners insight into brain functionality using a non-invasive imaging technique that capitalises on the coupling between neuronal activity and blood oxygen concentration. FMRI connectivity utilises fMRI data to ascertain how spatially remote neuronal regions cooperate to provide functionality in response to a task or when the subject is at ‘rest’. Connectivity methods have traditionally been categorised into data-driven and modeldriven methods, also termed functional and effective connectivity, respectively. Datadriven methods conventionally extract whole-brain connectivity maps using contemporaneous correlation-based dependence measures, while model-driven methods examine hypothesised networks founded on a parametric model of regional relationships that typically incorporate contemporaneous and directed influence. Traditionally the data-driven/model-driven dichotomy has been considered incontrovertible and the two classes regarded as mutually exclusive. However, indistinct categorisation of several methods has prompted a discernable shift in this perception, with recent recognition that the demarkation between modalities is not entirely clear, motivating proposals of a continuous scale from data-driven to model-driven. This thesis scrutinises the validity of the data-driven/model-driven dichotomy by clarifying methodological dependencies between linear techniques drawn from both modalities. In particular, Granger causality measures, which model instantaneous and directed influence, are demonstrated to be remappings of correlation-based metrics. This result highlights the centrality of partial correlation and partial variance in linear connectivity analyses and bridges the gap between data-driven and model-driven connectivity techniques. Consequently, assignment of a linear Gaussian connectivity method into the data-driven/model-driven dichotomy is ultimately a function of node selection and model configuration, rather than a distinction derived from methodological difference. Linear Gaussian connectivity methods introduce data assumptions, conformance to which is necessary to guarantee integrity of results. A problematic assumption for fMRI is that of sample independence, which requires an absence of autocorrelation in voxel timeseries. iii Temporal filtering, employed to address the high noise content of fMRI data, exacerbates the problem by filtering out components of the frequency spectra, necessarily introducing autocorrelation. In this thesis, temporal filtering is shown to induce artificial connectivity by reducing the effective degrees of freedom contributing to a sample correlation estimate. An analytic derivation for the distribution of sample correlation as a function of the complex filter frequency response is detailed, and a correction proposed to re-establish valid statistical inference testing of correlation estimates. The utility of the correction for mitigating artificial correlation is demonstrated both analytically and empirically. Linear Gaussian models assume stationarity of timeseries, requiring the mean and variance to remain constant with time. FMRI data is known to contain non-stationary processes, typically modelled as time-varying noise variance. In this thesis, a model for non-stationary signal power is introduced to address variability in power across slice acquisition. The distribution of voxel intensity in the presence of non-stationary variance is analytically derived to be a generalised Student’s-t distribution. Additionally, the impact of non-stationary signal power on correlation is deduced and the expected value of sample correlation shown to differ to the true correlation from which the signals were generated. A correction is proposed to restore signal stationarity and rectify the change in the expected value of sample correlation.