Directed Dynamical Connectivity At Multiple Scales In Neuroimaging Datasets: Theory And Tools

The last decade has witnessed a continuous rise in studies of complex networks,which have now become an established paradigm to study complex systems, amongwhich the brain, with its balance between anatomical segregation and functionalintegration, is a most prominent example. Although initial efforts focused ondisentangling the intricate topological properties of complex networks, the interest hasnow shifted towards the study of dynamical processes at different temporal and spatialscales and the co-evolution of network structures with those processes.One of the big challenges to date is to understand the non-trivial topologicalorganization of the brain at the structural/anatomical and the functional level. Asidefrom structural connectivity, that typically corresponds to white matter tracts, severalmethods have been employed to infer connectivity in the brain. Functional connectivityis usually inferred on the basis of correlations among neural activity and defined asstatistical dependencies among remote neurophysiological events. Another importantfamily of methods aims to reveal directed information transfer between brain regions(effective connectivity). In recent years, many approaches have been proposed, amongwhich Granger Causality (GC) emerged as a powerful data driven method.My thesis work has been dedicated to the development, implementation andrigorous validation of approaches to make GC more solid and amenable to be applied toneuroimaging datasets in order to extract from them the maximum amount of reliableinformation on the directed information transfer among the variables. These approacheswere then extensively applied to data with the goal of answering specific questions andof providing a novel insight on brain function and malfunctioning.One of the main issues with GC is how to deal with the redundant and confoundinginformation arising in multivariate datasets. Addressing this issue was a constantconcern throughout all the project.In the first part, dynamical networks of moderate size (100~102nodes) werereconstructed by means of a canonical correlation approach to GC. This approach,capable to detect multivariate/groupwise/blockwise information interaction was appliedto simultaneously recorded scalp and depth electroencephalographic (EEG) data fromone epileptic patient during an interictal period (Chapter2). Then I extended the capability of canonical correlation to include the estimation ofnonlinear causal interaction using the kernel trick, which projects the data into a higherdimensional feature space and provides a convenient way for generalization of the linearcanonical correlation GC. After testing feasibility and effectiveness tested on simulateddata, the approach was applied to intracranial EEG data in epilepsy, resulting in animproved identification of the spatio-temporal causal connectivity network associated tothe disease (Chapter3).In the second part the issue of redundancy and curse of dimensionality wasaddressed for networks of medium size (102~103nodes). This is the typical size of theparcellation of the brain surface, so the natural target of this phase were datasets whosetime series corresponded to the blood-oxygenation level-dependent (BOLD) recorded infunctional magnetic resonance imaging (fMRI) and averaged across brain regions.These datasets are typically noisy and short. For networks of this size, standardconditional GC (CGC) is no longer effective. I applied a technique that identifies thevariables that share common information with each candidate driver to perform partiallyconditioned GC (PCGC). This approach was tested on simulated data and high densityEEG. Furthermore when evaluating dynamical directed interactions from BOLD timeseries, one is faced to another critical issue, namely the confounding effect ofhemodynamic response function (HRF). I addressed this problem by implementing anovel blind deconvolution technique for BOLD-fMRI signal (Chapter4). This jointapproach (deconvolution and PCGC) proved useful in retrieving dynamical interactionsin resting-state fMRI datasets. The results show that the distributions of conditioningvariable follow a stable spatial pattern, across different session and repetition time (TR,0.645s,1.4s and2.5s)(Chapter5).In the last part I addressed the reconstruction of large networks (from104nodesonwards). This is the typical number of voxels in a fMRI dataset. I developed anadditional strategy to reduce the number of conditioning variables in a faster and moreefficient way. With this approach it was possible to uncover the architecture of directednetworks at the voxel level and investigate its degree, betweenness and clusteringcoefficient hubs (Chapter6).