Modelling effective brain connectivity using manifolds in optical functional neuroimaging

The development of analytical approaches for decoding brain’s effective connectivity from neuroimages remains open to improvement as existing model assumptions depart from physiological processes. Manifold based topological approaches are surprisingly underexplored considering the powerful mathematical abstraction they represent. This research hypothesizes that the brain function abides to the topological abstraction of a manifold, and thus the subsequent interactions among brain regions underpinning functional and effective connectivity can be expressed either as locations within the manifold or as trips along the manifold surface. In seeking to confirm this hypothesis, the aim is to develop a model of brain effective connectivity capitalizing on topological modelling of neurophysiological processes so that the connectivity network can retrieved from experimental neuroimaging data. As the physics of the image formation shall determine the topological characteristics of the dataset, the modelling will have to consider such modality-specific demands; in the case at hand, those of functional near infrared spectroscopy (fNIRS). To realize this goal, first the topological properties (continuity, differentiality and existence of a suitable metric) of the data will be characterized and the needs to represent the segregational response attended. It will be shown how the ambient Euclidean distance is insufficient for these purposes. Later, the integrational information will be univocally integrated within the direction of the flow of information first along a Riemann manifold by means of imposing a metric inspired on causal principles. Finally the inherent causal structure of certain manifolds such as the Lorentzian, will be harness to afford a computationally efficient modelling solution. Verification against synthetic scenarios and posterior validation against gold standard Dynamic Causal Modeling (DCM) over experimental observation will be carried out for the two modelling proposals. One important contribution in computational neuroscience of this thesis shall be the establishment of the foundations for topological modelling of brain function; an approach which has been hinted in literature but it is thus far lacking robust foundational mathematical support . Also, two major manifold-based modelling approaches i.e. Riemmanian and Lorentzian, will be explored. Finally, additional definition and establishment of topological constraints to be demanded to the resulting manifolds will be characterized so to ensure compliance with neurophysiological conditions and the exploitation of existing, or imposition of causal structure of manifolds to encode brain’s effective connectivity. Successful completion of this research will provide new computational insights about topological modelling that should in principle be transferable to other domains, and it will further offer a new highly expressive causal modelling approach for one of the most important phenomenon to understand brain behaviour, effective connectivity.