Directed Network Recovery from Large Systems with Applications in Functional Magnetic Resonance Imaging (fMRI)

Adora DSouza

Supervised by Professor Axel Wismuller

Goergen Hall, Room 108

Existence of networks are ubiquitous in natural as well as man made systems. Identifying the underlying network structure of components of a complex system, especially from simultaneously observed signals, is an actively growing area of research. One of the biggest challenges encountered with network modeling from time-series data is that we rarely know the underlying network structure governing interactions amongst the signals. Thus, the task to be accomplished for such problems is that the network modeling technique should be well-equipped to characterize different types of interactions. Interactions (i) may be casual in nature, (ii) may have nonlinear dependencies,(iii) may take place with different components interacting directly or indirectly with others (iv) may be part of a large or small system. Hence, network modeling approaches should be formulated keeping these different characteristics of interaction in mind. To this end, this work presents three approaches that can detect causal relationships, in systems regardless of size. These approaches are first tested and validated on various simulations with a known underlying network structure of inter- actions. Subsequently, they are evaluated on real brain activity data recorded using functional magnetic resonance imaging (fMRI).

Studies on how the brain is connected and how different regions communicate is a growing and evolving field, as improvements in fMRI technology call for improved analysis techniques. One of the three investigated approaches that is nonlinear uses local models to extract the underlying network structure from fMRI data for both simulated and real data. Such an approach uses state space reconstruction to estimate causality. We also develop two extensions to Granger causality analysis that can determine network graphs for large systems. These approaches are not susceptible to falsely capturing indirect connections since they are multivariate. We first develop a linear multivariate Granger causality analysis approach called large-scale Granger causality (lsGC). Subsequently, we develop large-scale nonlinear Granger causality (lsNGC), which is an extension of lsGC as it accounts for nonlinear dependencies.

Methods currently adopted in fMRI literature are either too simplistic and unable to capture the various types of interactions or are too complex and cannot be ex- tended to large systems. With the aforementioned approaches, we demonstrate that the three investigated network modeling techniques can characterize complex inter- actions without being severely impacted by network size and limited observations. These methods can potentially replace traditional correlation-based approaches used to estimate the network structure in fMRI. Additionally, they can also be used to aid model-driven approaches that require a pre-specified network structure. Furthermore, the promising results on experimental fMRI data suggest that these approaches may aid in identifying imaging-derived biomarkers that can assist clinicians in monitoring disease progression and response to therapeutic intervention for patients with a wide range of neurological and psychiatric disorders.