Higher-order functional connectivity analysis of resting-state functional magnetic resonance imaging data using multivariate cumulants

Blood-level oxygenation-dependent (BOLD) functional magnetic resonance imaging (fMRI) is the most common modality to study functional connectivity in the human brain. Most research to date has focused on connectivity between pairs of brain regions. However, attention has recently turned towards connectivity involving more than two regions, that is, higher-order connectivity. It is not yet clear how higher-order connectivity can best be quantified. The measures that are currently in use cannot distinguish between pairwise (i.e., second-order) and higher-order connectivity. We show that genuine higher-order connectivity can be quantified by using multivariate cumulants. We explore the use of multivariate cumulants for quantifying higher-order connectivity and the performance of block bootstrapping for statistical inference. In particular, we formulate a generative model for fMRI signals exhibiting higher-order connectivity and use it to assess bias, standard errors, and detection probabilities. Application to resting-state fMRI data from the Human Connectome Project demonstrates that spontaneous fMRI signals are organized into higher-order networks that are distinct from second-order resting-state networks. Application to a clinical cohort of patients with multiple sclerosis further demonstrates that cumulants can be used to classify disease groups and explain behavioral variability. Hence, we present a novel framework to reliably estimate genuine higher-order connectivity in fMRI data which can be used for constructing hyperedges, and finally, which can readily be applied to fMRI data from populations with neuropsychiatric disease or cognitive neuroscientific experiments.