  Human brain function dynamically adjusts to ever-changing stimuli from the
external environment. Studies characterizing brain functional reconfiguration
are nevertheless scarce. Here we present a principled mathematical framework to
quantify brain functional reconfiguration when engaging and disengaging from a
stop signal task (SST). We apply tangent space projection (a Riemannian
geometry mapping technique) to transform functional connectomes (FCs) and
quantify functional reconfiguration using the correlation distance of the
resulting tangent-FCs. Our goal was to compare functional reconfigurations in
individuals at risk for alcohol use disorder (AUD). We hypothesized that
functional reconfigurations when transitioning in/from a task would be
influenced by family history of alcohol use disorder (FHA) and other AUD risk
factors. Multilinear regression model results showed that engaging and
disengaging functional reconfiguration were driven by different AUD risk
factors. Functional reconfiguration when engaging in the SST was negatively
associated with recent drinking. When disengaging from the SST, however,
functional reconfiguration was negatively associated with FHA. In both models,
several other factors contributed to the explanation of functional
reconfiguration. This study demonstrates that tangent-FCs can characterize
task-induced functional reconfiguration, and that it is related to AUD risk.
