HONeD-in on Brain Activity: Deconvolving Passive Diffusion on the Structural Network from Functional Brain Signals

Brain regions perform distinct computations, and their signals propagate through the whole-brain white matter network. Yet, mathematical models that describe this signal propagation via <i>purely passive diffusion</i> can predict a considerable amount of the observed functional connectivity between regions. This raises a critical question: if so much functional connectivity can be explained by a <i>passive</i> process, how can we isolate the <i>active</i> process? Here, we calculate in closed-form an estimate for such an active signal in functional MRI by spatially deconvolving the effect of passive signal spread over the brain's structural connectivity using a higher-order network diffusion (HONeD) model. Across 770 Human Connectome Project subjects, we show that the resulting HONeD-innovation (HONeD-in) signal 1) sparsifies functional connectivity while retaining a well-connected network, 2) remodels resting-state networks (RSNs), 3) mixes the unimodal-multimodal hierarchical organization of RSNs into a circle with no clear hierarchy, and 4) deblurs task-activation maps. Together, our results highlight HONeD deconvolution as a generalizable new way to study resting-state and task fMRI brain signals.