Deconvolving Passive Diffusion on the Structural Network from Functional Brain Signals

It is commonly understood that brain regions perform re-gionally specific computations that are then transmitted glob-ally through the whole-brain white matter network. However, the success of network diffusion models for predicting the brain's functional connectivity suggests that a significant portion of recorded brain signal is attributable to passive diffusion through the structural network. We can therefore inter-pret the global signal as a convolution of an innovation sig-nal from novel regional computations with a passive signal merely flowing through the network. Since the innovation signal contains the information of interest, there is a need to deconvolve the innovation signal from the passive signal in functional brain recordings. Here, we estimate the innovation signal in functional MRI by using the Network Diffusion Model (NDM) to measure the amount of global signal dif-fusion in data from 64 Human Connectome Project (HCP) subjects, then invert the NDM to perform a Network Diffusion Deconvolution (NDD). We show that the estimated in-novation signal has different BOLD power gradients, forms a more segregated functional network, reorganizes resting -state networks, and constrains the signal in a motor task to the expected motor regions. Overall, NDD highlights a promising new approach to study fMRI and connectivity.