Is fMRI "noise" really noise? Resting state nuisance regressors remove variance with network structure

Noise correction is a critical step towards accurate mapping of resting state BOLD fMRI connectivity. Noise sources related to head motion or physiology are typically modelled by nuisance regressors, and a generalised linear model is applied to regress out the associated signal variance. In this study, we use independent component analysis (ICA) to characterise the data variance typically discarded in this pre-processing stage in a cohort of 12 healthy volunteers. The signal variance removed by 24, 12, 6, or only 3 head motion parameters demonstrated network structure typically associated with functional connectivity, and certain networks were discernable in the variance extracted by as few as 2 physiologic regressors. Simulated nuisance regressors, unrelated to the true data noise, also removed variance with network structure, indicating that any group of regressors that randomly sample variance may remove highly structured "signal" as well as "noise." Furthermore, to support this we demonstrate that random sampling of the original data variance continues to exhibit robust network structure, even when as few as 10% of the original volumes are considered. Finally, we examine the diminishing returns of increasing the number of nuisance regressors used in pre-processing, showing that excessive use of motion regressors may do little better than chance in removing variance within a functional network. It remains an open challenge to understand the balance between the benefits and confounds of noise correction using nuisance regressors.