Mapping dependencies of BOLD signal change to end-tidal CO2: Linear and nonlinear modeling, and effect of physiological noise correction

Background: Disentangling physiological noise and signal of interest is a major issue when evaluating BOLD-signal changes in response to breath holding. Currently-adopted approaches for retrospective noise correction are general-purpose, and have non-negligible effects in studies on hypercapnic challenges. New method: We provide a novel approach to the analysis of specific and non-specific BOLD-signal changes related to end-tidal CO2 (PETCO2) in breath-hold fMRI studies. Multiple-order nonlinear predictors for PETCO2 model a region-dependent nonlinear input-output relationship hypothesized in literature and possibly playing a crucial role in disentangling noise. We explore Retrospective Image-based Correction (RETROICOR) effects on the estimated BOLD response, applying our analysis both with and without RETROICOR and analyzing the linear and non-linear correlation between PETCO2 and RETROICOR regressors. Results: The RETROICOR model of noise related to respiratory activity correlated with PETCO2 both linearly and non-linearly. The correction affected the shape of the estimated BOLD response to hypercapnia but allowed to discard spurious activity in ventricles and white matter. Activation clusters were best detected using non-linear components in the BOLD response model. Comparison with existing method: We evaluated the side-effects of standard physiological noise correction procedure, tailoring our analysis on challenging understudied brainstem and subcortical regions. Our novel approach allowed to characterize delays and non-linearities in BOLD response. Conclusions: RETROICOR successfully avoided false positives, still broadly affecting the estimated non-linear BOLD responses. Non-linearities in the model better explained CO2-related BOLD signal fluctuations. The necessity to modify the standard procedure for physiological-noise correction in breath-hold studies was addressed, stating its crucial importance.