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Journal of Neuroscience Methods
Volume 362, 2021, 109317

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

Simone Cauzzoa, Alejandro L. Callarab, Maria Sole Morellia,f, Valentina Hartwigd,f, Fabrizio Espositoe, Domenico Montanarof, Claudio Passinoa, Michele Emdina, Alberto Giannonia,f, Nicola Vanelloc

Institute of Life Sciences, Sant’Anna School of Advanced Studies, Pisa, Italy.



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.


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.


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.

Keywords: Functional MRI, Physiological noise, Central respiratory network, RETROICOR, Voluntary breath hold.

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