Bayesian Modelling Approaches for Breath-Hold Induced Cerebrovascular Reactivity

Cerebrovascular reactivity (CVR) reflects the ability of blood vessels to dilate and constrict in response to a vasoactive stimulus and is an important indicator of cerebrovascular health. CVR can be mapped non-invasively with functional magnetic resonance imaging (fMRI) based on blood oxygen level-dependent (BOLD) contrast in combination with a breath-hold (BH) task. There are several ways to analyse this type of data and retrieve individual CVR amplitude and timing information. The most common approach involves employing a time-shifted general linear model with the measured end-tidal carbon dioxide signal as a regressor of interest. In this work, we introduce a novel method for CVR mapping based on a variational Bayesian approach. We analysed BOLD fMRI data from six participants that performed a BH task in ten different sessions each, and computed the corresponding CVR amplitude and delay maps for each session/subject. No statistically significant differences were observed between the modelling approaches in the CVR delay and amplitude maps in grey matter. Notably, the largest difference between methods was apparent in the case of low CVR amplitude, attributed to how each method addressed noisy voxels, particularly in white matter and cerebral spinal fluid. Both approaches showed highly reproducible CVR amplitude maps where between-subject variability was significantly larger than between-session variability. Furthermore, our results illustrated that the Bayesian approach is more computationally efficient, and future implementations could incorporate more complex noise models, non-linear fitting, and physiologically meaningful information into the model in the form of priors. This work demonstrates the utility of variational Bayesian modelling for CVR mapping and highlights its potential for characterising BOLD fMRI dynamics in the study of cerebrovascular health and its application to clinical settings.