Physiologically Informed PCA-Partial Correlation for highly Collinear Brainstem fMRI Networks

Functional connectivity (FC) approaches from resting-state fMRI (rs-fMRI) are amply spread to investigate the cortical organization, yet the brainstem remains relatively underexplored despite its pivotal roles in both physiological and pathological conditions. The highly collinear network, in which the strongly interconnected nodes and the widespread neuromodulatory influences induce indirect or mediated interactions, make the estimation of direct brainstem FC challenging. Standard bivariate methods fail to recover the true network structure in such complex topologies, causing false positive interactions. On the other hand, partial correlation can potentially estimate the direct FC, but multicollinearity issues and collider-induced spurious correlations limit its application in high-dimensional scenarios. Here, we propose a physiologically informed framework in which the conditioning strategy for partial correlation estimation is tailored for the investigation of the brainstem and its direct interactions within the network and with whole-brain regions. Specifically, we employed a PCA-regularized partial correlation (PCA - {rho}PC) approach, where PCA is applied to the brainstem covariates to mitigate multicollinearity and model shared modulatory variance. We show that PCA - {rho}PC improves the robustness and interpretability of brainstem FC, yielding sparser and more physiologically plausible connectomes compared with conventional (regularized) approaches. Both simulation and real fMRI data raise the possibility that Pearsons and PCA-regularized approaches may complement each other in an effort to unravel the pattern of direct vs. indirect effects in highly collinear settings, paving the way for future extensions in a wide range of multivariate neuroimaging applications.