Brainstem Exploration: PCA-Based Partial Correlation for Sparse and Direct Functional Connectivity Networks

In vivo brain functional connectivity (FC) analysis plays a pivotal role in studying brain activity in both health and disease. Since the brainstem is strongly involved in fundamental physiological processes as well as in pathological conditions, it is important to characterise both its direct and mediated functional connectivity. However, given a complex brain network topology and their strong neuromodulatory role, brainstem nuclei can act as confounders, chain system elements, and colliders (i.e., mediator regions) within brain networks, making the estimation of direct FC an open challenge. In this work, we propose a partial correlation approach exploiting principal component analysis (PCA) to address the multicollinearity issue and alleviate the effects of mediator regions. Specifically, the partial correlation is implemented to focus on brainstem-to-brainstem and brainstem-to-brain direct connectivity, thus highlighting the contribution of specific brainstem nuclei. The methodology was applied to resting-state fMRI data and compared with commonly used regularization approaches, revealing direct and sparse networks between brainstem nuclei and whole-brain regions.