We propose a novel methodology to extract the main sources of variability from a collection of space-time dependent signals observed over complicated geometries. The methodology is developed in the context of functional Principal Component Analysis (fPCA), and proposes an estimation problem combining a rank-one approximation of the data matrix with a roughness penalty. The computed principal components are smooth spatio-temporal functions over the domain of interest, which are easy to interpret and can lead to interesting insights in the spatio-temporal dynamic of the phenomenon under study. The model is applied to the study of neuroimaging data. In particular, we explore the main sources of variability in neuronal connectivity in a population of healthy and pathological subjects, starting from functional Magnetic Resonance Imaging scans.