Time-resolved instantaneous functional loci estimation (TRIFLE): Estimating time-varying allocation of spatially overlapping sources in functional magnetic resonance imaging

In functional magnetic resonance imaging, multivariate proxies of functional brain networks are commonly extracted using spatial independent component analysis. The theoretical premises of spatial overlap among functional processes and the time-varying nature of functional connectivity prompt the question of how to accurately model spatially overlapping and time-varying functional sources. Well-known functional networks have previously been shown to divide into spatially overlapping and functionally distinct subprocesses termed Temporal Functional Modes (TFM) using temporal independent component analysis on the time courses obtained via spatial independent component analysis. In this model, spatial and temporal modes of organisation interact through a single mixing matrix with fixed coefficients. Here, we introduce a time-resolved version termed Time-Resolved Instantaneous Functional Loci Estimation (TRIFLE) to estimate time-varying changes in source allocation. We analytically demonstrate that the originally fixed TFM mixing matrix can be expressed as the temporal average of a time-resolved mixing matrix, which in turn can be obtained in closed form and provides instantaneous estimates of brain network reconfigurations involved in distinct temporal functional modes. We apply TRIFLE to a high-temporal resolution functional magnetic resonance imaging dataset. We demonstrate that spatial source allocation aligns with expectations based on the experimental task design and that successful and unsuccessful trials have different allocation profiles. The proposed method sheds light on the temporal evolution of brain network reconfigurations while explicitly accounting for potential neuroanatomical overlap.