Transformer-aided dynamic causal model for scalable estimation of effective connectivity

Dynamic Causal Models (DCMs) in functional Magnetic Resonance Imaging (fMRI) decipher causal interactions, known as Effective Connectivity, among neuronal populations. However, their utility is often constrained by computational limitations, restricting analysis to a small subset of interacting brain areas, typically fewer than 10, thus lacking scalability. While the regression DCM (rDCM) has emerged as a faster alternative to traditional DCMs, it is not without its limitations, including the linearization of DCM terms, reliance on a fixed Hemodynamic Response Function (HRF), and an inability to accommodate modulatory influences. In response to these challenges, we propose a novel hybrid approach named Transformer encoder DCM decoder (TREND), which combines a Transformer encoder with state-of-the-art physiological DCM (P-DCM) as decoder. This innovative method addresses the scalability issue while preserving the nonlinearities inherent in DCM equations. Through extensive simulations, we validate TREND's efficacy by demonstrating its ability to accurately predict effective connectivity values with dramatically reduced computational time relative to original P-DCM even in networks comprising up to, for instance, 100 interacting brain regions. Furthermore, we showcase TREND on an empirical fMRI dataset demonstrating the superior accuracy and/or speed of TREND compared with other DCM variants. In summary, by amalgamating P-DCM with Transformer, we introduce and validate a pioneering approach for determining effective connectivity values among brain regions, extending its applicability seamlessly to large-scale brain networks.