A fast dynamic causal modeling regression method for fMRI

•Compared with traditional methods, the calculation time of GSD algorithm can be reduced by >50 %.•Utilized Fourier transform symmetry for real-valued time series to enhance GSD computational efficiency.•Frequency domain filtering techniques are applied to enhance the inversion scheme to ensure compliance with the dual principles of Bayes optimality.•GSD affords an extremely efficient form of complex system modelling for sparsely coupled nodes, under mild prior constraints on the dynamics. Dynamic Causal Modeling (DCM) is a crucial tool for studying brain effective connectivity, offering valuable insights into brain network dynamics through functional magnetic resonance imaging (fMRI) and electrophysiology (EEG and MEG). However, its high computational complexity limits its applicability in large-scale network analysis. To address this issue, we propose a regression algorithm that integrates the Generalized Linear Model (GLM) with Sparse DCM, termed GSD. This algorithm enhances computational performance through three key optimizations: (1) utilizing the symmetry of the Fourier transform to convert complex frequency domain calculations into real number operations, thereby reducing computational complexity; (2) applying GLM and filtering techniques to minimize the effects of noise and confounds, enhancing parameter estimation accuracy; and (3) defining a new cost function to optimize variational inference and filter parameters, further improving parameter estimation accuracy. We validated the GSD algorithm using three public fMRI datasets: simulated Smith small-world network data, attention and motion measured data, and face recognition repetition effect measured data. The experimental results demonstrate that the GSD algorithm reduces computation time by over 50 % while maintaining parameter estimation performance comparable to traditional methods. These findings offer a new perspective on balancing model interpretability and computational efficiency, potentially broadening the application of DCM across various fields. [Display omitted]