Continuous-time causal distribution learning with identifiability for brain dynamic effective connectivity inference

Dynamic effective connectivity (dEC) analysis provides an approach for revealing the causal mechanism of information transmission in human brain. However, existing discrete-time dEC learning models suffer a mismatch between sampling and causal frequencies as well as low efficiency in data utilization. Based on a continuous-time dynamic causality distribution learning framework, we propose a dEC distribution learning model, which uses free energy principle to ensure more proper parameter learning than maximum likelihood estimation. Theoretically, the identifiability of the proposed model is proved, which guarantees the uniqueness of the learned dEC given the same data distribution. Results from the synthetic dataset show that the ability in both causality learning and time series reconstruction of the proposed model outperforms the comparison methods. The dEC results learned from the task functional magnetic resonance imaging (fMRI) data reveal the changing information transmission patterns in brain when dealing with picture-sentence matching tasks. Additionally, during the transition from resting state to task state, information flow in the brain's dEC network becomes increasingly organized around the left supramarginal gyrus, a hub known for the language processing and information integration in parietal lobe. When applied to resting-state fMRI data on Alzheimer's disease, the learned dEC patterns reveal distinct alterations in brain networks associated with Alzheimer's disease. The results suggest that Alzheimer's disease is associated with abnormalities not only in memory and emotion-related networks, but also in networks underlying executive control and visual integration. The source code of the proposed model are available at https://github.com/Yiding00/IDECD-CT.