An MCMC-Based Method for Dynamic Causal Modeling of Effective Connectivity in Functional MRI

2026-05-13

AI Summary

Traditional dynamic causal modeling (DCM) for effective connectivity analysis in fMRI suffers from low computational efficiency, underestimated parameter uncertainty, and imprecise solutions due to its complex observation model. This work proposes Canonical DCM (CDCM), which streamlines the observation model, employs the No-U-Turn Sampler for posterior inference, and—uniquely—enables piecewise analytical solutions of neural ordinary differential equations (ODEs). The approach substantially improves computational efficiency and establishes sufficient conditions for parameter identifiability, thereby enhancing uncertainty quantification. Experiments on both synthetic and real fMRI datasets (from the Wellcome Centre and the Human Connectome Project) demonstrate that CDCM reliably estimates task-related parameters and yields consistent, reproducible patterns of effective connectivity.

Abstract

Effective connectivity analysis in functional magnetic resonance imaging (fMRI) studies directional interactions among brain regions and experimental stimuli. Dynamic causal modeling (DCM) is a widely used method to estimate effective connectivity, based on a state-space representation consisting of a latent neural signal model and an observation model transforming the neural signal into the observed blood-oxygen-level-dependent (BOLD) response. A standard DCM combines ordinary differential equation (ODE) dynamics for the latent signal with a complex neural-hemodynamic system for the observation model, and typically uses variational Bayes for parameter estimation. While physically well-motivated, this approach can lead to practical challenges such as inexact solutions and underestimated uncertainty. We introduce Canonical DCM (CDCM), a Markov chain Monte Carlo (MCMC)-based method that adopts a simpler observation model and the No-U-Turn Sampler for posterior sampling. The simpler observation model admits a piecewise analytic solution to the neural ODE, increasing computational efficiency and enabling explicit derivation of sufficient conditions for parameter identifiability. The results indicate that CDCM provides reliable uncertainty quantification and consistent estimation of parameters related to experimental inputs for simulated and real data. We use publicly available data from the Wellcome Centre for Human Neuroimaging and the Human Connectome Project (HCP) to benchmark CDCM against standard DCM methods and examine replicability of estimated connectivity patterns in small- and large-scale neuroimaging settings.

Problem

• effective connectivity
• dynamic causal modeling
• fMRI
• parameter estimation
• uncertainty quantification

Innovation

• Dynamic Causal Modeling
• Markov chain Monte Carlo
• fMRI effective connectivity
• No-U-Turn Sampler
• parameter identifiability