A spectral sampling algorithm in dynamic causal modelling for resting‐state fMRI

Resting‐state functional magnetic resonance imaging (rs‐fMRI) is widely utilized to study the directed influences among neural populations which were called effective connectivity (EC), and the spectral dynamic causal modelling (spDCM) is the state‐of‐the‐art framework to identify them. However, spDCM used variational Laplace to approximate the posterior density by maximizing the free energy, which might underestimate the variability of posterior density and get locked to the local minima. A spectral sampling algorithm (SS‐DCM) was proposed to improve the estimation accuracy of the dynamic causal model for rs‐fMRI. In SS‐DCM, a naïve Bayesian model was constructed in the spectral domain, which described the probabilistic relationship between the sampled parameters and cross spectra of the observed blood oxygen level‐dependent signals, and the parameters were sampled using randomly walked Markov Chain Monto Carlo scheme. The root mean square errors of the estimation of EC and hemodynamic parameters of SS‐DCM, spDCM and generalized filter scheme were compared in the synthetic data, and SS‐DCM was the most accurate and stable. A comparative evaluation using empirical rs‐fMRI data was performed to study the EC pattern of the default mode network and compare the accuracy of classification between typically developed subjects and inattentive attention deficit and hyperactivity disorder patients. The results showed high consistency of positivity and negativity of EC between spDCM and SS‐DCM, and SS‐DCM also provided higher classification accuracy. It is highlighted that SS‐DCM improves the accuracy of the estimation of EC and provides accurate information of discrepancies between diseased and healthy subjects using rs‐fMRI.