Correction to: Improved dynamic functional connectivity estimation with an alternating hidden Markov model

Dynamic functional connectivity (DFC) analysis has been widely applied to functional magnetic resonance imaging (fMRI) data to reveal the time-varying functional interactions between brain regions. Although the sliding window (SW) method is popular for DFC analysis, the selection of window length is hard, and the temporal resolution is limited by the window length. The hidden Markov model (HMM) without the limitation of window length has been proven to be able to estimate time-varying brain states from fMRI data. However, HMM tends to be overfitted in DFC analysis of fMRI data because of the high spatial dimension and the limited sample size of fMRI data. In this study, we proposed an alternating HMM (aHMM) method that used the functional connectivity estimation of SW to initialize the covariance matrix of HMM and adopted an alternating HMM procedure to reduce the number of parameters during each optimization. The simulated and real fMRI resting data from the Human Connectome Projects showed that aHMM produced better robustness to noise, parameter number and sample size in DFC estimation than SW and HMM. For the real fMRI resting data of cerebral small vessel disease (CSVD), results of aHMM revealed that amnesia and mild cognitive impairment (aMCI) caused the CSVD with aMCI (CSVD-aMCI) group tended to spend more time on the brain state with overall weak connections and less time on the state with overall strong connections than the CSVD-controls. Moreover, CSVD-aMCI showed significantly lower connectivity amplitude and higher connectivity fluctuation than CSVD-control. In contrast, HMM did not detect intergroup differences of the connectivity amplitude and fluctuations and SW did not detect intergroup differences of connectivity fluctuations and fraction of time. The results further indicated that aHMM outperformed HMM and SW in detecting inter-group differences of temporal properties of DFC and connectivity fluctuations.