Fig. 2

Flow diagram of the graph modelling and analysis pipeline. Following preprocessing of the fMRI data we obtain multivariate regional brain activity time series for all N subjects. Variational Bayes inference is then used to train HMMs (using the HMM-MAR package (Vidaurre et al. 2016)). A is a sketch of an HMM fitted to the \(X_{n,t}\) data for subject n and time point t. Each hidden brain state \(S_{n,t}\) \(\Sigma (S_{n,t})\) has mean activity \(\mu (S_{n,t})\) and covariance \(\Sigma (S_{n,t})\) (after backprojection). State change from \(S_{n,t}\) is determined by the transition matrix P. B The number of hidden states, K, is determined using mean subjectwise cross-validated maximum entropy, which is calculated over the fractional occupancies, \(\kappa _{s,n,k}\) for each subject-state pair up to K states. C Adjacency matrix of the interlayer temporal directed transition graph determined by the Markov transition matrix of the HMM, with temporal communities in red along the diagonal. D Each state itself can be considered a layer with edges relating brain regions by their correlation in activity derived from their modelled covariance \(\Sigma (s)\), with node weights (regional mean activity) determined by \(\mu (s)\). Of the states, some are highly connected state hubs, h(U), belonging to a temporal community U (red shading). E Each hub state (layer) h(U) is analysed and internal spatial communities are determined. F Internal communities are ranked according to their level of coherent brain activity compared to many repeated random walk samples from the multiplex model. G The results of ranking summarised by the community T-score. High T-score corresponds to a higher than expected level of community coherent activity when compared to the rest of the multiplex graph in this brain area. We propose functions for highly ranked communities by mapping these regions onto a 3D functional activity map and compared them to maps and terms drawn from the neuroscience literature with NeuroSynth