Temporal Dynamics and Developmental Maturation of Salience, Default and Central-Executive Network Interactions Revealed by Variational Bayes Hidden Markov Modeling
Our ability to adapt to a constantly changing environment is thought to depend on the dynamic and flexible organization of intrinsic brain networks 1 , 2 ., Characterizing the temporal dynamics of interactions between distributed brain regions is fundamental to our understanding of human brain organization and its development 2–8 ., However , most of our current knowledge of functional brain organization in adults and children is based on investigations of time-independent functional coupling ., Progress in the field has been impeded by both a lack of appropriate computational techniques to investigate brain dynamics as well as an inadequate focus on core brain systems involved in higher-order cognition 3 , 4 , 9 , 10 ., In particular , progress has been limited by weak analytical models for identifying time-varying brain states , and their occurrence rates and mean lifetimes , for quantifying transition probabilities between brain states , and for characterizing the dynamic evolution of functional connectivity patterns over time 9–11 ., Here we overcome limitations of extant methods by developing and applying novel computational techniques for characterizing dynamic functional interactions between distributed brain regions and address two key neuroscientific goals ., The first scientific goal of our study was to investigate the dynamic functional connectivity of the salience network ( SN ) , the central-executive network ( CEN ) and the default mode network ( DMN ) , three core neurocognitive systems that play a central role in cognitive and affective information processing 1 , 12 ., Our second scientific goal was to characterize the maturation of the dynamic functional connectivity of the SN , CEN and DMN between childhood and adulthood in order to address important gaps in the literature regarding the nature of dynamic cross-network interactions over development and the question of how brain systems become more flexible during the period between childhood and adulthood ., The SN is a limbic-paralimbic network anchored in the anterior insula and dorsal anterior cingulate cortex with prominent subcortical nodes in affective and reward processing regions including the amygdala and ventral striatum 13 , 14 ., The SN plays an important role in orienting attention to behaviorally and emotionally salient and rewarding stimuli and facilitating goal-directed behavior 12 , 14–16 ., The fronto-parietal CEN is anchored in the dorsolateral prefrontal cortex and supramarginal gyrus and is critical for actively maintaining and manipulating information in working memory 17 , 18 ., The DMN is anchored in the posterior cingulate cortex , medial prefrontal cortex , medial temporal lobe , and angular gyrus 19–21 and is involved in self-referential mental activity and autobiographical memory 22 ., In adults , task-based fMRI studies have consistently demonstrated that SN , CEN and DMN nodes are involved in a wide range of cognitive tasks , with the strength of their responses increasing or decreasing proportionately with task demands 12 , 23 , 24 ., Analysis of causal interactions between these networks has also shown that high-level attention and cognitive control processes rely on dynamic interactions between these three core neurocognitive networks 16 , 25–27 ., Thus , far from operating independently , these three brain networks , which have only been probed using static time-invariant connectivity analysis , must form transient dynamic functional networks ( DFNs ) allowing for flexible within- and cross-network interactions ., While the SN , CEN and DMN can be reliably identified in most individuals using static network analysis of rs-fMRI data 26 , 28 , progress in characterizing their dynamic temporal properties has been limited by currently available computational tools and procedures ., Most current studies of dynamic brain connectivity use a sliding window approach 29 , 30 , which is problematic because of arbitrary parameters such as window size , which can lead to erroneous estimates of dynamic connectivity 7 , 9 , 11 ., Furthermore , extant methods do not provide information about the occurrence and lifetimes of individual dynamic brain states , transition probabilities between network states or unique dynamic network configurations associated with each brain connectivity state ., To address these weaknesses , we developed a novel variational Bayesian hidden Markov model ( VB-HMM ) 31 to uncover time-varying functional connectivity ., HMM uses a state-space approach to model multivariate non-stationary time series data 32 , 33 and cluster them into distinct states , each with a different covariance matrix reflecting the functional connectivity between specific brain regions ., Importantly , VB-HMM automatically prunes redundant states , retaining only those that significantly contribute to the underlying dynamics of the fMRI data , and provides the posterior distribution of parameters rather than point estimates of maximum likelihood-based methods ., We then used VB-HMM to characterize dynamic functional interactions between the SN , CEN and DMN to address our two neuroscientific goals ., VB-HMM allowed us to examine for the first time several important metrics of brain dynamics: the number of distinct brain states , their occupancy rates and mean lifetimes , and switching probabilities between brain states and DFNs ., Crucially , VB-HMM enabled us to investigate the temporal dynamics and evolution of states where the SN , DMN and CEN are fully segregated from each other , and states where they interact with each other ., We hypothesized that segregation of the SN , DMN and CEN would constitute a dominant state with high occupancy rates and mean lifetimes ., We further hypothesized that states with high occupancy rates would be temporally stable and marked by a higher probability of switching within the state compared to switching across states ., We use sub-second resting-state fMRI ( rs-fMRI ) datasets acquired as part of the Human Connectome Project ( HCP ) ( http://www . humanconnectome . org ) and demonstrate the robustness of our findings across two independent cohorts of healthy adults ., Next , we used VB-HMM and insights from our analyses of the adult brain to characterize the maturation of dynamic functional networks and connectivity associated with the SN , DMN and CEN between childhood and adulthood ., Flexible and dynamic cross-network functional interactions are essential for mature brain function 5 , 34 , yet little is known about the nature of dynamic organization and time-varying connectivity in children relative to adults ., Studies using static connectivity analyses suggest that functional brain networks undergo significant reconfiguration from childhood to adulthood , with analysis of time-averaged whole-brain connectivity patterns suggesting prominent increases as well as decreases in connectivity between childhood and adulthood ., In a previous study we showed that time-averaged connectivity within key nodes of the SN and DMN as well as their inter-network interactions is weaker in children relative to adults 28 ., Recent reports suggest that time-varying connectivity between distributed brain areas changes significantly with age , with greater temporal variability of connection strengths in children compared to adults34 ., Based on these observations , we hypothesized that compared to adults , children would show immature and less flexible patterns of dynamic connectivity between the SN , CEN and DMN ., Crucially , VB-HMM allowed us to , for the first time , probe developmental changes in dynamic networks properties including the occurrence rates and mean lifetimes of distinct brain states , such as those in which the SN , CEN and DMN are fully segregated from each other with decreased switching probabilities ., This study was approved by the Stanford University Institutional Review Board ., Written informed consent was obtained from all the subjects ., We first describe a novel VB-HMM framework we developed for characterizing dynamic brain networks in human fMRI data ., In the following sections , we represent matrices by using uppercase letters while scalars and vectors are represented using lowercase letters ., Let Y={{yts}t=1T}s=1S be the observed voxel time series , where T is the number of time samples and S is the number of subjects ., yts is an M dimensional time sample at time t for subject s , where M is the number of brain regions or nodes of the dynamic functional network under investigation ., Let Z={{zts}t=1T}s=1S be the underlying hidden/latent discrete states , where zts is the state label at time t for subject s ., Let Z be a first order Markov chain , with stationary transition ( A ) and initial distributions ( π ) defined as:, p ( zts=k|zt−1s=j ) =Ajk, ( 1 ), p ( z1s=k ) =πk, ( 2 ), where 0≤Ajk≤1 , ∑k=1KAjk=1 , and πk≥0 , ∑k=1Kπk=1 ., We assume the probability of the observation yts given its state zts=k to be a multivariate normal distribution with parameters mean μk and covariance Σk:, p ( yts|zts=k ) =N ( μk , Σk ), ( 3 ), Here we assume that the number of possible states K is not known a priori ., Each state k has M μk and an M x M Σk ., Let Φ = {π , A , Θ} ( where Θ={μk , Σk}k=1K ) be the unknown parameters of the HMM model ., Using the factorization property 35 of the Bayesian network shown in Fig 1A , the joint probability distribution of the observations , hidden states , and parameters can be written as, p ( Y , Z , Φ ) =∏s=1Sp ( z1s|π ) ∏t=2Tsp ( zts|zt−1s , A ) ∏t=1Tsp ( ( yts|zts , Θ ) P ( Φ ), ( 4 ), In maximum likelihood methods , the parameters Φ of the model are assumed to be unknown deterministic quantities , whereas in the Bayesian approach they are treated as random variables with prior probability distributions ., Here we assume that conjugate priors 35 for Φ and Z are defined as in 31 with the goal of estimating the joint posterior distribution p ( Z , Φ|Y ) of the hidden states and parameters ., Estimating this posterior distribution is analytically intractable but inference methods , such as sampling or variational methods , can instead be used 31 , 35 ., Here , to estimate p ( Z , Φ|Y ) , we use a variational Bayesian ( VB ) method 31 , which not only provides an elegant analytical approximation to the required posterior distribution but is also computationally faster than sampling approaches ., Let q ( Z , Φ|Y ) be any arbitrary probability distribution and p ( Z , Φ|Y ) be the true posterior probability distribution ., Then the log of the marginal distribution of observations Y can be written as, log\u2061P ( Y ) =F ( q ) +KL ( q||p ), ( 5 ), where F ( q ) is known as the negative free energy and KL ( q||p ) is the Kullback-Leibler ( KL ) divergence between the approximate and true posterior ., These quantities are given by, F ( q ) =∫dZdΦq ( Z , Φ|Y ) log\u2061p ( Y , Z , Φ ) q ( Z , Φ|Y ), ( 6 ), KL ( q||p ) =−∫dZdΦq ( Z , Φ|Y ) log\u2061p ( Z , Φ|Y ) q ( Z , Φ|Y ), ( 7 ), Since KL ( q||p ) is nonnegative , F ( q ) serves as the strict lower bound on log P ( Y ) ., F ( q ) and log P ( Y ) are equal if and only if the approximate posterior q ( Z , Φ|Y ) is equal to the true posterior p ( Z , Φ|Y ) for which KL ( q||p ) = 0 ., The goal of VB approximation is to find the approximate posterior for which the lower bound F ( q ) is maximized ., We make a mean field approximation on the approximate posterior 31 wherein it factorizes as, q ( Z , Φ|Y ) =q ( Z , A , Θ , π|Y ) =q ( Z|Y ) q ( π|Y ) q ( A|Y ) q ( Θ|Y ), ( 8 ), The functional forms of these factors are defined by the priors on the parameters and the likelihood of the data ., We assume conjugate priors for the priors , which results in elegant analytical approximations to the required posterior distributions of the Eq ( 8 ) ., Accordingly , the conjugate prior for π and rows of A is the Dirichlet ( Dir ) distribution , while the prior over the parameters of the Gaussian distribution Θ is the Normal-Wishart ( NW ) distribution ., We further assume that the prior distribution over Φ factorizes as, P ( Φ ) =p ( π ) p ( A ) p ( Θ ), ( 9 ), The forms of the Dirichlet and Normal-Wishart distributions are defined in 31 ., We provide the values of the hyper-parameters of these distributions in the Appendix ., Since we define conjugate priors on the model parameters , q ( π|Y ) and q ( A|Y ) follow multinomial distributions and q ( Θ|Y ) follows the Normal-Wishart distribution 31 ., The update equations for the posterior parameters are provided in the Supplementary Material ., The posterior distribution of the hidden states can be estimated using an efficient forward-backward method similar to the Baum-Welch algorithm for ML-HMM 33 , 35 ., Furthermore , our VB-HMM estimates the parameters of Normal-Wishart distribution for each state ., VB-HMM therefore discovers states for which the parameters of the Normal-Wishart distributions are distinct for each state ., A new state will be discovered if either mean or covariance or both are different in that state with respect to other states ., In task-based fMRI studies it is important to discover states with both mean and covariance differences ., However , in resting-state fMRI studies , as in the current study , differences in absolute signal levels are not relevant and states are based solely on changes in covariance over time ., This can be accomplished elegantly in our Bayesian framework using the hyperparameter λk in the joint Normal-Wishart distribution ., A non-informative prior value ( say , λk = 0 . 001 ) allows the data to determine the joint posterior distributions for the mean and covariance ., However , setting it to a very high value ( λk = 1000 ) biases the posterior to the prior mean which is 0 in our case ( equation S . 10 ) ., This ensures that our states are discovered only by the changes in covariance/inverse covariance in each state ., Similar to the expectation maximization algorithm for ML-HMM , the posterior distributions for the latent and model parameters are iteratively updated in VB-HMM as follows: We iterate steps, ( b ) and, ( c ) until the fractional lower bound F ( q ) between two consecutive thresholds is below a set threshold value of tol = 10−3 ., We initialize the states using the K-means algorithm with the number of clusters/states K set to a high value ( K = 25 ) ., The sparsity property of VB-HMM prunes away unwanted clusters/states in the model ., Like ML-HMM , VB-HMM provides suboptimal estimates of the posterior distributions , and these estimates are sensitive to the initial estimates of states using K-means initialization ., To account for this , we repeat VB-HMM with 100 different random initializations and choose the solution for which the lower bound F ( q ) is maximum ., We validated VB-HMM using three different simulation models; the details of each are provided in the Supplementary Materials ., Briefly , in Simulation-1 , we created datasets with two nodes and two hidden states ., The hidden states were constructed using a typical block design with two conditions ( or states ) : “OFF” and “ON” as shown in S2A Fig . We simulated observations with two nodes where the nodes are negatively correlated in the “OFF” state and uncorrelated in the “ON” state ., In Simulation-2 , we simulated data with six nodes and two hidden states using the HMM generative model given by Eqs 1–3 ., In this case , the two hidden states were constructed using a specified state transition matrix A and six nodes/ROIs with observations drawn from a zero-mean multivariate Gaussian distribution and state specific covariance matrices ( S3A Fig ) ., Simulation-3 also consisted of six nodes and two hidden states ., Here , however , the first three nodes/ROIs were correlated in the first half ( 116 samples ) of the experiment ( state 1 ) while the other three ROIs were correlated in the second half ( 116 samples ) of the experiment ( state 2 ) ( S4A Fig ) ., Five datasets were simulated ( akin to a group size of five subjects in fMRI studies ) for each simulation type ., We first validated VB-HMM using computer-simulated datasets generated from three different simulation models ., Here we briefly summarize the results from these simulations; details are in the Supplementary Materials ., For all three simulations , we applied VB-HMM with the number of hidden states ( K ) initialized to 25 and used VB-HMM to automatically determine the optimal number of states from the data ., S2 Fig shows the actual states , the estimated posterior probabilities and the Viterbi decoded states for Simulation-1 ., Among the 25 states , the occupancy rates of 18 states are zero suggesting that VB-HMM penalizes redundant states ., Further analysis suggests that among the seven with non-zero occupancy rates , four states together constitute 98% of the total occupancy rate and these states match the underlying true states in terms of their associated estimated Pearson correlation matrices and their occurrences with respect to their respective true states ., Similarly , 21 out of the 25 states in Simulation-2 had zero occupancy rates ( S3 Fig ) ., The top two most dominant states comprise 98% of the total occupancy rate and are well matched with the temporal occurrence of the underlying actual states ., Lastly , Simulation-3 yielded 21 out of 25 states with an occupancy rate of zero ( S4 Fig ) ., Of the four states with non-zero occupancy rates , the top two account for 99 . 2% of the total occupancy rate and match the true states used to generate the data ., These simulations demonstrate that VB-HMM can accurately discover the optimal number of states and the underlying dynamic connectivity across different models of simulated data ., We applied VB-HMM on rs-fMRI data to uncover dynamic functional interactions between the SN , CEN and DMN in two cohorts of HCP data ., Our first goal here was to identify dynamic brain states and their associated functional networks ., We computed the occupancy rates and mean lifetimes of each state as well as the switching probabilities between states ., A particular theoretical focus was on the occurrence of brain states in which the three networks were disconnected from each other ., We conducted separate analyses on Cohorts 1 and 2 and investigated the robustness and consistency of our key findings across the two cohorts ., To characterize the connectivity patterns associated with each functional state , we used a community detection algorithm on the estimated partial correlations in each state and examined the functional connectivity between ROIs ., Below we describe the salient features of the dynamic functional network structure in each cohort ., Given our focus on the temporal properties of the state in which the SN , CEN , and DMN were disconnected from each other , we combined states with a similar community structure into distinct DFNs ( see S1 Text ) ., We then examined the occupancy rates , mean lifetimes and switching probabilities of these DFNs ., Based on our primary goal of characterizing the network structure associated with segregated SN , CEN and DMN as encapsulated by DFN-1 ( Fig 3B ) and the common patterns of network structure involving DFN-1 and DFN-2 in both cohorts ( see previous sections ) , we next examined state transitions between these networks ., In each cohort , network structures corresponding to all other functional states were combined together into a mixed DFN-M ., As in previous sections , these analyses were conducted separately in the two cohorts with the aim of elucidating replicable findings ., We next used VB-HMM to characterize the maturation of dynamic functional interactions between the SN , CEN and DMN in a Stanford cohort of IQ- and gender-matched adults and children ., We used the same analytic procedures as described above on data from adults and children and then compared dynamic network properties between the two groups ., To investigate whether DFN occupancy rates and mean lifetimes differ between children and adults , we focused on DFN-1 and DFN-2 , the two dominant DFNs with identical community structures in adults and children that together account for about 77% occupancy rates in both groups ., Network configurations corresponding to all other functional states were combined into DFN-M ., The mean lifetimes , but not the occupancy rates , of all three DFNs were significantly greater in children compared to adults ( p < 0 . 05 , FDR corrected ) ( Fig 6A and 6B ) ., These findings indicate that children tend to persist longer in the same DFN than adults , as illustrated by the time evolution of the three DFNs ( Fig 5A and 5F ) ., Below we further investigate this pattern of developmental differences in terms of transition probabilities between DFNs ., To further investigate whether children tend to stay in one DFN configuration longer than adults , we computed transition probabilities in children and adults and compared them between the groups ., The probability of within-DFN transitions was not significantly different between the two groups ( p > 0 . 05 , FDR corrected ) ., However , transition probabilities to the fully disconnected SN-CEN-DMN configuration ( DFN-1 ) from both connected network configurations ( DFN-2 and DFN-M ) were significantly higher in adults compared to children ( p < 0 . 05 , FDR corrected ) ( Fig 6D ) ., In contrast , children showed a higher probability of switching between the two connected network configurations ( p < 0 . 05 , FDR corrected ) ., These findings demonstrate that , compared to children , adults switch back more frequently to DFN-1 , in which the SN , DMN and CEN are completely segregated from each other ., Finally , to investigate how dynamic functional connectivity matures with age we compared the strength of DFN connectivity assessed using within- and cross-network links as described above ., In this analysis , we further excluded participants with DFN connectivity beyond 3 standard deviations from their specific group or for whom both DFNs were not present ., After exclusion , our sample consisted of 22 adults and 16 children ., We found a significant three-way interaction between DFN ( DFN-1 vs . DFN-2 ) , link type ( within- vs . cross-network ) , and participant groups ( children vs . adults ) ( F1 , 36 = 10 . 99 , p = 0 . 002 ) ( Fig 6C ) , such that DFN-1 and DFN-2 configurations differed in connection strength by link type in adults ( F1 , 21 = 119 . 5 , p < 0 . 001 ) but not in children ( F1 , 15 = 0 . 491 , p = 0 . 494 ) ., These results demonstrate that DFN connectivity is weaker and less differentiated in children relative to adults ., The main scientific aims of our study were to ( 1 ) investigate the temporal properties of dynamic functional connectivity between the SN , CEN and DMN , three core neurocognitive networks implicated in a wide range of goal directed behaviors 12 , 15 , 16 , 26 , 48 , 49 , and ( 2 ) investigate how the temporal properties of dynamic functional connectivity between these core networks change from childhood to adulthood ., To accomplish this , we first developed a novel Bayesian HMM ( VB-HMM ) model for quantifying dynamic changes in functional connectivity ., A variational Bayes approach for estimating latent states and unknown HMM model parameters allowed us to overcome weaknesses associated with conventional methods and to investigate dynamic changes in intrinsic functional connectivity between three networks , which have previously only been investigated using static network analysis ., VB-HMM allowed us to quantify the temporal evolution of distinct brain states and probe the dynamic functional organization of the SN , CEN and DMN in an analytically rigorous manner ., Contrary to previous observations based on static time-averaged connectivity analysis 20 , 50 , we found that temporal coupling between the SN , CEN and DMN varies considerably over time and that these networks exist in a completely segregated state only intermittently with relatively short mean lifetimes ., VB-HMM also revealed immature and inflexible dynamic interactions between the SN , CEN and DMN characterized by higher mean lifetimes in individual states and reduced transition probability between states , in children relative to adults ., VB-HMM is a novel machine learning approach for identifying dynamic changes in functional brain connectivity ., VB-HMM has several advantages over existing methods 6 , 9 , 29 , 51 , 52:, ( i ) the automated estimation of latent states and their temporal evolution;, ( ii ) estimation of posterior probabilities of latent states and model parameters;, ( iii ) selection of models based on a trade-off between the model complexity and fit of the data , thereby reducing overfitting;, ( iv ) use of sparsity constraints resulting in pruning of weak states without having to specify the number of states a priori; and, ( v ) a generative model that has the potential to provide a more mechanistic understanding of human brain dynamics ., Our approach also overcomes weaknesses of existing HMM methods that are based on a maximum likelihood estimation approach and require a priori specification of the number of hidden states ., Furthermore , in contrast to conventional HMM methods , VB-HMM can discover dynamic changes in states based on signal mean or covariance or both ., This flexibility can be useful in uncovering latent brain dynamics during cognitive task processing , where states typically differ in both signal mean and covariance , as well as rs-fMRI , where states are better characterized by changes in covariance rather than mean signal levels ., In applications to rs-fMRI , as in the present study , this is accomplished in VB-HMM by setting the prior hyperparameter value λk = 1000 for each state k ., This choice forces the posterior mean values for each state ( μk ) close to prior mean ( which is zero ) ( Equation S . 10 ) and ensure that states are characterized by differences in the covariance matrices ( Σk ) , but not the mean ( μk ) ., Another advantage of our Bayesian approach is that the covariance ( or inverse covariance ) estimates are regularized and the extent of regularization is determined by the data ( Eqs S11–S . 13 ) ., This regularization ensures that the covariance matrices are full rank and therefore invertible to estimate partial correlations ., Such regularized estimation is not possible with maximum likelihood approaches ., Our simulations using three different simulation models demonstrate that VB-HMM can accurately discover the number of states , their temporal evolution , the transition probabilities between states and dynamic connectivity patterns associated with each state ( see S1 Text for details ) ., We next used VB-HMM to characterize the temporal evolution of dynamic brain states in two independent cohorts of adult participants from the HCP ., VB-HMM identified multiple stable states in both cohorts of participants ., The observation that the number of states is strictly greater than one is consistent with previous results demonstrating that the rs-fMRI time series is not stationary29 , 53 ., Importantly , VB-HMM identified similar patterns of stable brain states in both cohorts and provided reliable and replicable estimates of occupancy rates , mean lifetimes , and state transition probabilities associated with each brain state ., Although VB-HMM identified 16–19 states in both adult cohorts , only three states had occupancy rates greater than 10% ( Fig 2C and 2G ) , and these states demonstrated the highest mean lifetimes ., However , even these dominant states had short mean lifetimes ranging from 7–10 s , demonstrating that brain states are temporally persistent over durations far shorter than the length of a typical rs-fMRI scan session ., These features were observed in both adult cohorts , demonstrating the robustness of our findings ., Furthermore , analysis of the state transition probability indicated that each state had the highest probability of transitioning to itself rather than other states ( Fig 2D and 2H ) , suggesting that temporal stability of individual states does occur ., Taken together , these results demonstrate the existence of dynamic , yet stable , brain states in rs-fMRI and identify distinct connectivity patterns associated with each state ., We suggest that this balance of temporal stability and dynamic connectivity is a fundamental principle of brain organization ., By construction , VB-HMM states are characterized by distinct patterns of inter-node connectivity ( Figs 2 and 3 ) ., To test specific hypotheses related to the dynamic interactions between the SN , CEN and DMN and interpret the neurobiological relevance of connectivity profiles , we identified dynamic functional connectivity profiles associated with the three previously known static networks ., To accomplish this we applied modularity-based community detection algorithms 36 on the functional connectivity matrix estimated by VB-HMM for each state ( Fig 1B ) ., This analysis revealed that , in some cases , states with non-identical connectivity matrices had similar overall community structures ( S5 , S6 , S8 and S9 Figs ) ., For example , multiple states ( S5 and S6 Figs ) demonstrated a pattern in which the SN , CEN and DMN formed separate , segregated communities , reminiscent of the static functional networks previously identified by independent components analysis 50 ., We next combined states with identical community structures into dynamic functional networks ( DFNs ) and examined the temporal properties of segregated and non-segregated DFNs as well as the dynamic interactions between key nodes of the SN , CEN and DMN ., The SN , CEN and DMN formed separate communities and were segregated from each other ( DFN-1 in Fig 3 ) approximately 31% of the time ( 31% and 27% in Cohorts 1 and 2 , respectively ) ., In this case , all three networks maintained their within-network connectivity structure–AI and ACC nodes of the SN were connected with each other , PMC and VMPFC nodes of the DMN were connected with each other , and DLPFC and PPC nodes of the CEN were connected with each other ., Crucially , VB-HMM also revealed that this DFN had a mean lifetime of about 7–10 s ( 8 . 3 s and 8 . 8 s in Cohorts 1 and 2 , respectively ) ( Fig 3C and 3G ) ., These findings suggest that although this particular DFN configuration is a prominent feature of SN , CEN and DMN organization , it has a relatively short lifetime ., The second dominant DFN identified by VB-HMM had a community structure in which the CEN and DMN were interconnected in one community , while the SN nodes remained segregated from the CEN and DMN , forming an independent network ( DFN-2 in Fig 3 ) ., This DFN configuration had occurrence rates of 36% and 18% in Cohorts 1 and 2 , respectively ( Fig 3 ) ., The remaining states had distinct DFN configurations ( S5 and S6 Figs ) , with varying levels of cross-network interactions , but their occurrence rates were lower and not consistent across the two cohorts ., Previous work from our lab 12 39 and recent work by other labs 54 , 55 has indicated that the SN plays a critical role in switching between the DMN and the CEN ., Our results suggest that this switching is transient ( i . e . doesn’t persist for a long time ) and may occur not very frequently ., Finally , analysis of the switching probability between DFNs revealed that each DFN had a high probability ( 0 . 91 in Cohort 1 and 0 . 93 in Cohort 2 ) of making self-transitions ( Fig 3D and 3H ) ., Thus , as with individual brain states , the two dominant DFN configurations ( DFN-1 and DFN-2 in Fig 3 ) were stable over time but persistent only for short time intervals ., Taken together , these findings identify key features of dynamic functional interactions associated with the SN , CEN and DMN and confirm that the static segregated networks previously identified using independent component analysis occur only about 30% of the time ., The organization of brain networks in adults is shaped by years of development , learning and brain plasticity 5 ., Previous stud
Little is currently known about dynamic brain networks involved in high-level cognition and their ontological basis ., Here we develop a novel Variational Bayesian Hidden Markov Model ( VB-HMM ) to investigate dynamic temporal properties of interactions between salience ( SN ) , default mode ( DMN ) , and central executive ( CEN ) networks—three brain systems that play a critical role in human cognition ., In contrast to conventional models , VB-HMM revealed multiple short-lived states characterized by rapid switching and transient connectivity between SN , CEN , and DMN ., Furthermore , the three “static” networks occurred in a segregated state only intermittently ., Findings were replicated in two adult cohorts from the Human Connectome Project ., VB-HMM further revealed immature dynamic interactions between SN , CEN , and DMN in children , characterized by higher mean lifetimes in individual states , reduced switching probability between states and less differentiated connectivity across states ., Our computational techniques provide new insights into human brain network dynamics and its maturation with development .
Characterizing the temporal dynamics of functional interactions between distributed brain regions is of fundamental importance for understanding human brain organization and its development ., Progress in the field has been hampered both by a lack of strong computational techniques to investigate brain dynamics and an inadequate focus on core brain systems involved in higher-order cognition ., Here we address these gaps by developing a novel variational Bayesian Hidden Markov Model ( VB-HMM ) that uncovers non-stationary dynamical functional networks in human fMRI data ., In two cohorts of adults , VB-HMM revealed multiple short-lived states characterized by rapid switching and transient connectivity between the salience ( SN ) , default mode ( DMN ) , and central executive ( CEN ) networks—three brain systems critical for higher-order cognition ., In children , relative to adults , VB-HMM revealed immature dynamic interactions between SN , CEN , and DMN , characterized by higher mean lifetimes in individual states , reduced switching probability between states and less differentiated connectivity across states ., Our findings suggest that the flexibility of switching between distinct brain states is weaker in childhood , and they provide a novel framework for modeling immature brain network organization in children ., More generally , the approach used here may prove useful to the investigation of dynamic brain organization in neurodevelopmental and psychiatric disorders .
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