Brain Network Constraints and Recurrent Neural Networks reproduce unique Trajectories and State Transitions seen over the span of minutes in resting state fMRI

Large scale patterns of spontaneous whole brain activity seen in resting state functional Magnetic Resonance Imaging (rsfMRI), are in part believed to arise from neural populations interacting through the structural fiber network [18]. Generative models that simulate this network activity, called Brain Network Models (BNM), are able to reproduce global averaged properties of empirical rsfMRI activity such as functional connectivity (FC) [7, 27]. However, they perform poorly in reproducing unique trajectories and state transitions that are observed over the span of minutes in whole brain data [20]. At very short timescales between measurements, it is not known how much of the variance these BNM can explain because they are not currently synchronized with the measured rsfMRI. We demonstrate that by solving for the initial conditions of BNM from an observed data point using Recurrent Neural Networks (RNN) and integrating it to predict the next time step, the trained network can explain large amounts of variance for the 5 subsequent time points of unseen future trajectory. The RNN and BNM combined system essentially models the network component of rsfMRI, and where future activity is solely based on previous neural activity propagated through the structural network. Longer instantiations of this generative model simulated over the span of minutes can reproduce average FC and the 1/f power spectrum from 0.01 to 0.3 Hz seen in fMRI. Simulated data also contain interesting resting state dynamics, such as unique repeating trajectories, called QPPs [22] that are highly correlated to the empirical trajectory which spans over 20 seconds. Moreover, it exhibits complex states and transitions as seen using k-Means analysis on windowed FC matrices [1]. This suggests that by combining BNMs with RNN to accurately predict future resting state activity at short timescales, it is learning the manifold of the network dynamics, allowing it to simulate complex resting state trajectories at longer time scales. We believe that our technique will be useful in understanding the large-scale functional organization of the brain and how different BNMs recapitulate different aspects of the system dynamics.