Author Summary Brain network models have become a promising theoretical framework for simulating signals that are representative of whole-brain activity such as resting-state fMRI. However, it has been difficult to compare the complex brain activity obtained from simulations with empirical data. Previous studies have used simple metrics to characterize coordination between regions such as functional connectivity. In this manuscript, we extend this work by utilizing modern machine learning techniques to fit the brain network models to observed data and train on the mismatch between the model and observed signal. Our results show that our system training on these new metrics generalizes to a system that is able to reproduce trajectories and complex state transitions seen in rs-fMRI over the span of minutes. Our results will be useful in constraining and developing more realistic simulations of whole-brain activity. Abstract Large-scale patterns of spontaneous whole-brain activity seen in resting-state functional magnetic resonance imaging (rs-fMRI) are in part believed to arise from neural populations interacting through the structural network (Honey, Kötter, Breakspear, & Sporns, 2007 ). Generative models that simulate this network activity, called brain network models (BNM), are able to reproduce global averaged properties of empirical rs-fMRI activity such as functional connectivity (FC) but perform poorly in reproducing unique trajectories and state transitions that are observed over the span of minutes in whole-brain data (Cabral, Kringelbach, & Deco, 2017 ; Kashyap & Keilholz, 2019 ). The manuscript demonstrates that by using recurrent neural networks, it can fit the BNM in a novel way to the rs-fMRI data and predict large amounts of variance between subsequent measures of rs-fMRI data. Simulated data also contain unique repeating trajectories observed in rs-fMRI, called quasiperiodic patterns (QPP), that span 20 s and complex state transitions observed using k-means analysis on windowed FC matrices (Allen et al., 2012 ; Majeed et al., 2011 ). Our approach is able to estimate the manifold of rs-fMRI dynamics by training on generating subsequent time points, and it can simulate complex resting-state trajectories better than the traditional generative approaches.

Brain network models (BNMs) have become a promising theoretical framework for simulating signals that are representative of whole-brain activity such as resting-state fMRI. However, it has been difficult to compare the complex brain activity obtained from simulations to empirical data. Previous studies have used simple metrics to characterize coordination between regions such as functional connectivity. We extend this by applying various different dynamic analysis tools that are currently used to understand empirical resting-state fMRI (rs-fMRI) to the simulated data. We show that certain properties correspond to the structural connectivity input that is shared between the models, and certain dynamic properties relate more to the mathematical description of the brain network model. We conclude that the dynamic properties that explicitly examine patterns of signal as a function of time rather than spatial coordination between different brain regions in the rs-fMRI signal seem to provide the largest contrasts between different BNMs and the unknown empirical dynamical system. Our results will be useful in constraining and developing more realistic simulations of whole-brain activity. Author Summary The development of more sophisticated models of the brain will allow us to address some of the most challenging questions in neuroscience, such as how the physical structure of the brain can give rise to behavior, consciousness, and memory. Our focus in this manuscript is on simulating the relatively slow brain signals that coordinate information transfer across large scales in the brain and that can be measured using fMRI. Previous measures used averaged measures of functional connectivity in the simulated brain signals to compare with the empirical signal. In order to extend previous findings, we use dynamic analysis techniques developed for these fMRI signals to understand more transient events that occur naturally during normal brain activity. We show that these dynamic properties are better in differentiating models from each other and from the measured brain activity. These results will be useful in constraining and developing more realistic simulations of whole-brain activity.