A DEEP LEARNING APPROACH TO ESTIMATING INITIAL CONDITIONS OF BRAIN NETWORK MODELS IN REFERENCE TO MEASURED FMRI DATA

Abstract

1.Brain Network Models (BNMs) are a family of dynamical systems that simulate whole brain activity using neural mass models to represent local activity in different brain regions that influence each other via a global structural network. Research has been interested in using these network models to explain measured whole brain activity measured via resting state functional magnetic resonance imaging (rs-fMRI). Properties computed over longer periods of simulated and measured data such as average functional connectivity (FC), have shown to be comparable with similar properties estimated from measured rs-fMRI data. While this shows that these network models have similar properties over the dynamical landscape, it is unclear how well simulated trajectories compare with empirical trajectories on a timepoint-by-timepoint basis. Previous studies have shown that BNMs are able to produce relevant features at shorter timescales, but analysis of short-term trajectories or transient dynamics as defined by synchronized predictions from BNM made at the same timescale as the collected data has not yet been conducted. Relevant neural processes exist in the time frame of measurements and are often used in task fMRI studies to understand neural responses to behavioral cues. Therefore, it is important to investigate how much of these dynamics are captured by our current brain simulations. To test the nature of BNMs short term trajectories against observed data, we utilize a deep learning technique known as Neural ODE that based on an observed sequence of fMRI measurements, estimates the initial conditions such that the BNMs simulation is synchronized to produce the closest trajectory relative to the observed data. We test to see if the parameterization of a specific well studied BNM, the Firing Rate Model, calculated by maximizing its accuracy in reproducing observed short term trajectories matches with the parameterized model that produces the best average long-term metrics. Our results show that such an agreement between parameterization using long and short simulation analysis exists if also considering other factors such as the sensitivity in accuracy with relative to changes in structural connectivity. Therefore, we conclude that there is evidence that by solving for initial conditions, BNMs can be simulated in a meaningful way when comparing against measured data trajectories, although future studies are necessary to establish how BNM activity relate to behavioral variables or to faster neural processes during this time period.