COMMSVAE: LEARNING THE BRAIN'S MACROSCALE COMMUNICATION DYNAMICS USING COUPLED SE-QUENTIAL VAES

Abstract

Communication within or between complex systems is commonplace in the natural sciences and fields such as graph neural networks. The brain is a perfect example of such a complex system, where communication between brain regions is constantly being orchestrated. To analyze communication, the brain is often split up into anatomical regions that each perform certain computations. These regions must interact and communicate with each other to perform tasks and support higher-level cognition. On a macroscale, these regions communicate through signal propagation along the cortex and along white matter tracts over longer distances. When and what types of signals are communicated over time is an unsolved problem and is often studied using either functional or structural data. In this paper, we propose a non-linear generative approach to communication from functional data. We address three issues with common connectivity approaches by explicitly modeling the directionality of communication, finding communication at each timestep, and encouraging sparsity. To evaluate our model, we simulate temporal data that has sparse communication between nodes embedded in it and show that our model can uncover the expected communication dynamics. Subsequently, we apply our model to temporal neural data from multiple tasks and show that our approach models communication that is more specific to each task. The specificity of our method means it can have an impact on the understanding of psychiatric disorders, which are believed to be related to highly specific communication between brain regions compared to controls. In sum, we propose a general model for dynamic communication learning on graphs, and show its applicability to a subfield of the natural sciences, with potential widespread scientific impact.

1. INTRODUCTION

Characterizing macroscale communication between brain regions is a complex and difficult problem, but is necessary to understand the connection between brain activity and behavior. The effect of neural systems on each other, or connectivity, has also been linked to psychiatric disorders, such as schizophrenia Friston (2002) . Hence, gaining a deeper understanding of the dynamics underlying the communication between brain regions is both from the perspective of understanding how our brain facilitates higher-order cognition and also to provide insight into and consequently how psychiatric disorders arise. Static functional network connectivity (sFNC) and dynamic functional network connectivity (dFNC), computed respectively as the Pearson correlation between regional activation timeseries over the full scan duration (sFNC) or on shorter sliding windows (dFNC), are among the most widely reported measures of connectivity between brain regions Hutchison et al. (2013) . These approaches calculate the correlation between the timeseries of each brain region to find their coherence, either across the full timeseries (sFNC) or by windowing the timeseries and calculating the correlation within each window (dFNC). Although extensions have been proposed Hutchison et al. (2013) , along with more complex connectivity measures, such as wavelet coherence Yaesoubi et al. (2015) , multiplication of temporal derivates Shine et al. (2015) , and Granger causality Roebroeck et al. (2005); Seth et al. (2015) , Pearson correlation remains the most prevalent measure of brain network connectivity. And even the less commonly employed metrics have issues stemming from some combination of sensitivity to noise, linearity, symmetry, or coarse timescales. Most im-portantly, these approaches do not directly model the communication, but rather analyze it post-hoc. The pursuit of instantaneous communication between brain regions Sporns et al. ( 2021) and generative approaches to model communication can potentially lead to models that closely resemble effective connectivity Avena-Koenigsberger et al. (2018) . An important advantage of generative models is that they allow us to move away from post-hoc inference from context-naïve metrics toward simulating macroscale brain communication. We propose the use of recurrent neural networks as generative models of communication on both simulated data and functional magnetic resonance imaging (fMRI) data to validate and demonstrate the specificity of our model. Our method complements connectivity metrics, since it does more than quantify the aggregation of communication Avena-Koenigsberger et al. (2018) , but directly simulates it, and can thus be analyzed using those same connectivity metrics. Creating an accurate generative model of the macroscale communication dynamics in the brain is hard, due to its complexity. However, there are some general design principles the brain follows Sterling & Laughlin (2015) . Generally, the brain tries to minimize its energy use, which is likely also true for communication in the brain. Macroscale communication is an energy-intensive process and involves white matter tracts, which are essentially highways that connect spatially separate parts of the brain. Hence, the amount of information and the number of times information is sent should generally be limited. The bits needed to convey are limited by the brain using sparse coding, which at a lower scale is how neurons encode and communicate information Olshausen & Field (2004) . Although mechanistically different, due to metabolic and volume constraints, macroscale communication presumably exhibits strategies similar to sparse coding to efficiently transfer information between neural populations Bullmore & Sporns (2012); Sterling & Laughlin (2015) . To incorporate this inductive bias into our model, we regularize the communication from one region in our model to another using a KL-divergence term to a Laplace distribution. The communication itself is modeled as a Laplace distribution and by minimizing its divergence from a Laplace distribution we encourage sparser temporal communication. Encouraging sparse temporal communication implies that information is only sent when necessary, and lower rates of communication lead to reductions in the brain's energy requirements. As far as we are aware, this is the first model that explicitly models communication dynamics between vertices on a graph, specifically between brain regions. The connectivity metrics that are used currently assume that the connectivity between brain regions is stationary, e.g. Granger causality, and lack a generative model. Although non-linear generative models have been proposed for connectivity Stephan et al. (2008) , however, determining the correct model is intractable Lohmann et al. (2012) . Furthermore, most methods quantify the coupling between brain regions and do not consider potentially rapid changes in fMRI signals that can be traced from region to region. In this paper, we specifically try to model the communication between brain regions, which likely relates to these abrupt and parsimonious changes in the signal. This means that our model is finding a type of interaction between brain regions, or more generally nodes on a graph, that has never been studied in this way before, to the best of our knowledge. The assumptions we make thus also differ from commonly used connectivity metrics. Firstly, we assume directionality and communication with the same temporal resolution as the original signal. Hence, we completely move away from windowed approaches, that quantify the coupling between brain regions within windows. Secondly, we assume that brain regions are largely independent and can be modeled by a dynamical system with sparse inputs. Lastly, we aim to learn a fully generative model of fMRI data, where the communications and initial state of each brain region's dynamical system can be sampled from a simple distribution. This also implies that our method is hard to compare with more common connectivity metrics, and we expect it to exhibit different behavior since it is modeled under different assumptions. We propose this model because we believe it has tremendous value and complements many connectivity metrics in a meaningful way, not only in the neuroimaging community, but also in other scientific fields, such as sociology Barnes (1969) , computational biology or chemistry Balaban (1985) , and traffic prediction models Zhao et al. (2019) . The goal of our model is to get a better idea of communication dynamics in the brain. To evaluate whether our model is equipped to find the underlying dynamics of a known generative model, we first train it on simulated data. After we show that our model finds the correct generative model from the simulated data, we apply our model to neuroimaging data with fairly well-established neural pathways. Although the pathways are well-established, we do not know the exact ground truth communication underlying fMRI data. We do know that communication dynamics depend on

