![]() Graph diffusion models naturally employ the Laplacian of SC and have been generalized to yield spectral graph models whereby Laplacian eigenspectra were sufficient to reproduce functional patterns of brain activity using only a few eigenmodes ( Atasoy et al., 2016 Abdelnour et al., 2018 Raj et al., 2020). An early example of this was our proposal of using low-dimensional processes involving diffusion or random walks on the structural graph as a simple means of simulating FC from SC ( Abdelnour et al., 2014). The key driving insight here is that the brain's activity is macroscopically linear to a large extent ( Abdelnour et al., 2014 Nozari et al., 2020 Raj et al., 2020). However, stochastic simulations are unable to provide a closed form solution and inherently suffer from lack of interpretability since dynamics are only achieved from iterative optimizations of high dimensional NMM parameters.ĭue to these challenges many laboratories are exploring parsimonious models that leverage the brain's macroscale linearity through a relationship between structural and functional network eigenmodes. Using these techniques such simulation methods are able to achieve moderate correlation between simulated and empirical FC ( Nunez, 1974 Jirsa and Haken, 1997 Valdes et al., 1999 Honey et al., 2009 Spiegler and Jirsa, 2013). Structurally coupled neural mass models (NMMs) use the brain's connections to couple anatomically connected neuronal assemblies and perform lengthy numerical simulations to approximate the brain's local and global activity. Evolution of the structural and functional networks have been investigated using graph theoretical statistics ( Chatterjee et al., 2008 Bullmore and Sporns, 2009 He et al., 2010 Bassett and Bullmore, 2017 Liang and Wang, 2017). ![]() Recently, graph based methods have been employed to relate the brain's SC to FC. While complex dynamic neural activity must propagate over a static structural network, whether and to what extent the correlation structure of the latter can be directly predicted from the former is a subject of active interest. We also investigate the impact of local activity diffusion and long-range interhemispheric connectivity on the structure-function model and show an improvement in functional connectivity prediction when accounting for such latent variables which are often excluded from traditional diffusion tensor imaging (DTI) methods.ĭetermining the correspondence between the brain's structural white matter connectivity (SC) network and its temporally dependent functional connectivity (FC) network is of fundamental import in neuroscience and may inform characteristics of brain disease. ![]() Here we show a simple model relating the eigenvalues of the structural connectivity and functional networks using the Gamma function, producing a reliable prediction of functional connectivity with a single model parameter. Previous work has demonstrated that linear graph-theoretic models perform as well as non-linear neural simulations in predicting functional connectivity with the added benefits of low dimensionality and a closed-form solution which make them far less computationally expensive. Understanding how complex dynamic activity propagates over a static structural network is an overarching question in the field of neuroscience.
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