Advances in magnetic resonance imaging (MRI) allow to gain critical insight into the structure of neural networks and their functional dynamics. To relate structural connectivity [as quantified by diffusion-weighted imaging (DWI) tractography] and functional connectivity [as obtained from functional MRI (fMRI)], increasing emphasis has been put on computational models of brain activity. In the present study, we use structural equation modeling (SEM) with structural connectivity to predict functional connectivity. The resulting model takes the simple form of a spatial simultaneous autoregressive model (sSAR), whose parameters can be estimated in a Bayesian framework. On synthetic data, results showed very good accuracy and reliability of the inference process. On real data, we found that the sSAR performed significantly better than two other reference models as well as than structural connectivity alone, but that the Bayesian procedure did not bring significant improvement in fit compared to two simpler approaches. Nonetheless, we also found that the values of the region-specific parameters inferred using Bayesian inference differed significantly across resting-state networks. These results demonstrate 1) that a simple abstract model is able to perform better that more complex models based on more realistic assumptions, 2) that the parameters of the sSAR can be estimated and can potentially be used as biomarkers, but also 3) that the sSAR, while being the best-performing model, is at best still a very crude model of the relationship between structure and function in MRI.
