Dynamic Causal Modeling for fMRI With Wilson-Cowan-Based Neuronal Equations

Abstract

Dynamic causal modeling (DCM) is an analysis technique that has been successfully used to infer about directed connectivity between brain regions based on imaging data such as functional magnetic resonance imaging (fMRI). Most variants of DCM for fMRI rely on a simple bilinear differential equation for neural activation, making it difficult to interpret the results in terms of local neural dynamics. In this work, we introduce a modification to DCM for fMRI by replacing the bilinear equation with a non-linear Wilson-Cowan based equation and use Bayesian Model Comparison (BMC) to show that this modification improves the model evidences. Improved model evidence of the non-linear model is shown for our empirical data (imitation of facial expressions) and validated by synthetic data as well as an empirical test dataset (attention to visual motion) used in previous foundational papers. For our empirical data, we conduct the analysis for a group of 42 healthy participants who performed an imitation task, activating regions putatively containing the human mirror neuron system (MNS). In this regard, we build 540 models as one family for comparing the standard bilinear with the modified Wilson-Cowan models on the family-level. Using this modification, we can interpret the sigmoid transfer function as an averaged f-I curve of many neurons in a single region with a sigmoidal format. In this way, we can make a direct inference from the macroscopic model to detailed microscopic models. The new DCM variant shows superior model evidence on all tested data sets.