Bypassing the volume conduction effect by multilayer neural network for effective connectivity estimation

Differentiation of real interactions between different brain regions from spurious ones has been a challenge in neuroimaging researches. While using electroencephalographic data, those spurious interactions are mostly caused by the volume conduction (VC) effect between the recording sites. In this study, we address the problem by jointly modeling the causal relationships among brain regions and the mixing effects of volume conduction. The VC effect is formulated with a time-invariant linear equation, and the causal relationships between the brain regions are modeled with a nonlinear multivariate autoregressive process. These two models are simultaneously implemented by a multilayer neural network. The internal hidden layers represent the interactions among the regions, while the external layers are devoted for the relationship between the source activities and observed EEG measurements at the scalp. The causal interactions are estimated by the causality coefficient measure, which is based on the information (weights and parameters) embedded in the network. The proposed method is verified using various simulated data. It is then applied to the real EEG signals collected from a memory retrieval test. The results showed that the method is able to eliminate the volume conduction interferences and consequently leads to higher accuracy in identification of true causal interactions. Graphical abstract The proposed network structure used to simultaneously model the volume conduction and source interactions. By this special structure, we first move from the sensor space to the source space at the first layer. Then, within internal hidden layers, the interactions between the sources are represented in the form of a general (nonlinear) multivariate autoregressive (nMVAR) model. Finally, we return from the source space to the sensor space at the last layer of the network. The proposed method bypasses the effect of volume conduction and causes more accurate connectivity estimation.