Figure 1
From: A graph neural network framework for causal inference in brain networks
An overview of the DCRNN model. The model consists of an encoder and decoder (a), modified to process graph structured signals (b). In our context, vertices (nodes) \({\mathcal {V}}, |{\mathcal {V}}| = N\) of the graph \(\mathcal {G}\) are defined as N brain regions, derived from an atlas (b2). Structural connections between brain regions are derived from DTI, quantifying the strength of edge connections in the graph (b1). The signal on the graph \({\mathbf {x}}(t)\) at a certain time point t is the average BOLD signal in brain regions/nodes, obtained by the fMRI measurement at time t (b3). The encoder (a) receives an input sequence \([{\mathbf {x}}(1),\ldots ,{\mathbf {x}}(T_p)]\), and iteratively updates its hidden state H(t). The final encoder state \(H(T_p)\) is passed to the decoder part, which learns to recursively predict the output sequence of graph signals \([{\mathbf {x}}(T_p+1),\ldots ,{\mathbf {x}}(T_p + T_f)]\) in the future. The encoder, as well as the decoder (c) consist of diffusion convolution gated recurrent unit cells (DCGRU). The first encoder and decoder cell receive the input graph signal, and they pass their hidden state to the subsequent cell. In the decoding part, the final cell of the decoder generates then the predicted signal (c). During testing and validation, the decoder uses its own outputs as inputs, to generate the subsequent output. The first input of the decoder (\(<GO>\) symbol) is simply a vector of zeros. Figure (b1) was created with the MRtrix3 software package35 (version 3.0) : https://www.mrtrix.org/, and figure (b2) and (b3) with the Connectome Workbench (version 1.4.2): https://www.humanconnectome.org/software/connectome-workbench.
