Nonlinear Conditional Time-Varying Granger Causality of Task fMRI via Deep Stacking Networks and Adaptive Convolutional Kernels

Abstract

Time-varying Granger causality refers to patterns of causal relationships that vary over time between brain functional time series at distinct source and target regions. It provides rich information about the spatiotemporal structure of brain activity that underlies behavior. Current methods for this problem fail to quantify nonlinear relationships in source-target relationships, and require ad hoc setting of relationship time lags. This paper proposes deep stacking networks (DSNs), with adaptive convolutional kernels (ACKs) as component parts, to address these challenges. The DSNs use convolutional neural networks to estimate nonlinear source-target relationships, ACKs allow these relationships to vary over time, and time lags are estimated by analysis of ACKs coefficients. When applied to synthetic data and data simulated by the STANCE fMRI simulator, the method identified ground-truth time-varying causal relationships and time lags more robustly than competing methods. The method also identified more biologically-plausible causal relationships in a real-world task fMRI dataset than a competing method. Our method is promising for modeling complex functional relationships within brain networks.