Analysing Effective Connectivity of the Math-gifted Brain with Nonlinear Granger Causality

As the cornerstone of natural sciences, mathematics influences and changes our technology oriented world in systematic and progressive ways. The importance of fostering and developing mathematically gifted children/adolescents has been acknowledged widely. Spectral measures of linear Granger causality have been widely applied to study the causal connectivity between time series data in neuroscience, biology, and economics. Traditional Granger causality measures are based on linear autoregressive with exogenous inputs models of time series data, which cannot truly reveal nonlinear effects in the data especially in the frequency domain. In this paper, we used nonlinear Granger causality based on kernel methods to study the effective connectivity between the frontal brain area and the posterior brain area in the mathematical frontoparietal network system during deductive reasoning tasks. It was founded that the frontoparietal regions of the math-gifted show stronger working memory information processing at the θ-band and math-gifted group show more significant increase in the mid-front brain area and the posterior parietal area compared with control group.