Componential Granger causality, and its application to identifying the source and mechanisms of the top-down biased...

We describe a new measure of Granger causality, componential Granger causality, and show how it can be applied to the identification of the directionality of influences between brain areas with functional neuroimaging data. Componential Granger causality measures the effect of y on x, but allows interaction effects between y and x to be measured. In addition, the terms in componential Granger causality sum to 1, allowing causal effects to be directly compared between systems. We show using componential Granger causality analysis applied to an fMRI investigation that there is a top-down attentional effect from the anterior dorsolateral prefrontal cortex to the orbitofrontal cortex when attention is paid to the pleasantness of a taste, and that this effect depends on the activity in the orbitofrontal cortex as shown by the interaction term. Correspondingly there is a top-down attentional effect from the posterior dorsolateral prefrontal cortex to the insular primary taste cortex when attention is paid to the intensity of a taste, and this effect depends on the activity of the insular primary taste cortex as shown by the interaction term. Componential Granger causality thus not only can reveal the directionality of effects between areas (and these can be bidirectional), but also allows the mechanisms to be understood in terms of whether the causal influence of one system on another depends on the state of the system being causally influenced. Componential Granger causality measures the full effects of second order statistics by including variance and covariance effects between each time series, thus allowing interaction effects to be measured, and also provides a systematic framework within which to measure the effects of cross, self, and noise contributions to causality. The findings reveal some of the mechanisms involved in a biased activation theory of selective attention.