The effect of intra- and inter-subject variability of hemodynamic responses on group level Granger causality analyses.

Granger causality analyses aim to reveal the direction of influence between brain areas by analyzing temporal precedence: if a signal change in area A consistently precedes a signal change in area B, then A Granger-causes B. fMRI-based Granger causality inferences are mediated by the hemodynamic response function which can vary across brain regions. This variability might induce a bias in Granger causality analyses. Here we use simulations to investigate the effect of hemodynamic response variability on Granger causality analyses at the level of a group of twenty participants. We used a set of hemodynamic responses measured by Handwerker et al. (Neuroimage, 2004) and simulated 200 experiments in which time series with known directions of influence are convolved with these hemodynamic responses and submitted to Granger causality analysis. Results show that the average chance to find a significant Granger causality effect when no actual influence is present in the data stays well below the p-level imposed on the second level statistics. Most importantly, when the analyses reveal a significant directed influence, this direction was accurate in the vast majority of the cases. The sensitivity of the analyses however depended on the neuronal delay between the source and target regions and their relative hemodynamic delay. Influences flowing from regions to one with the same or a slower hemodynamic response function were detected in over 80% of the cases when the neuronal delay was at least 100 ms. Influences flowing to a region with a faster hemodynamic delay were detected in over 80% of the cases when delays are above 1s.