Effect of HRF spatial variability on the accuracy of multivariate Granger causal networks obtained from fMRI data

Introduction The hemodynamic response function (HRF) of fMRI data is known to vary across subjects and brain regions [1]. Since HRF variability may be dictated, in part, by nonneuronal considerations, it has the potential to confound inferences about directional neuronal influences obtained from Granger causality (GC) analysis of fMRI data [2]. However, a systematic investigation of this confound and its effect on the accuracy of Granger-based networks obtained from fMRI is lacking. Here, we investigate this aspect in a multivariate fashion using a simulated neuronal system. Methods The ground truth for the causal interactions between neuronal systems was established using local field potentials (LFPs) obtained from the macaque cortex sampled at 1 KHz, owing to the very high temporal resolution they offer and the fact that they represent a direct measure of neuronal activity. In order to simulate multivariate causal relationships, we first sliced each LFP time series x(n) of length l into three parts, x1(n), x2(n) and x3(n) with lengths l1, l2 and l3 ms, respectively, such that