Lag-based effective connectivity applied to fMRI: a simulation study highlighting dependence on experimental parameters and formulation

A vast repertoire of methods is currently available to study effective brain connectivity based on neuroimaging data, among which lag-based measures can be distinguished. Although several studies have previously assessed the performance of such measures, their validity in different conditions remains unclear. In the current study, several lag-based effective connectivity measures are tested and benchmarked using simulated fMRI data, conceived to reflect a broad range of different situations with practical interest. The main goal is two-fold: 1) to provide a thorough overview of lag-based effective connectivity measures, and 2) to assess their performance in specific experimental conditions, thereby providing guidance for future effective connectivity studies involving fMRI. We focus on well-known lag-based measures, cover existing improvements and alternative formulations in some cases: Granger causality (GC), Geweke's Granger causality (GGC), directed transfer function (DTF), partial directed coherence (PDC), phase slope index (PSI), and transfer entropy (TE). Benchmarking consists in identifying causal relations in local field potential (LFP) networks that have their output convolved with a canonical hemodynamic response function (HRF) with varying node number, topology, coupling strength, neuronal delay, repetition time (TR), signal-to-noise ratio (SNR) and HRF variability. In a first set of simulations, we cover all possible combinations of discretized values of the previous variables, for networks with 2 and 3 nodes, and find that the measure with best performance (time-domain Granger Causality) is able to detect neuronal delays of a few hundreds of milliseconds with TRs between 0.25 and 2s and neuronal delays below 100ms for TRs that are also below 100ms, with more than 80% accuracy in realistic conditions. For networks with more than 3 nodes, we find that the number of nodes and the density of causal links degrade sensitivity, especially if the number of observations does not compensate for the increase in nodes, and that clustered networks can be more easily identified. In conclusion, this study argues in favor of the applicability of lag-based measures in the context of fMRI, provided that a stringent set of experimental specifications is met and that the chosen measure is applied with full knowledge of its limitations and specific constraints.