On time delay estimation and sampling error in resting-state fMRI.

Accumulating evidence indicates that resting-state functional magnetic resonance imaging (rsfMRI) signals correspond to propagating electrophysiological infra-slow activity (<0.1 Hz). Thus, pairwise correlations (zero-lag functional connectivity (FC)) and temporal delays among regional rsfMRI signals provide useful, complementary descriptions of spatiotemporal structure in infra-slow activity. However, the slow nature of fMRI signals implies that practical scan durations cannot provide sufficient independent temporal samples to stabilize either of these measures. Here, we examine factors affecting sampling variability in both time delay estimation (TDE) and FC. Although both TDE and FC accuracy are highly sensitive to data quantity, we use surrogate fMRI time series to study how the former is additionally related to the magnitude of a given pairwise correlation and, to a lesser extent, the temporal sampling rate. These contingencies are further explored in real data comprising 30-min rsfMRI scans, where sampling error (i.e., limited accuracy owing to insufficient data quantity) emerges as a significant but underappreciated challenge to FC and, even more so, to TDE. Exclusion of high-motion epochs exacerbates sampling error; thus, both sides of the bias-variance (or data quality-quantity) tradeoff associated with data exclusion should be considered when analyzing rsfMRI data. Finally, we present strategies for TDE in motion-corrupted data, for characterizing sampling error in TDE and FC, and for mitigating the influence of sampling error on lag-based analyses.