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Resting-state (rs) functional magnetic resonance imaging (fMRI) is used to detect low-frequency fluctuations in the blood oxygen-level dependent (BOLD) signal across brain regions. Correlations between temporal BOLD signal fluctuations are commonly used to infer functional connectivity. However, because BOLD is based on the dilution of deoxyhemoglobin, it is sensitive to veins of all sizes, and its amplitude is biased by draining veins. These biases affect local BOLD signal location and amplitude, and may also influence BOLD-derived connectivity measures, but the magnitude of this venous bias and its relation to vein size and proximity is unknown. Here, veins were identified using high-resolution quantitative susceptibility maps and utilized in a biophysical model to investigate systematic venous biases on common local rsfMRI-derived measures. Specifically, we studied the impact of vein diameter and distance to veins on the amplitude of low-frequency fluctuations (ALFF), fractional ALFF (fALFF), Hurst exponent (HE), regional homogeneity (ReHo), and eigenvector centrality values in the grey matter. Values were higher across all distances in smaller veins, and decreased with increasing vein diameter. Additionally, rsfMRI values associated with larger veins decrease with increasing distance from the veins. ALFF and ReHo were the most biased by veins, while HE and fALFF exhibited the smallest bias. Across all metrics, the amplitude of the bias was limited in voxel-wise data, confirming that venous structure is not the dominant source of contrast in these rsfMRI metrics. Finally, the models presented can be used to correct this venous bias in rsfMRI metrics.