Theoretical noise model for oxygenation‐sensitive magnetic resonance imaging

Contrast‐to‐noise ratio (CNR) in blood oxygenation level‐dependent (BOLD) based functional MRI (fMRI) studies is a fundamental parameter to determine statistical significance and therefore to map functional activation in the brain. The CNR is defined here as BOLD contrast with respect to temporal fluctuation. In this study, a theoretical noise model based on oxygenation‐sensitive MRI signal formation is proposed. No matter what the noise sources may be in the signal acquired by a gradient‐echo echo‐planar imaging pulse sequence, there are only three noise elements: apparent spin density fluctuations, S0(t); transverse relaxation rate fluctuations, R  2* (t); and thermal noise, n(t). The noise contributions from S0(t), R  2* (t), and n(t) to voxel time course fluctuations were evaluated as a function of echo time (TE) at 3 T. Both noise contributions caused by S0(t) and R  2* (t) are significantly larger than that of thermal noise when TE = 30 ms. In addition, the fluctuations between S0(t) and R  2* (t) are cross‐correlated and become a noise factor that is large enough and cannot be ignored. The experimentally measured TE dependences of noise, temporal signal‐to‐noise ratio, and BOLD CNR in finger‐tapping activation regions were consistent with the proposed model. Furthermore, the proposed theoretical models not only unified previously proposed BOLD CNR models, but also provided mechanisms for interpreting apparent controversies and limitations that exist in the literature. Magn Reson Med 53:1046–1054, 2005. © 2005 Wiley‐Liss, Inc.