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International Journal of Biomedical Imaging
Volume 2006 (2006), Article ID 12014, 11 pages

BOLD Noise Assumptions in fMRI

1Brain Mapping Unit, Department of Psychiatry, University of Cambridge, Addenbrooke's Hospital, Hills Road, Cambridge CB2 2QQ, United Kingdom
2Institute for Mathematics and Computing Science, University of Groningen, P.O. Box 800, Groningen 9700 AV, The Netherlands
3Institute for Behavioral and Cognitive Neurosciences and BCN Neuroimaging Center, University of Groningen, The Netherlands

Received 30 January 2006; Revised 13 June 2006; Accepted 17 June 2006

Copyright © 2006 Alle Meije Wink and Jos B. T. M. Roerdink. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper discusses the assumption of Gaussian noise in the blood-oxygenation-dependent (BOLD) contrast for functional MRI (fMRI). In principle, magnitudes in MRI images follow a Rice distribution. We start by reviewing differences between Rician and Gaussian noise. An analytic expression is derived for the null (resting-state) distribution of the difference between two Rician distributed images. This distribution is shown to be symmetric, and an exact expression for its standard deviation is derived. This distribution can be well approximated by a Gaussian, with very high precision for high SNR, and high precision for lower SNR. Tests on simulated and real MR images show that subtracting the time-series mean in fMRI yields asymmetrically distributed temporal noise. Subtracting a resting-state time series from the first results in symmetric and nearly Gaussian noise. This has important consequences for fMRI analyses using standard statistical tests.