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Introduction
Functional Magnetic Resonance Imaging (fMRI) is a widely applied method for measuring brain activation in humans. For some purposes of fMRI, such as the planning for neurosurgery (Rutten et al., 2002 ), the definition of phenotypes in genetic studies (Turetsky et al., 2007 ), or clinical trials predicting the outcome of pharmacological treatment (Chen et al., 2007 ), a high degree of reliability is demanded, meaning that differences with retesting should be minimal. However, it is well known that activation maps in the same subjects can contain substantial variation across sessions (McGonigle et al., 2000 ).
This is not surprising, as the fMRI signal not only contains activation related signal (i.e. Blood Oxygen Level Dependent (BOLD) signal) but also noise. This noise is produced both by the scanner and by human physiological processes such as heartbeat and respiration (Kruger and Glover, 2001; van Buuren et al., 2009 ). Because of this noise, the estimate of the true BOLD signal in a certain voxel will fluctuate around the true underlying mean BOLD signal. We postulate that this true underlying BOLD signal would be revealed should one obtain a number of scans that approaches infinity during each experimental session. We believe however, in regular fMRI experiments the number of obtainable samples is limited, so noise in the fMRI signal is an important factor for determining reliability (Bennett and Miller, 2010 ).
Besides noise, the estimates of the underlying BOLD signal can also differ because there are in fact true underlying BOLD signal changes between sessions. This true variation, as opposed to variation due to noise, refers to between-session signal changes that are larger than would be expected based on noise alone. More specifically, we define the true variation as the variation in signal that would be measured when we have a number of scans that approaches infinity. In this study we want to estimate the amount of true variation. An estimate of true variation in the underlying BOLD signal can yield a theoretical limit of fMRI reliability of individual measurements. A theoretical limit of fMRI reliability is an important piece of knowledge not only for assessing feasibility of future fMRI studies, but also for providing a more elaborate background for...