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IntroductionFunctional magnetic-resonance imaging (fMRI) based on the blood oxygenation-level dependent (BOLD) signal is a powerful technique for studying the neural response in the cortex. Most previous work has been based on the assumption that the BOLD signal is a unitary response to a single form of stimulus S(t), usually in the form of a linear convolution of a hemodynamic response function (HRF) with the temporal waveform of the stimulus time sequence (Bandettini et al., 1993;Friston et al., 1994;Boynton et al., 1996). In most cases, it is assumed that the HRF incorporates both the cortical response to the stimulus and the hemodynamic response of the blood to the oxygen requirements of the cortical response. However, the situation may be much more complicated, with multiple components of neural response to the stimulus weighted differentially across the cortex (Zacks et al., 2001;d'Avossa et al., 2003;Bellgowan et al., 2003;Calhoun et al., 2004a;Fox et al., 2005), such that any one voxel contains contributions from more than one neural time course. If these time course variations are small relative to the BOLD temporal resolution, they may be negligible for an overall analysis of response strength, but the cited studies show non-negligible variations that require a more detailed analysis. For this reason, consistent with Friston et al. (1998Friston et al. ( , 2000, Buxton et al. (2004) and others, we restrict the term HRF to the dynamics of the blood response to the metabolic demands of the neural processing and consider the neural response to the stimulus as a separate process. This leads to the model of the BOLD mechanisms shown in Fig. 1.