Background: The blood oxygenation-level dependent (BOLD) functional magnetic resonance imaging (fMRI)\r\nmodality has been numerically simulated by calculating single voxel signals. However, the observation on single\r\nvoxel signals cannot provide information regarding the spatial distribution of the signals. Specifically, a single BOLD\r\nvoxel signal simulation cannot answer the fundamental question: is the magnetic resonance (MR) image a replica\r\nof its underling magnetic susceptibility source? In this paper, we address this problem by proposing a multivoxel\r\nvolumetric BOLD fMRI simulation model and a susceptibility expression formula for linear neurovascular coupling\r\nprocess, that allow us to examine the BOLD fMRI procedure from neurovascular coupling to MR image formation.\r\nMethods: Since MRI technology only senses the magnetism property, we represent a linear neurovascular-coupled\r\nBOLD state by a magnetic susceptibility expression formula, which accounts for the parameters of cortical\r\nvasculature, intravascular blood oxygenation level, and local neuroactivity. Upon the susceptibility expression of a\r\nBOLD state, we carry out volumetric BOLD fMRI simulation by calculating the fieldmap (established by susceptibility\r\nmagnetization) and the complex multivoxel MR image (by intravoxel dephasing). Given the predefined\r\nsusceptibility source and the calculated complex MR image, we compare the MR magnitude (phase, respectively)\r\nimage with the predefined susceptibility source (the calculated fieldmap) by spatial correlation.\r\nResults: The spatial correlation between the MR magnitude image and the magnetic susceptibility source is about\r\n0.90 for the settings of TE = 30 ms, B0 = 3 T, voxel size = 100 micron, vessel radius = 3 micron, and blood volume\r\nfraction = 2%. Using these parameters value, the spatial correlation between the MR phase image and the\r\nsusceptibility-induced fieldmap is close to 1.00.\r\nConclusion: Our simulation results show that the MR magnitude image is not an exact replica of the magnetic\r\nsusceptibility source (spatial correlation Ã?Å? 0.90), and that the MR phase image conforms closely with the\r\nsusceptibility-induced fieldmap (spatial correlation Ã?Å? 1.00).
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