Figure 1.

(a) A small vessel relative to the acquisition voxel size will suffer from partial-volume effects. (b) Such a voxel with partial-volume effects overlays two distinct tissue regions: vein and parenchyma (eg gray matter). (c) A voxel containing entirely gray matter has a complex signal with magnitude M_a and phase φ_a. (d) A voxel containing entirely venous blood has a complex signal with magnitude M_b and phase φ_b. (e) A voxel containing regions of each tissue consists of a fraction α of blood, and a fraction 1 − α of gray matter. (f) The partial-volume voxel signal will be the sum of the signals in (c) and (d) weighted by the fractions in (e). φ_a, φ_b, M_a, M_b, α, φ_vox, and M_vox are defined in Table 1. (g) Simplified 1D example where the vessel binary mask b(x) coincides with the main lobe of the voxel function v(x), and α > 1. (h) 1D example where b(x) coincides with a negative lobe of v(x), and α < 0. In (g) and (h), the different limits of integration represent the different spatial extents of the respective blood vessels. (i) For the same system as in (h), an adjacent voxel has positive α with a larger magnitude.