Figure 3.

The effects of chemical shift phase (φ _CS) on quantitative PC-MRI measurements. (a) In the absence of chemical shift and other phase errors, flowing spins are encoded with an amount of phase proportional to their velocity (φ_v, black arrow). When chemical shift effects are taken into consideration the choice of high or low bandwidth (HBW or LBW) scales the magnitude (radius of the gray circles in (a)) of the complex fat factor because it controls the percent of partial-volume fat. HBW results in a lower percent of partial-volume fat (reduced magnitude) than LBW, which for a fixed TE results in φ _CS,HBW < φ _CS,LBW. In (b) it is apparent that the TE determines the phase of the complex fat factor (dashed arrow), which adds to the blood velocity vector (black arrow) to produce the Z_C or Z_E complex signal (gray arrow) and subsequently impacts the magnitude of the phase error. TE_IN leads the fat vector to be closely aligned with the blood vector when the blood velocity is low, which is typical of the vessel lumen periphery where CS effects are likely to be problematic. The use of TE_IN leads to reduced error from chemical shift (φ _CS,TE−π/2 < φ _CS,TEIN < φ _v,Blood < φ _CS,TEOUT < φ_CS,TE+π/2) for slow flowing blood near the vessel lumen periphery. In summary, the chemical shift error (φ_CS) depends on the magnitude and phase of the fat vector the phase of the water vector (φ_v). The use of HBW and TE_IN can minimize CS effects in PC-MRI.