In-vivo distortion of through-plane flow by spiral phase-contrast imaging

To explain previously unrecognised consequences of two sources of phase curvature over the vessel cross-section in spiral imaging i.e. off-resonance and the velocity-encoded phase-shift.


Summary
To explain previously unrecognised consequences of two sources of phase curvature over the vessel cross-section in spiral imaging i.e. off-resonance and the velocityencoded phase-shift.

Background
The effects of off-resonance frequency errors during spiral readouts [Yudilevich and Stark, 1987] are known. Here we explain previously unrecognised intra-voxel dephasing consequences of two sources of phase curvature over the vessel cross-section in through-plane flow imaging using spirals i.e. off-resonance and the velocityencoded phase-shift, including the consequences for invivo measurements.

Figure 1 shows magnitude and phase images for Ref and
Vel scans with corresponding velocity maps (VM). For low flow rates the off-resonance blurring at +40Hz and -40Hz is similar for both Ref. and Vel. images. However, high velocities cause an apparent "implosion" (Figure 1-I) and "explosion" (Figure 1-E) of the vessel for opposite off-resonance frequencies. From the distorted VMs, peak velocity was measured at 37.8, 48.6, 56.3cm/s for -40, 0, 40Hz off-resonance respectively.
For theoretical explanation, Figure 2a) depicts the ideal diametrical phase line profile across a tube velocity-compensated spiral imaging, red line = on-resonance and blue/green lines = phase curvature induced by ±40Hz off-resonance error. Figure 2b)-red shows velocity-encoded phase over the vessel with parabolic flow. Figure 2b)-blue shows the consequence of their addition: the increased radial slope worsens intra-voxel dephasing in all but the central pixels of a laminar flow ("implosion" effect, Figure 1-I). In Figure 2b)-green the opposing phase curvatures lead to a cancellation of the radial phase slope at some radius, which can lie outside the true lumen ("explosion" effect, Figure 1-E).

Conclusions
The distortion of the velocity distribution over the invivo vessel distorts peak velocity by~20% at -40Hz offresonance at these sequence parameters. Separate tests eliminated through-plane gradient fields as a cause, including eddy-current effects after the velocity-encoding pulses.
These effects on magnitude images and velocity distributions at <1ppm off-resonance are potentially difficult for >20ms spiral readouts in small vessel applications at least, perhaps more so near B0-distortions such as lungs. Shorter spirals and avoiding large intra-voxel radial phase shear are some-what incompatible with rapid flow work.   The phase across a small vessel with no flow is ideally flat with infinitely steep sides (a-red); off-resonance causes a distortion of the flat phase such that it becomes curved (simulated off-resonance) (a-blue/green) and can be seen in the LOW flow phase images in Figure 2 where both Ref ph and Vel ph are similar. Velocity mapping induces phase relative to velocity within a pixel, the ideal Ref. phase over the vessel with laminar flow remains flat (a-red) and for Vel. phase has parabolic profile (b-red). When the Vel. image is acquired with off-resonance, the phase from these 2 effects can add constructively or destructively resulting in distortion of the velocity profile (Figure 1-PEAK VM). Signal loss in edge pixels with high velocity shear can be increased (b-blue) or decreased (b-green) depending on the direction of the off-resonance phase resulting in the implosion (Figure 1-I) and explosion (Figure 1-E) artefacts in Vel. mg images.