= Magnetic resonance velocity encoding
<Magnetic resonance velocity encoding> makes a component of motion measurable through the <phase> of a <nuclear magnetic resonance> signal. Controlled <magnetic field gradients> give different phase shifts to spins with different trajectories. <Phase-contrast magnetic resonance imaging> compares encodings to extract a <velocity> component, rather than interpreting ordinary image brightness as speed.<A flow velocity zeugmatographic interlace for NMR imaging in humans by P. R. Moran>[Primary abstract: phase-sensitive flow encoding and reconstructed motion information]{ref}
In an original idealized model, assume constant <velocity> $v$ along one encoding axis and effective gradients with equal <gradient zeroth moments>. Then the encoding difference obeys
$$
\Delta\phi=\gamma v\Delta m_1,
$$
where $\gamma$ is the angular <gyromagnetic ratio> and $\Delta m_1$ is the <gradient first moment> difference. For $\gamma=2\pi\cdot42.58\times10^6\,\mathrm{rad\,s^{-1}T^{-1}}$, $\Delta m_1=2\times10^{-8}\,\mathrm{T\,s^2/m}$ and $v=0.10\,\mathrm{m/s}$, this gives $\Delta\phi\simeq0.535\,\mathrm{rad}$. These stipulated values illustrate the conversion, rather than a particular scanner experiment.
Reversing the moment difference reverses the phase sign under this convention. Reducing its magnitude decreases sensitivity to a given <velocity> while increasing the <velocity encoding limit>. A measured voxel can contain a range of velocities, and background phase or phase <aliasing> can complicate reconstruction.
The encoded component also differs from <volumetric flow rate>: estimating transported volume requires combining the appropriate normal <velocity> with area and time, not merely recording one peak speed.
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