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.^[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 obeyswhere $\gamma$ is the angular gyromagnetic ratio and $\Delta m_1$ is the gradient first moment difference. For $\gamma =2\pi \cdot 42.58\times 10^6\mathrm{rad}{\mathrm{s}}^{-1}{\mathrm{T}}^{-1}$, $\Delta m_1=2\times 10^{-8}\mathrm{T}{\mathrm{s}}^2/m$ and $v=0.10m/s$, this gives $\Delta \varphi \simeq 0.535\mathrm{rad}$. 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.