Optimisation of velocity encoding gradients for phase contrast gas velocity taking diffusion into account

Introduction Phase contrast MRI which is commonly used to map blood [1]has been applied more recently to map gas velocities using hyperpolarized tracers[2, 3].The bipolar gradient used to induce a phase shift proportional to velocity also introduces diffusion weighting. This can be safely neglected considering diffusion coefficients of liquids. However, for a gas, diffusion can no longer be neglected [3]. As an illustration on helium, considering an encoding time of 10ms for spins moving at 20 cm.s, the displacement (2mm) becomes the same as the mean diffusion length. Blurring is introduced and a loss of precision in the phase measurement is obtained. While the precision on the velocity measurement can be enhanced by increasing the gradient 1st moment, there is a competition with the loss introduced by diffusion weighting. Here, considering both phenomena, we derive theoretically and verify experimentally the bipolar gradient characteristics for an optimized velocity measurement.