Optimal control flow encoding for time-efficient magnetic resonance velocimetry

Abstract

Phase contrast velocimetry relies on bipolar gradients to establish a direct and linear relationship between the phase of the magnetic resonance signal, and the corresponding fluid motion. Despite its utility, several limitations and drawbacks have been reported, the most important being the extended echo time due to the encoding after the excitation. In this study, we elucidate a new approach based on optimal control theory that circumvents some of these disadvantages. An excitation pulse, termed FAUCET (flow analysis under controlled encoding transients), is designed to encode velocity into phase already during the radiofrequency excitation. As a result of concurrent excitation and flow encoding, and hence elimination of post-excitation flow encoding, FAUCET achieves a shorter echo time than the conventional method. This achievement is a matter of significance not only because it decreases the loss of signal due to spin–spin relaxation and B0 inhomogeneity, but also because a shorter echo time is always preferred in order to reduce the dimensionless dephasing parameter and the required residence time of the flowing sample in the detection coil. The method is able to establish a non-linear bijective relationship between phase and velocity, which can be employed to enhance the resolution over a specific range of velocities, for example along flow boundaries. A computational comparison between the phase contrast and optimal control methods reveals that the latter’s encoding is more robust against remnant higher-order-moment terms of the Taylor expansion for faster voxels, such as acceleration, jerk, and snap.