Velocity vector reconstruction for real‐time phase‐contrast MRI with radial Maxwell correction

Purpose To develop an auto‐calibrated image reconstruction for highly accelerated multi‐directional phase‐contrast (PC) MRI that compensates for (1) reconstruction instabilities occurring for phase differences near ±π and (2) phase errors by concomitant magnetic fields that differ for individual radial spokes. Theory and Methods A model‐based image reconstruction for real‐time PC MRI based on nonlinear inversion is extended to multi‐directional flow by exploiting multiple flow‐encodings for the estimation of velocity vectors. An initial smoothing constraint during iterative optimization is introduced to resolve the ambiguity of the solution space by penalizing phase wraps. Maxwell terms are considered as part of the signal model on a line‐by‐line basis to address phase errors by concomitant magnetic fields. The reconstruction methods are evaluated using simulated data and cross‐sectional imaging of a rotating‐disc, as well as in vivo for the aortic arch and cervical spinal canal at 3T. Results Real‐time three‐directional velocity mapping in the aortic arch is achieved at 1.8 × 1.8 × 6 mm3 spatial and 60 ms temporal resolution. Artificial phase wraps are avoided in all cases using the smoothness constraint. Inter‐spoke differences of concomitant magnetic fields are effectively compensated for by the model‐based image reconstruction with integrated radial Maxwell correction. Conclusion Velocity vector reconstructions based on nonlinear inversion allow for high degrees of radial data undersampling paving the way for multi‐directional PC MRI in real time. Whether a spoke‐wise treatment of Maxwell terms is required or a computationally cheaper frame‐wise approach depends on the individual application.