Time‐optimal multidimensional gradient waveform design for rapid imaging

Magnetic resonance imaging (MRI) is limited in many cases by long scan times and low spatial resolution. Recent advances in gradient systems hardware allow very rapid imaging sequences, such as steady-state free precession (SSFP), which has repetition times (TRs) of 2-5 ms. The design of these rapid sequences demands time-optimal preparatory gradient waveforms to provide maximum readout duty-cycle, and preserve spatial resolution and SNR while keeping TRs low. Time-optimal gradient waveforms can be synthesized analytically for certain simple cases. However, certain problems, such as time-optimal 2D and 3D gradient design with moment constraints, either may not have a solution or must be solved numerically. We show that time-optimal gradient design is a convex-optimization problem, for which very efficient solution methods exist. These methods can be applied to solve gradient design problems for oblique gradient design, spiral imaging, and flow-encoding using either a constant slew rate or the more exact voltage-limited gradient models. Ultimately, these methods provide a time-optimal solution to many 2D and 3D gradient design problems in a sufficiently short time for interactive imaging.