The Fastest Arbitrary k-space Trajectories

Introduction: We present a method to compute the fastest possible gradient waveforms for a given k-space trajectory. In our design, we exploit the fact that each gradient set has its own limitation. This is an extension of our previous method described in [1]. In that solution, the worst-case magnitude gradient and slew constraints were considered. This has the advantage of resulting in waveforms that are invariant to any rotation of the trajectory, at the expense of sub-utilizing the hardware. Here, we present an improvement of the algorithm. We constraint the waveforms for each gradient set separately, while still requiring that the trajectory follows the desired kspace path. This produces the fastest waveforms. A redesign is needed when the trajectory is rotated, as the solution depends on the orientation of the curve. Our algorithm is fast and non-iterative and can compute waveforms on-the-fly.