The fastest gradient waveforms for arbitrary and optimized k-space trajectories

A method for finding the fastest possible gradient waveforms for any given k-space trajectory is presented. It is an extension of our previously introduced solution. The original scheme provides an efficient and non-iterative method for designing the fastest freely rotatable gradient waveforms. Here, the hardware constraints are relaxed so that each axis is constrained independently. This produces the fastest possible non-rotatable waveforms that can be up to 10% faster than their previous counterparts. In addition, for circular trajectories we relax the path constraints. This results in new diamond-shaped trajectories, which are more optimized than circles for separable gradient sets, reducing the total travel time by up to an additional 11%. Analysis of performance for a variety of parameters including the sensitivity to field inhomogeneity compared to freely rotatable circle trajectories is presented.