Fast imaging sequences exploit higher gradient magnetic field amplitudes, slew rates, and efficient non-Cartesian k-space trajectories.  With these improvements comes greater safety concerns as PNS, acoustic noise, and the risk of system damage increase. To address these problems we introduce a framework for optimizing time-domain properties, while adhering to an arbitrary specified trajectory. 

OPTIKS optimizes the speed along a trajectory as a function of arclength. This speed uniquely determines the time parameterization of the trajectory and therefore the gradient waveforms. By approximating the arclength-time domain transformation as differentiable we are able to simultaneously impose constraints and loss terms in both domains and guarantee no trajectory deviation (neglecting system imperfections).