OPTIKS: Optimized Gradient Properties Through Timing in k-Space

A customizable method (OPTIKS) for designing fast trajectory-constrained gradient waveforms with optimized time domain properties was developed. Given a specified multidimensional $k$ -space trajectory, the method optimizes traversal speed (and therefore timing) with position along the trajectory. OPTIKS facilitates optimization of objectives dependent on the time domain gradient waveform and the arc-length domain $k$ -space speed. OPTIKS is applied to design waveforms which limit peripheral nerve stimulation (PNS), minimize mechanical resonance excitation, and reduce acoustic noise. A variety of trajectory examples are presented including spirals, circular echo-planar-imaging, and rosettes. Design performance is evaluated based on duration, standardized PNS models, field measurements, gradient coil back-EMF measurements, and calibrated acoustic measurements. We show reductions in back-EMF of up to 94% and field oscillations up to 91.1%, acoustic noise decreases of up to 9.22 dB, and with efficient use of PNS models speed increases of up to 11.4%. The design method implementation is made available as an open source Python package through GitHub (https://github.com/mamccready/optiks).