Volumetric k-Space Trajectories Via Genetic Algorithms

A pseudo-random, velocity-insensitive, volumetric k-space sampling trajectory is designed for use with balanced steady state imaging. Individual arcs are designed independently and do not fit together in the way that multi-shot spiral, radial or echo-planar trajectories do. Previously, it was shown that second-order cone optimization problems can be defined for each arc independent of the others, that nulling of zeroth and higher moments can be encoded as constraints, and that individual arcs can be optimized in seconds. For use in steady state imaging, sampling duty cycles exceed 95 percent. Using such pseudo-random trajectories, aliasing caused by undersampling manifests itself as incoherent noise. In this paper, a genetic algorithm is formulated and numerically evaluated. A large set of arcs is designed using previous methods, and the genetic algorithm choses particular fit subsets of a given size, corresponding to a desired acquisition time. Numerical simulations of 1s acquisitions show good detail and acceptable noise for large-volume imaging with 32 coils.