Three dimensional k-space trajectory design using genetic algorithms

Image quality and total scan time in MRI are determined in large part by the trajectory employed to sample the Fourier space. Each trajectory has different properties like coverage of k-space, scan time, sensitivity to off-resonance conditions, etc. These properties are often contradictory, therefore a universal optimal trajectory does not exist and ultimately, it will depend on the image characteristics sought. Most trajectories used today are designed based on intuition and k-space analysis more than with optimization methods. This work presents a 3D k-space trajectory design method based on Genetic Algorithm optimization. Genetic Algorithms have been chosen because they are particularly good for searching large solution spaces. They emulate the natural evolutionary process allowing better offsprings to survive. The objective function searches the maximum of the trajectory's k-space coverage subject to hardware constraints for a fixed scanning time using the trajectory's torsion as its optimization variable. The method proved to be effective for generating k-space trajectories. They are compared with well-established trajectories. The results of simulated experiments show that they can be appropriate for image acquisition under certain special conditions, like off-resonance and undersampling. This design method can be extended to include other objective functions for different behaviors.