Automatic Design of Radial Trajectories for Parallel MRI and Anisotropic Fields-of-View

Introduction: In recent years, non-Cartesian k-space trajectories such as radials and spirals have gained increased attention owing to mild appearance of artifacts from flow, chemical shift and undersampling, increased efficiency and intrinsic self-navigating properties. Remaining challenges of imaging with non-Cartesian trajectories include the lack of practical methods to optimize their performance under objectand system-specific imaging constraints. The examples include optimization to anisotropic Fields-of-View (FOV) arising from slab-selective excitation and anatomy, and design maximizing parallel imaging performance for a given coil array. Heuristic optimization of radials to anisotropic FOV [1] demonstrated potential of such designs to decrease significantly data sampling overhead for many existing nonCartesian trajectories. While Cartesian scans may be readily tuned to perform efficiently with both anisotropic FOV and a given coil array in parallel imaging mode [2], no general automatic method exists to perform such optimization for non-Cartesian trajectories. We propose a new approach to the design of non-Cartesian trajectories based on the analysis of properties of matrix inversion underlying non-Cartesian data reconstruction. We reduce the complexity of matrix inversion by approximating the matrix inverse with a local k-space based reconstruction such as PARS/GRAPPA [3, 4]. The design of optimized trajectories is guided by probing the ability of the inverse to reliably solve the inverse problem of restoring image content from samples on a k-space trajectory. We apply the developed theory to create a fast method that optimizes radials for arbitrary FOV and parallel MRI with a given coil array.