Electric Potential Energy Optimized 3D Radial Sampling Trajectories for MRI

Abstract

The purpose of this work was to develop and analyze a novel method for creating “golden” 3D center-out radial MRI sampling trajectories, called ELECTRO (ELECTRic potential energy Optimized). This method is based on using repulsive forces to minimize electric potential energy. An objective function G(S) was proposed that contains the electric potential energies of all subsets of consecutive readouts in a 3D radial trajectory. G(S) and its reduced form were minimized using a multi-stage optimization strategy. A new measure called Normalized Mean Nearest neighbor Angular distance (NMNA) was proposed for describing distributions of points on a sphere. ELECTRO and other relevant golden trajectories were compared in silico using NMNA and point spread function analysis. This work demonstrated that any subset of consecutive readouts from an ELECTRO trajectory were well spread out, as indicated by the consistency of NMNA values across sphere sizes (σNMNA=0.005) and between regions on the sphere (NMNA ≈ 1.49 over most regions). Conversely, the commonly used supergolden trajectory had poor consistency in NMNA values (σNMNA=0.090) and had severe clustering of readouts (for instance, NMNA = 1.28 at the pole with 40,000 readouts) that lead to structured aliasing artifact in the point spread function. Compared to performing the optimization all in a single stage, a multi-stage optimization strategy was faster and obtained lower values of G(S) (eg, 0.87 vs. 0.91, for a sphere size of 40). Minimizing a reduced version of G(S) can significantly reduce computation time but may result in a more uneven readout distribution. In conclusion, ELECTRO trajectories are more golden than other 3D center-out radial trajectories, making them a suitable candidate for dynamic 3D MR imaging.