Electric potential energy optimized 3D radial sampling trajectories for MRI

A novel method for creating "golden" 3D center-out radial MRI sampling trajectories was developed and analyzed. This method, called ELECTRO (ELECTRic potential energy Optimized), uses repulsive forces to minimize electric potential energy. An objective function \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:G\left(S\right)$$\end{document}, the electric potential energies of all subsets of consecutive readouts in a 3D radial trajectory, and its reduced form were minimized using a multi-stage optimization strategy. A metric 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. Consecutive readouts from an ELECTRO trajectory were well spread out, with consistent NMNA values across sphere sizes (sigma NMNA = 0.005) and between regions on the sphere (NMNA approximate to 1.49). Conversely, the supergolden trajectory had poor consistency in NMNA values (sigma NMNA = 0.090) and clustering (NMNA = 1.28 at the pole with 40,000 readouts) that lead to artifact in the point spread function. Multi-stage optimization was faster than single-stage and obtained lower values of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:G\left(S\right)$$\end{document} (e.g., 0.87 vs. 0.91, for a sphere size of 40). In conclusion, ELECTRO trajectories are more golden than other 3D center-out radial trajectories, making them a suitable candidate for dynamic 3D MR imaging.