Temporal Stability of 3D-PR based on Multidimensional Golden Means: Simulation and Implementation

INTRODUCTION Adaptive sampling of k-space allows images in dynamic contrast-enhanced (DCE)-MRI to be reconstructed at various spatial and temporal resolutions from the same dataset. Golden-angle radial kspace sampling achieves this flexibility in-plane with samples incremented by the golden angle, φ = (√5 1)/2 * 180° [1,2]. These projections fill 2D k-space with projections that have a relatively uniform angular distribution for any time interval. We extend this method to 3D Projection Reconstruction (3DPR) using multidimensional golden means, which are derived from modified Fibonacci sequences by an eigenvalue-eigenvector approach [3,4,5]. Successive 3D radial projections are chosen based on two ratios from the two-dimensional golden means. Conventional 3D-PR schemes restrict reconstruction to specific commensurate projection sets that form a spherically-isotropic set of radial directions in k-space. On the other hand, the golden 3D-PR approach provides a relatively uniform coverage of 3D radial k-space directions for any number of projections including incommensurate projection numbers, that, in conventional schemes, have incomplete sets of radial directions.