Natural reconstruction coordinates for imperfect TRASE MRI

Abstract

TRansmit Array Spatial Encoding (TRASE) Magnetic Resonance Imaging (MRI) encodes image information in the Nuclear Magnetic Resonance (NMR) signal using spatially varying phases in a multiple spin-echo radio frequency (RF) pulse sequence. When the TRASE transmit coils are perfect, the spatial isophase RF contours produced are straight and orthogonal for a UXY TRASE sequence and the data produced fall into a well-understood k-space of spatial frequencies. When the TRASE coils are imperfect the spatial isophase RF contours will be non-orthogonal and/or curved. In that case the data produced by the TRASE sequence no longer falls into the traditional k-space. Here we show that the data fall into an alternative k-space relative to non-Cartesian coordinates in the image space that are naturally defined by the spatial isophase RF contours produced by the imperfect TRASE coils. With the construction of these natural image space coordinates, a direct image reconstruction transform may be defined. Simulated TRASE MRI cases with imperfect virtual transmit coils were computed and images reconstructed using the direct image reconstruction transform. The mathematical set-up here is a new one for MRI and may be amenable to further mathematical development as TRASE technology evolves.