An analytical SMASH procedure (ASP) for sensitivity-encoded MRI.
The simultaneous acquisition of spatial harmonics (SMASH) method of imaging with detector arrays can reduce the number of phase-encoding steps, and MRI scan time several-fold. The original approach utilized numerical gradient-descent fitting with the coil sensitivity profiles to create a set of composite spatial harmonics to replace the phase-encoding steps. Here, an analytical approach for generating the harmonics is presented. A transform is derived to project the harmonics onto a set of sensitivity profiles. A sequence of Fourier, Hilbert, and inverse Fourier transform is then applied to analytically eliminate spatially dependent phase errors from the different coils while fully preserving the spatial-encoding. By combining the transform and phase correction, the original numerical image reconstruction method can be replaced by an analytical SMASH procedure (ASP). The approach also allows simulation of SMASH imaging, revealing a criterion for the ratio of the detector sensitivity profile width to the detector spacing that produces optimal harmonic generation. When detector geometry is suboptimal, a group of quasi-harmonics arises, which can be corrected and restored to pure harmonics. The simulation also reveals high-order harmonic modulation effects, and a demodulation procedure is presented that enables application of ASP to a large numbers of detectors. The method is demonstrated on a phantom and humans using a standard 4-channel phased-array MRI system.
Lee
R F
RF
Division of MR Research, Department of Radiology, Johns Hopkins University, Baltimore, MD 21205, USA. leer@mri.jhu.edu
Westgate
C R
CR
Weiss
R G
RG
Bottomley
P A
PA
D005583:Fourier Analysis; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D007866:Leg / Q000033:anatomy & histology; D008279:Magnetic Resonance Imaging; D008433:Mathematics; D019047:Phantoms, Imaging