Magnetic Resonance Imaging:Single Coil Sensitivity Mapping and Correction using Spatial Harmonics
Eric Peterson, Ryan Lipscomb
Problem:
Current Magnetic Resonance Imaging (MRI) systems are finely tuned machines which typically have very uniform coil sensitivities. However, when using some types of movable vest coils, the sensitivity is not uniform over the field of view. One specific example of this is functional lung imaging using Hyperpolarized Helium-3 MRI.
Proposal:
A MRI imaging and reconstruction method using multiple coils called Generalized SMASH(SiMultaneous Acquisition of Spatial Harmonics)[1], which is itself an extension of SMASH[2], proposed a method by which coil sensitivity maps can be generated by using linear combinations of spatial harmonics.
Equation 1: Spatial Harmonic Equation [1]
Where p and q are integers determined to provide an adequate coil sensitivity representation, am is the mth complex Fourier coefficient.
In this project, we propose a novel application of this method asan image restoration algorithm for non-ideal single coil geometries. This algorithm consists of using few (small p and q from Equation 1) low frequency harmonics as an estimate of the coil sensitivity.
Equation 2: Image Degradation Model
As seen in Equation 2, the signal(S) is the product of the Nuclear Magnetic Resonance (NMR) signal (M) and the coil sensitivity map (C) with η being theadditive noise. The proposed method is to use equation 1 to approximate the coil sensitivity map. From the calculated sensitivity map, the inverse will be computed and modulated to attenuate high amplification elements. The inverted and modulated sensitivity map will be multiplied by the original image to produce the corrected image.
One of the most useful quantitative metrics of functional lung imaging is the spatial distribution of the Apparent Diffusion Coefficient (ADC)[4]. A metric of this restoration algorithm’s utility is the preservation of the spatial distribution of the ADC.
References:
1. Bydder M, Larkman DJ, Hajnal JV. Generalized SMASH imaging. Magn Reson Med 2002;47:160-170
2. Sodickson DK, Manning WJ. Simultaneous acquisition of spatial harmonics (SMASH): fast imaging with radiofrequency coil arrays. Magn Reson Med 1997;38:591-603
3. Griswold MA, Jakob PM, Heidemann RM, Nittka M, Jellus V, Wang J, Kiefer B, Haase A. Generalized Autocalibrating Partially Parallel Acquisitions (GRAPPA). Magn Reson Med 2002;47:1202-1210
4. Chen XJ, Moller HE, Chawla MS, Cofer GP, Driehuys B, Hedlund LW, JohnsonGA.Spatially Resolved Measurements of Hyperpolarized Gas Properties in the Lung In Vivo. Part I: Diffusion Coefficient. Magn Reson Med 1999;42:721–728