Lineshape Accommodation in Quantitation of Magnetic Resonance Spectroscopy Signals

Introduction Lineshape distortions due to residual eddy currents and magnetic field inhomogeneities are often present in short echo-time H spectroscopic data. If left uncorrected, these lineshape distortions lead to errors in metabolite concentration estimates when using quantification methods that incorporate model functions with specific lineshapes (i.e., Lorentzian or Gaussian). Several methods have been proposed for lineshape correction, 1) The distorted in vivo signal can be given a purely Lorentzian lineshape by using methods such as QUALITY deconvolution and eddy current correction (ECC) or the hybrid method QUECC, see [1] and references therein. These methods use a separate reference spectrum for lineshape correction, for instance unsuppressed water; 2) The lineshape distortions with respect to the basis-set spectra are corrected in the fitting procedure, see e.g.[2, 3]. In this study a new method is investigated, namely the lineshape of the simulated metabolite basis-set signals is given the estimated lineshape of a reference spectrum before the quantitation step. Analytical formulae for the Cramér-Rao lower bounds (CRBs) on model function parameters of a Lorentzian and Gaussian singlet are also derived and provide insights in the lineshape accommodation strategy to be used. Method Monte Carlo Studies: The influence of different lineshape accommodation strategies on QUEST [2] quantitation results are investigated through Monte-Carlo studies. To assess the performances – including bias – of QUEST, a H signal (2048 data points) mimicking an in vivo spectrum of rat brain at 9.4 Tesla was simulated, see Fig.1. This signal comprises contributions from eleven metabolites and lipids whose amplitudes correspond to a healthy rat-brain. Voigt lineshapes were imposed (damping factor of the form exp(−αt − βt)). The damping factors of the Lorentzian part range from 5Hz to 20Hz and that of the strong Gaussian part is 4 s. To this simulated noiseless signal, 200 different realisations of white Gaussian noise were added. The noise level was chosen as in in vivo conditions so that the SNR of the Cr singlet be 8.6:16. Quantitation: Signals were processed in the time domain. The metabolite basis-set signals used in QUEST were simulated with NMR-SCOPE using spin parameters given in [3]. Eleven metabolites – aspartate (Asp), choline (Cho), creatine (Cr), γ-amino-butyric acid (GABA), glucose (Glc), glutamate (Glu), glutamine (Gl), myoInositol (mI), N-acetylaspartate (NAA and NAAG), taurine (Tau) and lipids (Lip) at 0.9 and 1.3 ppm – were included. Three methods were investigated and compared, 1) a Lorentzian basis-set is used, 2) the Monte Carlo signals were given a purely Lorentzian lineshape using a deconvolution approach prior to quantitation and the basis-set was Lorentzian too, 3) an ’adapted’ basis set which was given the Voigt lineshape of a reference singlet, was used. Note that without reference, the lineshape signal can also be estimated from the data. Analytical Formulae for the Cramér-Rao Bounds on Model Parameters of a Singlet To help in finding the best lineshape accommodation strategy for quantitation, we derived (with Maple) analytical formulae for the CRBs on parameters of a singlet