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Simultaneous linear-combination modeling of MEGA-PRESS sum and difference spectra without soft constraints1Russell H. Morgan Department of Radiology and Radiological Science, The Johns Hopkins University School of Medicine, Baltimore, MD, United States, 2F. M. Kirby Research Center for Functional Brain Imaging, Kennedy Krieger Institute, Baltimore, MD, United States, 3Institute of Pathophysiology, Medical Faculty, University of Ljubljana, Ljubljana, Slovenia
Synopsis
J-difference edited magnetic resonance spectroscopy is widely used to estimate levels of low-concentration metabolites with overlapping signals. Quantification is commonly performed on the difference spectra only, either using single-resonance fitting or linear-combination modeling based on simulated basis functions. Here, simultaneous linear-combination modeling of GABA-edited MEGA-PRESS sum and difference spectra is demonstrated. Simultaneous modeling incorporates all available spectral information, and does not require the definition of soft constraints on the low-concentration metabolite estimates. Across a large dataset, this new approach gave lower coefficients of variation for estimates of GABA, glutamate, and glutamine than modeling of the difference and sum spectra only.
Introduction
MEGA-PRESS1 is commonly used to measure the inhibitory neurotransmitter GABA at 3T. Aside from the primary target GABA, the difference spectrum contains poorly separated signals from glutamate (Glu) and glutamine (Gln). Linear-combination modeling algorithms such as LCModel2 are widely used to quantify both edited MRS data and non-edited MRS data, attempting to separate the individual contributions from GABA, Glu and Gln in spite of partial overlap. By default, LCModel often relies on soft constraints on GABA measures to quantify spectra, potentially making reproducibility of GABA measures misleadingly high. Here, we present a method for simultaneous modeling of the sum and difference spectra. This approach represents a self-constraining model, since all available spectral information is incorporated, without the need for a priori soft constraints.Methods
101 MEGA-PRESS datasets acquired on Philips 3T scanners at 9 sites3 were analyzed. Common parameters were TR/TE = 2000/68 ms; 15-ms editing pulses at 1.9 ppm (ON) and 7.5 ppm (OFF); 320 averages; 3 × 3 × 3 cm3 voxel in midline-parietal cortex. Preprocessing including frequency-and-phase correction4 was performed with FID-A5. The ON and OFF spectra were subtracted to yield the difference spectrum (‘DIFF’), and added to yield the sum spectrum (‘SUM’). Full-density matrix simulations were performed on a 21 × 21 × 21 spatial grid to compute metabolite basis functions for 26 spin systems6, and a Gaussian peak at 3.0 ppm was added to the GABA basis function to mimic co-edited macromolecules. In-vivo data were modeled from the basis functions using non-linear least-squares optimization in the frequency domain $$$\nu$$$ between 0.2 and 4.2 ppm, according to:
$$y(\nu )=\Gamma(\lambda_{1},\lambda_{2})\ast[\sum_{m=1}^{M}e^{i\varphi m}C_{m}\Psi _{m}(\nu,\delta _{m} )] + [\sum_{j=1}^{J}\beta _{j}B_{j}(\nu )]$$
Here, small frequency ($$$\delta _{m}$$$) and phase shifts ($$$\varphi _{m}$$$) are applied to the $$$M$$$ basis functions $$$\Psi _{m}$$$, weighted by the concentration estimates $$$C _{m}$$$. The linear combination is convolved with a normalized function $$$\Gamma$$$ containing Lorentzian ($$$\lambda_{1}$$$) and Gaussian ($$$\lambda_{2}$$$) lineshape contributions, and added to a baseline constructed from $$$J$$$ cubic B-splines with coefficients $$$\beta_{j}$$$ and knot-spacing of 0.4 ppm, preventing excessive baseline flexibility.
For each dataset, three different spectra were modeled: (A) DIFF-only, (B) SUM-only, (C) the concatenation of DIFF and SUM. GABA, Glu, and Gln were quantified relative to total creatine (tCr). Since the DIFF spectrum does not contain Cr, it was quantified relative to tCr from the SUM. Overall mean coefficients of variation (CV) across all 101 datasets, and mean within-site CVs (across all 9 sites) were calculated.
Results
All fitting approaches consistently produced plausible models (Fig. 1). GABA/tCr ratios from the concatenated model agreed with results from the DIFF-only model, while GABA/tCr from the SUM-only model was grossly overestimated (Fig. 2). The concatenated model gave the lowest overall mean CVs for GABA/tCr (14%), Glu/tCr (14%), and Gln/tCr (43%), and also gave the lowest mean within-site CVs for all three metabolites: 10%, 9%, and 35% (Fig. 3).Discussion
GABA/tCr ratios and CVs obtained with the concatenated model agreed well with published values3. The gross overestimation of GABA in the SUM-only fit demonstrates how necessary soft constraints are for linear-combination modeling of un-edited spectra.
Compared to only fitting the difference spectrum, the simultaneous fit of sum and difference adds information back into the model that has been lost during subtraction. These additional constraints provided by considering the whole dataset likely benefits the separated estimation of Glu and Gln, as evidenced by the lower CVs for both metabolites. Since the 2.25 ppm resonances of Glu and Gln are partially inverted by the editing pulse, the sum spectrum can be thought of as an artificially ‘TE-averaged’ spectrum (over two ‘virtual echo times’), and Glu/Gln overlap is considerably reduced. Incorporation of simulated or measured macromolecular background – particularly in the heavy-overlap region around 2.25 ppm – may further increase the precision with which GABA, Glu, and Gln can be separated.
Conclusion
Simultaneous linear-combination modeling of MEGA-PRESS spectra may improve quantification accuracy of low-concentration metabolites without requiring soft constraints.Acknowledgements
This work was supported by NIH grants R01 EB016089, R01 EB023963, and P41 EB015909.References
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