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Spectral quality differentially affects apparent concentrations of individual metabolites as estimated by linear combination modeling of in vivo MR spectroscopy data at 7 Tesla
Kelley M. Swanberg1,2, Hetty Prinsen2, and Christoph Juchem1,2,3,4

1Biomedical Engineering, Columbia University School of Engineering and Applied Science, New York, NY, United States, 2Radiology and Biomedical Imaging, Yale School of Medicine, New Haven, CT, United States, 3Radiology, Columbia University Medical Center, New York, NY, United States, 4Neurology, Yale School of Medicine, New Haven, CT, United States

Synopsis

In vivo magnetic resonance spectroscopy currently lacks data-driven quality control standards, the development of which can be informed by characterizing the effects of spectral quality on metabolite quantification. We assess the influences of spectral line width and signal-to-noise ratio on both simulated and experimentally derived in vivo resonances from twenty-one metabolites measured by short-echo-time STEAM and J-difference editing for glutathione and GABA at 7 Tesla. We show that spectral quality exerts distinct effects on apparent concentrations of different metabolites, underlining the importance of explicit quality analysis in studies employing in vivo magnetic resonance spectroscopy, especially cross-sectional investigations of physiologically distinct groups.

Purpose

The in vivo magnetic resonance spectroscopy (1H-MRS) field needs data-driven quality control standards.1 Such standards can be informed by quantifying the effects of spectral quality, including full width at half maximum (FWHM; frequency width of a resonance at the ordinate point halfway between baseline and apex) and signal-to-noise ratio (SNR; a prominent singlet amplitude normalized by noise intensity standard deviation) on metabolite quantification.

Understanding the numerical influences of spectral quality on metabolite quantification informs both quality control and experimental integrity. Brain water or metabolite spectral FWHM has demonstrated increases in multiple sclerosis,2 Wilson’s disease,3 and normal maturation.4 Additionally, any cohort who might compromise magnetic field homogeneity by increased motion between shim optimization and signal acquisition, like children, may also exhibit broader lines. It is important to determine how this may influence metabolite quantification by 1H-MRS. Some previous work has addressed this question with simulation experiments,5-7 but these findings are not generalizable to higher field strengths or to metabolite signals isolated by spectral editing.

Glutathione (GSH) is an antioxidant synthesized in neurons and glia,8 while γ-amino butyric acid (GABA) is an inhibitory neurotransmitter and potential immunomodulator9 and glutamate the central nervous system's predominating excitatory neurotransmitter. All three compounds play key mechanistic roles in neurological health and disease. Reduced peak amplitude and complex line shapes due to J-coupling-induced signal splitting, plus spectral overlap with nearby resonances, complicate the spectroscopic quantification of these molecules, predicting its strong influence by spectral quality.

To facilitate data-driven quality assessment for 1H-MRS experimental planning and interpretation, we applied linear combination modeling and quantification error analysis to 25,250 simulated and measured MEGA-sLASER and STEAM spectra based on previously published sequences at 7 Tesla10 and calculated the effects of spectral quality measures FWHM and SNR on the quantification accuracy of these three metabolites, plus common concentration references total creatine and N-acetyl aspartate (NAA).

Methods

We analyzed the accuracy of linear combination model fits to proton spectra of varying complexity to examine how FWHM and SNR affect apparent metabolite concentration as quantified by in vivo 1H-MRS at 7 T. Linear combination modeling routines exploited functionality from INSPECTOR;11 additional scripting was implemented in MATLAB (Mathworks, Natick, MA, USA). Quantification errors were calculated relative to apparent concentrations output by perfect model fits to noiseless spectra at each FWHM and signal amplitude combination (Figure 1A).

Condition 1 comprised fits at 5 FWHM, 10 starting signal amplitudes, and 100 Gaussian noise patterns, based on a simulated Lorentzian singlet at 3.01 ppm, or GSH or GABA difference resonances from MEGA-sLASER experiments (TE = 72 ms) with J-difference editing (glutathione 4.56 ppm; GABA 1.89 ppm)10 simulated using SpinWizard12 (Figure 1B). Actual concentration was kept constant across FWHM. Noise patterns were matched across signal amplitude and line width conditions for each resonance; noise amplitude remained constant within each experiment. Condition 2 consisted of fits at 5 FWHM and 5 starting signal amplitudes, also with 100 Gaussian noise patterns, based on GSH or GABA difference spectra plus co-edited resonances (NAA or NAA, glutamate, and glutamine, respectively), or full metabolite spectra (STEAM, TE = 10 ms)10 including twenty-one metabolites, in approximately physiological ratios (Figure 1C). Condition 3 repeated GSH J-difference spectral fits with an in vivo baseline averaged from fit residuals to similar acquisitions in the frontal cortex of healthy adults (N = 7). This enabled the calculation of quantification error under spectral conditions resembling those seen in vivo against a perfect gold standard without noise or baseline (Figure 1D).

Results

Fit error standard deviation decreased with SNR (Figures 2, 3B) and increased with FWHM (Figures 2, 3C) in all fits of singlets, GABA, and GSH and varied positively with metabolite amplitude Cramér-Rao Lower Bound (CRLB) (Figures 2, 3D-E). In vivo baseline conditions introduced systematic asymmetry into quantification errors expected from linear combination model fits plus linear baseline to GSH J-difference spectra (Figure 3B, C), and glutamate fit errors exhibited greater influence by spectral quality than those of total creatine or NAA (Figure 4). Underestimation of actual fit errors by reported CRLB varied with fit frequency range and baseline complexity (Figure 5).

Conclusions

SNR and FWHM predictably affect the standard deviation of quantification errors expected from linear combination model fitting of isolated and overlapping singlet, J-difference-edited, and unedited metabolite resonances. Complex baseline shapes may introduce systematic quantification errors that could influence conclusions based on comparisons of groups exhibiting disparate spectral quality. These results motivate further work on the effects of fitting algorithms, particularly baseline modeling routines, on conditions exhibiting such systematic errors here. All told, the relationship between spectral quality and fit error differs by metabolite, arguing against the use of one-size-fits-all quality control thresholds for in vivo 1H-MRS experiments.

Acknowledgements

This research was made possible by the National Multiple Sclerosis Society (NMSS, RG-5319) and the Yale Center for Clinical Investigation. In vivo measurements were conducted in accordance with Yale School of Medicine Human Investigation Committee protocol #1107008743.

References

1. Wilson MOA, Barker PB, Bartha R, Bizzi A, et al. A Methodological consensus on clinical proton MR spectroscopy of the brain: Review and recommendations. Under review at Magn Reson Med. Unpublished manuscript.

2. Geurts JJ, Reuling IE, Vrenken H, Uitdehaag BM, Polman CH, Castelijns JA, Barkhof F, Pouwels PJ. MR spectroscopic evidence for thalamic and hippocampal, but not cortical, damage in multiple sclerosis. Magn Reson Med 2006; 55(3): 478-483.

3. Lucato LT, Concepcion M, Otaduy G, Barbosa ER, Machado AAC, McKinney A, Bacheschi LA, Scaff M, Cerri GG, Leite CC. Proton MR spectroscopy in Wilson Disease: Analysis of 36 cases. Am J Neuroradiol 2005; 26(5): 1066-1071.

4. Pouwels PJW, Brockmann K, Kruse B, Wilken B, Wick M, Hanefeld F, Frahm J. Regional age dependence of human brain metabolites from infancy to adulthood as detected by quantitative localized proton MRS. Pediatr Res 1999; 46(4): 474-485.

5. Bartha R. Effect of signal-to-noise ratio and spectral linewidth on metabolite quantification at 4 T. NMR Biomed 2007; 20(5): 512-521.

6. Kanowski M, Kaufmann J, Braun J, Bernarding J, Tempelmann C. Quantitation of simulated short echo time 1H human brain spectra by LCModel and AMARES. Magn Reson Med 2004; 51(5): 904-912.

7. Kreis R, Boesch C. Bad spectra can be better than good spectra. 11th Annual Meeting of the International Society of Magnetic Resonance in Medicine, 2003; Toronto, Canada. p 264.

8. Cooper AJL. Role of astrocytes in maintaining cerebral glutathione homeostasis and in protecting the brain against xenobiotics and oxidative stress. In: Shaw CA, editor. Glutathione in the nervous system. Washington, D.C.: Taylor and Francis; 1998.

9. Bhat R, Axtell R, Mitra A, Miranda M, Lock C, Tsien RW, Steinman L. Inhibitory role for GABA in autoimmune inflammation. Proc Natl Acad Sci USA 2010;107(6): 2580-2585.

10. Prinsen H, de Graaf RA, Mason GF, Pelletier D, Juchem C. Reproducibility measurement of glutathione, GABA, and glutamate: Towards in vivo neurochemical profiling of multiple sclerosis with MR spectroscopy at 7T. J Magn Reson Imaging 2017; 45(1): 187-198.

11. Swanberg KM, Prinsen H, Coman D, de Graaf RA, Juchem C. Quantification of glutathione transverse relaxation time T2 using echo time extension with variable refocusing selectivity and symmetry in the human brain at 7 Tesla. J Magn Reson 2018; 290: 1-11.

12. de Graaf RA, Chowdhury GMI, Behar KL. Quantification of High-Resolution H-1 NMR Spectra from Rat Brain Extracts. Anal Chem 2011; 83(1): 216-224.

Figures

Figure 1. Simulation parameters. We analyzed spectral quality effects on fit accuracy, or the error of quantified concentration relative to that of a noiseless standard at the same line width and signal amplitude conditions (A), of linear combination model fits to B) single resonances (Lorentzian singlets and J-difference spectra of 2.95-ppm glutathione 7’CH2 and 3.01-ppm GABA 4CH2); C) overlapping resonances (GABA with co-edited molecules or a STEAM spectrum including 21 metabolites) resembling in vivo concentration ratios; or D) overlapping resonances with in vivo baselines (glutathione plus co-edited molecules with and without a baseline derived from an identical sequence in the frontal cortex of 7 volunteers).

Figure 2. Error changes predictably with signal-to-noise ratio and line width in linear combination model fits of single resonances or GABA J-difference spectra with overlap. Linear combination model fit (A) error decreases with signal-to-noise ratio (SNR) (B) and increases with full width at half maximum (FWHM) (C) in Lorentzian singlets or GABA spectra with J-difference editing (JDE) to isolate the 3.01-ppm 4CH2. Amplitude Cramér-Rao Lower Bounds (CRLB) exhibit positive relationships with magnitude quantification error (D), with regular influence by FWHM, and positive relationships with quantification error standard deviation (SD) (E). NAA: N-acetyl aspartate; Glu: glutamate; Gln: glutamine.

Figure 3. In vivo baseline conditions introduce systematic asymmetry in quantification errors expected from linear combination model fits of glutathione J-difference spectra. Linear combination model fit (A) error decreases with signal-to-noise ratio (SNR) (B) and increases with full width at half maximum (FWHM) (C), and its magnitude and standard deviation associate positively with Cramér-Rao Lower Bound (CRLB) (D, E), in glutathione (GSH) spectra with J-difference editing (JDE) to isolate the 2.95-ppm 7’CH2. Including a spectral baseline averaged from in vivo JDE acquisitions in the human frontal cortex (N=7) introduces asymmetries into fit errors and their relationships with spectral quality. NAA: N-acetyl aspartate.

Figure 4. Linear combination model fit errors for total creatine, N-acetyl aspartate, and glutamate as measured by STEAM exhibit distinct relationships with spectral quality. Linear combination model fit errors exhibit differential sensitivity to spectral quality depending on the metabolite quantified, with glutamate quantification accuracy exhibiting higher sensitivity to full width at half maximum (FWHM) than that of either total creatine or NAA. With the 100 noise patterns applied here, glutamate also exhibited the strongest tendency among the three metabolites to systematic underestimation, especially at high FWHM and low signal-to-noise ratio (SNR).

Figure 5. Underestimation of fit error standard deviation by Cramér-Rao Lower Bound is exacerbated by insufficient fit range and complicated baseline shapes. As evidenced by the greater deviation from identity (depicted as a blue line) of the relationship between Cramér-Rao Lower Bound (CRLB) and quantification error standard deviation, reported CRLB represents actual fit error more poorly when fits exhibit an insufficient frequency range for determining the spectral baseline (C to B) and inadequate information about complicated baseline shapes (B to D) in linear combination modeling of GSH with J-difference editing (JDE) to isolate the 2.95-ppm 7’CH2. NAA: N-acetyl aspartate.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)
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