Assessment of ¹H-MRS spectra via multiset canonical correlation analysis and empirical mode decomposition

Proton magnetic resonance spectroscopy (¹H-MRS) is a valuable non-invasive method for quantifying brain metabolites. Most MRS spectra are pre-processed by taking the mean of several single-acquisition transients, ultimately resulting in peaks associated with biologically significant molecules. However, simply taking the mean of the transients is prone to errors due to outliers and the non-independence of sequential data acquisitions. Furthermore, this approach cannot identify whether peaks corresponding to different metabolites tend to co-vary across acquisitions. Averaging also assumes a single underlying true signal that is variably corrupted with noise. In this study, we propose a novel analytic approach that models each transient as a combination of deterministic components. This method allows for the extraction of distinct orthogonal components of the MRS spectrum that variably contribute to each transient signal. First, complex Empirical Mode Decomposition (EMD) is applied to extract intrinsic mode functions from the free induction decay (FID) signals. Subsequently, Multiset Canonical Correlation Analysis (MCCA) is employed to obtain the linear combination of intrinsic mode functions from each FID signal that produce the most consistent temporal waveforms across all transients. We applied this method to time-domain ¹H-MRS data from 21 Alzheimer's disease (AD) subjects. Using the MCCA method, three significant orthogonal components were extracted. Regression analyses revealed that each of these components significantly contributed to the transient signals. To interpret the isolated spectra contained in the MCCA components, we utilized the LCModel program. The first component was qualitatively similar to the grand mean spectrum but demonstrated a dramatic 40.7 % increase in signal-to-noise ratio (SNR; p < 0.001). This component also exhibited lower Cramer-Rao Lower Bound (CRLB) values and statistically significant differences in the concentrations of key metabolites, including N-acetyl aspartate (NAA), myo-inositol (mI), and glutamate (Glu) (p < 0.05). The second component contained similar peak values to the first, except for the NAA peak. A judicious combination of the first two components enabled selective variability in the NAA peak height across transients. The third component primarily extracted peaks related to total creatine (tCr) and total choline (tCho). These findings indicate that ¹H-MRS spectra consist of a combination of deterministic components. By isolating these components, the signal-to-noise ratio (SNR) of the spectra is enhanced, and the Cramer-Rao Lower Bound (CRLB) values for most metabolites are improved. This approach offers a novel framework for increasing the utility of ¹H-MRS in both clinical and research applications.