Covariance J-resolved spectroscopy: Theory and application in vivo

Enhanced spectral resolution for correlated spectroscopic imaging using inner-product and covariance transform: a pilot analysis of metabolites and lipids in breast cancer in vivo

Acquisition duration of correlated spectroscopy in vivo can be longer due to a large number of t1 increments along the indirect (F1) dimension. Limited number of t1 increments on the other hand leads to poor spectral resolution along F1. Covariance transformation (CT) instead of Fourier transform along t1 is an alternative way of increasing the resolution of the 2D COSY spectrum. Prospectively undersampled five-dimensional echo-planar correlated spectroscopic imaging (EP-COSI) data from ten malignant patients and ten healthy women were acquired and reconstructed using compressed sensing. The COSY spectrum at each voxel location was then generated using FFT, CT and a variant of CT called Inner Product (IP). Metabolite and lipid ratios were computed with respect to water from unsuppressed one-dimensional spectrum. The effects of t1-ridging artifacts commonly seen with FFT were not observed with CT/IP. Statistically significant differences were observed in the fat cross peaks measured with CT/IP/FFT. Spectral resolution was increased ~ 8.5 times (~ 19.53 Hz in FFT, ~ 2.32 Hz in CT/IP) without affecting the spectral width along F1 was possible with CT/IP. CT and IP enabled substantially increased F1 resolution effectively with significant gain in scan time and reliable measure of unsaturation index as a biomarker for malignant breast cancer.

Deep learning can accelerate and quantify simulated localized correlated spectroscopy

Nuclear magnetic resonance spectroscopy (MRS) allows for the determination of atomic structures and concentrations of different chemicals in a biochemical sample of interest. MRS is used in vivo clinically to aid in the diagnosis of several pathologies that affect metabolic pathways in the body. Typically, this experiment produces a one dimensional (1D) 1H spectrum containing several peaks that are well associated with biochemicals, or metabolites. However, since many of these peaks overlap, distinguishing chemicals with similar atomic structures becomes much more challenging. One technique capable of overcoming this issue is the localized correlated spectroscopy (L-COSY) experiment, which acquires a second spectral dimension and spreads overlapping signal across this second dimension. Unfortunately, the acquisition of a two dimensional (2D) spectroscopy experiment is extremely time consuming. Furthermore, quantitation of a 2D spectrum is more complex. Recently, artificial intelligence has emerged in the field of medicine as a powerful force capable of diagnosing disease, aiding in treatment, and even predicting treatment outcome. In this study, we utilize deep learning to: (1) accelerate the L-COSY experiment and (2) quantify L-COSY spectra. All training and testing samples were produced using simulated metabolite spectra for chemicals found in the human body. We demonstrate that our deep learning model greatly outperforms compressed sensing based reconstruction of L-COSY spectra at higher acceleration factors. Specifically, at four-fold acceleration, our method has less than 5% normalized mean squared error, whereas compressed sensing yields 20% normalized mean squared error. We also show that at low SNR (25% noise compared to maximum signal), our deep learning model has less than 8% normalized mean squared error for quantitation of L-COSY spectra. These pilot simulation results appear promising and may help improve the efficiency and accuracy of L-COSY experiments in the future.

Covariance NMR: Theoretical concerns, practical considerations, contemporary applications and related techniques

The family of resolution enhancement and spectral reconstruction techniques collectively known as covariance NMR continues to expand, along with the list of applications for these techniques. Recent advances in covariance NMR include the utilization of covariance to reconstruct pure shift NMR spectra, and the growing use of covariance NMR in processing non-uniformly sampled data, especially in solid state NMR and metabolomics. This review describes theoretical and practical considerations for direct and indirect covariance NMR techniques, and summarizes recent additions to the covariance NMR family. The review also outlines some of the applications of covariance NMR, and places covariance NMR in the larger context of methods that use statistical and algebraic approaches to enhance and combine various kinds of spectroscopic data, including tensor-based approaches for multidimensional NMR and heterocovariance spectroscopy.