NMR spectroscopy at high magnetic fields: Derivative reconstructions of components from envelopes using encoded time signals

Abstract

For in vitro magnetic resonance spectroscopy (MRS) in medical diagnostics, strong fields (say 10T and above) are usually viewed as the panacea for the two major progress-hampering problems, low resolution and high noise. While total shape spectra or envelopes from time signals encoded with high magnetic fields show sharp resonances, these are still superimposed on the visibly elevated background baselines. This obstacle prevents reliable quantification by e.g. a numerical quadrature due to the equivocal integration limits. Most critically, there is no guarantee whatsoever that the detected seemingly isolated peaks in an envelope are not composite. Therefore, fitting such an envelope with some Lorentzians (or similar mathematical functions) would invariably lead to ambiguous metabolite concentrations. This would fail to secure the promise of MRS in delivering the diagnostically reliable information for helping the decision making about the health condition of the examined patient. These stumbling blocks are even enhanced with ’spectral crowding’ in narrower frequency bands packed with closely spaced resonances. The same fundamental limitations are shared by the envelopes from time signals encoded with the high-resolution magic-angle spinning (HRMAS) variant of MRS. In the present study, we investigate the possibilities to simultaneously surmount all these hurdles while considering only the envelopes (shape estimations) and, moreover, not resorting to any fittings. The most appropriate rescue is in subjecting the given envelope to an additional transformation, the operators of successive derivatives with respect to frequency. In principle, these derivatives can be used with any shape estimators. However, practice shows that the optimal results are obtained when the derivative operators are applied to the envelopes from the nonparametric fast Padé transform (FPT). The ensuing derivative fast Padé transform (dFPT) solves all the mentioned problems with in vitro MRS by narrowing the peak widths and concomitantly enhancing the peak heights, while flattening the background baseline. The net result of this simultaneously improved resolution and suppressed noise is a ’purified’ envelope with the bottoms of all the peaks descended to the chemical shift axis and all the overlapped resonances completely separated. Hence, this derivative envelope represents the unfolded form of the nonderivative envelope. In other words, the dFPT as a shape estimator can quantify the input nonderivative envelope from encoded time signals by resolving it into its components with no recourse to fitting. The found components are assignable to the true metabolites contained in the scanned tissue or biofluid. This is confirmed by applying the same derivative operator to the explicitly available components due to the parametric FPT. There is more to these achievements by shape estimations with the dFPT. Namely, this same dFPT performs equally well for time signals encoded by in vivo MRS at clinical scanners (1.5, 3T). After all, the ultimate goal of MRS in the clinic is to analyze and interpret the data encoded directly from the patient. The better the data analyzer, the better the clinical end point: the differential diagnosis, benign versus cancerous samples. The nonparametric dFPT is anticipated to give its important contributions to these vital applications in medical diagnostics. Furthermore, because of the versatility and general performance of this estimator, its usefulness is expected to extend to the entire field of signal processing ranging from basic and applied sciences all the way to technologies and industries.