The topic of this study is in vitro proton magnetic resonance spectroscopy (MRS). The theme is on theoretical analysis of time signals encoded at a high magnetic field 14.1T, using a Bruker spectrometer, operating at a Larmor frequency of 600 MHz. The samples, dissolved in a D$${}_2$$
2
O buffer, are from histopathologically analyzed ovarian cyst fluid from two patients. The benign and malignant diagnoses were serous cystadenoma and serous cystadenocarcinoma, respectively. It is of vital clinical importance to determine whether certain specific patterns, inferred from the analyzed/interpreted MRS data could be correlated with this and similar histopathologic findings for other patients. Encoded time signals contain the fingerprint of the examined sample, its metabolic content. Therefore, to detect the sought patterns from MRS data, the salient characteristics of a malignant tumor, implied by the diagnostically most relevant metabolites (including recognized cancer biomarkers, e.g. lactic acids, cholines, ...), need to be unambiguously identified by their significant departures from the associated control data of benign biomaterial, ovarian cyst fluid (serous cystadenoma) in the diagnostic problem under the present consideration. Such identifications are unfeasible by visualization in the domain of encoding (time domain). A direct inspection of the graphed waveforms of an encoded time signal would give no clue about its structure nor about the sample content. However, merely visualizing the plots of the equivalent, information-preserving spectral lineshape profiles in the frequency domain would make transparent at least some of clinically useful, discernible features of MRS data, a number of resonances assignable to the known and unknown metabolites. For instance, the size of each resonance (peak area) is proportional to the concentration of the given metabolite. This is a key quantitative measure, which could help differentiate a malignant from a benign specimen by reference to the normal standards. A number of metabolites (choline, alanine, lactate, threonine, $$\beta $$
β
-hydroxybuturate, valine, isolecine, leucine, ...) have substantially different concentrations in the malignant compared with normal samples. Time signals can be processed by two substantially different categories of mathematical transforms, shape and parameter estimators. The former processors are alternatively called nonparametric estimators. They have been employed for envelopes in our recent study on this problem, which will presently be addressed with the prime focus on reconstructions of the corresponding components. Components and envelopes are partial and total shape spectra, respectively. The sum of all the component lineshapes (one per metabolite) yields the envelope nondegenerate spectrum representation of the entire sample. Presently, a deeper diagnostically valid insight is gained about the metabolic content of the scanned sample through the reported exact component spectra. The employed parameter estimators are the high-resolution, noise-suppressing nonderivative and derivative fast Padé transforms. Detailed are several critical achievements by the parametric Padé processing of direct clinical relevance. Importantly, all the accomplishments are shared by the nonparametric derivative Padé estimations. Three examples are highlighted here as follows.
Confirmation of our recent nonparametric derivative detection of an unassigned metabolite (a singlet peak) co-resonating with free choline near chemical shift 3.19 ppm (parts per million). Therein, with the nonderivative envelope, only one compound peak usually appears and is conventionally assigned to a free choline singlet. However, such an oversight would yield about twice larger value of the true concentration of this key cancer biomarker.
The concentration level of another cancer biomarker (lactate) is also overestimated by any nonparametric nonderivative envelope. In sharp contrast, the parametric nonderivative Padé estimation unequivocally detects six usually invisible resonances (assignable to other metabolites) beneath the lactate doublet, around chemical shift 1.41 ppm. At least two of the strongest among these invisible six resonances can be also identified in the nonparametric fourth derivative Padé envelope.
Regularization of the spectral compound for the water residual (4.71 ppm), which deforms the neighboring resonance lineshapes and impacts adversely on the concentration assessments of other nearby metabolites. This is accomplished by the fourth derivative envelope (coincident with the components) whose narrowing of the widths, cutting off the long tails and the background flattening generate a quantifiable singlet of water. This can serve as a reliable calibration reference resonance. After such a localization, no distortion appears around water, so that even very near 4.71 ppm, several smaller resonances are detected (assignable to a multiplet of nitrogen acetyl asparate), totally invisible in the nonparametric nonderivative envelope.
