Derivative NMR Spectroscopy for J-Coupled Multiplet Resonances using Short Time Signals (0.5KB) Encoded at Low Magnetic Field Strengths (1.5T). Part II: Water Unsuppressed

2021

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The theme of this study is derivative nuclear magnetic resonance (dNMR) spectroscopy. This versatile methodology of peering into the molecular structure of general matter is common to e.g. analytical chemistry and medical diagnostics. Theoretically, the potential of dNMR is huge and the art is putting it into practice. The implementation of dNMR (be it in vitro or in vivo) is wholly dependent on the manner in which the encoded time signals are analyzed. These acquired data contain the entire information which is, however, opaque in the original time domain. Their frequency-dependent dual representation, a spectrum, can be transparent, provided that the appropriate signal processors are used. In signal processing, there are shape and parameter estimators. The former processors are qualitative as they predict only the forms of the lineshape profiles of spectra. The latter processors are quantitative because they can give the peak parameters (positions, widths, heights, phases). Both estimators can produce total shape spectra or envelopes. Additionally, parameter estimators can yield the component spectra, based on the reconstructed peak quantifiers. In principle, only parameter estimators can solve the quantification problem (harmonic inversion) to determine the structure of the time signal and, hence, the quantitative content of the investigated matter. The derivative fast Fourier transform (dFFT) and the derivative fast Padé transform (dFPT) are the two obvious candidates to employ for dNMR spectroscopy. To make fair comparisons between the dFFT and dFPT, the latter should also be applied as a shape estimator. This is what is done in the present study, using the time signals encoded from a patient with brain tumor (glioma) using a 1.5T clinical scanner. Moreover, within the dFPT itself, the shape estimations are compared to the parameter estimations. The goal of these testings is to see whether, for in vivo dNMR spectroscopy, shape estimations by the dFPT could quantify (without fitting), similarly to parameter estimations. We check this key point in two successive steps. First, we compare the envelopes from the shape and parameter estimations in the dFPT. The second comparison is between the envelopes and components from the shape and parameter estimations, respectively, in the dFPT. This plan for benchmarking shape estimations by the dFPT is challenging both on the level of data acquisition and data analysis. The data acquisition reported here provides encoded time signals of short length, only 512 as compared to 2048, which is customarily employed. Moreover, the encoding echo time was long (272 ms) at which most of resonances assigned to metabolites with shorter spin-spin relaxations are likely to be obliterated from the frequency spectra. Yet, in face of such seemingly insurmountable obstacles, we are looking into the possibility to extract diagnostically relevant information, having particularly in focus the resonances for recognized cancer biomarkers, notably lactate, choline and phosphocholine. Further, we want to see how many of the remaining resonances in the spectra could accurately be identified with clinical reliability as some of them could also be diagnostically relevant. From the mathematical stance, we are here shaking the sharp border between shape and parameter estimators. That border stood around for a long time within nonderivative estimations. However, derivative shape estimations have a chance to tear the border down. Recently, shape estimations by the dFPT have been shown to lead such a trend as this processor could quantify using the time signals encoded from a phantom (a test sample of known content). Further, the present task encounters a number of additional challenges, including a low signal-to-noise ratio (SNR) and, of course, the unknown content of the scanned tissue. Nevertheless, we are determined to find out whether the nonparametric dFPT can deliver the unique quantification-equipped shape estimation and, thus, live up to the expectation of derivative processing: a long-sought simultaneous improvement of resolution and SNR. In every facet of in vivo dNMR, we found that shape estimations by the dFPT has successfully passed the outlined most stringent tests. It begins with transforming itself to a parameter estimator (already with the 3rd and 4th derivatives). It ends with reconstructing some 54 well-isolated resonances. These include the peaks assigned to recognized cancer biomarkers. In particular, a clear separation of choline from phosphocholine is evidenced for the first time by reliance upon the dFPT with its shape estimations alone.

In vivo derivative NMR spectroscopy for simultaneous improvements of resolution and signal-to-noise-ratio: Case study, Glioma

2021

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High-resolution at 3T for in vivo derivative NMR spectroscopy in medical diagnostics of ovarian tumor: exact quantification by shape estimations

2021

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Time signals are measured experimentally throughout sciences, technologies and industries. Of particular interest here is the focus on time signals encoded by means of magnetic resonance spectroscopy (MRS). The great majority of generic time signals are equivalent to auto-correlation functions from quantum physics. Therefore, a quantum-mechanical theory of measurements of encoded MRS time signals is achievable by performing quantum-mechanical spectral analysis. When time signals are measured, such an analysis becomes an inverse problem (harmonic inversion) with the task of reconstruction of the fundamental frequencies and the corresponding amplitudes. These complex-valued nodal parameters are the building blocks of the associated resonances in the frequency spectrum. Customarily, the MRS literature reports on fitting some ad hoc mathematical expressions to a set of resonances in a Fourier spectrum to extract their positions, widths and heights. Instead, an alternative would be to diagonalize the so-called data matrix with the signal points as its elements and to extract the resonance parameters without varying any adjusting, free constants as these would be absent altogether. Such a data matrix (the Hankel matrix) is from the category of the evolution matrix in the Schrödinger picture of quantum mechanics. Therefore, the spectrum of this matrix, i.e. the eigenvalues and the corresponding amplitudes, as the Cauchy residues (that are the squared projections of the full wave functions of the system onto the initial state) are equivalent to the sought resonance parameters, just mentioned. The lineshape profile of the frequency-dependent quantum-mechanical spectral envelope is given by the Heaviside partial fraction sum. Each term (i.e. every partial fraction) in this summation represents a component lineshape to be assigned to a given molecule (metabolite) in the tissue scanned by MRS. This is far reaching, since such a procedure allows reconstruction of the most basic quantum-mechanical entities, e.g. the total wave function of the investigated system and its ’Hamiltonian’ (a generator of the dynamics), directly from the encoded time signals. Since quantum mechanics operates with abstract objects, it can be applied to any system including living species. For example, time signals measured from the brain of a human being can be analyzed along these lines, as has actually been done e.g. by own our research. In this way, one can arrive at a quantum-mechanical description of the dynamics of vital organs of the patient by retrieving the interactions as the most important parts of various pathways of the tissue functions and metabolism. Of practical importance is that the outlined quantum-mechanical prediction of the frequency spectrum coincides with the Padé approximant, which is in signal processing alternatively called the fast Padé transform (FPT) for nonderivative estimations. Further, there is a novelty called the derivative fast Padé transform (dFPT). The FPT and dFPT passed the test of time with three fundamentally different time signals, synthesized (noise-free, noise-contaminated) as well as encoded from phantoms and from patients. Such systematics are necessary as they permit robust and reliable benchmarkings of the theory in a manner which can build confidence of the physician, while interpreting the patient’s data and making the appropriate diagnosis. In the present study, we pursue further this road paved earlier by applying the FPT and dFPT (both as shape and parameter estimators) to time signals encoded by in vivo proton MRS from an ovarian tumor. A clinical 3T scanner is used for encoding at a short echo time (30 ms) at which most resonances have not reached yet their decay mode and, as such, could be detected to assist with diagnostics. We have two goals, mathematical and clinical. First, we want to find out whether particularly the nonparametric dFPT, as a shape estimator, can accurately quantify. Secondly, we want to determine whether this processor can provide reliable information for evaluating an ovarian tumor. From the obtained results, it follows that both goals have met with success. The nonparametric dFPT, from its onset as a shape estimator, transformed itself into a parameter estimator. Its quantification capabilities are confirmed by reproducing the components reconstructed by the parametric dFPT. Thereby, fully quantified information is provided to such a precise extent that a large number of sharp resonances (more than 160) appear as being well isolated and, thus, assignable to the known metabolites with no ambiguities. Importantly, some of these metabolites are recognized cancer biomarkers (e.g. choline, phosphocholine, lactate). Also, broader resonances assigned to macromolecules are quantifiable by a sequential estimation (after subtracting the formerly quantified sharp resonances and processing the residual spectrum by the nonparametric dFPT). This is essential too as the presence of macromolecules in nonoderivative envelopes deceptively exaggerates the intensities of sharper resonances and, hence, can be misleading for diagnostics. The dFPT, as the quantification-equipped shape estimator, rules out such possibilities as wider resonances can be separately quantified. This, in turn, helps make adequate assessment of the true yield from sharp resonances assigned to metabolites of recognized diagnostic relevance.

In vitro proton magnetic resonance spectroscopy at 14T for benign and malignant ovary: Part I, signal processing by the nonparametric fast Padé transform

2021

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The present study deals with two different kinds of time signals, encoded by in vitro proton magnetic resonance spectroscopy (MRS) with a high external static magnetic field, 14.1T (Bruker 600 MHz spectrometer). These time signals originate from the specific biofluid samples taken from two patients, one with benign and the other with malignant ovarian cysts. The latter two diagnoses have been made by histopathologic analyses of the samples. Histopathology is the diagnostic gold standard in medicine. The obtained results from signal processing by the nonparametric derivative fast Padé transform (dFPT) show that a number of resonances assignable to known metabolites are considerably more intense in the malignant than in the benign specimens. Such conclusions from the dFPT include the recognized cancer biomarkers, lactic acid and choline-containing compounds. For example, the peak height ratio for the malignant-to-benign samples is about 18 for lactate, Lac. This applies equally to doublet Lac(d) and quartet Lac(q) resonating near 1.41 and 4.36 ppm (parts per million), respectively. For the choline-containing conglomerate (3.19-3.23 ppm), the dFPT with already low-derivative orders (2nd, 3rd) succeeds in clearly separating the three singlet component resonances, free choline Cho(s), phosphocholine PC(s) and glycerophosphocholine GPC(s). These constituents of total choline, tCho, are of critical diagnostic relevance because the increased levels, particularly of PC(s) and GPC(s), are an indicator of a malignant transformation. It is gratifying that signal processing by the dFPT, as a shape estimator, coheres with the mentioned histopathology findings of the two samples. A very large number of resonances is identifiable and quantifiable by the nonparametric dFPT, including those associated with the diagnostically most important low molecular weight metabolites. This is expediently feasible by the automated sequential visualization and quantification that separate and isolate sharp resonances first and subsequently tackle broad macromolecular lineshape profiles. Such a stepwise workflow is not based on subtracting nor annulling any part of the spectrum, in sharp contrast to controversial customary practice in the MRS literature. Rather, sequential estimation exploits the chief derivative feature, which is a faster peak height increase of the thin than of the wide resonances. This is how the dFPT simultaneously improves resolution (linewidth narrowing) and reduces noise (background flattening). Such a twofold achievement makes the dFPT-based proton MRS a high throughput strategy in tumor diagnostics as hundreds of metabolites can be visualized/quantified to offer the opportunity for a possible expansion of the existing list of a handful of cancer biomarkers.