| 21. |
|
|
| 22. |
- Belkic, D, et al.
(författare)
-
In vitro proton magnetic resonance spectroscopy at 14T for benign and malignant ovary: Part I, signal processing by the nonparametric fast Pade transform
- 2022
-
Ingår i: JOURNAL OF MATHEMATICAL CHEMISTRY. - : Springer Science and Business Media LLC. - 0259-9791 .- 1572-8897. ; 60:2, s. 373-416
-
Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- 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.
|
|
| 23. |
|
|
| 24. |
- Belkic, D, et al.
(författare)
-
In vivo derivative NMR spectroscopy for simultaneous improvements of resolution and signal-to-noise-ratio: Case study, Glioma
- 2021
-
Ingår i: JOURNAL OF MATHEMATICAL CHEMISTRY. - : Springer Science and Business Media LLC. - 0259-9791 .- 1572-8897. ; 59:9, s. 2133-2178
-
Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- 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.
|
|
| 25. |
|
|
| 26. |
|
|
| 27. |
- Belkic, D, et al.
(författare)
-
Inverse problem for reconstruction of components from derivative envelope in ovarian MRS: Citrate quartet as a cancer biomarker with considerably decreased levels in malignant vs benign samples
- 2023
-
Ingår i: JOURNAL OF MATHEMATICAL CHEMISTRY. - : Springer Science and Business Media LLC. - 0259-9791 .- 1572-8897. ; 61:3, s. 569-599
-
Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- The harmonic inversion (HI) problem in nuclear magnetic resonance spectroscopy (NMR) is conventionally considered by means of parameter estimations. It consists of extracting the fundamental pairs of complex frequencies and amplitudes from the encoded time signals. This problem is linear in the amplitudes and nonlinear in the frequencies that are entrenched in the complex damped exponentials (harmonics) within the time signal. Nonlinear problems are usually solved approximately by some suitable linearization procedures. However, with the equidistantly sampled time signals, the HI problem can be linearized exactly. The solution is obtained by relying exclusively upon linear algebra, the workhorse of computer science. The fast Padé transform (FPT) can solve the HI problem. The exact analytical solution is obtained uniquely for time signals with at most four complex harmonics (four metabolites in a sample). Moreover, using only the computer linear algebra, the unique numerical solutions, within machine accuracy (the machine epsilon), is obtained for any level of complexity of the chemical composition in the specimen from which the time signals are encoded. The complex frequencies in the fundamental harmonics are recovered by rooting the secular or characteristic polynomial through the equivalent linear operation, which solves the extremely sparse Hessenberg or companion matrix eigenvalue problem. The complex amplitudes are obtained analytically as a closed formula by employing the Cauchy residue calculus. From the frequencies and amplitudes, the components are built and their sum gives the total shape spectrum or envelope. The component spectra in the magnitude mode are described quantitatively by the found peak positions, widths and heights of all the physical resonances. The key question is whether the same components and their said quantifiers can be reconstructed by shape estimations alone. This is uniquely possible with the derivative fast Padé transform (dFPT) applied as a nonparametric processor (shape estimator) at the onset of the analysis. In the end, this signal analyzer can determine all the true components from the input nonparametric envelope. In other words, it can quantify the input time signal. Its performance is presently illustrated utilizing the time signals encoded at a high-field proton NMR spectrometer. The scanned samples are for ovarian cyst fluid from two patients, one histopathologically diagnosed as having a benign lesion and the other with a malignant lesion. These findings are presently correlated with the NMR reconstruction results from the Padé-based solution of the HI problem. Special attention is paid to the citrate metabolites in the benign and malignant samples. The goal of this focus is to see whether the citrates could also be considered as cancer biomarkers as they are now for prostate (low in cancerous, high in normal or benign tissue). Cancer biomarkers are metabolites whose concentration levels can help discriminate between benign and malignant lesions.
|
|
| 28. |
|
|
| 29. |
|
|
| 30. |
|
|
