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Derivative NMR spectroscopy for J-coupled multiplet resonances using short time signals (0.5 KB) encoded at low magnetic field strengths (1.5T). I: Water suppressed. (English) Zbl 07346601

Summary: The theme of this study is within the realm of basic nuclear magnetic resonance (NMR) spectroscopy. It relies upon the mathematics of signal processing for NMR in analytical chemistry and medical diagnostics. Our objective is to use the fast Padé transform (both derivative and nonderivative as well as parametric and nonparametric) to address the problem of multiplets from J-coupling appearing in total shape spectra as completely unresolved resonances. The challenge is exacerbated especially for short time signals (0.5 KB, no zero filling), encoded at a standard clinical scanner with the lowest magnetic field strengths (1.5T), as is the case in the present investigation. Water has partially been suppressed in the course of encoding. Nevertheless, the residual water content is still more than four times larger than the largest among the other resonances. This challenge is further sharpened by the following question: Can the J-coupled multiplets be resolved by an exclusive reliance upon shape estimation alone (nonparametric signal processing)? In this work, the mentioned parametric signal processing is employed only as a gold standard aimed at cross-validating the reconstructions from nonparametric estimations. A paradigm shift, the derivative NMR spectroscopy, is at play here through unprecedentedly parametrizing total shape spectra (i.e. solving the quantification problem) by sole shape estimators without fitting any envelope.

MSC:

92C55 Biomedical imaging and signal processing
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[1] Estermann, I.; Stern, O., Beugung von molekularstrahlen, Z. Phys., 61, 95-125 (1930) · doi:10.1007/BF01340293
[2] Rabi, II, Space quantization in a gyrating magnetic field, Phys. Rev., 51, 652-654 (1937) · JFM 64.1483.04 · doi:10.1103/PhysRev.51.652
[3] Rabi, II; Zacharias, JR; Millman, S.; Kusch, P., A new method of measuring nuclear magnetic moment, Phys. Rev., 53, 318 (1938) · doi:10.1103/PhysRev.53.318
[4] Rabi, II; Millman, S.; Kusch, P.; Zacharias, JR, The molecular beam resonance method for measuring nuclear magnetic moments. The magnetic moments of \({^3{\text{Li}}^6, {}^3{\text{Li}}^7}\) and \({^9{\text{F}}^{19}} \), Phys. Rev., 55, 526 (1939) · doi:10.1103/PhysRev.55.526
[5] Groter, CJ, Negative results of an attempt to detect nuclear magnetic spins, Physica, 9, 995-998 (1936) · doi:10.1016/S0031-8914(36)80324-3
[6] Bloch, F.; Hansen, WW; Packard, M., Nuclear induction, Phys. Rev., 69, 127 (1946) · doi:10.1103/PhysRev.69.127
[7] Bloch, F., Nuclear induction, Phys. Rev., 70, 460-474 (1946) · doi:10.1103/PhysRev.70.460
[8] Bloch, F.; Hansen, WW; Packard, M., The nuclear induction experiment, Phys. Rev., 70, 474-485 (1946) · doi:10.1103/PhysRev.70.474
[9] Purcell, EM; Torrey, HC; Pound, RV, Resonance absorption by nuclear moments in a solid, Phys. Rev., 69, 37-38 (1946) · doi:10.1103/PhysRev.69.37
[10] Purcell, EM; Bloembergen, N.; Pound, RV, Resonance absorbtion by nuclear magnetic moments in a single crystal of \({\text{ CaF}_2} \), Phys. Rev., 69, 988 (1946) · doi:10.1103/PhysRev.70.988
[11] Siegbahn, K.; Lindström, G., Magnetic moments of deuterium-2, lithium-7 and fluorine-19, Nature, 163, 211 (1949) · doi:10.1038/163211a0
[12] Siegbahn, K.; Lindström, G., The nuclear magnetic moments of \({\text{ D}^2}, {\text{ Li}^7}\) and \({\text{ F}^{19}}\) studied by the magnetic resonance absorption method, Arkiv f. Fysik, 1, 193-213 (1949)
[13] Proctor, WG; Yu, FC, On the Magnetic Moments of \({\text{Mn}}^{55}, {\text{Co}}^{59}, {\text{Cl}}^{37}, {\text{N}}^{15}\) and \({\text{N}}^{14} \), Phys. Rev., 77, 716-717 (1950) · doi:10.1103/PhysRev.77.716
[14] Proctor, WG; Yu, FC, The dependence of a nuclear magnetic resonance frequency upon chemical compound, Phys. Rev., 77, 717 (1950) · doi:10.1103/PhysRev.77.717
[15] Dickinson, WC, Dependence of the \({\text{ F}^{19}}\) nuclear resonance position on chemical compound, Phys. Rev., 77, 736-737 (1950) · doi:10.1103/PhysRev.77.736.2
[16] Lindström, G., An experimental investigation of the nuclear magnetic moments of \({\text{ D}^2}\) and \({\text{ H}^1} \), Phys. Rev., 78, 817-818 (1950) · doi:10.1103/PhysRev.78.817
[17] Thomas, HA, The diamagnetic correction for protons in water and mineral oil, Phys. Rev., 77, 901-902 (1950) · doi:10.1103/PhysRev.80.901.2
[18] Lindström, G., Nuclear resonance absorption applied to precise measurements of nuclear magnetic moments and the establishment of an absolute energy scale in \(\beta -\) spectroscopy, Arkiv f. Fysik, 4, 1-80 (1951)
[19] Gutowsky, HC; McClure, RE, Magnetic shielding of the proton resonance in \({\text{ H}_2, \text{ H}_20}\) and mineral oil, Phys. Rev., 81, 276-277 (1951) · doi:10.1103/PhysRev.81.276
[20] Dickinson, WC, The time average magnetic field at the nucleus in nuclear magnetic resonance experiments, Phys. Rev., 81, 717-731 (1951) · doi:10.1103/PhysRev.81.717
[21] Arnold, JT; Dharmatti, SS; Packard, ME, Chemical effects on nuclear induction signals from organic compounds, J. Chem. Phys., 19, 507 (1951) · doi:10.1063/1.1748264
[22] Manual, Spectroscopy Application Guide Gyroscan ACS-NT. Philips Medical System Nederland B.V. (1989)
[23] Manual, Philips Medical System Nederland B.V. (2014). Release 5-US-Version (www.philips.com/healthcare)
[24] Drost, DJ; Riddle, WR; Clarke, GD, Proton magnetic resonance spectroscopy in the brain: Report of AAPM MR Task Group #9, Med. Phys., 29, 2177-2197 (2002) · doi:10.1118/1.1501822
[25] Belkić, Dž; Belkić, K., Quantification by the fast Padé transform of magnetic resonance spectroscopic data encoded at 1.5T: implications for brain tumor diagnostics, J. Math. Chem., 54, 602-655 (2016) · Zbl 1351.92025 · doi:10.1007/s10910-015-0578-3
[26] Dž. Belkić, K. Belkić, Derivative NMR spectroscopy for J-coupled multiplet resonances with short time signals (0.5 KB) encoded at low magnetic field strengths (1.5T): Part II, Water Unsuppressed. J. Math. Chem. (2020). doi:10.1007/s10910-020-0199-y
[27] Belkić, Dž; Belkić, K., Exact quantification by the nonparametric fast Padé transform using only shape estimation of high-order derivatives of envelopes, J. Math. Chem., 56, 268-314 (2018) · Zbl 1381.92054 · doi:10.1007/s10910-017-0837-6
[28] Belkić, Dž; Belkić, K., Explicit extraction of absorption peak positions, widths and heights using higher order derivatives of total shape spectra by nonparametric processing of time signals as complex damped multi-exponentials, J. Math. Chem., 56, 932-977 (2018) · Zbl 1384.92042 · doi:10.1007/s10910-017-0852-7
[29] Belkić, Dž; Belkić, K., Validation of reconstructed component spectra from non-parametric derivative envelopes: comparison with component lineshapes from parametric derivative estimations with the solved quantification problem, J. Math. Chem., 56, 2537-2578 (2018) · Zbl 1401.92119 · doi:10.1007/s10910-018-0906-5
[30] Belkić, Dž; Belkić, K., Review of recent applications of the conventional and derivative fast Padé transform for magnetic resonance spectroscopy, J. Math. Chem., 57, 385-464 (2019) · Zbl 1414.92155 · doi:10.1007/s10910-019-01001-8
[31] Belkić, Dž; Belkić, K., Feasibility study for applying the lower-order derivative fast Padé transform to measured time signals, J. Math. Chem., 58, 146-177 (2020) · Zbl 1455.94048 · doi:10.1007/s10910-019-01077-2
[32] Belkić, Dž, Quantum-Mechanical Signal Processing and Spectral Analysis (2005), London: Taylor & Francis via CRC Press, London · Zbl 1143.94003
[33] Belkić, Dž; Belkić, K., Signal Processing in Magnetic Resonance Spectroscopy with Biomedical Applications (2010), London: Taylor & Francis via CRC Press, London · doi:10.1201/9781439806456
[34] Belkić, Dž; Belkić, K., Robust high-resolution quantification of time signals encoded by in vivo magnetic resonance spectroscopy, Nucl. Instr. Phys. Res. A, 878, 99-128 (2018) · doi:10.1016/j.nima.2017.07.034
[35] Belkić, Dž, Exact signal-noise separation by Froissart doublets in fast Padé transform for magnetic resonance spectroscopy, Adv. Quantum Chem., 56, 95-179 (2009) · doi:10.1016/S0065-3276(08)00403-6
[36] Belkić, Dž; Belkić, K., The general concept of signal-noise separation (SNS): mathematical aspects and implementation in magnetic resonance spectroscopy, J. Math. Chem., 45, 563-597 (2009) · Zbl 1197.92030 · doi:10.1007/s10910-007-9344-5
[37] Arnold, JT, Magnetic resonance of protons in ethyl alcohol, Phys. Rev., 102, 136-150 (1956) · doi:10.1103/PhysRev.102.136
[38] Ramsey, NF, Magnetic shielding of nuclei in molecules, Phys. Rev., 78, 699-703 (1950) · Zbl 0037.42303 · doi:10.1103/PhysRev.78.699
[39] Belkić, Dž; Belkić, K., In vivo magnetic resonance spectroscopy for ovarian cancer diagnostics: quantification by the fast Padé transform, J. Math. Chem., 55, 349-405 (2017) · Zbl 1360.92063 · doi:10.1007/s10910-016-0694-8
[40] Liang, B.; Tamm, LK, NMR as a tool to investigate membrane protein structure, dynamics and function, Nat. Struct. Mol. Biol., 23, 468-474 (2016) · doi:10.1038/nsmb.3226
[41] Perez Santero, S.; Favretto, F.; Zanzoni, S.; Chignola, R.; Assfalg, M.; D’Onofrio, M., Effects of macromolecular crowding on a small lipid binding protein probed at the single-amino acid level, Arch. Biochem. Biophys., 606, 99-110 (2016) · doi:10.1016/j.abb.2016.07.017
[42] Govindaraju, V.; Young, K.; Maudsley, AA, Proton NMR chemical shifts and coupling constants for brain metabolites, NMR Biomed., 13, 129-153 (2000) · doi:10.1002/1099-1492(200005)13:3<129::AID-NBM619>3.0.CO;2-V
[43] Seeger, U.; Klose, U.; Mader, I.; Grodd, W.; Nagele, T., Parametrized evaluation of macromolecules and lipids in proton MR spectroscopy of brain diseases, Magn. Res. Med., 49, 19-28 (2003) · doi:10.1002/mrm.10332
[44] Wolinsky, JS; Narayana, PA; Fernstermacher, MJ, Proton magnetic resonance spectroscopy in multiple sclerosis, Neurology, 40, 1764-1769 (1990) · doi:10.1212/WNL.40.11.1764
[45] Narayana, PA; Wolinsky, JS; Jackson, EF; McCarthy, M., Proton MR spectroscopy of gadolinium-enhanced multiple sclerosis plaques, J. Magn. Reson. Imag., 2, 263-270 (1992) · doi:10.1002/jmri.1880020303
[46] Narayana, PA; Dyle, TJ; Wolinsky, JS, Serial proton magnetic resonance spectroscopic imaging, contrast-enhanced magnetic resonance imaging and quantitative lesion volumetry in multiple sclerosis, Ann. Neurol., 43, 56-71 (1998) · doi:10.1002/ana.410430112
[47] Larsson, HB; Christiansen, P.; Jensen, M.; Fredriksen, J.; Heltberg, A.; Olesen, J.; Henriksen, O., Localized in vivo proton spectroscopy in the brain of patients with multiple sclerosis, Magn. Reson. Med., 22, 23-31 (1991) · doi:10.1002/mrm.1910220104
[48] Davie, CA; Hawkins, CP; Barker, GJ; Brennan, A.; Tofts, PS; Miller, DH; McDonald, WI, Detection of myelin breakdown products by proton magnetic resonance spectroscopy, Lancet (Letter to the Editor), 341, 630-631 (1993) · doi:10.1016/0140-6736(93)90390-3
[49] Davie, CA; Hawkins, CP; Barker, GJ; Brennan, A.; Tofts, PS; Miller, DH; McDonald, WI, Serial proton magnetic resonance spectroscopy in acute multiple sclerosis lesions, Brain, 117, 49-58 (1994) · doi:10.1093/brain/117.1.49
[50] Koopmans, RA; Li, DK; Zhu, G.; Allen, PS; Penn, A.; Paty, DW, Magnetic resonance spectroscopy of multiple sclerosis: in-vivo detection of myelin breakdown products, Lancet (Letter to the Editor), 341, 631-632 (1993) · doi:10.1016/0140-6736(93)90391-S
[51] Roser, W.; Hagberg, G.; Mader, I.; Brunnschweiler, H.; Radue, EW; Seelig, J.; Kappos, L., Proton MRS of gadolinium-enhancing MS plaques and metabolic changes in normal-appearing white matter, Magn. Reson. Med., 33, 811-817 (1995) · doi:10.1002/mrm.1910330611
[52] Behar, KL; Ogino, T., Characterization of macromolecule resonances in the 1H NMR spectrum of rat brain, Magn. Reson. Med., 30, 38-44 (1993) · doi:10.1002/mrm.1910300107
[53] Behar, KL; Rothman, DL; Spencer, DD; Petroff, OA, Analysis of macromolecule resonances in 1H NMR spectra of human brain, Magn. Reson. Med., 32, 294-302 (1994) · doi:10.1002/mrm.1910320304
[54] Mader, I.; Seeger, U.; Weissert, R.; Close, U.; Nagele, T.; Melms, A.; Grodd, W., Proton MR spectroscopy with metabolite-nulling reveals elevated macromolecules in acute multiple sclerosis, Brain, 124, 953-961 (2001) · doi:10.1093/brain/124.5.953
[55] Seeger, U.; Mader, I.; Nagele, T.; Grodd, W.; Lutz, O.; Klose, U., Reliable detection of macromolecules in single-volume 1H NMR Spectra of the human brain, Magn. Res. Med., 45, 948-954 (2001) · doi:10.1002/mrm.1127
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