1
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Babenko SV, Sviyazov SV, Burueva DB, Koptyug IV. Hyperpolarized long-lived spin state of methylene protons of 2-bromoethanol obtained from ethylene with non-equilibrium nuclear spin order. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2024; 360:107648. [PMID: 38401476 DOI: 10.1016/j.jmr.2024.107648] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2023] [Revised: 02/05/2024] [Accepted: 02/10/2024] [Indexed: 02/26/2024]
Abstract
In this work we achieve a significant overpopulation (PLLS≈1%) of the long-lived spin state (LLS) of methylene protons in 2-bromoethan(2H)ol (BrEtOD) obtained in a reaction between ethylene with non-equilibrium nuclear spin order and bromine water. Given all protons in ethylene are magnetically equivalent, its nuclear states are classified into nuclear spin isomers (NSIM) with total spin I = 2,1,0. Addition of parahydrogen to acetylene produces ethylene with a population of only those NSIMs with I = 1,0. As a result of the reaction with bromine water the non-equilibrium spin order of ethylene is partly transferred to the singlet LLS involving the two methylene groups of BrEtOD. The 1H NMR signal enhancement (SE≈200) obtained as a result of the LLS readout is approximately equal to the SE of the hyperpolarized BrEtOD obtained with a single π/4 pulse. The LLS relaxation time (TLLS) was shown to be approximately 40 s (≈8T1) in the argon-bubbled sample.
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Affiliation(s)
- Simon V Babenko
- Laboratory of Magnetic Resonance Microimaging, International Tomography Center, SB RAS, Novosibirsk 630090, Russia; V.V. Voevodsky Institute of Chemical Kinetics and Combustion, SB RAS, Novosibirsk 630090, Russia.
| | - Sergey V Sviyazov
- Laboratory of Magnetic Resonance Microimaging, International Tomography Center, SB RAS, Novosibirsk 630090, Russia; Novosibirsk State University, Novosibirsk 630090, Russia
| | - Dudari B Burueva
- Laboratory of Magnetic Resonance Microimaging, International Tomography Center, SB RAS, Novosibirsk 630090, Russia
| | - Igor V Koptyug
- Laboratory of Magnetic Resonance Microimaging, International Tomography Center, SB RAS, Novosibirsk 630090, Russia
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2
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Eills J, Budker D, Cavagnero S, Chekmenev EY, Elliott SJ, Jannin S, Lesage A, Matysik J, Meersmann T, Prisner T, Reimer JA, Yang H, Koptyug IV. Spin Hyperpolarization in Modern Magnetic Resonance. Chem Rev 2023; 123:1417-1551. [PMID: 36701528 PMCID: PMC9951229 DOI: 10.1021/acs.chemrev.2c00534] [Citation(s) in RCA: 62] [Impact Index Per Article: 62.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
Abstract
Magnetic resonance techniques are successfully utilized in a broad range of scientific disciplines and in various practical applications, with medical magnetic resonance imaging being the most widely known example. Currently, both fundamental and applied magnetic resonance are enjoying a major boost owing to the rapidly developing field of spin hyperpolarization. Hyperpolarization techniques are able to enhance signal intensities in magnetic resonance by several orders of magnitude, and thus to largely overcome its major disadvantage of relatively low sensitivity. This provides new impetus for existing applications of magnetic resonance and opens the gates to exciting new possibilities. In this review, we provide a unified picture of the many methods and techniques that fall under the umbrella term "hyperpolarization" but are currently seldom perceived as integral parts of the same field. Specifically, before delving into the individual techniques, we provide a detailed analysis of the underlying principles of spin hyperpolarization. We attempt to uncover and classify the origins of hyperpolarization, to establish its sources and the specific mechanisms that enable the flow of polarization from a source to the target spins. We then give a more detailed analysis of individual hyperpolarization techniques: the mechanisms by which they work, fundamental and technical requirements, characteristic applications, unresolved issues, and possible future directions. We are seeing a continuous growth of activity in the field of spin hyperpolarization, and we expect the field to flourish as new and improved hyperpolarization techniques are implemented. Some key areas for development are in prolonging polarization lifetimes, making hyperpolarization techniques more generally applicable to chemical/biological systems, reducing the technical and equipment requirements, and creating more efficient excitation and detection schemes. We hope this review will facilitate the sharing of knowledge between subfields within the broad topic of hyperpolarization, to help overcome existing challenges in magnetic resonance and enable novel applications.
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Affiliation(s)
- James Eills
- Institute
for Bioengineering of Catalonia, Barcelona
Institute of Science and Technology, 08028Barcelona, Spain,
| | - Dmitry Budker
- Johannes
Gutenberg-Universität Mainz, 55128Mainz, Germany,Helmholtz-Institut,
GSI Helmholtzzentrum für Schwerionenforschung, 55128Mainz, Germany,Department
of Physics, UC Berkeley, Berkeley, California94720, United States
| | - Silvia Cavagnero
- Department
of Chemistry, University of Wisconsin, Madison, Madison, Wisconsin53706, United States
| | - Eduard Y. Chekmenev
- Department
of Chemistry, Integrative Biosciences (IBio), Karmanos Cancer Institute
(KCI), Wayne State University, Detroit, Michigan48202, United States,Russian
Academy of Sciences, Moscow119991, Russia
| | - Stuart J. Elliott
- Molecular
Sciences Research Hub, Imperial College
London, LondonW12 0BZ, United Kingdom
| | - Sami Jannin
- Centre
de RMN à Hauts Champs de Lyon, Université
de Lyon, CNRS, ENS Lyon, Université Lyon 1, 69100Villeurbanne, France
| | - Anne Lesage
- Centre
de RMN à Hauts Champs de Lyon, Université
de Lyon, CNRS, ENS Lyon, Université Lyon 1, 69100Villeurbanne, France
| | - Jörg Matysik
- Institut
für Analytische Chemie, Universität
Leipzig, Linnéstr. 3, 04103Leipzig, Germany
| | - Thomas Meersmann
- Sir
Peter Mansfield Imaging Centre, University Park, School of Medicine, University of Nottingham, NottinghamNG7 2RD, United Kingdom
| | - Thomas Prisner
- Institute
of Physical and Theoretical Chemistry and Center of Biomolecular Magnetic
Resonance, Goethe University Frankfurt, , 60438Frankfurt
am Main, Germany
| | - Jeffrey A. Reimer
- Department
of Chemical and Biomolecular Engineering, UC Berkeley, and Materials Science Division, Lawrence Berkeley National
Laboratory, Berkeley, California94720, United States
| | - Hanming Yang
- Department
of Chemistry, University of Wisconsin, Madison, Madison, Wisconsin53706, United States
| | - Igor V. Koptyug
- International Tomography Center, Siberian
Branch of the Russian Academy
of Sciences, 630090Novosibirsk, Russia,
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3
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Dagys L, Bengs C, Moustafa GAI, Levitt MH. Deuteron-Decoupled Singlet NMR in Low Magnetic Fields: Application to the Hyperpolarization of Succinic Acid. Chemphyschem 2022; 23:e202200274. [PMID: 35925559 PMCID: PMC9804268 DOI: 10.1002/cphc.202200274] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2022] [Revised: 06/23/2022] [Indexed: 01/05/2023]
Abstract
The reaction of unsaturated substrates with hydrogen gas enriched in the para spin isomer leads to products with a high degree of nuclear singlet spin order. This leads to greatly enhanced NMR signals, with important potential applications such as magnetic resonance imaging (MRI) of metabolic processes. Although parahydrogen-induced polarization has the advantage of being cheap, compact, and mobile, especially when performed in ultralow magnetic fields, efficiency is lost when more than a few protons are involved. This strongly restricts the range of compatible substances. We show that these difficulties may be overcome by a combination of deuteration with the application of a sinusoidally modulated longitudinal field as a well as a transverse rotating magnetic field. We demonstrate a six-fold enhancement in the 13 C hyperpolarization of [1-13 C, 2,3-d2 ]-succinic acid, as compared with standard hyperpolarization methods, applied in the same ultralow field regime.
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Affiliation(s)
- Laurynas Dagys
- School of ChemistryHighfield CampusSouthamptonSO17 1BJUnited Kingdom
| | - Christian Bengs
- School of ChemistryHighfield CampusSouthamptonSO17 1BJUnited Kingdom
| | | | - Malcolm H. Levitt
- School of ChemistryHighfield CampusSouthamptonSO17 1BJUnited Kingdom
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4
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Tickner BJ, Zhivonitko VV. Advancing homogeneous catalysis for parahydrogen-derived hyperpolarisation and its NMR applications. Chem Sci 2022; 13:4670-4696. [PMID: 35655870 PMCID: PMC9067625 DOI: 10.1039/d2sc00737a] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2022] [Accepted: 03/21/2022] [Indexed: 12/18/2022] Open
Abstract
Parahydrogen-induced polarisation (PHIP) is a nuclear spin hyperpolarisation technique employed to enhance NMR signals for a wide range of molecules. This is achieved by exploiting the chemical reactions of parahydrogen (para-H2), the spin-0 isomer of H2. These reactions break the molecular symmetry of para-H2 in a way that can produce dramatically enhanced NMR signals for reaction products, and are usually catalysed by a transition metal complex. In this review, we discuss recent advances in novel homogeneous catalysts that can produce hyperpolarised products upon reaction with para-H2. We also discuss hyperpolarisation attained in reversible reactions (termed signal amplification by reversible exchange, SABRE) and focus on catalyst developments in recent years that have allowed hyperpolarisation of a wider range of target molecules. In particular, recent examples of novel ruthenium catalysts for trans and geminal hydrogenation, metal-free catalysts, iridium sulfoxide-containing SABRE systems, and cobalt complexes for PHIP and SABRE are reviewed. Advances in this catalysis have expanded the types of molecules amenable to hyperpolarisation using PHIP and SABRE, and their applications in NMR reaction monitoring, mechanistic elucidation, biomedical imaging, and many other areas, are increasing.
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Affiliation(s)
- Ben J Tickner
- NMR Research Unit, Faculty of Science, University of Oulu P.O. Box 3000 Oulu 90014 Finland
- Department of Chemical and Biological Physics, Faculty of Chemistry, Weizmann Institute of Science Rehovot 7610001 Israel
| | - Vladimir V Zhivonitko
- NMR Research Unit, Faculty of Science, University of Oulu P.O. Box 3000 Oulu 90014 Finland
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5
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Barker SJ, Dagys L, Hale W, Ripka B, Eills J, Sharma M, Levitt MH, Utz M. Direct Production of a Hyperpolarized Metabolite on a Microfluidic Chip. Anal Chem 2022; 94:3260-3267. [PMID: 35147413 PMCID: PMC9096798 DOI: 10.1021/acs.analchem.1c05030] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Abstract
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Microfluidic systems hold great potential
for the study of live
microscopic cultures of cells, tissue samples, and small organisms.
Integration of hyperpolarization would enable quantitative studies
of metabolism in such volume limited systems by high-resolution NMR
spectroscopy. We demonstrate, for the first time, the integrated generation
and detection of a hyperpolarized metabolite on a microfluidic chip.
The metabolite [1-13C]fumarate is produced in a nuclear
hyperpolarized form by (i) introducing para-enriched hydrogen into
the solution by diffusion through a polymer membrane, (ii) reaction
with a substrate in the presence of a ruthenium-based catalyst, and
(iii) conversion of the singlet-polarized reaction product into a
magnetized form by the application of a radiofrequency pulse sequence,
all on the same microfluidic chip. The microfluidic device delivers
a continuous flow of hyperpolarized material at the 2.5 μL/min
scale, with a polarization level of 4%. We demonstrate two methods
for mitigating singlet–triplet mixing effects which otherwise
reduce the achieved polarization level.
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Affiliation(s)
- Sylwia J Barker
- School of Chemistry, University of Southampton, Southampton SO17 1BJ, United Kingdom
| | - Laurynas Dagys
- School of Chemistry, University of Southampton, Southampton SO17 1BJ, United Kingdom
| | - William Hale
- School of Chemistry, University of Southampton, Southampton SO17 1BJ, United Kingdom.,Department of Chemistry, University of Florida, Gainesville 32611, United States
| | - Barbara Ripka
- School of Chemistry, University of Southampton, Southampton SO17 1BJ, United Kingdom
| | - James Eills
- Institute for Physics, Johannes Gutenberg University, D-55090 Mainz, Germany.,GSI Helmholtzzentrum für Schwerionenforschung GmbH, Helmholtz-Institut Mainz, 55128 Mainz, Germany
| | - Manvendra Sharma
- School of Chemistry, University of Southampton, Southampton SO17 1BJ, United Kingdom
| | - Malcolm H Levitt
- School of Chemistry, University of Southampton, Southampton SO17 1BJ, United Kingdom
| | - Marcel Utz
- School of Chemistry, University of Southampton, Southampton SO17 1BJ, United Kingdom
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6
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Eills J, Hale W, Utz M. Synergies between Hyperpolarized NMR and Microfluidics: A Review. PROGRESS IN NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY 2022; 128:44-69. [PMID: 35282869 DOI: 10.1016/j.pnmrs.2021.09.001] [Citation(s) in RCA: 13] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2021] [Revised: 09/10/2021] [Accepted: 09/11/2021] [Indexed: 06/14/2023]
Abstract
Hyperpolarized nuclear magnetic resonance and lab-on-a-chip microfluidics are two dynamic, but until recently quite distinct, fields of research. Recent developments in both areas increased their synergistic overlap. By microfluidic integration, many complex experimental steps can be brought together onto a single platform. Microfluidic devices are therefore increasingly finding applications in medical diagnostics, forensic analysis, and biomedical research. In particular, they provide novel and powerful ways to culture cells, cell aggregates, and even functional models of entire organs. Nuclear magnetic resonance is a non-invasive, high-resolution spectroscopic technique which allows real-time process monitoring with chemical specificity. It is ideally suited for observing metabolic and other biological and chemical processes in microfluidic systems. However, its intrinsically low sensitivity has limited its application. Recent advances in nuclear hyperpolarization techniques may change this: under special circumstances, it is possible to enhance NMR signals by up to 5 orders of magnitude, which dramatically extends the utility of NMR in the context of microfluidic systems. Hyperpolarization requires complex chemical and/or physical manipulations, which in turn may benefit from microfluidic implementation. In fact, many hyperpolarization methodologies rely on processes that are more efficient at the micro-scale, such as molecular diffusion, penetration of electromagnetic radiation into a sample, or restricted molecular mobility on a surface. In this review we examine the confluence between the fields of hyperpolarization-enhanced NMR and microfluidics, and assess how these areas of research have mutually benefited one another, and will continue to do so.
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Affiliation(s)
- James Eills
- Institute for Physics, Johannes Gutenberg University, D-55090 Mainz, Germany; GSI Helmholtzzentrum für Schwerionenforschung GmbH, Helmholtz-Institut Mainz, 55128 Mainz, Germany.
| | - William Hale
- Department of Chemistry, University of Florida, 32611, USA
| | - Marcel Utz
- School of Chemistry, University of Southampton, SO17 1BJ, UK.
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7
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Ostrowska SJ, Rana A, Utz M. Spatially Resolved Kinetic Model of Parahydrogen Induced Polarisation (PHIP) in a Microfluidic Chip. Chemphyschem 2021; 22:2004-2013. [PMID: 33929791 PMCID: PMC8518753 DOI: 10.1002/cphc.202100135] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2021] [Revised: 04/23/2021] [Indexed: 01/19/2023]
Abstract
We report a spatially resolved kinetic finite element model of parahydrogen-induced polarisation (PHIP) in a microfluidic chip that was calibrated using on-chip and off-chip NMR data. NMR spectroscopy has great potential as a read-out technique for lab-on-a-chip (LoC) devices, but is often limited by sensitivity. By integrating PHIP with a LoC device, a continuous stream of hyperpolarised material can be produced, and mass sensitivities of pmol s have been achieved. However, the yield and polarisation levels have so far been quite low, and can still be optimised. To facilitate this, a kinetic model of the reaction has been developed, and its rate constants have been calibrated using macroscopic kinetic measurements. The kinetic model was then coupled with a finite element model of the microfluidic chip. The model predicts the concentration of species involved in the reaction as a function of flow rate and position in the device. The results are in quantitative agreement with published experimental data.
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Affiliation(s)
| | - Aabidah Rana
- School of ChemistryUniversity of SouthamptonSouthamptonUK
| | - Marcel Utz
- School of ChemistryUniversity of SouthamptonSouthamptonUK
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8
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Bengs C, Dagys L, Moustafa GAI, Whipham JW, Sabba M, Kiryutin AS, Ivanov KL, Levitt MH. Nuclear singlet relaxation by chemical exchange. J Chem Phys 2021; 155:124311. [PMID: 34598559 DOI: 10.1063/5.0066182] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Abstract
The population imbalance between nuclear singlet states and triplet states of strongly coupled spin-1/2 pairs, also known as nuclear singlet order, is well protected against several common relaxation mechanisms. We study the nuclear singlet relaxation of 13C pairs in aqueous solutions of 1,2-13C2 squarate over a range of pH values. The 13C singlet order is accessed by introducing 18O nuclei in order to break the chemical equivalence. The squarate dianion is in chemical equilibrium with hydrogen-squarate (SqH-) and squaric acid (SqH2) characterized by the dissociation constants pK1 = 1.5 and pK2 = 3.4. Surprisingly, we observe a striking increase in the singlet decay time constants TS when the pH of the solution exceeds ∼10, which is far above the acid-base equilibrium points. We derive general rate expressions for chemical-exchange-induced nuclear singlet relaxation and provide a qualitative explanation of the TS behavior of the squarate dianion. We identify a kinetic contribution to the singlet relaxation rate constant, which explicitly depends on kinetic rate constants. Qualitative agreement is achieved between the theory and the experimental data. This study shows that infrequent chemical events may have a strong effect on the relaxation of nuclear singlet order.
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Affiliation(s)
- Christian Bengs
- School of Chemistry, University of Southampton, Southampton, United Kingdom
| | - Laurynas Dagys
- School of Chemistry, University of Southampton, Southampton, United Kingdom
| | - Gamal A I Moustafa
- School of Chemistry, University of Southampton, Southampton, United Kingdom
| | - James W Whipham
- School of Chemistry, University of Southampton, Southampton, United Kingdom
| | - Mohamed Sabba
- School of Chemistry, University of Southampton, Southampton, United Kingdom
| | | | | | - Malcolm H Levitt
- School of Chemistry, University of Southampton, Southampton, United Kingdom
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9
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Eills J, Cavallari E, Kircher R, Di Matteo G, Carrera C, Dagys L, Levitt MH, Ivanov KL, Aime S, Reineri F, Münnemann K, Budker D, Buntkowsky G, Knecht S. Singlet-Contrast Magnetic Resonance Imaging: Unlocking Hyperpolarization with Metabolism*. Angew Chem Int Ed Engl 2021; 60:6791-6798. [PMID: 33340439 PMCID: PMC7986935 DOI: 10.1002/anie.202014933] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2020] [Indexed: 11/21/2022]
Abstract
Hyperpolarization-enhanced magnetic resonance imaging can be used to study biomolecular processes in the body, but typically requires nuclei such as 13 C, 15 N, or 129 Xe due to their long spin-polarization lifetimes and the absence of a proton-background signal from water and fat in the images. Here we present a novel type of 1 H imaging, in which hyperpolarized spin order is locked in a nonmagnetic long-lived correlated (singlet) state, and is only liberated for imaging by a specific biochemical reaction. In this work we produce hyperpolarized fumarate via chemical reaction of a precursor molecule with para-enriched hydrogen gas, and the proton singlet order in fumarate is released as antiphase NMR signals by enzymatic conversion to malate in D2 O. Using this model system we show two pulse sequences to rephase the NMR signals for imaging and suppress the background signals from water. The hyperpolarization-enhanced 1 H-imaging modality presented here can allow for hyperpolarized imaging without the need for low-abundance, low-sensitivity heteronuclei.
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Affiliation(s)
- J. Eills
- Helmholtz Institute MainzGSI Helmholtzzentrum für Schwerionenforschung64291DarmstadtGermany
- Johannes Gutenberg University55090MainzGermany
| | - E. Cavallari
- Dept. of Molecular Biotechnology and Health SciencesUniversity of TorinoTorino10126Italy
| | - R. Kircher
- Technical University of Kaiserslautern67663KaiserslauternGermany
| | - G. Di Matteo
- Dept. of Molecular Biotechnology and Health SciencesUniversity of TorinoTorino10126Italy
| | - C. Carrera
- Institute of Biostructures and BioimagingNational Research Council of ItalyTorino10126Italy
| | - L. Dagys
- School of ChemistryUniversity of SouthamptonSouthamptonSO17 1BJVereinigtes Königreich
| | - M. H. Levitt
- School of ChemistryUniversity of SouthamptonSouthamptonSO17 1BJVereinigtes Königreich
| | - K. L. Ivanov
- International Tomography CenterSiberian Branch of the Russian Academy of ScienceNovosibirsk630090Russia
- Novosibirsk State UniversityNovosibirsk630090Russia
| | - S. Aime
- Dept. of Molecular Biotechnology and Health SciencesUniversity of TorinoTorino10126Italy
| | - F. Reineri
- Dept. of Molecular Biotechnology and Health SciencesUniversity of TorinoTorino10126Italy
| | - K. Münnemann
- Technical University of Kaiserslautern67663KaiserslauternGermany
| | - D. Budker
- Helmholtz Institute MainzGSI Helmholtzzentrum für Schwerionenforschung64291DarmstadtGermany
- Johannes Gutenberg University55090MainzGermany
| | - G. Buntkowsky
- Eduard-Zintl-Institute for Inorganic Chemistry and Physical, ChemistryTechnical University Darmstadt64287DarmstadtGermany
| | - S. Knecht
- Eduard-Zintl-Institute for Inorganic Chemistry and Physical, ChemistryTechnical University Darmstadt64287DarmstadtGermany
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10
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Eills J, Cavallari E, Kircher R, Di Matteo G, Carrera C, Dagys L, Levitt MH, Ivanov KL, Aime S, Reineri F, Münnemann K, Budker D, Buntkowsky G, Knecht S. Singulett‐Kontrast‐Magnetresonanztomographie: Freisetzung der Hyperpolarisation durch den Metabolismus**. Angew Chem Int Ed Engl 2021. [DOI: 10.1002/ange.202014933] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
Affiliation(s)
- J. Eills
- Helmholtz Institute Mainz GSI Helmholtzzentrum für Schwerionenforschung 64291 Darmstadt Deutschland
- Johannes Gutenberg University 55090 Mainz Deutschland
| | - E. Cavallari
- Dept. of Molecular Biotechnology and Health Sciences University of Torino Torino 10126 Italien
| | - R. Kircher
- Technical University of Kaiserslautern 67663 Kaiserslautern Deutschland
| | - G. Di Matteo
- Dept. of Molecular Biotechnology and Health Sciences University of Torino Torino 10126 Italien
| | - C. Carrera
- Institute of Biostructures and Bioimaging National Research Council of Italy Torino 10126 Italien
| | - L. Dagys
- School of Chemistry University of Southampton Southampton SO17 1BJ Vereinigtes Königreich
| | - M. H. Levitt
- School of Chemistry University of Southampton Southampton SO17 1BJ Vereinigtes Königreich
| | - K. L. Ivanov
- International Tomography Center Siberian Branch of the Russian Academy of Science Novosibirsk 630090 Russland
- Novosibirsk State University Novosibirsk 630090 Russland
| | - S. Aime
- Dept. of Molecular Biotechnology and Health Sciences University of Torino Torino 10126 Italien
| | - F. Reineri
- Dept. of Molecular Biotechnology and Health Sciences University of Torino Torino 10126 Italien
| | - K. Münnemann
- Technical University of Kaiserslautern 67663 Kaiserslautern Deutschland
| | - D. Budker
- Helmholtz Institute Mainz GSI Helmholtzzentrum für Schwerionenforschung 64291 Darmstadt Deutschland
- Johannes Gutenberg University 55090 Mainz Deutschland
| | - G. Buntkowsky
- Eduard-Zintl-Institute for Inorganic Chemistry and Physical, Chemistry Technical University Darmstadt 64287 Darmstadt Deutschland
| | - S. Knecht
- Eduard-Zintl-Institute for Inorganic Chemistry and Physical, Chemistry Technical University Darmstadt 64287 Darmstadt Deutschland
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11
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Bengs C. Markovian exchange phenomena in magnetic resonance and the Lindblad equation. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2021; 322:106868. [PMID: 33253960 DOI: 10.1016/j.jmr.2020.106868] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/22/2020] [Revised: 10/28/2020] [Accepted: 10/30/2020] [Indexed: 06/12/2023]
Abstract
Nuclear Magnetic Resonance (NMR) experiments involve coherent and incoherent dynamics. Incoherent dynamics give rise to nuclear spin relaxation typically accounted for by a differential equation known as a quantum master equation. Out of the existing master equations the Lindblad equation is particularly important. A central theorem of open quantum theory states that a relaxation process represents a quantum Markovian process if and only if it can be described by a Lindblad master equation. This in turn raises serious questions regarding the compatibility of conventional NMR relaxation theory and one of the most fundamental results of open quantum theory. The NMR treatment of important Markovian relaxation mechanisms such as Brownian motion or chemical exchange events do in general not result in a master equation in Lindblad form and would therefore be at odds with the mathematically rigorous theory of open quantum systems. We explore this apparent conflict for two important chemical exchange phenomena and show that their conventional treatment may be recast into a suitable Lindblad equation. Similarities between spatial diffusion and multi-site exchange events allow us to extend our results to nuclear spin relaxation due to translational diffusion. As a result we are able to show that the NMR treatment of intramolecular exchange and translational diffusion represent valid quantum Markovian processes compatible with the rigorous definitions of open quantum theory.
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Affiliation(s)
- Christian Bengs
- School of Chemistry, Southampton University, University Road, SO17 1BJ, UK.
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