Tensor operator formalism for multiple-quantum NMR. 1. Spin-1 nuclei

Bowden, G. J.; Hutchison, W. D.

doi:10.1016/0022-2364(86)90378-1

Cited by 71 publications

(82 citation statements)

References 12 publications

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“…1 nuclei, and for a pair of I = 1/2 nuclei are given in Table 1. 7 The irreducible tensor representation has the advantage that it facilitates the understanding of the processes occurring during the pulse sequences. In order to follow the sequence of events one should bear in mind a few simple rules that are applicable at high magnetic fields: (a) a non-selective radiofrequency pulse can change the coherence p within the limits of jpj l; (b) changes in the rank l can occur by relaxation and modulation by quadrupolar, dipolar or J-coupling, keeping the same value of p.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Multiquantum filters and order in tissues

et al. 2001

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In ordered systems, where the molecular motion is anisotropic, quadrupolar and dipolar interactions are not averaged to zero. In such cases, double quantum (DQ) coherences can be formed. This review deals mainly with the effect of anisotropic motion of water molecules and sodium ions in intact biological tissues on 2 H, 1 H and 23 Na NMR spectroscopy and its application to NMR imaging (MRI).Double quantum filtered (DQF) spectra of water molecules and sodium ions were detected in a variety of ordered biological tissues. In collagen-containing tissues such as ligaments, tendons, cartilage, skin, blood vessels and nerves, the DQ coherences are formed as a result of the interaction with the collagen fibers. In red blood cells and presumably also in nerve axons it stems from the interaction with the cytoskeleton.For 23 Na, an I = 3/2 nucleus, the DQ coherences can also be formed in isotropic media. By a judicial choice of the pulse angle in the DQ pulse sequence only the DQ coherences arising from anisotropic motion are detected. For I = 1 nuclei such as 2 H, DQF spectra can be observed only in ordered structures. Thus, the observation of 2 H DQF spectra is an indication of order. The same is true for pairs of equivalent 1 H nuclei.The dependence of the DQF signal on the creation time of the double quantum coherences is characteristic to each tissue and allows signals to be resolved from different tissues by performing the measurements at different creation times. In this way, the 2 H DQF signals of the different compartments of sciatic nerve were resolved and water diffusion in each compartment was studied independently. In the axon, the diffusion was heavily restricted perpendicular to the axon's long axis, a result from which the axon diameter could be deduced. In blood vessel walls, this characteristic enabled the different layers of the vessel to be viewed and studied under strain.For 2 H, a DQF spectroscopic imaging sequence was used to study the orientation of the collagen fibers in the different zones of articular cartilage and bone plug. The effect of pressure on the fibers and their return to equilibrium was studied as well. In blood vessels, a DQF image was obtained and strain maps of the different layers were calculated.The efficiency of the 1 H DQF imaging technique was demonstrated on a phantom of rat tail where only the four tendons were detected at short creation times. 1 H DQF imaging and spectroscopy followed the healing of a rabbit's ruptured Achilles tendon and the results were far more sensitive to the process than conventional imaging. Finally, the method was implemented on a commercial whole body MRI spectrometer. Images of human wrist and ankle showed a positive contrast for the tendons and ligaments, indicating the potential of the method for clinical imaging.

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Section: Theoretical Backgroundmentioning

confidence: 99%

Multiquantum filters and order in tissues

et al. 2001

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“…However, for some complicated pulse sequences in zero field, the common procedure for taking a powder average is complicated due to many integrations over trigonometric functions. In this section, we will describe a general method which can greatly simplify the calculation of the zero field NMR and NQR spectra by using the irreducible tensor theory and properties of Wigner rotation matrices [20,21,22,23,24]. We will show some particular cases where the theoretical spectrum after a particular pulse sequence can be straightforwardly calculated by our method without performing any detailed integrations in the powder average.…”

Section: Calculation Of Zero Field Nmr and Nqr Spectramentioning

confidence: 99%

“…• the product properties of two irreducible tensors [20,21], the secular part of the first order average Hamiltonian may be rewritten as:…”

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Scalar operators in solid-state NMR

Sun

1991

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“…Abragam andBleaney 1970, Hutchings 1964) but rather the set of tensor operators T n q given by Buckmaster et al (1972), Bowden and Hutchison (1986 (Bowden and Hutchison 1986). Fourth, they obey well-known rotation laws (Edmonds 1957).…”

Section: Theory: Magneto-crystalline Magnetic Anisotropymentioning

confidence: 99%

Magnetic anisotropy terms in [110] MBE-grown REFe₂films involving the strain term ε_xy

Bowden

Groot

Rainford

et al. 2006

J. Phys.: Condens. Matter

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The magnetic anisotropy parameters in [110] MBE-grown films of REFe 2 (RE, rare earth) compounds are not the same as those in the bulk. This is due to the presence of a shear strain ε xy , frozen-in during crystal growth. In this paper, magnetic anisotropy parameters for [110] MBE-grown REFe 2 films, that directly involve the shear strain ε xy , are presented and discussed. In addition to the usual first-order Callen and Callen termK 2 , there are nine second-order terms, six of which involve cross-terms between ε xy and the cubic crystal field terms B 4 and B 6 . Two of the second-order cross-terms are identified as being important:K 242 (T ) andK 264 (T ). Of these, the rank-two termK 242 (T ) dominates over a large temperature range. It has the same angular dependence as the first-order termK 2 , but with a more rapid temperature dependence. The correction at T = 0 K for TbFe 2 , DyFe 2 , HoFe 2 , ErFe 2 and TmFe 2 , amounts to ∼+9.2%, −13.9%, −11.6%, +14.3%, and 27.1%, respectively. Similar comments are made concerning the rank-fourK 264 (T ) term.

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Tensor operator formalism for multiple-quantum NMR. 1. Spin-1 nuclei

Cited by 71 publications

References 12 publications

Multiquantum filters and order in tissues

Multiquantum filters and order in tissues

Scalar operators in solid-state NMR

Magnetic anisotropy terms in [110] MBE-grown REFe₂films involving the strain term ε_xy

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Tensor operator formalism for multiple-quantum NMR. 1. Spin-1 nuclei

Cited by 71 publications

References 12 publications

Multiquantum filters and order in tissues

Multiquantum filters and order in tissues

Scalar operators in solid-state NMR

Magnetic anisotropy terms in [110] MBE-grown REFe2films involving the strain term εxy

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Product

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Magnetic anisotropy terms in [110] MBE-grown REFe₂films involving the strain term ε_xy