Steady-State Magnetic Resonance

Figure 10 shows effects of a pulse in the rotating frame described in the previous section. When the sample (containing magnetically equivalent spin-5 species) is placed in the Bq field the steady state magnetization Mq develops by spin-lattice interactions, and the spin vectors come to rest in the rotating frame with random orientation (Fig. 10b). A 5, (rf) pulse at the resonance frequency ( o supplies a field in the x direction that rotates the vector M in the y z plane through a pulse angle (or flip angle) ao/rad given by...

Figure B2.4.6. Results of an offset-saturation expermient for measuring the spin-spin relaxation time, T. In this experiment, the signal is irradiated at some offset from resonance until a steady state is achieved. The partially saturated z magnetization is then measured with a kH pulse. This figure shows a plot of the z magnetization as a fiinction of the offset of the saturating field from resonance. Circles represent measured data the line is a non-linear least-squares fit. The signal is nonnal when the saturation is far away, and dips to a minimum on resonance. The width of this dip gives T, independent of magnetic field inliomogeneity.

If the rate of sweep through the resonance frequeney is small (so-called slow passage), a steady-state solution, in which the derivatives are set to zero, is ob-tained. The result expresses M,., and as funetions of cu. These magnetization components are not actually observed, however, and it is more useful to express the solutions in terms of the susceptibility, a complex quantity related to the magnetization. The solutions for the real (x ) and imaginary (x") components then are... 

In the previous section was given the experimental demonstration of two sites. Here the steady state scheme and equations necessary to calculate the single channel currents are given. The elemental rate constants are thereby defined and related to experimentally determinable rate constants. Eyring rate theory is then used to introduce the voltage dependence to these rate constants. Having identified the experimentally required quantities, these are then derived from nuclear magnetic resonance and dielectric relaxation studies on channel incorporated into lipid bilayers. 

The phenomenological equations proposed by Felix Bloch in 19462 have had a profound effect on the development of magnetic resonance, both ESR and NMR, on the ways in which the experiments are described (particularly in NMR), and on the analysis of line widths and saturation behavior. Here we will describe the phenomenological model, derive the Bloch equations and solve them for steady-state conditions. We will also show how the Bloch equations can be extended to treat inter- and intramolecular exchange phenomena and give examples of applications. 

In a continuous wave (CW) magnetic resonance experiment, the radiation field B is continuous and BQ is changed only slowly compared with the relaxation rates (so-called slow passage conditions). Thus a steady-state solution to eqns... 

Gruetter, R., Novotny, E. J., Boulware, S. D. etal. Non-inva-sive measurements of the cerebral steady-state glucose concentration and transport in humans by 13C magnetic resonance. In L. Drewes and A. Betz (eds), Frontiers in Cerebral Vascular Biology Transport and its Regulation, vol. 331. New York Plenum Press, 1993, pp. 35-40. 

J. B. Weaver, E. E. Van Houten, M. I. Miga, F. E. Kennedy and K. D. Paulsen, Magnetic resonance elastography using 3D gradient echo measurements of steady-state motion, Med. Rhys., 2001, 28, 1620-1628. 

The steady-state methods involve theoretical analysis of magnetic resonance spectra observed under steady-state conditions. This typically involves assumptions regarding the adequacy of magnetic resonance line shape theory, some model for molecular motions and distances of closest approach on collision, and a comparison of calculated spectra for various assumed diffusion constants, and observed spectra. In general, the agreement between diffusion constants calculated using the transient and steady-state methods has been excellent. 

A second steady-state method involves the analysis of the broadening of the nuclear magnetic resonance spectra of phospholipids in bilayers containing low concentrations of spin-labeled phospholipids. A theoretical analysis of the relation between this line broadening and diffusion rates has been given by Brulet and McConnell.3 [In this paper (6) is not correct the subsequent equations are nonetheless correct. For an alternative derivation, see Brulet.2] In this paper it is shown that a number of measurements of nuclear relaxation rates T71 of nuclei in phospholipids are consistent with lateral diffusion constants in the range 10 7 to 10 R cm2/s. 

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