Magnetization steady state

Measurement by quasi - constant current (steady - state value of pulse current) providing a compete tuning out from the effect of not only electric but also magnetic material properties. 

The mathematical description of the echo intensity as a fiinction of T2 and for a repeated spin-echo measurement has been calculated on the basis that the signal before one measurement cycle is exactly that at the end of the previous cycle. Under steady state conditions of repeated cycles, this must therefore equal the signal at the end of the measurement cycle itself For a spin-echo pulse sequence such as that depicted in Figure B 1.14.1 the echo magnetization is given by [17]... 

Flow which fluctuates with time, such as pulsating flow in arteries, is more difficult to experimentally quantify than steady-state motion because phase encoding of spatial coordinate(s) and/or velocity requires the acquisition of a series of transients. Then a different velocity is detected in each transient. Hence the phase-twist caused by the motion in the presence of magnetic field gradients varies from transient to transient. However if the motion is periodic, e.g., v(r,t)=VQsin (n t +( )q] with a spatially varying amplitude Vq=Vq(/-), a pulsation frequency co =co (r) and an arbitrary phase ( )q, the phase modulation of the acquired data set is described as follows ... 

The observable NMR signal is the imaginary part of the sum of the two steady-state magnetizations, and Mg. The steady state implies that the time derivatives are zero and a little fiirther calculation (and neglect of T2 tenns) gives the NMR spectrum of an exchanging system as equation (B2.4.6)). 

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 presence of Hq but the absence of H, a steady state is established, the magnetization vector having component Mq along the z axis, but because of symmetry owing to randomization there is no net magnetization in the x y plane. This situation is shown in Fig. 4-9A. 

Figure 4-9. (Ai Precessing moment vectors in field tfo creating steady-state magnetization vector Afo. with//i = 0. (B) Immediately following application of a 90° pulse along the x axis in the rotating frame. (C) Free induction decay of the induced magnetization showing relaxation back to the configuration in A.

Now with Hx turned off, the induced magnetization must relax to its steady-state value. This is the free induction decay phase. Figure 4-9C shows an intermediate stage in the FID is increasing ftom zero toward Mq, and My is decreasing toward zero. As we have seen, relaxes with rate constant l/Ti, and My relaxes with rate constant l/T 2. 

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. 

The deposition is performed at a potential where the current is diffusion controlled at a steady state. The steady-state diffusion is maintained for a deposition time, t, by stirring the solution, usually with a magnetic stirrer. At the end of the deposition time, the stirrer is turned off for a quiet time, q (about 30 s) while the deposition potential is held. 

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. 

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