Fast adiabatic passage

The quick adiabatic passage ( English adiabatic fast passage , AFP) is a method for reversing nuclear spin orientations. It has established itself as a technique in nuclear magnetic resonance tomography , in nuclear magnetic resonance spectroscopy and in magnetic resonance therapy. A reversal of the spin orientations is a prerequisite for nuclear magnetic resonance . With the fast adiabatic passage, a reversal can be brought about, which is less sensitive with regard to the magnetic field homogeneity and generates nuclear magnetic resonance even at low flux densities. An adiabatic pulse can invert very large bandwidths with little power. The principle also enables experimental imperfections to be minimized.

Physical basics

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→ Main article : Nuclear spin  and nuclear magnetic resonance

Atoms have their own mechanical angular momentum, called nuclear spin . Through its spin possess atomic nuclei also a magnetic moment . After applying a static magnetic field, these nuclei generate a measurable magnetization in the direction of the static field. In addition, the energy level of the core is split up. There are therefore predefined possible values ​​for the orientation of the spins, which are determined by the quantization condition.

An additional high-frequency alternating field in the radio frequency range with a certain frequency allows this magnetization to be deflected from the direction of the static field. The frequency has to match the Larmor frequency of the atom. As a result of the deflection, the magnetization of the spins begins to precess around the field direction of the static magnetic field . ${\displaystyle \omega }$

The magnetic moment precesses with the following frequency around the direction of the applied magnetic field.

${\displaystyle \omega =\gamma \cdot \left|B\right|={\frac {g\,q}{2\,m}}\cdot \left|B\right|\ }$

Here is the Larmor frequency and the gyromagnetic ratio . ${\displaystyle \omega }$ ${\displaystyle \gamma }$

The condition for the fast adiabatic passage must then apply:

${\displaystyle {\frac {1}{T_{1}}}\ll {\frac {1}{B_{1}}}\cdot {\frac {{\text{d}}B_{0}}{{\text{d}}t}}\ll \gamma B_{1}}$

Here is the irradiated magnetic flux density and the rate of change of the flux density of the main field and the relaxation time. ${\displaystyle B_{1}}$ ${\displaystyle {\tfrac {{\text{d}}B_{0}}{{\text{d}}t}}}$ ${\displaystyle T}$

There are two conditions: the first condition is also called the “adiabatic condition”. The rotation of the effective flux density vector must be very much slower than the precession frequency of the magnetization so that the magnetization follows the flux density. The second condition is called the “quick condition”. The rotation of the effective flux density vector must be much faster than the relaxation time .

The naming goes back to: When viewed strictly, the method is not “ adiabatic ”, since the entropy for all pulses is not zero.

application

Various nuclear magnetic resonance techniques have made it one of the most advanced and established scientific and medical procedures. A large number of related methods, such as rapid adiabatic passage, have also been developed. They are used in the following technologies:

Magnetic resonance imaging (MRI)

→ Main article : Magnetic resonance imaging

Magnetic resonance imaging is an imaging technique used to visualize tissue. The sensitivity and the quality of the resolution can be realized by a suitable pulse shape. With the fast adiabatic passage, the spins can be reversed over a large area without the underlying magnetic field having to be homogeneous.

Nuclear magnetic resonance spectroscopy (NMR)

→ Main article : Nuclear magnetic resonance spectroscopy

Nuclear magnetic resonance spectroscopy of solids has established itself in the last few decades as a method with great potential for the characterization of materials. It is necessary to excite the entire spectral width homogeneously in a large frequency range. The fast adiabatic passage enables this required homogeneous excitation in a wide frequency range. A suitable choice of AFP pulses can optimize the analysis of solids. Various so-called adiabatic pulse sequences are in use. B. " hyperbolic secant " pulses or WURST pulses. Furthermore, effects from dipolar spin-spin interactions can be reduced and thus the resolution of NMR in solids can be increased.

Magnetic resonance therapy

The generation of repeated spin resonance sequences according to the principle of rapid adiabatic passage allows the generation of the nuclear magnetic resonance condition in weak magnetic fields. This means that the nuclear resonance condition can also be used in small and medium-sized systems. The procedure is used in nuclear magnetic resonance therapy.

There are three interacting magnetic fields required for magnetic resonance therapy. Firstly, a static main magnetic field, secondly, a modulated magnetic field parallel to it, and thirdly, an alternating field that meets the Larmor condition and is perpendicular to the other two. A sweep of the magnetic field strength of the modulated magnetic field around the static field is then brought about, while the frequency remains constant. When the strength drops, the alternating field is also activated. The aim is to correlate the frequency of the modulated magnetic field with the spin-lattice relaxation time . The typical magnetic field is generated in a Helmholtz coil . ${\displaystyle {\text{d}}B/{\text{d}}t}$

Individual evidence

1. ↑ Malcolm H. Levitt, Ray Freeman: NMR population inversion using a composite pulse . In: Journal of Magnetic Resonance (1969) . tape 33 , no. 2 , February 1979, p. 473-476 , doi : 10.1016 / 0022-2364 (79) 90265-8 .
2. ↑ ^{a b c} A. Abragam: Principles of Nuclear Magnetism. Oxford University Press, 2000.
3. ↑ http://www.medcyclopaedia.com/library/topics/volume_i/a/adiabatic_fast_passage_afp_.aspx?s=adiabatic+fast+passage&mode=1&syn=&scope=
4. ↑ CJ Hardy, WA Edelstein, D. Vatis: Efficient adiabatic fast passage for NMR population inversion in the presence of radiofrequency field inhomogeneity and frequency offsets . In: Journal of Magnetic Resonance (1969) . tape 66 , no. 3 , February 15, 1986, p. 470-482 , doi : 10.1016 / 0022-2364 (86) 90190-3 .
5. ^ F. Bloch, WW Hansen, M. Packard: The Nuclear Induction Experiment . In: Physical Review . tape 70 , no. 7–8 , October 1946, pp. 474-485 , doi : 10.1103 / PhysRev.70.474 .
6. ↑ ^{a b} Alberto Tannus, Michael Garwood: Adiabatic pulses . In: NMR in Biomedicine . tape 10 , no. 8 , December 1997, p. 423-434 , doi : 10.1002 / (SICI) 1099-1492 (199712) 10: 8 <423 :: AID-NBM488> 3.0.CO; 2-X .
7. ^ Matt A. Bernstein, Kevin F. King, Xiaohong Joe Zhou: Handbook of MRI Pulse Sequences . illustrated ed. Academic Press, 2004, ISBN 0-12-092861-2 .
8. ↑ ^{a b} S. L. Chaplot, T. Sakuntala, SM Yusuf: Solid State Physics . Taylor & Francis, 2002.
9. ^ E. Kupce, R. Freeman: Adiabatic Pulses for Wideband Inversion and Broadband Decoupling . In: Journal of Magnetic Resonance, Series A . tape 115 , no. 2 , August 1995, p. 273-276 , doi : 10.1006 / jmra.1995.1179 .
10. ↑ Michael Ryan Hansen, Michael Brorson, Henrik Bildsøe, Jørgen Skibsted, Hans J. Jakobsen: Sensitivity enhancement in natural-abundance solid-state 33S MAS NMR spectroscopy employing adiabatic inversion pulses to the satellite transitions . In: Journal of Magnetic Resonance . tape 190 , no. 2 , February 2008, p. 316–326 , doi : 10.1016 / y.jmr.2007.11.014 .
11. ^ ^{A b} D. Krpan (2011) Nuclear Magnetic Resonance Therapy. The new possible of osteoarthritis and osteoporosis treatment. Balneoclimatologia. Volume 35 Broj 3
12. ↑ Hendrik Jansen, Sönke P. Frey, Jürgen Paletta, Rainer H. Meffert: Effects of low-energy NMR on posttraumatic osteoarthritis: observations in a rabbit model . In: Archives of Orthopedic and Trauma Surgery . tape 131 , no. 6 , November 10, 2010, p. 863-868 , doi : 10.1007 / s00402-010-1205-1 , PMID 21063883 .
13. ^ I. Digel et al.: Decrease in extracellular collagen crosslinking after NMR magnetic field application in skin fibroblasts . In: Medical & Biological Engineering & Computing . tape 45 , no. 1 , January 3, 2007, p. 91-97 , doi : 10.1007 / s11517-006-0144-z , PMID 7203317 .