Spin–lattice relaxation in the rotating frame

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Spin–lattice relaxation in the rotating frame is the mechanism by which Mxy, the transverse component of the magnetization vector, exponentially decays towards its equilibrium value of zero, under the influence of a radio frequency (RF) field in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI). It is characterized by the spin–lattice relaxation time constant in the rotating frame, T. It is named in contrast to T1, the spin-lattice relaxation time.

T MRI is an alternative to conventional T1 and T2 MRI by its use of a long-duration, low-power radio frequency referred to as spin-lock (SL) pulse applied to the magnetization in the transverse plane. The magnetization is effectively spin-locked around an effective B1 field created by the vector sum of the applied B1 and any off-resonant component. The spin-locked magnetization will relax with a time constant T, which is the time it takes for the magnetic resonance signal to reach 37% (1/e) of its initial value, . Hence the relation: , where tSL is the duration of the RF field.

Measuring Spin–lattice relaxation in the rotating frame[edit]

T can be quantified (relaxometry) by curve fitting the signal expression above as a function of the duration of the SL pulse while the amplitude of SL pulse (γB1~0.1-few kHz) is fixed. Quantitative T MRI relaxation maps reflect the biochemical composition of tissues.[1]

T MR images[edit]

T MRI has been used to image tissues such as cartilage,[2][3] intervertebral discs,[4] brain,[5][6] and heart,[7] as well as certain types of cancers.[8][9]


  • Malcolm H. Levitt (2001). Spin Dynamics: Basics of Nuclear Magnetic Resonance. Wiley. ISBN 978-0-471-48922-1. 
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