Spin–spin relaxation

Origin

When excited nuclear spins—i.e., those lying partially in the transverse plane—interact with each other by sampling local magnetic field inhomogeneities on the micro- and nanoscales, their respective accumulated phases deviate from expected values. While the slow- or non-varying component of this deviation is reversible, some net signal will inevitably be lost due to short-lived interactions such as collisions and random processes such as diffusion through heterogeneous space.

T2 decay does not occur due to the tilting of the magnetization vector away from the transverse plane. Rather, it is observed due to the interactions of an ensemble of spins dephasing from each other. Unlike spin-lattice relaxation, considering spin-spin relaxation using only a single isochromat is trivial and not informative.

Determining parameters

Like spin-lattice relaxation, spin-spin relaxation can be studied using a molecular tumbling autocorrelation framework. Some frequency shifts, such as the NMR chemical shift, occur at frequencies proportional to the Larmor frequency, and the related but distinct parameter T2* can be heavily dependent on field strength due to the difficulty of correcting for inhomogeneity in stronger magnet bores.

Assuming isothermal conditions, spins tumbling faster through space will generally have a longer T2. Since slower tumbling displaces the spectral energy at high tumbling frequencies to lower frequencies, the relatively low beat frequency will experience a monotonically increasing amount of energy as \tau_c increases, decreasing relaxation time. The figure at the left illustrates this relationship. Fast tumbling spins, such as those in pure water, have similar T1 and T2 relaxation times, while slow tumbling spins, such as those in crystal lattices, have very distinct relaxation times.

Measurement

A spin echo experiment can be used to reverse time-invariant dephasing phenomena such as millimeter-scale magnetic inhomogeneities. The resulting signal decays exponentially as the echo time (TE), i.e., the time after excitation at which readout occurs, increases. In more complicated experiments, multiple echoes can be acquired simultaneously in order to quantitatively evaluate one or more superimposed T2 decay curves. In MRI, T2-weighted images can be obtained by selecting an echo time on the order of the various tissues' T2s. In order to reduce the amount of T1 information and therefore contamination in the image, excited spins are allowed to return to near-equilibrium on a T1 scale before being excited again. (In MRI parlance, this waiting time is called the "repetition time" and is abbreviated TR). Pulse sequences other than the conventional spin echo can also be used to measure T2; gradient echo sequences such as steady-state free precession (SSFP) and multiple spin echo sequences can be used to accelerate image acquisition or inform on additional parameters.

References

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• McRobbie D., et al. MRI, From picture to proton. 2003
• Hashemi Ray, et al. MRI, The Basics 2ED. 2004.

References

1. (September 2009). "Principles, Techniques, and Applications of T2*-based MR Imaging and Its Special Applications". RadioGraphics.
2. (October 1999). "High Resolution NMR". Academic Press.
3. (September 2011). "Structure and dynamics of hydrogels and organogels: An NMR spectroscopy approach". Progress in Polymer Science.
4. (October 1999). "High Resolution NMR". Academic Press.
5. (January 1994). "MR diffusion tensor spectroscopy and imaging". Biophysical Journal.