Spin–lattice relaxation in the rotating frame

Spin–lattice relaxation in the rotating frame is the mechanism by which M_xy, 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_1ρ. It is named in contrast to T₁, the spin-lattice relaxation time.[1]

T_1ρ 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_1ρ, which is the time it takes for the magnetic resonance signal to reach 37% (1/e) of its initial value, ${\displaystyle M_{xy}(0)}$. Hence the relation: ${\displaystyle M_{xy}(t_{\rm {SL}})=M_{xy}(0)e^{-t_{\rm {SL}}/T_{1\rho }}\,}$ , where t_SL is the duration of the RF field.