A Fast and Convenient Way to Predict Relaxation during a Frequency-Selective Adiabatic Hyperbolic Secant Pulse (HS1 Sech Pulse)

Frequency-selective inversion of magnetization is often achieved by long, low-power adiabatic RF pulses. Because these pulses can last hundreds of milliseconds, substantial relaxation of magnetization can occur during their application. Recently, a numerical model was introduced that allows an approximation of relaxation during frequency-selective adiabatic pulses for fast-tumbling small molecules in non-viscous solutions using only standard T ₁ and T ₂ relaxation times. This model is now extended to conditions in which net magnetization is not at its thermodynamic equilibrium prior to the adiabatic inversion. Simulated and experimental data reveal that the amplitude of net magnetization after an adiabatic inversion with the HS1 hyperbolic secant pulse can be approximated by a linear function of the magnetization before the pulse, depending only on T ₁ and T ₂ relaxation. The model presented here is particularly applicable to solvent-suppression sequences that utilize multiple adiabatic inversions, such as the multiple inversion-recovery nulling sequence EXCEPT. Tabulated slope and intercept values for the linear relationship are provided to facilitate a convenient optimization of pulse sequences that utilize HS1 frequency-selective adiabatic inversions.