Michaeli Shalom
Center for Magnetic Resonance Research, University of Minnesota, Minneapolis, MN, USA.
J Magn Reson. 2025 Jan;370:107809. doi: 10.1016/j.jmr.2024.107809. Epub 2024 Dec 2.
During adiabatic full passage (AFP) radiofrequency (RF) pulses the relaxation functions are conventionally treated in the Tilting Doubly Rotating Frame (TDRF), or the second rotating frame (SRF) of reference. Such a description is adequate when during the adiabatic passage the magnetization M is perfectly aligned with the time dependent effective magnetic field, B(t), leading to T(t) relaxation, or evolves on a plane perpendicular to B(t), leading to T(t) relaxation. Time evolution of B(t) results in formation of a fictitious magnetic field, which is typically neglected during the AFP pulses operating in adiabatic regime, i.e., given that the adiabatic condition |γdα(t)/dt| ≪ B(t) is well satisfied. Here α(t) is the angle between B(t) and the axis of quantization of the first rotating frame (FRF) z', and dα(t)/dt is the angular velocity. When the fictitious field component cannot be neglected, for the adequate description of relaxation during AFP pulses the solutions for the relaxation functions in a multi-fold rotating frame are necessary. Such a general treatment is currently unavailable for adiabatic RF pulses. Here, we obtain the solution for the relaxation functions in the Tilting Triply Rotating Frame (TTRF) during the Hyperbolic Secant (HS) pulses of the HSn family, HS1 and HS4, where n is the stretching factor. We show that the contribution to the relaxations originating from the non-negligible magnitude of the fictitious field depends on the pulse modulation functions of the AFP pulses and the parameters of the pulses. The corrections to describe the relaxations are given, which may be relevant in specific experimental setups especially for high-resolution NMR.
在绝热全通过（AFP）射频（RF）脉冲期间，弛豫函数通常在倾斜双旋转框架（TDRF）或第二参考旋转框架（SRF）中进行处理。当在绝热通过期间磁化强度M与随时间变化的有效磁场B(t)完美对齐，导致T(t)弛豫，或者在垂直于B(t)的平面上演变，导致T(t)弛豫时，这样的描述是足够的。B(t)的时间演变会导致形成一个虚拟磁场，在绝热状态下运行的AFP脉冲期间，该虚拟磁场通常被忽略，即假设绝热条件|γdα(t)/dt| ≪ B(t)得到很好的满足。这里α(t)是B(t)与第一旋转框架（FRF）z'的量化轴之间的夹角，dα(t)/dt是角速度。当虚拟场分量不可忽略时，为了充分描述AFP脉冲期间的弛豫，需要在多重旋转框架中求解弛豫函数。目前对于绝热RF脉冲还没有这样的通用处理方法。在这里，我们得到了在HSn族的双曲正割（HS）脉冲HS1和HS4期间倾斜三旋转框架（TTRF）中弛豫函数的解，其中n是拉伸因子。我们表明，源自不可忽略的虚拟场大小对弛豫的贡献取决于AFP脉冲的脉冲调制函数和脉冲参数。给出了描述弛豫的修正，这在特定的实验设置中可能是相关的，特别是对于高分辨率核磁共振。
