Sorce Dennis J, Michaeli Shalom
Independent Researcher, 6 Stonegate Court, Cockeysville, MD 21030, USA.
Center for Magnetic Resonance Research, University of Minnesota, 2021 6th Street SE, Minneapolis, MN 55455, USA.
J Magn Reson. 2025 Mar;372:107840. doi: 10.1016/j.jmr.2025.107840. Epub 2025 Jan 23.
In this work the effect of the geometric phase on time evolution of the density matrix was evaluated during nonadiabatic radiofrequency (RF) pulses with Sine amplitude modulation (AM) and Cosine frequency modulation (FM) functions of the RAFF (Relaxations Along a Fictitious Field) family, and the polarization between two energy level ½ spin system coupled by dipolar interaction was evaluated during the application of RF irradiation. The dependencies of the diagonal density matrix elements and the polarization on the rotational correlation times and the time during RF pulses were evaluated. The general treatment of the density matrix elements along with the polarization generated during RF pulses was unavailable thus far, and for the first time was here derived for the nonadiabatic case of the RAFF pulses. The current formalism could be extended to other AM and FM RF waveforms, including the adiabatic RF pulses which are widely used in magnetic resonance (MR). We demonstrate that the sub-geometric phases (SGP) influence the density matrix elements and thus the polarization generated during the application of RF AM and FM pulses. The corrections to describe the SGP influence of the density matrix elements developed in this work could be essential for determination of MR fundamental parameters necessary for evaluation of tissue contrasts in vivo in MRI and for protein dynamics characterization in high resolution NMR, where AM and FM RF pulses are frequently utilized.
在这项工作中，评估了几何相位对密度矩阵时间演化的影响，该影响发生在具有正弦幅度调制（AM）和余弦频率调制（FM）函数的非绝热射频（RF）脉冲期间，这些函数属于RAFF（沿虚拟场的弛豫）族；并且在施加RF辐射期间，评估了由偶极相互作用耦合的两个能级1/2自旋系统之间的极化。评估了对角密度矩阵元素和极化对旋转相关时间以及RF脉冲期间时间的依赖性。迄今为止，对于RF脉冲期间产生的密度矩阵元素以及极化还没有通用的处理方法，本文首次针对RAFF脉冲的非绝热情况进行了推导。当前的形式体系可以扩展到其他AM和FM RF波形，包括在磁共振（MR）中广泛使用的绝热RF脉冲。我们证明了亚几何相位（SGP）会影响密度矩阵元素，进而影响在施加RF AM和FM脉冲期间产生的极化。在这项工作中所开发的用于描述SGP对密度矩阵元素影响的修正，对于确定在MRI中评估体内组织对比度以及在高分辨率NMR中表征蛋白质动力学所需的MR基本参数可能至关重要，在这些领域中经常会使用AM和FM RF脉冲。
