纵向弛豫对核磁共振线型的影响

The effects of longitudinal relaxation on NMR lineshape

根据经典Bloch方程的解析解以及考虑辐射阻尼效应的Bloch方程的数值解 ,通过解析分析和数值模拟 ,从理论上研究了在射频场扰动下以及在辐射阻尼效应的作用下纵向弛豫对核磁共振线型的影响。结果表明 :①射频场的扰动和辐射阻尼效应将导致纵向磁化与横向磁化的耦合 ,从而使纵向弛豫对线型产生了一定的影响。②在射频场的扰动下 ,峰强和线宽分别为 2M0 sin(θ)T1 T2 / (T1 +T2 )和 (T1 +T2 ) / (2πT1 T2 ) ,即纵向弛豫将使谱线的峰强增大、线宽变窄 ,且影响程度随着比值T2 /T1 的减小而增大 ,峰强最大可增加 1倍而线宽最多可减小 1 / 2。③在强辐射阻尼效应的作用下 ,纵向弛豫会使谱线的峰强降低 ,降低的幅度与扳转角θ以及比值T2 /T1 密切相关。当θ从 0到 3π/ 4时 ,降低的幅度均较小 ,只有当θ >3π/ 4时 ,降低的幅度才开始逐渐变大 ,且当θ接近π时 ,降低的幅度急剧增大。谱线峰强降低的幅度与T2 /T1 呈较严格的正比关系 ,即T1 越接近T2 。

According to the analytical solutions of classical Bloch equations and the numeric solutions of extended Bloch equations with radiation damping (RD) effects, the effects of longitudinal relaxation on nuclear magnetic resonance (NMR) lineshape are theoretically studied when radio frequency (RF) field irradiation or RD effects must be considered. By a series of analytical deduction and numeric simulation, the following detailed conclusions are presented:① NMR lineshape will be quite different because of the coupling between the transverse magnetization and the longitudinal magnetization by RF field or RD effects. The lineshape will be dependent not only on the transverse relaxation time T_2, but also on the longitudinal relaxation time T_1. ② The computation formulas of peak height and line width are respectively 2M_0sin(θ)T_1T_2/(T_1+T_2) and (T_1+T_2)/(2πT_1T_2) in the presence of the RF field irradiation. T_1 have such effects as increasing the peak height and narrowing the line. The effects of T_1 on lineshape grow with the decreasing ratio of T_2/T_1. ③When RD effects must be considered, T_1 will reduce the peak height. The smaller τ_r, the bigger ratio of T_2/T_1 and pulse flip angle θ, the effects of T_1 on lineshape more obviously.