Universal equations for linear adiabatic pulses and characterization of partial adiabaticity
Universal equations for linear adiabatic pulses and characterization of partial adiabaticity
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DOI：
10.1006/jmre.2002.2531
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发表时间：
2002-05-01
影响因子：
2.2
通讯作者：
Bendall, MR
中科院分区：
文献类型：
--
作者：
Tesiram, YA;Bendall, MR
sech/tanh（或双曲正割）和 tanh/tan 绝热反演脉冲的数值分析为每种类型的脉冲提供了一组主方程，保证了它们在各种实际条件下的最佳实现，而无需进一步模拟脉冲的反演剖面。这些简单的方程确定了在选定的有效带宽 (bw(eff)) 上和选定的脉冲长度 (T-p) 上预选反转程度所需的必要最大射频幅度 (RFmax)。两种类型的脉冲功能不同：sech/tanh 脉冲提供矩形反演轮廓，其中 bw(eff) 是绝热频率扫描 (bwdth) 的很大一部分，而 tanh/tanh bw(eff) 小于或等于 bwdth /20。如果反演质量定义为在 bw(eff) 边界处的最小允许反演范围 iota(bw)，则可以找到两种脉冲类型的两个基本线性方程，其形式为 (RFmaxTp)(2) = m(1)T(p)bwdth + c(1) 和 T(p)bwdth = m(3)T(p)bw(eff) + c(3)。两个脉冲的不同行为表示为斜率 m(n) 和截距 c(n) 对 iota(bw) 的不同依赖性，并且在这些方程中考虑了二阶效应。这些主关系的可用性使得能够直接比较两种类型的绝热脉冲，并且发现 tanh/tanh 需要等效 sech/tanh 脉冲的大约一半的脉冲长度，并且还具有对标量耦合的影响不太敏感的优点。相比之下，sech/tanh 提供的总 RF 功率约为等效 tanh/tanh 脉冲的一半。预计这两个基本线性方程的形式通常适用于绝热反演脉冲，从而定义了“线性绝热性”的概念。在 T(p)wdth 或 T(p)bw(eff) 值较低时，线性方程不再适用，从而定义了“部分绝热”区域。该部分区域中间的正常绝热脉冲在 RFmax 或 T-p 方面更有效，但对 RF 不均匀性的容忍度稍差。最近开发出了一类数值优化脉冲，专门以绝热性为代价来获得 RFmax 或 T-p 效率。与在最佳条件下实施的正常绝热脉冲相比，这些新的部分绝热脉冲仅显示出微小的改进；它们仅限于 T-p bw(eff) 的单个值，并且对 RF 不均匀性的容忍度要低得多。这些比较以及任何类型的反转脉冲（绝热或其他）之间的直接比较可以使用 (RFmax T-p)(2) 或（总功率）T-p 与 T-p bw(eff) 的关系图进行。 (C) 2002 年爱思唯尔科学（美国）。
A numerical analysis of the sech/tanh (or hyperbolic secant) and tanh/tan adiabatic inversion pulses provides a set of master equations for each type of pulse that guarantee their optimal implementation over a wide range of practical conditions without needing to further simulate the inversion profiles of the pulses. These simple equations determine the necessary maximum R-F amplitude (RFmax) required for a preselected degree of inversion across a chosen effective bandwidth (bw(eff)) and for a chosen pulse length (T-p). The two types of pulse function differently: The sech/tanh pulse provides a rectangular inversion profile with bw(eff) being a large fraction of the adiabatic frequency sweep (bwdth), whereas for tanh/tan bw(eff) is less than or equal tobwdth /20. If the quality of inversion is defined as the minimum allowable extent of inversion, iota(bw), at the boundaries of bw(eff), two basic linear equations are found for both types of pulse and these are of the form (RFmaxTp)(2) = m(1)T(p)bwdth + c(1) and T(p)bwdth = m(3)T(p)bw(eff) + c(3). The different behavior of the two pulses is expressed as different dependencies of the slopes m(n) and intercepts c(n) on iota(bw) and allowances are made for second order effects within these equations. The availability of these master relationships enables a direct comparison of the two types of adiabatic pulse and it is found that tanh/tan requires about half the pulse length of an equivalent sech/tanh pulse and also has the advantage of being less sensitive to the effects of scalar coupling. In contrast sech/tanh delivers about half the total RF power of an equivalent tanh/tan pulse. It is expected that the forms of these two basic linear equations are generally applicable to adiabatic inversion pulses and thus define the concept of "linear adiabaticity." At low values of T(p)wdth or T(p)bw(eff) the linear equations no longer apply, defining a region of "partial adiabaticity." Normal adiabatic pulses in the middle of this partial region are more efficient in terms of RFmax or T-p but are moderately less tolerant to RF inhomogeneity. A class of numerically optimized pulses has recently been developed that specifically trades adiabaticity in an attempt to gain RFmax or T-p efficiency. In comparison to normal adiabatic pulses implemented under optimal conditions, these new partially adiabatic pulses show only marginal improvements; they are restricted to single values of T-p bw(eff), and they are vastly less tolerant to RF inhomogeneity. These comparisons, and direct comparisons between any types of inversion pulse, adiabatic or otherwise, can be made using plots of (RFmax T-p)(2) or (Total Power) T-p versus T-p bw(eff). (C) 2002 Elsevier Science (USA).