International Tomography Center SB RAS, Institutskaya 3a, Novosibirsk 630090, Russia.
J Magn Reson. 2011 Oct;212(2):330-43. doi: 10.1016/j.jmr.2011.07.013. Epub 2011 Jul 27.
Exact explicit analytical expression for echoes in the Carr-Purcell-Meiboom-Gill sequence with arbitrary excitation and refocusing angles and resonance offset of RF pulses was obtained, employing the generating functions formalism developed earlier by authors. Asymptotic form and analytical approximation for echoes were derived in an elegant way and analyzed in details. In particular, it was shown that depending on T(1), T(2) and parameters of the pulse sequence, oscillatory behavior of echoes can take place. Accuracy of asymptotic forms and approximations were tested by comparison with exactly calculated echo amplitudes. Besides, it was shown, that the generating function approach can be applied to the consideration of terminated pulse sequences, when after-pulses echoes are registered.
已获得具有任意激励和聚焦角以及 RF 脉冲的共振偏移的 Carr-Purcell-Meiboom-Gill 序列中回波的精确显式解析表达式，采用作者先前开发的生成函数形式。以优雅的方式推导出了回波的渐近形式和解析近似，并进行了详细分析。特别是，结果表明，取决于 T(1)、T(2)和脉冲序列的参数，回波可能会出现振荡行为。通过与精确计算的回波幅度进行比较，测试了渐近形式和近似的准确性。此外，还表明，生成函数方法可应用于已终止的脉冲序列的考虑，在这种情况下会记录到后脉冲回波。
