IEEE Trans Med Imaging. 1986;5(2):106-15. doi: 10.1109/TMI.1986.4307754.
Most magnetic resonance imaging sequences employ field gradients and amplitude modulated RF pulses to excite only those spins lying in a specific plane. The fidelity of the resulting magnetization distribution is crucial to overall image resolution. Conventional RF-pulse design techniques rely on the small tip-angle approximation to Bloch's equation, which is inadequate for the design of 90 degrees and 180 degrees pulses. This paper demonstrates the existence of a selective pulse, and provides a sound mathematical and computational basis for pulse design. It is shown that the pulses are optimal in the class of piecewise continuous functions of duration T. An optimal pulse is defined as the pulse on the interval that achieves a magnetization profile "closest" to the desired distribution. Optimal control theory provides the mathematical basis for the new pulse design technique. Computer simulations have verified the efficacy of the 90 degrees and the 180 degrees inversion and "pancake-flip" optimal pulses.
大多数磁共振成像序列采用磁场梯度和幅度调制射频脉冲来仅激发位于特定平面内的那些自旋。所得磁化分布的保真度对整体图像分辨率至关重要。传统的射频脉冲设计技术依赖于 Bloch 方程的小顶角近似，对于 90 度和 180 度脉冲的设计来说，这是不够的。本文证明了选择性脉冲的存在，并为脉冲设计提供了合理的数学和计算基础。结果表明，在持续时间为 T 的分段连续函数类中，这些脉冲是最优的。最佳脉冲定义为在间隔上实现“最接近”所需分布的磁化轮廓的脉冲。最优控制理论为新的脉冲设计技术提供了数学基础。计算机模拟已经验证了 90 度和 180 度反转以及“薄饼翻转”最优脉冲的有效性。
