Simonetti O P, Wendt R E, Duerk J L
Department of Radiology, MetroHealth Medical Center, Cleveland, OH.
J Magn Reson Imaging. 1991 Sep-Oct;1(5):569-77. doi: 10.1002/jmri.1880010510.
The relationship between magnetic field gradient waveform moments and the motion sensitivity of magnetic resonance imaging was explored analytically and by computer simulation. The analysis and simulations revealed several key points. In general, waveform time moments define sensitivity to the time derivatives of position of moving material only at a single time point: the time about which the moments are computed. A Taylor series description of instantaneous position is expanded about this same time point to compute the phase acquired due to specific derivatives of position. A moment is proportional to phase sensitivity to a particular derivative of position throughout the waveform only when sensitivity to all lower-order derivatives is zero. Under restricted conditions of waveform symmetry and motion characteristics, the phase due to motion may be expressed in terms of the average value of a derivative of position over the duration of the waveform. The choice of the moment center, or point of expansion, adds a degree of freedom that may be used advantageously in the design of motion-compensating and motion phase-encoding gradient waveforms. These results facilitate a more complete understanding of the effects of motion through a magnetic field gradient.
通过分析和计算机模拟，探讨了磁场梯度波形矩与磁共振成像运动敏感性之间的关系。分析和模拟揭示了几个关键点。一般来说，波形时间矩仅在单个时间点定义对运动物质位置时间导数的敏感性：即计算矩的时间点。关于这个相同时间点展开瞬时位置的泰勒级数描述，以计算由于位置的特定导数而获得的相位。仅当对所有低阶导数的敏感性为零时，矩才与整个波形中对位置特定导数的相位敏感性成比例。在波形对称性和运动特性的受限条件下，由于运动产生的相位可以根据波形持续时间内位置导数的平均值来表示。矩中心或展开点的选择增加了一个自由度，可在运动补偿和运动相位编码梯度波形设计中有利地使用。这些结果有助于更全面地理解通过磁场梯度的运动效应。
