Department of Radiology, Washington University, St. Louis, Missouri 63110, USA.
J Magn Reson. 2013 Sep;234:135-40. doi: 10.1016/j.jmr.2013.06.016. Epub 2013 Jun 29.
The apparent diffusion coefficient (ADC) is analyzed for the case of oscillating diffusion sensitizing gradients. Exact analytical expressions are obtained in the high-frequency expansion of the ADC for an arbitrary number of oscillations N. These expressions are universal and valid for arbitrary system geometry. The validity conditions of the high-frequency expansion of ADC are obtained in the framework of a simple 1D model of restricted diffusion. These conditions are shown to be substantially different for cos- and sin-type gradients: for the cos-type gradients, the high-frequency expansion is valid when the period of a single oscillation is smaller than the characteristic diffusion time, the frequency dependence of ADC being practically the same for any N. In contrast, for the sin-type gradients, the high-frequency regime can be achieved only when the total diffusion time is smaller than the characteristic diffusion time, the frequency dependence of ADC being different for different N.
对于振荡扩散敏感梯度的情况，分析表观扩散系数（ADC）。对于任意数量的 N 个振荡，在 ADC 的高频展开中获得了精确的解析表达式。这些表达式是通用的，适用于任意系统几何形状。在受限扩散的简单 1D 模型框架内，获得了 ADC 的高频展开的有效性条件。结果表明，对于余弦和正弦类型的梯度，这些条件有很大的不同：对于余弦类型的梯度，当单个振荡的周期小于特征扩散时间时，高频展开是有效的，对于任何 N，ADC 的频率依赖性实际上是相同的。相比之下，对于正弦类型的梯度，只有当总扩散时间小于特征扩散时间时，才能达到高频状态，对于不同的 N，ADC 的频率依赖性也不同。
