磁共振中位置-相位概率密度的动力学
Dynamics of position-phase probability density in magnetic resonance
摘要：
我们认为行为的进动角（相位）下的扩散样品的分子进行典型的磁共振实验的磁场。建立了粒子系综的演化方程，将分子的相位和位置视为随机变量。这种“位置-相位（概率）密度”（PPD）被示出为编码横向磁化强度密度的布洛赫-托里方程（BTE）族的解决方案，这是因为PPD是比磁化强度密度更基本量;后者出现在前者平均后。本范例代表了一个概念上的优势，因为PPD是一个真正的概率密度服从马尔可夫动力学，而不是一个总的磁化密度的演变是不太直观的。对于适当的特殊情况，我们也给出了解析解。
英文摘要：
We consider the behaviour of precessional angle (phase) carried by molecules of a diffusing specimen under magnetic fields typical of magnetic resonance experiments. An evolution equation for the ensemble of particles is constructed, which treats the phase as well as the position of the molecules as random variables. This "position-phase (probability) density" (PPD) is shown to encode solutions to a family of Bloch-Torrey equations (BTE) for transverse magnetization density, which is because the PPD is a more fundamental quantity than magnetization density; the latter emerges from the former upon averaging. The present paradigm represents a conceptual advantage, since the PPD is a true probability density subject to Markovian dynamics, rather than an aggregate magnetization density whose evolution is less intuitive. We also work out the analytical solution for suitable special cases.
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