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首页> 外文会议>ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2007 >NMR MEASUREMENTS OF ANOMALOUS DIFFUSION REFLECT FRACTIONAL ORDER DYNAMICS
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NMR MEASUREMENTS OF ANOMALOUS DIFFUSION REFLECT FRACTIONAL ORDER DYNAMICS

机译：异常扩散反射分数阶动力学的NMR测量

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摘要

Diffusion weighted MRI is often used to detect and stage neurodegenerative, malignant and ischemic diseases. The correlation between developing pathology and localized diffusion measurements relies on the design of selective phase encoding pulses that alter the intensity of the acquired signal according to biophysical models of spin diffusion in tissue. The most common approach utilizes a bipolar or Stejskal-Tanner gradient pulse sequence to encode the apparent diffusion coefficient as an exponential, multi-exponential or stretched exponential function of experimentally-controlled parameters. Several studies have investigated the ability of the stretched exponential to provide an improved fit to diffusion-weighted imaging data. These results were recently analyzed by establishing a direct link between water diffusion, as measured using NMR, and fractal structural models of tissues. In this paper we suggest an alternative description for stretched exponential behavior that reflects fractional order dynamics of a generalized Bloch-Torrey equation in either space or time. Such generalizations are the basis for similar anomalous diffusion phenomena observed in optical spectroscopy, polymer dynamics and electrochemistry. Here we demonstrate a correspondence between the detected NMR signal and anomalous diffusional dynamics of water through the Riesz fractional order space derivative and the Caputo form of the fractional order Riemann-Liouville time derivative.
机译：弥散加权MRI通常用于检测和分级神经退行性，恶性和缺血性疾病。发展中的病理学与局部扩散测量之间的相关性依赖于选择性相位编码脉冲的设计，该脉冲根据组织中自旋扩散的生物物理模型来改变获取信号的强度。最常见的方法是利用双极性或Stejskal-Tanner梯度脉冲序列将视在扩散系数编码为实验控制参数的指数，多指数或拉伸指数函数。几项研究研究了拉伸指数为扩散加权成像数据提供改进拟合的能力。最近，通过建立使用NMR测量的水扩散与组织的分形结构模型之间的直接联系来分析这些结果。在本文中，我们为延伸的指数行为提出了另一种描述，该描述反映了时空上广义Bloch-Torrey方程的分数阶动力学。这种概括是在光谱学，聚合物动力学和电化学中观察到的类似异常扩散现象的基础。在这里，我们证明了检测到的NMR信号与通过Riesz分数阶空间导数和分数阶Riemann-Liouville时间导数的Caputo形式的水的异常扩散动力学之间的对应关系。

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