Ingo Carson, Sui Yi, Chen Yufen, Parrish Todd B, Webb Andrew G, Ronen Itamar
Department of Radiology, C.J. Gorter Center for High Field MRI, Leiden University Medical Center, Leiden, Netherlands.
Department of Bioengineering, University of Illinois at Chicago, Chicago, IL, USA.
Front Phys. 2015 Mar;3. doi: 10.3389/fphy.2015.00011. Epub 2015 Mar 16.
In this paper, we provide a context for the modeling approaches that have been developed to describe non-Gaussian diffusion behavior, which is ubiquitous in diffusion weighted magnetic resonance imaging of water in biological tissue. Subsequently, we focus on the formalism of the continuous time random walk theory to extract properties of subdiffusion and superdiffusion through novel simplifications of the Mittag-Leffler function. For the case of time-fractional subdiffusion, we compute the kurtosis for the Mittag-Leffler function, which provides both a connection and physical context to the much-used approach of diffusional kurtosis imaging. We provide Monte Carlo simulations to illustrate the concepts of anomalous diffusion as stochastic processes of the random walk. Finally, we demonstrate the clinical utility of the Mittag-Leffler function as a model to describe tissue microstructure through estimations of subdiffusion and kurtosis with diffusion MRI measurements in the brain of a chronic ischemic stroke patient.
在本文中，我们为已开发出的用于描述非高斯扩散行为的建模方法提供了一个背景，这种行为在生物组织中水分子的扩散加权磁共振成像中普遍存在。随后，我们聚焦于连续时间随机游走理论的形式体系，通过对米塔格 - 莱夫勒函数进行新颖的简化来提取亚扩散和超扩散的特性。对于时间分数阶亚扩散的情况，我们计算米塔格 - 莱夫勒函数的峰度，这为常用的扩散峰度成像方法提供了联系和物理背景。我们提供蒙特卡罗模拟以说明反常扩散作为随机游走的随机过程的概念。最后，我们通过对一名慢性缺血性中风患者大脑进行扩散磁共振成像测量来估计亚扩散和峰度，从而证明米塔格 - 莱夫勒函数作为描述组织微观结构模型的临床实用性。
