Parsimonious continuous time random walk models and kurtosis for diffusion in magnetic resonance of biological tissue

Frontiers in Physics

Sui, Yi¹  Ronen, Itamar²  Ingo, Carson²  Webb, Andrew G.²  Parrish, Todd B.³  Chen, Yufen³ 

[1] Department of Bioengineering, University of Illinois at Chicago, Chicago, IL, USA;Department of Radiology, C.J. Gorter Center for High Field MRI, Leiden University Medical Center, Leiden, Netherlands;Department of Radiology, Northwestern University, Chicago, IL, USA

关键词: anomalous diffusion;    kurtosis;    Mittag-Leffler function;    Continuous time random walk;    Fractional derivative;    Stroke;    Magnetic Resonance Imaging;    tissue microstructure;   

DOI  :  10.3389/fphy.2015.00011

学科分类：物理（综合）

来源: Frontiers

【 摘 要 】

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.

【 授权许可】

CC BY