title: Parsimonious continuous time random walk models and kurtosis for diffusion in magnetic resonance of biological tissue.
abstract: 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.
authors.affiliation: Department of Radiology, C.J. Gorter Center for High Field MRI, Leiden University Medical Center, Leiden, Netherlands.
authors.forename: Carson
authors.initials: C
authors.lastname: Ingo
authors.affiliation: Department of Bioengineering, University of Illinois at Chicago, Chicago, IL, USA.
authors.forename: Yi
authors.initials: Y
authors.lastname: Sui
authors.affiliation: Department of Radiology, Northwestern University, Chicago, IL, USA.
authors.forename: Yufen
authors.initials: Y
authors.lastname: Chen
authors.affiliation: Department of Radiology, Northwestern University, Chicago, IL, USA.
authors.forename: Todd B
authors.initials: TB
authors.lastname: Parrish
authors.affiliation: Department of Radiology, C.J. Gorter Center for High Field MRI, Leiden University Medical Center, Leiden, Netherlands.
authors.forename: Andrew G
authors.initials: AG
authors.lastname: Webb
authors.affiliation: Department of Radiology, C.J. Gorter Center for High Field MRI, Leiden University Medical Center, Leiden, Netherlands.
authors.forename: Itamar
authors.initials: I
authors.lastname: Ronen
keywords: Mittag-Leffler function; anomalous diffusion; continuous time random walk; fractional derivative; kurtosis; magnetic resonance imaging; stroke