Diffusion in Sephadex Gel Structures: Time Dependency Revealed by Multi-Sequence Acquisition over a Broad Diffusion Time Range.

Guangyu Dan,Kaibao Sun,M Muge Karaman,Weiguo Li,Richard L Magin,Qingfei Luo,Zheng Zhong,Xiaohong Joe Zhou

doi:10.3390/math9141688

Abstract

It has been increasingly reported that in biological tissues diffusion-weighted MRI signal attenuation deviates from mono-exponential decay, especially at high b-values. A number of diffusion models have been proposed to characterize this non-Gaussian diffusion behavior. One of these models is the continuous-time random-walk (CTRW) model, which introduces two new parameters: a fractional order time derivative α and a fractional order spatial derivative β. These new parameters have been linked to intravoxel diffusion heterogeneities in time and space, respectively, and are believed to depend on diffusion times. Studies on this time dependency are limited, largely because the diffusion time cannot vary over a board range in a conventional spin-echo echo-planar imaging sequence due to the accompanying T2 decays. In this study, we investigated the time-dependency of the CTRW model in Sephadex gel phantoms across a broad diffusion time range by employing oscillating-gradient spin-echo, pulsed-gradient spin-echo, and pulsed-gradient stimulated echo sequences. We also performed Monte Carlo simulations to help understand our experimental results. It was observed that the diffusion process fell into the Gaussian regime at extremely short diffusion times whereas it exhibited a strong time dependency in the CTRW parameters at longer diffusion times.

Highlights

Using water diffusion as a probe, diffusion-weighted MRI (DW-MRI) has become a promising technique to reveal the underlying micrometer-scale structural properties in millimeter-resolution MR images [1,2]
One way of characterizing the non-Gaussian diffusion behavior is to employ the continuous time random walk (CTRW) theory, in which the mean squared displacement (MSD) can be expressed by a composite power law as: hx2 i ~ t2α/β, where α and β are the fractional order time and space derivatives, respectively, in fractionalized Fick’s second law [7,8]
We investigated the diffusion time dependency of the CTRW model by employing oscillating-gradient spin-echo (OGSE), pulsed-gradient spin-echo (PGSE), and pulsed-gradient stimulated echo (PGSTE) pulse sequences

Summary

Introduction

Using water diffusion as a probe, diffusion-weighted MRI (DW-MRI) has become a promising technique to reveal the underlying micrometer-scale structural properties in millimeter-resolution MR images [1,2]. One way of characterizing the non-Gaussian diffusion behavior is to employ the continuous time random walk (CTRW) theory, in which the MSD can be expressed by a composite power law as: hx i ~ t2α/β , where α and β are the fractional order time and space derivatives, respectively, in fractionalized Fick’s second law [7,8]. This generalized description enables the CTRW model to provide a more realistic description of the complex diffusion pattern in biological tissues [8]

Methods

Results

Discussion

Conclusion