Understanding the Time-Dependent Effective Diffusion Coefficient Measured by Diffusion MRI: the Intra-Cellular Case - Archive ouverte HAL Access content directly
Journal Articles SIAM Journal on Applied Mathematics Year : 2017

Understanding the Time-Dependent Effective Diffusion Coefficient Measured by Diffusion MRI: the Intra-Cellular Case

(1) , (1) , (1)
1

Abstract

Diffusion Magnetic Resonance Imaging (dMRI) can be used to measure a time-dependent effective diffusion coefficient that can in turn reveal information about the tissue geometry. Recently a mathematical model for the time-dependent effective diffusion coefficient was obtained using homogenization techniques after imposing a certain scaling relationship for the time, the biological cell membrane permeability, the diffusion-encoding magnetic field gradient strength, and a periodicity length of the cellular geometry. With this choice of the scaling of the physical parameters, the effective diffusion coefficient of the medium can be computed after solving a diffusion equation subject to a time-dependent Neumann boundary condition, independently in the biological cells and in the extra-cellular space. In this paper, we analyze this new model, which we call the H-ADC model, in the case of finite domains, which is relevant to diffusion inside biological cells. We use both the eigenfunction expansion and the single layer potential representation for the solution of the above mentioned diffusion equation to obtain analytical expressions for the effective diffusion coefficient in different diffusion time regimes. These expressions are validated using numerical simulations in two dimensions.
Fichier principal
Vignette du fichier
article.pdf (620.02 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01421928 , version 1 (23-12-2016)

Identifiers

  • HAL Id : hal-01421928 , version 1

Cite

Houssem Haddar, Jing-Rebecca Li, Simona Schiavi. Understanding the Time-Dependent Effective Diffusion Coefficient Measured by Diffusion MRI: the Intra-Cellular Case. SIAM Journal on Applied Mathematics, 2017. ⟨hal-01421928⟩
484 View
210 Download

Share

Gmail Facebook Twitter LinkedIn More