| Issue |
ESAIM: M2AN
Volume 57, Number 4, July-August 2023
|
|
|---|---|---|
| Page(s) | 1953 - 1980 | |
| DOI | https://doi.org/10.1051/m2an/2023043 | |
| Published online | 03 July 2023 | |
A second order asymptotic model for diffusion MRI in permeable media
1
ESPRIT-School of Engineering, 1, 2 rue André Ampère – 2083 – Pôle Technologique – El Ghazala, Tunis, Tunisia
2
ENIT-LAMSIN, Université de Tunis El Manar, B.P. 37, Belvederem 1002, Tunis, Tunisia
3
Inria Saclay, IDEFIX Team, Institut Polytechnique de Paris, UMA, ENSTA Paris, Palaiseau, France
* Corresponding author: jingrebecca.li@inria.fr
Received:
27
July
2022
Accepted:
15
May
2023
Starting from a reference partial differential equation model of the complex transverse water proton magnetization in a voxel due to diffusion-encoding magnetic field gradient pulses, one can use periodic homogenization theory to establish macroscopic models. A previous work introduced an asymptotic model that accounted for permeable interfaces in the imaging medium. In this paper we formulate a higher order asymptotic model to treat higher values of permeability. We explicitly solved this new asymptotic model to obtain a system of ordinary differential equations that can model the diffusion MRI signal and we present numerical results showing the improved accuracy of the new model in the regime of higher permeability.
Mathematics Subject Classification: 35K10
Key words: Bloch–Torrey equation / diffusion MRI / Homogenization / higher-order diffusion tensor
© The authors. Published by EDP Sciences, SMAI 2023
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