New Transmission Condition Accounting For Diffusion Anisotropy In Thin Layers Applied To Diffusion MRI

Fabien Caubet 1 Houssem Haddar 2 Jing-Rebecca Li 2 Dang Van Nguyen 2
2 DeFI - Shape reconstruction and identification
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
Abstract : The Bloch-Torrey Partial Differential Equation (PDE) can be used to model the diffusion Magnetic Resonance Imaging (dMRI) signal in biological tissue. In this paper, we derive an Anisotropic Diffusion Transmission Condition (ADTC) for the Bloch-Torrey PDE that accounts for anisotropic diffusion inside thin layers. Such diffusion occurs, for example, in the myelin sheath surrounding the axons of neurons. This ADTC can be interpreted as an asymptotic model of order two with respect to the layer thickness and accounts for water diffusion in the normal direction that is low compared to the tangential direction. We prove uniform stability of the asymptotic model with respect to the layer thickness and a mass conservation property. We demonstrate the quadratic accuracy of the ADTC by numerical tests and show that it gives a better approximation of the dMRI signal than a simple transmission condition that assumes isotropic diffusion in the layers.
Document type :
Journal articles
Complete list of metadatas

Cited literature [36 references]  Display  Hide  Download

https://hal.inria.fr/hal-01110298
Contributor : Houssem Haddar <>
Submitted on : Wednesday, September 28, 2016 - 1:21:53 PM
Last modification on : Friday, October 25, 2019 - 1:57:49 AM

File

New transmission condition acc...
Files produced by the author(s)

Identifiers

Citation

Fabien Caubet, Houssem Haddar, Jing-Rebecca Li, Dang Van Nguyen. New Transmission Condition Accounting For Diffusion Anisotropy In Thin Layers Applied To Diffusion MRI. Modelisation Mathématique et Analyse Numérique, EDP sciences SMAI, 2016, ⟨10.1051/m2an/2016060⟩. ⟨hal-01110298v2⟩

Share

Metrics

Record views

561

Files downloads

890