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.
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Modelisation Mathématique et Analyse Numérique, EDP sciences SMAI, 2016, 〈10.1051/m2an/2016060〉
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Soumis le : mercredi 28 septembre 2016 - 13:21:53
Dernière modification le : jeudi 15 novembre 2018 - 01:22:23

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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〉

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