New Transmission Condition Accounting For Diffusion Anisotropy In Thin Layers Applied To Diffusion MRI - Inria - Institut national de recherche en sciences et technologies du numérique
Journal Articles ESAIM: Mathematical Modelling and Numerical Analysis Year : 2016

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

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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Dates and versions

hal-01110298 , version 1 (27-01-2015)
hal-01110298 , version 2 (28-09-2016)

Identifiers

  • HAL Id : hal-01110298 , version 1

Cite

Fabien Caubet, Houssem Haddar, Jing-Rebecca Li, Dang Van Nguyen. New Transmission Condition Accounting For Diffusion Anisotropy In Thin Layers Applied To Diffusion MRI. ESAIM: Mathematical Modelling and Numerical Analysis, 2016. ⟨hal-01110298v1⟩
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