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New Transmission Condition Accounting For Diffusion Anisotropy In Thin Layers Applied To Diffusion MRI
2017 (English)In: ESAIM: M2AN, Vol. 51, p. 1279-1301Article in journal (Refereed) Published
Abstract [en]

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 the uniform stability of the asymptotic model with respect to the layer thickness and a mass conservation property. We also prove the theoretical quadratic accuracy of the ADTC. Finally, numerical tests validate these results and show that our model gives a better approximation of the dMRI signal than a simple transmission condition that assumes isotropic diffusion in the layers.

Place, publisher, year, edition, pages
2017. Vol. 51, p. 1279-1301
Keywords [en]
Asymptotic expansion, Bloch-Torrey equation, anisotropic diffusion transmission condition, diffusion magnetic resonance imaging
National Category
Natural Sciences
Research subject
Applied and Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-225142DOI: 10.1051/m2an/2016060ISI: 000410567200006Scopus ID: 2-s2.0-85044202272OAI: oai:DiVA.org:kth-225142DiVA, id: diva2:1194340
Note

QC 20180411

Available from: 2018-03-31 Created: 2018-03-31 Last updated: 2018-04-11Bibliographically approved

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Publisher's full textScopushttps://www.esaim-m2an.org/articles/m2an/abs/2017/04/m2an150062/m2an150062.html

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Nguyen, Van-Dang
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Citation style
  • apa
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  • de-DE
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  • nn-NB
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  • Other locale
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