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Diffusion MRI simulation in thin-layer and thin-tube media using a discretization on manifolds
KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).ORCID iD: 0000-0002-3213-0040
KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).
CMAP, Polytechnique, France.
KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).
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2019 (English)In: Journal of magnetic resonance, ISSN 1090-7807, E-ISSN 1096-0856, Vol. 299, p. 176-187Article in journal (Refereed) Published
Abstract [en]

The Bloch-Torrey partial differential equation can be used to describe the evolution of the transverse magnetization of the imaged sample under the influence of diffusion-encoding magnetic field gradients inside the MRI scanner. The integral of the magnetization inside a voxel gives the simulated diffusion MRI signal. This paper proposes a finite element discretization on manifolds in order to efficiently simulate the diffusion MRI signal in domains that have a thin layer or a thin tube geometrical structure. The variable thickness of the three-dimensional domains is included in the weak formulation established on the manifolds. We conducted a numerical study of the proposed approach by simulating the diffusion MRI signals from the extracellular space (a thin layer medium) and from neurons (a thin tube medium), comparing the results with the reference signals obtained using a standard three-dimensional finite element discretization. We show good agreements between the simulated signals using our proposed method and the reference signals for a wide range of diffusion MRI parameters. The approximation becomes better as the diffusion time increases. The method helps to significantly reduce the required simulation time, computational memory, and difficulties associated with mesh generation, thus opening the possibilities to simulating complicated structures at low cost for a better understanding of diffusion MRI in the brain.

Place, publisher, year, edition, pages
Academic Press, 2019. Vol. 299, p. 176-187
Keywords [en]
Diffusion MRI; finite element method; Bloch-Torrey equation; FEniCS; thin layer; thin tube.
National Category
Medical and Health Sciences
Research subject
Applied and Computational Mathematics; Computer Science
Identifiers
URN: urn:nbn:se:kth:diva-235070DOI: 10.1016/j.jmr.2019.01.002Scopus ID: 2-s2.0-85059768594OAI: oai:DiVA.org:kth-235070DiVA, id: diva2:1248436
Funder
Swedish Energy Agency, P40435-1
Note

QC 20180919

Available from: 2018-09-14 Created: 2018-09-14 Last updated: 2019-02-14Bibliographically approved

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Publisher's full textScopushttp://www.csc.kth.se/~vdnguyen/preprints/DMRI_manifold.pdf

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Nguyen, Van Dang

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