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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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(English)Manuscript (preprint) (Other academic)
Abstract [en]

The Bloch-Torrey partial differential equation describes the evolution of the transverse magnetization under the influence of diffusion-encoding magnetic field gradients inside a three-dimensional medium. 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 simulate the diffusion MRI signal in domains that have a thin layer or a thin tube geometrical structure. Suppose that the three-dimensional domain has a thin layer geometrical structure: points in the domain can be obtained by starting on the two-dimensional manifold and moving along a depth (thickness) function. For this type of domains, we propose a finite element discretization formulated on a surface triangulation of the manifold. The variable thickness of the domain is included in the weak formulation on the surface triangular elements. A simple modification extends the approach to `thin tube' domains where a manifold in one direction and a two-dimensional variable cross-section describe the points in the domain. This discretization approach was implemented using the finite element platform FEniCS. We conduct 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) and compare the results with the reference signals obtained by using a standard three-dimensional finite element discretization. We show good agreement between the simulated signals using our proposed method and the reference signals. The method helps us to significantly reduce both the simulation cost and the complexity of mesh generation.

Keywords [en]
Diffusion MRI; finite element method; Bloch-Torrey equation; FEniCS; thin layer; thin tube.
National Category
Natural Sciences
Research subject
Applied and Computational Mathematics; Computer Science
Identifiers
URN: urn:nbn:se:kth:diva-235070OAI: oai:DiVA.org:kth-235070DiVA, id: diva2:1248436
Note

QC 20180919

Available from: 2018-09-14 Created: 2018-09-14 Last updated: 2018-09-19Bibliographically approved

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http://www.csc.kth.se/~vdnguyen/preprints/DMRI_manifold.pdf

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Nguyen, Van-DangJansson, JohanHoffman, Johan
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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
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Language
  • de-DE
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  • en-US
  • fi-FI
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Output format
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