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Publications (10 of 16) Show all publications
Nguyen, V. D., Jansson, J., Tran, H. T., Hoffman, J. & Li, J.-R. (2019). Diffusion MRI simulation in thin-layer and thin-tube media using a discretization on manifolds. Journal of magnetic resonance, 299, 176-187
Open this publication in new window or tab >>Diffusion MRI simulation in thin-layer and thin-tube media using a discretization on manifolds
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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
Keywords
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:nbn:se:kth:diva-235070 (URN)10.1016/j.jmr.2019.01.002 (DOI)000460655200018 ()2-s2.0-85059768594 (Scopus ID)
Funder
Swedish Energy Agency, P40435-1
Note

QC 20180919

Available from: 2018-09-14 Created: 2018-09-14 Last updated: 2019-03-27Bibliographically approved
Nguyen, V. D., Jansson, J., Goude, A. & Hoffman, J. (2019). Direct Finite Element Simulation of the Turbulent Flow Past a Vertical Axis Wind Turbine. Renewable energy, 135, 238-247
Open this publication in new window or tab >>Direct Finite Element Simulation of the Turbulent Flow Past a Vertical Axis Wind Turbine
2019 (English)In: Renewable energy, ISSN 0960-1481, E-ISSN 1879-0682, Vol. 135, p. 238-247Article in journal (Refereed) Published
Abstract [en]

There is today a significant interest in harvesting renewable energy, specifically wind energy, in offshore and urban environments. Vertical axis wind turbines get increasing attention since they are able to capture the wind from any direction. They are relatively easy to install and to transport, cheaper to build and maintain, and quite safe for humans and birds. Detailed computer simulations of the fluid dynamics of wind turbines provide an enhanced understanding of the technology and may guide design improvements. In this paper, we simulate the turbulent flow past a vertical axis wind turbine for a range of rotation angles in parked and rotating conditions. We propose the method of Direct Finite Element Simulation in a rotating ALE framework, abbreviated as DFS-ALE. The simulation results are validated against experimental data in the form of force measurements. We find that the simulation results are stable with respect to mesh refinement and that we capture well the general shape of the variation of force measurements over the rotation angles.

Place, publisher, year, edition, pages
Elsevier, 2019
Keywords
VAWT, Direct FEM simulation, ALE
National Category
Energy Systems
Research subject
Computer Science; Applied and Computational Mathematics; Vehicle and Maritime Engineering
Identifiers
urn:nbn:se:kth:diva-224801 (URN)10.1016/j.renene.2018.11.098 (DOI)000459365600021 ()2-s2.0-85058018814 (Scopus ID)
Note

QC 20180326

Available from: 2018-03-26 Created: 2018-03-26 Last updated: 2019-03-11Bibliographically approved
Nguyen, V. D., Jansson, J., Frachon, T., Degirmenci, C. & Hoffman, J. (2018). A fluid-structure interaction model with weak slip velocity boundary conditions on conforming internal interfaces. In: : . Paper presented at 6th European Conference on Computational Mechanics (ECCM), 7th European Conference on Computational Fluid Dynamics (ECFD 7), 1115 June 2018, Glasgow, UK.
Open this publication in new window or tab >>A fluid-structure interaction model with weak slip velocity boundary conditions on conforming internal interfaces
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2018 (English)Conference paper, Published paper (Other (popular science, discussion, etc.))
Abstract [en]

We develop a PUFEM–Partition of Unity Finite Element Method to impose slip velocity boundary conditions on conforming internal interfaces for a fluid-structure interaction model. The method facilitates a straightforward implementation on the FEniCS/FEniCS-HPC platform. We show two results for 2D model problems with the implementation on FEniCS: (1) optimal convergence rate is shown for a stationary Navier-Stokes flow problem, and (2) the slip velocity conditions give qualitatively the correct result for the Euler flow. 

Keywords
fluid-structure interaction, slip boundary conditions, conforming meshes, internal interfaces
National Category
Computational Mathematics
Research subject
Applied and Computational Mathematics; Computer Science
Identifiers
urn:nbn:se:kth:diva-225143 (URN)
Conference
6th European Conference on Computational Mechanics (ECCM), 7th European Conference on Computational Fluid Dynamics (ECFD 7), 1115 June 2018, Glasgow, UK
Note

QC 20190215

Available from: 2018-03-31 Created: 2018-03-31 Last updated: 2019-02-15Bibliographically approved
Nguyen, V. D., Jansson, J., Hoffman, J. & Li, J.-R. (2018). A partition of unity finite element method for computational diffusion MRI. Journal of Computational Physics, 375, 271-290
Open this publication in new window or tab >>A partition of unity finite element method for computational diffusion MRI
2018 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 375, p. 271-290Article in journal (Refereed) Published
Abstract [en]

The Bloch–Torrey equation describes the evolution of the spin (usually water proton) magnetization under the influence of applied magnetic field gradients and is commonly used in numerical simulations for diffusion MRI and NMR. Microscopic heterogeneity inside the imaging voxel is modeled by interfaces inside the simulation domain, where a discontinuity in the magnetization across the interfaces is produced via a permeability coefficient on the interfaces. To avoid having to simulate on a computational domain that is the size of an entire imaging voxel, which is often much larger than the scale of the microscopic heterogeneity as well as the mean spin diffusion displacement, smaller representative volumes of the imaging medium can be used as the simulation domain. In this case, the exterior boundaries of a representative volume either must be far away from the initial positions of the spins or suitable boundary conditions must be found to allow the movement of spins across these exterior boundaries.

Many approaches have been taken to solve the Bloch–Torrey equation but an efficient high-performance computing framework is still missing. In this paper, we present formulations of the interface as well as the exterior boundary conditions that are computationally efficient and suitable for arbitrary order finite elements and parallelization. In particular, the formulations are based on the partition of unity concept which allows for a discontinuous solution across interfaces conforming with the mesh with weak enforcement of real (in the case of interior interfaces) and artificial (in the case of exterior boundaries) permeability conditions as well as an operator splitting for the exterior boundary conditions. The method is straightforward to implement and it is available in FEniCS for moderate-scale simulations and in FEniCS-HPC for large-scale simulations. The order of accuracy of the resulting method is validated in numerical tests and a good scalability is shown for the parallel implementation. We show that the simulated dMRI signals offer good approximations to reference signals in cases where the latter are available and we performed simulations for a realistic model of a neuron to show that the method can be used for complex geometries.

Place, publisher, year, edition, pages
Elsevier, 2018
Keywords
Computational diffusion MRI, Bloch–Torrey equation, Partition of unity finite element method, Interface conditions, Weak pseudo-periodic conditions, FEniCS/FEniCS-HPC
National Category
Computational Mathematics
Research subject
Applied and Computational Mathematics; Biological Physics; Computer Science
Identifiers
urn:nbn:se:kth:diva-234286 (URN)10.1016/j.jcp.2018.08.039 (DOI)000450907600014 ()2-s2.0-85054048672 (Scopus ID)
Funder
Swedish Energy Agency, P40435-1
Note

QC 20180906

Available from: 2018-09-06 Created: 2018-09-06 Last updated: 2019-02-15Bibliographically approved
Tie, B., Mouronval, A.-S., Nguyen, V. D., Series, L. & Aubry, D. (2018). A unified variational framework for the space discontinuous Galerkin method for elastic wave propagation in anisotropic and piecewise homogeneous media. Computer Methods in Applied Mechanics and Engineering, 338, 299-332
Open this publication in new window or tab >>A unified variational framework for the space discontinuous Galerkin method for elastic wave propagation in anisotropic and piecewise homogeneous media
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2018 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 338, p. 299-332Article, review/survey (Refereed) Published
Abstract [en]

We present a unified multidimensional variational framework for the space discontinuous Galerkin method for elastic wave propagation in anisotropic and piecewise homogeneous media. Based on an elastic wave oriented formulation and using a tensorial formalism, the proposed framework allows a better understanding of the physical meaning of the terms involved in the discontinuous Galerkin method. The unified variational framework is written for first-order velocity-stress wave equations. An uncoupled upwind numerical flux and two coupled upwind numerical fluxes using respectively the Voigt and the Reuss averages of elastic moduli are defined. Two numerical fluxes that are exact solutions of the Riemann problem on physical interfaces are also developed and analyzed in the 1D case. The implemented solvers are then applied to different elastic media, especially to polycrystalline materials that present a particular case of piecewise homogeneous media. The use of the three upwind numerical fluxes, which only solve approximately the Riemann problem at element interfaces, is investigated.

Place, publisher, year, edition, pages
Elsevier, 2018
Keywords
Space discontinuous Galerkin method; Elastic wave propagation; Anisotropy; Piecewise homogeneous medium; Polycrystalline materials
National Category
Other Engineering and Technologies
Research subject
Applied and Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-227028 (URN)10.1016/j.cma.2018.04.018 (DOI)000436490700013 ()2-s2.0-85047003427 (Scopus ID)
Projects
MAPIE
Note

QC 20180523

Available from: 2018-05-01 Created: 2018-05-01 Last updated: 2019-02-14Bibliographically approved
Wassermann, D., Nguyen, V. D., Gallardo-Diez, G., Li, J.-R., Cai, W. & Menon, V. (2018). Sensing Spindle Neurons in the Insula with Multi-shell Diffusion MRI. In: : . Paper presented at Annual Meeting ISMRM-ESMRMB, June 16-21 2018, Paris, France. France: ISMRM-ESMRMB 2018
Open this publication in new window or tab >>Sensing Spindle Neurons in the Insula with Multi-shell Diffusion MRI
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2018 (English)Conference paper, Published paper (Refereed)
Abstract [en]

Sensing microstructural characteristics of human brain tissue with clinical scanners has been an area of heated debate in the diffusion MRI (dMRI) community. In this work, we propose that diffusion MRI on clinical scanners is sensitive to the presence of spindle neurons.

Spindle neurons, located in the insular and anterior cingular cortices, are only present in mammals with high cognitive functions. Albeit this neurons' role is not yet known, evidence suggests they facilitate rapid long-range information integration.

In this work, we provide theoretical and in-silico evidence that the dMRI signal is sensitive to the presence of spindle neurons as well as preliminary evidence on human dMRI images. 

Place, publisher, year, edition, pages
France: ISMRM-ESMRMB 2018, 2018
National Category
Natural Sciences
Research subject
Applied and Computational Mathematics; Applied Medical Technology
Identifiers
urn:nbn:se:kth:diva-225130 (URN)
Conference
Annual Meeting ISMRM-ESMRMB, June 16-21 2018, Paris, France
Note

QC 20180523

Available from: 2018-03-29 Created: 2018-03-29 Last updated: 2019-02-14Bibliographically approved
Nguyen, V. D. (2016). A FENICS-HPC framework for multi-compartment Bloch-Torrey models. In: : . Paper presented at ECCOMAS Congress 2016 (pp. 105-119). National Technical University of Athens, 1
Open this publication in new window or tab >>A FENICS-HPC framework for multi-compartment Bloch-Torrey models
2016 (English)Conference paper, Published paper (Refereed)
Place, publisher, year, edition, pages
National Technical University of Athens: , 2016
Keywords
Diffusion MRI; Diffusion NMR; FEniCS-HPC; Simulation
National Category
Computational Mathematics
Research subject
Applied and Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-202981 (URN)2-s2.0-84995394415 (Scopus ID)
Conference
ECCOMAS Congress 2016
Note

QC 20170509

Available from: 2017-03-10 Created: 2017-03-10 Last updated: 2017-06-15Bibliographically approved
Nguyen, V. D., Grebenkov, D., Le Bihan, D. & Li, J.-R. (2015). Numerical study of a cylinder model of diffusion MRI signal for neuronal dendrite trees. Journal of magnetic resonance, 252, 103-113
Open this publication in new window or tab >>Numerical study of a cylinder model of diffusion MRI signal for neuronal dendrite trees
2015 (English)In: Journal of magnetic resonance, ISSN 1090-7807, E-ISSN 1096-0856, Vol. 252, p. 103-113Article in journal (Refereed) Published
Abstract [en]

We study numerically how the neuronal dendrite tree structure can affect the diffusion magnetic resonance imaging (dMRI) signal in brain tissue. For a large set of randomly generated dendrite trees, synthetic dMRI signals are computed and fitted to a cylinder model to estimate the effective longitudinal diffusivity DL in the direction of neurites. When the dendrite branches are short compared to the diffusion length, DL depends significantly on the ratio between the average branch length and the diffusion length. In turn, DL has very weak dependence on the distribution of branch lengths and orientations of a dendrite tree, and the number of branches per node. We conclude that the cylinder model which ignores the connectivity of the dendrite tree can still be adapted to describe the apparent diffusion coefficient in brain tissue.

Place, publisher, year, edition, pages
Academic Press, 2015
Keywords
Diffusion MRI, Cylinder model, Neurites, Dendrite trees
National Category
Biochemistry and Molecular Biology
Research subject
Applied and Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-225140 (URN)10.1016/j.jmr.2015.01.008 (DOI)000352757200012 ()2-s2.0-84922745790 (Scopus ID)
Note

QC 20180403

Available from: 2018-03-31 Created: 2018-03-31 Last updated: 2019-02-14Bibliographically approved
Nguyen, H. T., Grebenkov, D., Nguyen, V. D., Poupon, C., Le Bihan, D. & Li, J.-R. (2015). Parameter estimation using macroscopic diffusion MRI signal models. Physics in Medicine and Biology, 60(8), 3389-3413
Open this publication in new window or tab >>Parameter estimation using macroscopic diffusion MRI signal models
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2015 (English)In: Physics in Medicine and Biology, ISSN 0031-9155, E-ISSN 1361-6560, Vol. 60, no 8, p. 3389-3413Article in journal (Refereed) Published
Abstract [en]

Macroscopic models of the diffusion MRI (dMRI) signal can be helpful in understanding the relationship between the tissue microstructure and the dMRI signal. We study the least squares problem associated with estimating tissue parameters such as the cellular volume fraction, the residence times and the effective diffusion coefficients using a recently developed macroscopic model of the dMRI signal called the Finite Pulse Kärger model that generalizes the original Kärger model to non-narrow gradient pulses. In order to analyze the quality of the estimation in a controlled way, we generated synthetic noisy dMRI signals by including the effect of noise on the exact signal produced by the Finite Pulse Kärger model. The noisy signals were then fitted using the macroscopic model. Minimizing the least squares, we estimated the model parameters. The bias and standard deviations of the estimated model parameters as a function of the signal to noise ratio (SNR) were obtained. We discuss the choice of the b-values, the least square weights, the extension to experimentally obtained dMRI data as well as noise correction.

Keywords
diffusion MRI, macroscopic model, parameter estimation
National Category
Medical and Health Sciences
Research subject
Applied and Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-240128 (URN)10.1088/0031-9155/60/8/3389 (DOI)000352525200027 ()2-s2.0-84927618778 (Scopus ID)
Note

QC 20181213

Available from: 2018-12-12 Created: 2018-12-12 Last updated: 2019-02-14Bibliographically approved
Nguyen, V. D., Li, J.-R., Grebenkov, D. & Le Bihan, D. (2014). A finite element method to solve the Bloch-Torrey equation applied to diffusion magnetic resonance imaging. Journal of Computational Physics, 263, 283-302
Open this publication in new window or tab >>A finite element method to solve the Bloch-Torrey equation applied to diffusion magnetic resonance imaging
2014 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 263, p. 283-302Article in journal (Refereed) Published
Abstract [en]

The complex transverse water proton magnetization subject to diffusion-encoding magnetic field gradient pulses in a heterogeneous medium can be modeled by the multiple compartment Bloch-Torrey partial differential equation (PDE). In addition, steady-state Laplace PDEs can be formulated to produce the homogenized diffusion tensor that describes the diffusion characteristics of the medium in the long time limit. In spatial domains that model biological tissues at the cellular level, these two types of PDEs have to be completed with permeability conditions on the cellular interfaces. To solve these PDEs, we implemented a finite elements method that allows jumps in the solution at the cell interfaces by using double nodes. Using a transformation of the Bloch-Torrey PDE we reduced oscillations in the searched-for solution and simplified the implementation of the boundary conditions. The spatial discretization was then coupled to the adaptive explicit Runge-Kutta-Chebyshev time-stepping method. Our proposed method is second order accurate in space and second order accurate in time. We implemented this method on the FEniCS C++ platform and show time and spatial convergence results. Finally, this method is applied to study some relevant questions in diffusion MRI.

Place, publisher, year, edition, pages
Academic Press, 2014
Keywords
Bloch–Torrey equation; Diffusion magnetic resonance imaging; Finite elements; RKC; Pseudo-periodic; Double-node; Interface problem
National Category
Computational Mathematics
Research subject
Applied and Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-225137 (URN)10.1016/j.jcp.2014.01.009 (DOI)000331716900016 ()2-s2.0-84893491013 (Scopus ID)
Note

QC 20180403

Available from: 2018-03-31 Created: 2018-03-31 Last updated: 2018-05-07Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-3213-0040

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