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  • 1. Caubet, Fabien
    et al.
    Haddar, Houssem
    Li, Jing-Rebecca
    Nguyen, Van-Dang
    New Transmission Condition Accounting For Diffusion Anisotropy In Thin Layers Applied To Diffusion MRI2017In: ESAIM: M2AN, Vol. 51, p. 1279-1301Article in journal (Refereed)
    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.

  • 2. Grebenkov, Denis
    et al.
    Nguyen, Van Dang
    Li, Jing-Rebecca
    Exploring diffusion across permeable barriers at high gradients. I. Narrow pulse approximation,2014In: Journal of magnetic resonance, ISSN 1090-7807, E-ISSN 1096-0856, Vol. 248, p. 153-163Article in journal (Refereed)
    Abstract [en]

    The adaptive variation of the gradient intensity with the diffusion time at a constant optimal b-value is proposed to enhance the contribution of the nuclei diffusing across permeable barriers, to the pulsed-gradient spin-echo (PGSE) signal. An exact simple formula the PGSE signal is derived under the narrow pulse approximation in the case of one-dimensional diffusion across a single permeable barrier. The barrier contribution to the signal is shown to be maximal at a particular b-value. The exact formula is then extended to multiple permeable barriers, while the PGSE signal is shown to be sensitive to the permeability and to the inter-barrier distance. Potential applications of the protocol to survey diffusion in three-dimensional domains with permeable membranes are illustrated through numerical simulations.

  • 3.
    Jansson, Johan
    et al.
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz). KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST). Basque Center for Applied Mathematics, Bilbao, Spain.
    Nguyen, Dang
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    Margarida, Moragues
    BCAM - Basque Center for Applied Mathematics.
    Castanon, Daniel
    BCAM - Basque Center for Applied Mathematics.
    Saavedra, Laura
    Universidad Politécnica de Madrid.
    Krishnasamy, Ezhilmathi
    BCAM - Basque Center for Applied Mathematics.
    Goude, Anders
    Uppsala University.
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST). Basque Center for Applied Mathematics, Bilbao, Spain.
    Direct finite element simulation of turbulent flow for marine based renewable energyManuscript (preprint) (Other academic)
    Abstract [en]

    In this article we present a computational framework for simulation ofturbulent flow in marine based renewable energy applications. Inparticular, we focus on floating structures and rotatingturbines. This work is an extension to multiphase turbulent flow, ofour existing framework of residual based turbulence modeling forsingle phase turbulent incompressible flow. We illustrate theframework in four examples: a regular wave test where we compareagainst an exact solution, the standard MARIN wave impact benchmarkwith experimental validation data, a vertical axis turbine withcomplex geometry from an existing turbine, and finally a prototypesimulation of decay test in a coupled moving boundary rigid-body andtwo-phase fluid simulation.

  • 4. Li, Jing-Rebecca
    et al.
    Nguyen, Van Dang
    KTH, School of Electrical Engineering and Computer Science (EECS).
    Nguyen, Van-Dang
    CEA Saclay Center, France.
    Haddar, Houssem
    Coatléven, Julien
    Le Bihan, Denis
    Numerical study of a macroscopic finite pulse model of the diffusion MRI signal2014In: Journal of magnetic resonance, ISSN 1090-7807, E-ISSN 1096-0856, Vol. 248, p. 54-65Article in journal (Refereed)
    Abstract [en]

    Diffusion magnetic resonance imaging (dMRI) is an imaging modality that probes the diffusion characteristics of a sample via the application of magnetic field gradient pulses. The dMRI signal from a heterogeneous sample includes the contribution of the water proton magnetization from all spatial positions in a voxel. If the voxel can be spatially divided into different Gaussian diffusion compartments with inter-compartment exchange governed by linear kinetics, then the dMRI signal can be approximated using the macroscopic Karger model, which is a system of coupled ordinary differential equations (ODEs), under the assumption that the duration of the diffusion-encoding gradient pulses is short compared to the diffusion time (the narrow pulse assumption). Recently, a new macroscopic model of the dMRI signal, without the narrow pulse restriction, was derived from the Bloch-Torrey partial differential equation (PDE) using periodic homogenization techniques. When restricted to narrow pulses, this new homogenized model has the same form as the Karger model. We conduct a numerical study of the new homogenized model for voxels that are made up of periodic copies of a representative volume that contains spherical and cylindrical cells of various sizes and orientations and show that the signal predicted by the new model approaches the reference signal obtained by solving the full Bloch-Torrey PDE in O(ε(2)), where ε is the ratio between the size of the representative volume and a measure of the diffusion length. When the narrow gradient pulse assumption is not satisfied, the new homogenized model offers a much better approximation of the full PDE signal than the Karger model. Finally, preliminary results of applying the new model to a voxel that is not made up of periodic copies of a representative volume are shown and discussed.

  • 5.
    Nguyen, Hang Tuan
    et al.
    NeuroSpin, CEA Saclay Center, 91191 Gif-sur-Yvette Cedex, France.
    Grebenkov, Denis
    Laboratoire de Physique de la Matière Condensée, CNRS—Ecole Polytechnique, F-91128 Palaiseau Cedex, France.
    Nguyen, Van Dang
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST). KTH, School of Electrical Engineering and Computer Science (EECS).
    Poupon, Cyril
    NeuroSpin, CEA Saclay Center, 91191 Gif-sur-Yvette Cedex, France.
    Le Bihan, Denis
    NeuroSpin, CEA Saclay Center, 91191 Gif-sur-Yvette Cedex, France.
    Li, Jing-Rebecca
    INRIA Saclay-Equipe DEFI, CMAP, Ecole Polytechnique Route de Saclay, 91128, Palaiseau Cedex, France.
    Parameter estimation using macroscopic diffusion MRI signal models2015In: Physics in Medicine and Biology, ISSN 0031-9155, E-ISSN 1361-6560, Vol. 60, no 8Article in journal (Refereed)
    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.

  • 6.
    Nguyen, Van Dang
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    A FENICS-HPC framework for multi-compartment Bloch-Torrey models2016Conference paper (Refereed)
  • 7.
    Nguyen, Van Dang
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    Implementation of MPI-based conjugate gradient methodfor solving the Poisson equation on Cartesian grid2015Report (Other academic)
    Abstract [en]

    In this project, we develop an MPI-based conjugate gradient method (CG) to solve the Poisson equation on Cartesian grids. The finite difference method will be used for space discretization. Thanks to the funtionalities of the MPI virtual topology, the computational domain is decomposed into subdomains and then each subdomain is assigned to an MPI process. The performance analysis will also be taken into account in this project.

  • 8.
    Nguyen, Van Dang
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).
    Jansson, Johan
    KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).
    Goude, Anders
    Uppsala University, Uppsala, Sweden.
    Hoffman, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Direct Finite Element Simulation of the Turbulent Flow Past a Vertical Axis Wind Turbine2019In: Renewable energy, ISSN 0960-1481, E-ISSN 1879-0682, Vol. 135, p. 238-247Article in journal (Refereed)
    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.

  • 9.
    Nguyen, Van Dang
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).
    Jansson, Johan
    KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).
    Hoffman, Johan
    KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).
    Li, Jing-Rebecca
    INRIA Saclay-Equipe DEFI, CMAP, Ecole Polytechnique Route de Saclay, 91128, Palaiseau Cedex, France.
    A partition of unity finite element method for computational diffusion MRI2018In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 375, p. 271-290Article in journal (Refereed)
    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.

  • 10.
    Nguyen, Van Dang
    et al.
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    Jansson, Johan
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    Li, Jing-Rebecca
    A partition of unity finite element method for computational diffusion MRIManuscript (preprint) (Other academic)
    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 efforts have been made to solve the equation but there is still missing an efficient high performance computing framework. In this work, 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 use extended finite elements with weak enforcement of real (in the case of interior interfaces) and artificial (in the case of exterior boundaries) permeability conditions as well as operator splitting for the exterior boundary conditions. The method appears to be straightforward to implement and it is implemented in the FEniCS for moderate-scale simulations and in the FEniCS-HPC for the large-scale simulations. The accuracy of the resulting method is validated numerically 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. Finally, we do simulations on a complex neuron to study how the signals decay under the effect of the permeable membrane and to show that the method can be used to simulate for complex geometries that we have not done before.

    Highlights:

    • The discontinuity in the magnetization across the interior interfaces of the medium is weakly imposed, allowing generalization to arbitrary order finite elements.
    • Spin exchange across the external boundaries is implemented by weakly imposing an artificial, high permeability, condition, allowing generalization to non-matching meshes.
    • Thus, optimal convergence with respect to the space discretization is achieved.
    • The second-order Crank-Nicolson method is chosen for the time discretization to reduce oscillations at high gradient strengths and allows for larger time-step sizes.
    • The method is of a high level of simplicity and suitable for parallelization.
    • An efficient open-source code is implemented in the FEniCS and FEniCS-HPC platforms.
  • 11.
    Nguyen, Van Dang
    et al.
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    Jansson, Johan
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    Leoni, Massimiliano
    Janssen, Barbel
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    Goude, Anders
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    Modelling of rotating vertical axis turbines using a multiphase finite element method2017In: MARINE 2017: Computational Methods in Marine Engineering VII15 - 17 May 2017, Nantes, France, 2017, p. 950-960Conference paper (Other academic)
  • 12.
    Nguyen, Van Dang
    et al.
    Ecole Polytechnique, France.
    Li, Jing-Rebecca
    Grebenkov, Denis
    Le Bihan, Denis
    A finite element method to solve the Bloch-Torrey equation applied to diffusion magnetic resonance imaging2014In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 263, p. 283-302Article in journal (Refereed)
    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.

  • 13.
    Nguyen, Van-Dang
    KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).
    High-Performance Finite Element Methods: with Application to Simulation of Diffusion MRI and Vertical Axis Wind Turbines2018Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    The finite element methods (FEM) have been developed over decades, and together with the growth of computer engineering, they become more and more important in solving large-scale problems in science and industry. The objective of this thesis is to develop high-performance finite element methods (HP-FEM), with two main applications in mind: computational diffusion magnetic resonance imaging (MRI), and simulation of the turbulent flow past a vertical axis wind turbine (VAWT). In the first application, we develop an efficient high-performance finite element framework HP-PUFEM based on a partition of unity finite element method to solve the Bloch-Torrey equation in heterogeneous domains. The proposed framework overcomes the difficulties that the standard approaches have when imposing the microscopic heterogeneity of the biological tissues. We also propose artificial jump conditions at the external boundaries to approximate the pseudo-periodic boundary conditions which allows for the water exchange at the external boundaries for non-periodic meshes. The framework is of a high level simplicity and efficiency that well facilitates parallelization. It can be straightforwardly implemented in different FEM software packages and it is implemented in FEniCS for moderate-scale simulations and in FEniCS-HPC for the large-scale simulations. The framework is validated against reference solutions, and implementation shows a strong parallel scalability. Since such a high-performance simulation framework is still missing in the field, it can become a powerful tool to uncover diffusion in complex biological tissues. In the second application, we develop an ALE-DFS method which combines advanced techniques developed in recent years to simulate turbulence. We apply a General Galerkin (G2) method which is continuous piecewise linear in both time and space, to solve the Navier-Stokes equations for a rotating turbine in an Arbitrary Lagrangian-Eulerian (ALE) framework. This method is enhanced with dual-based a posterior error control and automated mesh adaptation. Turbulent boundary layers are modeled by a slip boundary condition to avoid a full resolution which is impossible even with the most powerful computers available today. The method is validated against experimental data of parked turbines with good agreements. The thesis presents contributions in the form of both numerical methods for high-performance computing frameworks and efficient, tested software, published open source as part of the FEniCS-HPC platform.

  • 14.
    Nguyen, Van-Dang
    et al.
    Ecole Polytechnique, France.
    Grebenkov, Denis
    Le Bihan, Denis
    Li, Jing-Rebecca
    Numerical study of a cylinder model of diffusion MRI signal for neuronal dendrite trees2015In: Journal of magnetic resonance, ISSN 1090-7807, E-ISSN 1096-0856, Vol. 252, p. 103-113Article in journal (Refereed)
    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.

  • 15.
    Nguyen, Van-Dang
    et al.
    Ecole Polytechnique, France.
    Grebenkov, Denis
    LPMC, CNRS - Ecole Polytechnique, Palaiseau, France.
    Li, Jing-Rebecca
    Equipe DEFI, INRIA Saclay, Palaiseau, France.
    Le Bihan, Denis (Contributor)
    Neurospin, CEA Saclay, Gif-sur-Yvette, France.
    Effective diffusion tensor computed by homogenization2013In: Diffusion Fundamentals, ISSN 1862-4138, E-ISSN 1862-4138, Effective diffusion tensor computed by homogenization, Vol. 18, p. 1-6Article in journal (Refereed)
    Abstract [en]

    The convergence of the long-time apparent diffusion tensor of diffusion magnetic resonance imaging (dMRI) to the effective diffusion tensor obtained by mathematical homogenization theory was considered for two-compartment geometric models containing non-elongated cells of general shapes. A numerical study was conducted in two and three dimensions to demonstrate this convergence as a function of the diffusion time. 

  • 16.
    Nguyen, Van-Dang
    et al.
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    Jansson, Johan
    KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).
    Frachon, Thomas
    Degirmenci, Cem
    Hoffman, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    A fluid-structure interaction model with weak slip velocity boundary conditions on conforming internal interfaces2018Conference 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. 

  • 17.
    Nguyen, Van-Dang
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).
    Jansson, Johan
    KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).
    Tran, Hoang Trong An
    CMAP, Polytechnique, France.
    Hoffman, Johan
    KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).
    Li, Jing-Rebecca
    CMAP, Ecole Polytechnique, France.
    Diffusion MRI simulation in thin-layer and thin-tube media using a discretization on manifolds2019In: Journal of magnetic resonance, ISSN 1090-7807, E-ISSN 1096-0856Article in journal (Refereed)
    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.

  • 18.
    Nguyen, Van-Dang
    et al.
    Ecole Polytechnique, France.
    Li, Jing-Rebecca
    INRIA Saclay-Equipe DEFI, CMAP, Ecole Polytechnique, 91128, Palaiseau, France.
    Denis, Grebenkov
    LPMC, CNRS – Ecole Polytechnique, 91128, Palaiseau, France.
    Le Bihan, D.
    Modeling the diffusion magnetic resonance imaging signal inside neurons2014In: Journal of Physics, Conference Series, ISSN 1742-6588, E-ISSN 1742-6596, Vol. 490, no 1, article id UNSP 012013Article in journal (Refereed)
    Abstract [en]

    The Bloch-Torrey partial differential equation (PDE) describes the complex transverse water proton magnetization due to diffusion-encoding magnetic field gradient pulses. The integral of the solution of this PDE yields the diffusion magnetic resonance imaging (dMRI) signal. In a complex medium such as cerebral tissue, it is difficult to explicitly link the dMRI signal to biological parameters such as the cellular geometry or the cellular volume fraction. Studying the dMRI signal arising from a single neuron can provide insight into how the geometrical structure of neurons influences the measured signal. We formulate the Bloch-Torrey PDE inside a single neuron, under no water exchange condition with the extracellular space, and show how to reduce the 3D simulation in the full neuron to a 3D simulation around the soma and 1D simulations in the neurites. We show that this latter approach is computationally much faster than full 3D simulation and still gives accurate results over a wide range of diffusion times.

  • 19.
    Tie, B.
    et al.
    CentraleSupélec, Université Paris-Saclay, France.
    Mouronval, A.-S.
    CentraleSupélec, Université Paris-Saclay, France.
    Nguyen, Van Dang
    CentraleSupélec, Université Paris-Saclay, France.
    Series, L.
    CentraleSupélec, Université Paris-Saclay, France.
    Aubry, D.
    CentraleSupélec, Université Paris-Saclay, France.
    A unified variational framework for the space discontinuous Galerkin method for elastic wave propagation in anisotropic and piecewise homogeneous media2018In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 338, p. 299-332Article in journal (Refereed)
    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.

  • 20.
    Wassermann, Demian
    et al.
    Parietal, Inria, Paris, France.
    Nguyen, Van Dang
    KTH, School of Electrical Engineering and Computer Science (EECS).
    Gallardo-Diez, Guillermo
    Athena, Inria, Sophia-Antipolis, France.
    Li, Jing-Rebecca
    DEFI, Inria, Palaiseau, France.
    Cai, Weidong
    Stanford Medical School, Palo Alto, CA, United States.
    Menon, Vinod
    Stanford Medical School, Palo Alto, CA, United States.
    Sensing Spindle Neurons in the Insula with Multi-shell Diffusion MRI2018Conference 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. 

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