Publications by authors named "Van Dang Nguyen"

7 Publications

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Diffusion MRI simulation of realistic neurons with SpinDoctor and the Neuron Module.

Neuroimage 2020 11 27;222:117198. Epub 2020 Jul 27.

INRIA Saclay, Equipe DEFI, CMAP, Ecole Polytechnique, 91128 Palaiseau Cedex, France. Electronic address:

The diffusion MRI signal arising from neurons can be numerically simulated by solving the Bloch-Torrey partial differential equation. In this paper we present the Neuron Module that we implemented within the Matlab-based diffusion MRI simulation toolbox SpinDoctor. SpinDoctor uses finite element discretization and adaptive time integration to solve the Bloch-Torrey partial differential equation for general diffusion-encoding sequences, at multiple b-values and in multiple diffusion directions. In order to facilitate the diffusion MRI simulation of realistic neurons by the research community, we constructed finite element meshes for a group of 36 pyramidal neurons and a group of 29 spindle neurons whose morphological descriptions were found in the publicly available neuron repository NeuroMorpho.Org. These finite elements meshes range from having 15,163 nodes to 622,553 nodes. We also broke the neurons into the soma and dendrite branches and created finite elements meshes for these cell components. Through the Neuron Module, these neuron and cell components finite element meshes can be seamlessly coupled with the functionalities of SpinDoctor to provide the diffusion MRI signal attributable to spins inside neurons. We make these meshes and the source code of the Neuron Module available to the public as an open-source package. To illustrate some potential uses of the Neuron Module, we show numerical examples of the simulated diffusion MRI signals in multiple diffusion directions from whole neurons as well as from the soma and dendrite branches, and include a comparison of the high b-value behavior between dendrite branches and whole neurons. In addition, we demonstrate that the neuron meshes can be used to perform Monte-Carlo diffusion MRI simulations as well. We show that at equivalent accuracy, if only one gradient direction needs to be simulated, SpinDoctor is faster than a GPU implementation of Monte-Carlo, but if many gradient directions need to be simulated, there is a break-even point when the GPU implementation of Monte-Carlo becomes faster than SpinDoctor. Furthermore, we numerically compute the eigenfunctions and the eigenvalues of the Bloch-Torrey and the Laplace operators on the neuron geometries using a finite elements discretization, in order to give guidance in the choice of the space and time discretization parameters for both finite elements and Monte-Carlo approaches. Finally, we perform a statistical study on the set of 65 neurons to test some candidate biomakers that can potentially indicate the soma size. This preliminary study exemplifies the possible research that can be conducted using the Neuron Module.
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http://dx.doi.org/10.1016/j.neuroimage.2020.117198DOI Listing
November 2020

Practical computation of the diffusion MRI signal of realistic neurons based on Laplace eigenfunctions.

NMR Biomed 2020 10 29;33(10):e4353. Epub 2020 Jul 29.

Division of Computational Science and Technology, KTH Royal Institute of Technology, Sweden.

The complex transverse water proton magnetization subject to diffusion-encoding magnetic field gradient pulses in a heterogeneous medium such as brain tissue can be modeled by the Bloch-Torrey partial differential equation. The spatial integral of the solution of this equation in realistic geometry provides a gold-standard reference model for the diffusion MRI signal arising from different tissue micro-structures of interest. A closed form representation of this reference diffusion MRI signal called matrix formalism, which makes explicit the link between the Laplace eigenvalues and eigenfunctions of the biological cell and its diffusion MRI signal, was derived 20 years ago. In addition, once the Laplace eigendecomposition has been computed and saved, the diffusion MRI signal can be calculated for arbitrary diffusion-encoding sequences and b-values at negligible additional cost. Up to now, this representation, though mathematically elegant, has not been often used as a practical model of the diffusion MRI signal, due to the difficulties of calculating the Laplace eigendecomposition in complicated geometries. In this paper, we present a simulation framework that we have implemented inside the MATLAB-based diffusion MRI simulator SpinDoctor that efficiently computes the matrix formalism representation for realistic neurons using the finite element method. We show that the matrix formalism representation requires a few hundred eigenmodes to match the reference signal computed by solving the Bloch-Torrey equation when the cell geometry originates from realistic neurons. As expected, the number of eigenmodes required to match the reference signal increases with smaller diffusion time and higher b-values. We also convert the eigenvalues to a length scale and illustrate the link between the length scale and the oscillation frequency of the eigenmode in the cell geometry. We give the transformation that links the Laplace eigenfunctions to the eigenfunctions of the Bloch-Torrey operator and compute the Bloch-Torrey eigenfunctions and eigenvalues. This work is another step in bringing advanced mathematical tools and numerical method development to the simulation and modeling of diffusion MRI.
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http://dx.doi.org/10.1002/nbm.4353DOI Listing
October 2020

Microstructural organization of human insula is linked to its macrofunctional circuitry and predicts cognitive control.

Elife 2020 06 4;9. Epub 2020 Jun 4.

Parietal, Inria Saclay Île-de-France, CEA Université Paris Sud, Palaiseau, France.

The human insular cortex is a heterogeneous brain structure which plays an integrative role in guiding behavior. The cytoarchitectonic organization of the human insula has been investigated over the last century using postmortem brains but there has been little progress in noninvasive in vivo mapping of its microstructure and large-scale functional circuitry. Quantitative modeling of multi-shell diffusion MRI data from 413 participants revealed that human insula microstructure differs significantly across subdivisions that serve distinct cognitive and affective functions. Insular microstructural organization was mirrored in its functionally interconnected circuits with the anterior cingulate cortex that anchors the salience network, a system important for adaptive switching of cognitive control systems. Furthermore, insular microstructural features, confirmed in Macaca mulatta, were linked to behavior and predicted individual differences in cognitive control ability. Our findings open new possibilities for probing psychiatric and neurological disorders impacted by insular cortex dysfunction, including autism, schizophrenia, and fronto-temporal dementia.
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http://dx.doi.org/10.7554/eLife.53470DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7308087PMC
June 2020

Portable simulation framework for diffusion MRI.

J Magn Reson 2019 12 23;309:106611. Epub 2019 Sep 23.

INRIA Saclay-Equipe DEFI, CMAP, Ecole Polytechnique Route de Saclay, 91128 Palaiseau Cedex, France. Electronic address:

The numerical simulation of the diffusion MRI signal arising from complex tissue micro-structures is helpful for understanding and interpreting imaging data as well as for designing and optimizing MRI sequences. The discretization of the Bloch-Torrey equation by finite elements is a more recently developed approach for this purpose, in contrast to random walk simulations, which has a longer history. While finite element discretization is more difficult to implement than random walk simulations, the approach benefits from a long history of theoretical and numerical developments by the mathematical and engineering communities. In particular, software packages for the automated solutions of partial differential equations using finite element discretization, such as FEniCS, are undergoing active support and development. However, because diffusion MRI simulation is a relatively new application area, there is still a gap between the simulation needs of the MRI community and the available tools provided by finite element software packages. In this paper, we address two potential difficulties in using FEniCS for diffusion MRI simulation. First, we simplified software installation by the use of FEniCS containers that are completely portable across multiple platforms. Second, we provide a portable simulation framework based on Python and whose code is open source. This simulation framework can be seamlessly integrated with cloud computing resources such as Google Colaboratory notebooks working on a web browser or with Google Cloud Platform with MPI parallelization. We show examples illustrating the accuracy, the computational times, and parallel computing capabilities. The framework contributes to reproducible science and open-source software in computational diffusion MRI with the hope that it will help to speed up method developments and stimulate research collaborations.
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http://dx.doi.org/10.1016/j.jmr.2019.106611DOI Listing
December 2019

SpinDoctor: A MATLAB toolbox for diffusion MRI simulation.

Neuroimage 2019 11 27;202:116120. Epub 2019 Aug 27.

INRIA Saclay, Equipe DEFI, CMAP, Ecole Polytechnique, Route de Saclay, 91128 Palaiseau Cedex, France.

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. Under the assumption of negligible water exchange between compartments, the time-dependent apparent diffusion coefficient can be directly computed from the solution of a diffusion equation subject to a time-dependent Neumann boundary condition. This paper describes a publicly available MATLAB toolbox called SpinDoctor that can be used 1) to solve the Bloch-Torrey partial differential equation in order to simulate the diffusion magnetic resonance imaging signal; 2) to solve a diffusion partial differential equation to obtain directly the apparent diffusion coefficient; 3) to compare the simulated apparent diffusion coefficient with a short-time approximation formula. The partial differential equations are solved by P1 finite elements combined with built-in MATLAB routines for solving ordinary differential equations. The finite element mesh generation is performed using an external package called Tetgen. SpinDoctor provides built-in options of including 1) spherical cells with a nucleus; 2) cylindrical cells with a myelin layer; 3) an extra-cellular space enclosed either a) in a box or b) in a tight wrapping around the cells; 4) deformation of canonical cells by bending and twisting; 5) permeable membranes; Built-in diffusion-encoding pulse sequences include the Pulsed Gradient Spin Echo and the Oscillating Gradient Spin Echo. We describe in detail how to use the SpinDoctor toolbox. We validate SpinDoctor simulations using reference signals computed by the Matrix Formalism method. We compare the accuracy and computational time of SpinDoctor simulations with Monte-Carlo simulations and show significant speed-up of SpinDoctor over Monte-Carlo simulations in complex geometries. We also illustrate several extensions of SpinDoctor functionalities, including the incorporation of T relaxation, the simulation of non-standard diffusion-encoding sequences, as well as the use of externally generated geometrical meshes.
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http://dx.doi.org/10.1016/j.neuroimage.2019.116120DOI Listing
November 2019

Diffusion MRI simulation in thin-layer and thin-tube media using a discretization on manifolds.

J Magn Reson 2019 02 8;299:176-187. Epub 2019 Jan 8.

CMAP - Center for Applied Mathematics, Ecole Polytechnique, Palaiseau, France. Electronic address:

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.
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http://dx.doi.org/10.1016/j.jmr.2019.01.002DOI Listing
February 2019

Characteristics and mechanisms of cadmium adsorption onto biogenic aragonite shells-derived biosorbent: Batch and column studies.

J Environ Manage 2019 Jul 11;241:535-548. Epub 2018 Oct 11.

Sustainable Management of Natural Resources and Environment Research Group, Faculty of Environment and Labour Safety, Ton Duc Thang University, Ho Chi Minh City, Vietnam. Electronic address:

Calcium carbonate (CaCO)-enriched biomaterial derived from freshwater mussel shells (FMS) was used as a non-porous biosorbent to explore the characteristics and mechanisms of cadmium adsorption in aqueous solution. The adsorption mechanism was proposed by comparing the FMS properties before and after adsorption alongside various adsorption studies. The FMS biosorbent was characterized using nitrogen adsorption/desorption isotherm, X-ray diffraction, scanning electron microscopy with energy dispersive spectroscopy, Fourier-transform infrared spectroscopy, and point of zero charge. The results of batch experiments indicated that FMS possessed an excellent affinity to Cd(II) ions within solutions pH higher than 4.0. An increase in ionic strength resulted in a significant decrease in the amount of Cd(II) adsorbed onto FMS. Kinetic study demonstrated that the adsorption process quickly reached equilibrium at approximately 60 min. The FMS biosorbent exhibited the Langmuir maximum adsorption capacity as follows: 18.2 mg/g at 10 °C < 26.0 mg/g at 30 °C < 28.6 mg/g at 50 °C. The Cd(II) adsorption process was irreversible, spontaneous (-ΔG°), endothermic (+ΔH°), and more random (+ΔS°). Selective order (mmol/g) of metal cations followed as Pb > Cd > Cu > Cr > Zn. For column experiments, the highest Thomas adsorption capacity (7.86 mg/g) was achieved at a flow rate (9 mL/min), initial Cd(II) concentration (10 mg/L), and bed height (5 cm). The Cd(II) removal by FMS was regarded as non-activated chemisorption that occurred very rapidly (even at a low temperature) with a low magnitude of activation energy. Primary adsorption mechanism was surface precipitation. Cadmium precipitated in the primary (Cd,Ca)CO form with a calcite-type structure on the FMS surface. A crust of rhombohedral crystals on the substrate was observed by SEM. Freshwater mussel shells have the potential as a renewable adsorbent to remove cadmium from water.
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http://dx.doi.org/10.1016/j.jenvman.2018.09.079DOI Listing
July 2019