| 1. |
- Nguyen, Hang Tuan, et al.
(author)
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Parameter estimation using macroscopic diffusion MRI signal models
- 2015
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In: Physics in Medicine and Biology. - : IOP Publishing. - 0031-9155 .- 1361-6560. ; 60:8, s. 3389-3413
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Journal article (peer-reviewed)abstract
- 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.
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| 2. |
- Nguyen, Van Dang, et al.
(author)
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A finite element method to solve the Bloch-Torrey equation applied to diffusion magnetic resonance imaging
- 2014
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In: Journal of Computational Physics. - : Academic Press. - 0021-9991 .- 1090-2716. ; 263, s. 283-302
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Journal article (peer-reviewed)abstract
- 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.
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| 3. |
- Nguyen, Van Dang, 1985-, et al.
(author)
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Effective diffusion tensor computed by homogenization
- 2013
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In: Diffusion Fundamentals. - 1862-4138. ; 18, s. 1-6
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Journal article (peer-reviewed)abstract
- 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.
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| 4. |
- Nguyen, Van Dang, 1985-, et al.
(author)
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Numerical study of a cylinder model of diffusion MRI signal for neuronal dendrite trees
- 2015
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In: Journal of magnetic resonance. - : Academic Press. - 1090-7807 .- 1096-0856. ; 252, s. 103-113
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Journal article (peer-reviewed)abstract
- 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.
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| 5. |
- Grebenkov, Denis, et al.
(author)
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Exploring diffusion across permeable barriers at high gradients. I. Narrow pulse approximation
- 2014
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In: Journal of magnetic resonance. - : Elsevier BV. - 1090-7807 .- 1096-0856. ; 248, s. 153-163
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Journal article (peer-reviewed)abstract
- 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.
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| 6. |
- Moutal, Nicolas, et al.
(author)
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The Kärger vs bi-exponential model : Theoretical insights and experimental validations
- 2018
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In: Journal of Magnetic Resonance. - : Elsevier BV. - 1090-7807. ; 296, s. 72-78
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Journal article (peer-reviewed)abstract
- We revise three common models accounting for water exchange in pulsed-gradient spin-echo measurements: a bi-exponential model with time-dependent water fractions, the Kärger model, and a modified Kärger model designed for restricted diffusion, e.g. inside cells. The three models are compared and applied to experimental data from yeast cell suspensions. The Kärger model and the modified Kärger model yield very close results and accurately fit the data. The bi-exponential model, although less rigorous, has a natural physical interpretation and suggests a new experimental modality to estimate the water exchange time.
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| 7. |
- Nguyen, Van Dang, 1985-, et al.
(author)
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Modeling the diffusion magnetic resonance imaging signal inside neurons
- 2014
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In: Journal of Physics, Conference Series. - : Institute of Physics Publishing (IOPP). - 1742-6588 .- 1742-6596. ; 490:1
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Journal article (peer-reviewed)abstract
- 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.
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