Efficient GPU-based Monte-Carlo simulation of diffusion in real astrocytes reconstructed from confocal microscopy

Nguyen, Khieu Van; Hernández-Garzón, Edwin; Valette, Julien

doi:10.1016/j.jmr.2018.09.013

Cited by 20 publications

(28 citation statements)

References 39 publications

(66 reference statements)

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“…In 54 we performed an accuracy and computational timing study of the serial SpinDoctor finite element simulation and a GPU implementation of the Monte Carlo simulation. 32 We showed that at equivalent accuracy, if only one gradient direction needs to be simulated, SpinDoctor is faster than GPU Monte Carlo. Because the GPU Monte Carlo method is inherently parallel, if many gradient directions need to be simulated, there is a break-even point when GPU Monte Carlo becomes faster than SpinDoctor.…”

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confidence: 90%

“…The first group is referred to as Monte Carlo simulations in the literature and previous works include References. 4,[28][29][30][31] A GPU-based acceleration of Monte Carlo simulation was proposed in References 32,33 .…”

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confidence: 99%

“…4. we mention also that the GPU-based Monte Carlo simulation code described in Reference 32 is available upon request from the authors.…”

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confidence: 99%

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

Tran

Nguyen

2020

NMR in Biomedicine

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

Tran

Nguyen

2020

NMR in Biomedicine

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“…There might be a number of recent works with similar goals, this study however has some improvements such as successful simulation of permeability instead of assuming all microstructural walls are impermeable compared to [82] or lack of requirement any complex mathematical and time-consuming construction of microstructure such as in [63] and instead direct simulation of microsture from light microscopy data.…”

Section: Six Plates (Voxel)mentioning

confidence: 99%

Monte Carlo Simulation of Diffusion MRI in geometries constructed from two-photon microscopy of human cortical grey matter

Gilani

Hildebrand²,

Schueth

et al. 2019

Preprint

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Running title: Simulation of Diffusion in the CortexPurpose: Diffusion MRI of the cortical gray matter has shown to be sensitive to diseases such as Alzheimer's disease and multiple sclerosis. Additionally, there is a growing interest in remodelling, characterization and improvement of the understanding of different brain areas using a combination of quantitative MRI or 3D microscopy. The purpose of this study was to quantitatively characterize the cytoarchitecture of cortical tissue from fluorescence microscopy in order to simulate diffusion in the cortex and to better understand its diffusion signal characteristics Methods: Cellular volume fractions, and sizes of glial nuclei, and neurons were measured from 3D microscopy by volume segmentation and non-linear least squares ellipsoid fitting.Diffusion of water molecules in the cortex was simulated for variable permeability levels, free diffusion coefficients, cell (neuron, glia, dendrite or axon) densities, and sizes and diffusion times. Some parameters such as axonal density were extracted from the available literature. In an alternative method, the simulation geometry was directly extracted from available microscopy data of the cortex. The simulations were compared with fractional anisotropy, apparent diffusion and kurtosis values reported in vivo in the healthy brain. Results:Assuming a permeability of around 20-30 µms -1 and a free diffusion coefficient of around 1.6-1.7 µm 2 ms -1 , the simulated fractional anisotropy, diffusion coefficient and kurtosis of the cortical gray matter were on average around 0.2-0.4, 0.7-1.3 μ m 2 ms −1 , and 0.1-1.0, respectively, which are in ranges in agreement with previous in vivo reports. Conclusions:The Monte Carlo simulations of different layers or areas of the healthy cortex, and extrapolation of these simulations to other cell sizes or densities is an additional step in better quantitative characterization or remodelling of the healthy or diseased cortex from diffusion MRI.

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“…The first group is referred to as Monte-Carlo simulations in the literature and previous works include [13,[24][25][26][27]. A GPU-based acceleration of Monte-Carlo simulation was proposed in [28,29]. Some software packages using this approach include 1.…”

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confidence: 99%

SpinDoctor: A MATLAB toolbox for diffusion MRI simulation

Nguyen

Tran

et al. 2019

NeuroImage

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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.

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Efficient GPU-based Monte-Carlo simulation of diffusion in real astrocytes reconstructed from confocal microscopy

Cited by 20 publications

References 39 publications

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

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

Monte Carlo Simulation of Diffusion MRI in geometries constructed from two-photon microscopy of human cortical grey matter

SpinDoctor: A MATLAB toolbox for diffusion MRI simulation

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