A parametric finite element solution of the generalised Bloch–Torrey equation for arbitrary domains

Beltrachini, Leandro; Taylor, Zeike A.; Frangi, Alejandro F.

doi:10.1016/j.jmr.2015.08.008

Cited by 27 publications

(27 citation statements)

References 25 publications

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“…Additionally, combined analyses of histology and dMRI have been performed to further understand the development of certain diseases and the healthy brain (Budde and Frank, 2012;Kolasinski et al, 2012;Khan et al, 2016;Mollink et al, 2017). Information from histology can also help developing realistic in silico biomimetic phantoms of brain tissue (Cook et al, 2006;Beltrachini et al, 2015). Phantoms provide controlled ground truth that can test different dMRI acquisition schemes and post-processing methods.…”

Section: Introductionmentioning

confidence: 99%

Local volume fraction distributions of axons, astrocytes, and myelin in deep subcortical white matter

et al. 2018

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Article:Coelho, S. orcid.org/0000-0002-1039-4803, Pozo, J.M., Costantini, M. et This study aims to statistically describe histologically stained white matter brain sections to subsequently inform and validate diffusion MRI techniques. For the first time, we characterise volume fraction distributions of three of the main structures in deep subcortical white matter (axons, astrocytes, and myelinated axons) in a representative cohort of an ageing population for which well-characterized neuropathology data is available. We analysed a set of samples from 90 subjects of the Cognitive Function and Ageing Study (CFAS), stratified into three groups of 30 subjects each, in relation to the presence of age-associated deep subcortical lesions. This provides volume fraction distributions in different scenarios relevant to brain diffusion MRI in dementia. We also assess statistically significant differences found between these groups. In agreement with previous literature, our results indicate that white matter lesions are related with a decrease in the myelinated axons fraction and an increase in astrocytic fraction, while no statistically significant changes occur in axonal mean fraction. In addition, we introduced a framework to quantify volume fraction distributions from 2D immunohistochemistry images, which is validated against in silico simulations. Since a trade-off between precision and resolution emerged, we also performed an assessment of the optimal scale for computing such distributions.

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Section: Introductionmentioning

confidence: 99%

Local volume fraction distributions of axons, astrocytes, and myelin in deep subcortical white matter

et al. 2018

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“…More generally, numerical methods to solve the Bloch-Torrey PDE. with arbitrary temporal profiles have been proposed in [33][34][35][36]. The computational domain is discretized either by a Cartesian grid [33,34,37] or finite elements [30-32, 35, 36].…”

Section: Introductionmentioning

confidence: 99%

“…There is an example showing that the Runge-Kutta Chebyshev method is faster than the implicit Euler method in [35]. The Crank-Nicolson method was used in [36] to also allow for second order convergence in time. The efficiency of diffusion magnetic resonance imaging simulations is also improved by either a high-performance FEM computing framework [39,40] for large-scale simulations on supercomputers or a discretization on manifolds for thin-layer and thin-tube media [41].…”

Section: Introductionmentioning

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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“…The second group of simulations relies on solving the Bloch-Torrey PDE in a geometrical domain, either using finite difference methods (FDM) [7,8,9,10], typically on a Cartesian grid, or finite element methods (FEM), typically on a tetrahedral grid. Previous works on FEM include [11] for the short gradient pulse limit of some simple geometries, [12] for the multi-compartment Bloch-Torrey equation with general gradient pulses, and [13] with the flow and relaxation terms added. In [14], a simplified 1D manifold Bloch-Torrey equation was solved to study the diffusion MRI signal from neuronal dendrite trees.…”

Section: Introductionmentioning

confidence: 99%

Portable simulation framework for diffusion MRI

Nguyen

Leoni

Dancheva

et al. 2019

Journal of Magnetic Resonance

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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 elements 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 elements 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 elements 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. * I am corresponding author Email addresses: vdnguyen@kth.se (Van-Dang Nguyen ), jjan@kth.se (Johan Jansson), jhoffman@kth.se (Johan Hoffman), demian.wassermann@inria.fr (Demian Wassermann), jingrebecca.li@inria.fr (Jing-Rebecca Li)

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A parametric finite element solution of the generalised Bloch–Torrey equation for arbitrary domains

Cited by 27 publications

References 25 publications

Local volume fraction distributions of axons, astrocytes, and myelin in deep subcortical white matter

Local volume fraction distributions of axons, astrocytes, and myelin in deep subcortical white matter

SpinDoctor: A MATLAB toolbox for diffusion MRI simulation

Portable simulation framework for diffusion MRI

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