A Fenics-HPC Framework for Multi-Compartment Bloch-Torrey Models

Journal of Magnetic Resonance

Leoni

Dancheva

et al. 2019

Self Cite

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)

Section: Discussionmentioning

confidence: 99%

“…In [14], a simplified 1D manifold Bloch-Torrey equation was solved to study the diffusion MRI signal from neuronal dendrite trees. FEM in a high-performance computing framework was proposed in [15,16] for diffusion MRI simulations on supercomputers. An efficient simulation method for thin media was proposed in [17].…”

Section: Introductionmentioning

confidence: 99%

Portable simulation framework for diffusion MRI

Journal of Magnetic Resonance

Leoni

Dancheva

et al. 2019

Self Cite

“…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

Tran

et al. 2019

NeuroImage

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.

“…The second group of simulations, which up to now has been less often used by the diffusion MRI community, relies on solving the BT equation in a geometrical configuration using the FEM [40][41][42][43][44] (an alternative to the FEM is the finite difference method 45 ). Some of the recent works about FEM diffusion MRI simulations focused on improving its computational efficiency, by using high-performance computing 46,47 for large-scale simulations on supercomputers, by discretization on manifolds for thin-layer and thin-tube media, 48 and by integrating with Cloud computing resources. 49 Our previous works in neuron diffusion MRI simulations with FEM include the simulation of neuronal dendrites using a tree model 50 and the demonstration that diffusion MRI signals reflect the cellular organization of cortical gray matter, these signals being sensitive to cell size and the presence of large neurons such as the spindle (von Economo) neurons.…”

mentioning

confidence: 99%

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

Tran

2020

NMR in Biomedicine

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.