A finite elements method to solve the Bloch-Torrey equation applied to diffusion magnetic resonance imaging

DOI10.1016/j.jcp.2014.01.009zbMath1349.78070OpenAlexW2135130882MaRDI QIDQ348923

Denis Le Bihan, Dang Van Nguyen, Jing-Rebecca Li, Denis S. Grebenkov

Publication date: 5 December 2016

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2014.01.009

zbMATH Keywords

finite elementsinterface problemBloch-Torrey equationdiffusion magnetic resonance imagingdouble-nodepseudo-periodicRKC

Mathematics Subject Classification ID

Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory (78M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items (10)

An unstructured mesh finite difference/finite element method for the three-dimensional time-space fractional Bloch-Torrey equations on irregular domains ⋮ A finite elements method to solve the Bloch-Torrey equation applied to diffusion magnetic resonance imaging ⋮ Assessment of the effect of tissue motion in diffusion MRI: derivation of new apparent diffusion coefficient formula ⋮ Fourier Representation of the Diffusion MRI Signal Using Layer Potentials ⋮ A second order asymptotic model for diffusion MRI in permeable media ⋮ A robust computational framework for analyzing the Bloch-Torrey equation of fractional order ⋮ A partition of unity finite element method for computational diffusion MRI ⋮ A Macroscopic Model for the Diffusion MRI Signal Accounting for Time-Dependent Diffusivity ⋮ A finite volume method for the two-dimensional time and space variable-order fractional Bloch-Torrey equation with variable coefficients on irregular domains ⋮ Diffusion NMR in periodic media: efficient computation and spectral properties

Uses Software

• RKC
• FEniCS

Cites Work

• Unnamed Item
• A finite elements method to solve the Bloch-Torrey equation applied to diffusion magnetic resonance imaging
• Automated solution of differential equations by the finite element method. The FEniCS book
• Convergence properties of the Runge-Kutta-Chebyshev method
• RKC: An explicit solver for parabolic PDEs
• A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-α Method

This page was built for publication: A finite elements method to solve the Bloch-Torrey equation applied to diffusion magnetic resonance imaging