Numerical analysis of NMR diffusion measurements in the short gradient pulse limit

Moroney, Benjamin F; Stait‐Gardner, Timothy; Ghadirian, Bahman; Yadav, Nirbhay N.; Price, William S.

doi:10.1016/j.jmr.2013.06.019

Cited by 29 publications

(23 citation statements)

References 65 publications

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“…Figures and show several of these many sequences. A series of relatively recent publications deal with suggestions for improving the various aspects of the measurement . These include problems concerned with steady state effects in a two‐pulse diffusion‐weighted sequence, convection, band‐selective radio frequency pulses, J‐coupling peak distortion, short diffusion times, 3D DOSY, TOCSY, data processing for DOSY and high temperature measurements .…”

Section: Introductionmentioning

confidence: 99%

Applications of NMR diffusion methods with emphasis on ion pairing in inorganic chemistry: a mini‐review

Pregosin

2016

Magnetic Reson in Chemistry

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Section: Introductionmentioning

confidence: 99%

Applications of NMR diffusion methods with emphasis on ion pairing in inorganic chemistry: a mini‐review

Pregosin

2016

Magnetic Reson in Chemistry

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“…As the Bloch–Torrey equations inherently take the microscopic averaging into account solving them numerically better suits the task of simulating a dNMR experiment. The presence of complex boundary conditions (as a result of complex micro geometry in the sample) favours the use of finite elements method (FEM) for dNMR simulations . These allow solving the cases of more complicated microgeometries (e.g.…”

Section: Restricted Diffusionmentioning

confidence: 99%

Physical characterization using diffusion NMR spectroscopy

Zubkov

Dennis

Stait‐Gardner

et al. 2016

Magnetic Reson in Chemistry

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NMR diffusion measurements (or dNMR) provide a powerful tool for analysis of solution organization and microgeometry of the environment by probing random molecular motion. Being a very versatile method, dNMR can be applied to a large variety of samples and systems. Here, a brief introduction into dNMR and a summary of recent advances in the field are presented. The research topics include restricted diffusion, anisotropic diffusion, polymer dynamics, solution structuring and dNMR method development. The dNMR studied systems include plants, cells (cell models), liquid crystals, polymer solutions, ionic liquids, supercooled solutions, untreated water, amino acid solutions and more. It is demonstrated how a variety of dNMR methods can be applied to a system to extract the data on particular structures present among, formed by or surrounding the diffusing particles. It is also demonstrated how dNMR methods can be developed to allow probing larger geometries, low sample concentrations and faster processes. Copyright © 2016 John Wiley & Sons, Ltd.

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“…3a). A wide range of gradient strengths [3,13] is used. The signals are computed and plotted against b-values and q-values.…”

Section: Validation Of the Frameworkmentioning

confidence: 99%

“…Solving the full model, i.e Eqs. (2,7,8), is challenging and many efforts have been made [1,10,13,14,16,20]. However, large-scale problems for supercomputers with realistic applications have not been considered yet.…”

Section: Introductionmentioning

confidence: 99%

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

Nguyen¹,

Jansson²,

Hoffman³

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. In diffusion nuclear magnetic resonance (NMR) and diffusion magnetic resonance imaging (MRI), the multi-compartment Bloch-Torrey equation plays an important role in probing the diffusion characteristics from a nanometer scale to a macroscopic scale. The signal attenuation can be computed by solving the equation. If the volume of interest is composed by multiple compartments, interface conditions with permeability are imposed. Depending on applications, different gradient strengths can be used to capture the signal attenuation. In probing porous media, for instance, high gradient strengths are used. In diffusion MRI, since water molecules enter and exit the computational domain in realistic cases, pseudo-periodic boundary conditions are used. These conditions cause difficulties in solving the equation efficiently and many efforts have been made to develop an efficient numerical method. However, large-scale problems for supercomputers with realistic applications have not been considered yet. We propose a framework for the multi-compartment Bloch-Torrey models based on the FEniCS-HPC platform, a part of the FEniCS project that allows for automated discretization, automated error control with mesh adaptivity and high performance computing. The framework runs on supercomputers with near optimal weak and strong scaling. Our work includes two parts. First, we simplify the multi-compartment Bloch-Torrey model used in diffusion MRI by proposing an approximation to the pseudo-periodic boundary conditions to derive a general form for the interface and boundary conditions. The second part includes implementation and numerical validation of our method on the FEniCS-HPC platform. This simplified model is straightforward to implement and to parallelize and shows promise in validation against more realistic models.105

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Numerical analysis of NMR diffusion measurements in the short gradient pulse limit

Cited by 29 publications

References 65 publications

Applications of NMR diffusion methods with emphasis on ion pairing in inorganic chemistry: a mini‐review

Applications of NMR diffusion methods with emphasis on ion pairing in inorganic chemistry: a mini‐review

Physical characterization using diffusion NMR spectroscopy

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

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