A mixed basis approach in the SGP-limit

Nordin, Matias; Nilsson-Jacobi, Martin; Nydén, Magnus

doi:10.1016/j.jmr.2011.07.002

Cited by 6 publications

(8 citation statements)

References 35 publications

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“…However, for these methods the Laplace eigenvalues and eigenfunctions for the particular porous geometry must be known. Alternative methods well worth mentioning in this context are the Lattice path count method , the mixed basis , and finite element methods .…”

Section: Introductionmentioning

confidence: 99%

Finite difference diagonalization to simulate nuclear magnetic resonance diffusion experiments in porous media

Grombacher

Nordin

2015

Concepts Magnetic Resonance

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A finite difference approach for computing Laplacian eigenvalues and eigenvectors in discrete porous media is derived and used to approximately solve the Bloch-Torrey equations. Neumann, Dirichlet, and Robin boundary conditions are considered and applications to simulate nuclear magnetic resonance diffusion experiments are shown. The method is illustrated with MATLAB examples and computational tests in one and two dimensions and the extension to three dimensions is outlined.

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Section: Introductionmentioning

confidence: 99%

Finite difference diagonalization to simulate nuclear magnetic resonance diffusion experiments in porous media

Grombacher

Nordin

2015

Concepts Magnetic Resonance

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“…In this particular system the complication has been overcome through the use of Laplace transform [16]. Approximate eigenfunction-based approaches are also available [17]. (3) Finite element (FE) and finite difference (FD) methods: This is a broad family of numerical methods where the diffusion equation is solved numerically on a mesh.…”

Section: Techniques For Calculation Of the Diffusion Propagatormentioning

confidence: 99%

Further development of discrete computational techniques for calculation of restricted diffusion propagators in porous media

Momot

Powell

Tourell

2015

Microporous and Mesoporous Materials

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a b s t r a c tMagnetic resonance is a well-established tool for structural characterisation of porous media. Features of pore-space morphology can be inferred from NMR diffusion-diffraction plots or the time-dependence of the apparent diffusion coefficient. Diffusion NMR signal attenuation can be computed from the restricted diffusion propagator, which describes the distribution of diffusing particles for a given starting position and diffusion time.We present two techniques for efficient evaluation of restricted diffusion propagators for use in NMR porous-media characterisation. The first is the Lattice Path Count (LPC). Its physical essence is that the restricted diffusion propagator connecting points A and B in time t is proportional to the number of distinct length-t paths from A to B. By using a discrete lattice, the number of such paths can be counted exactly. The second technique is the Markov transition matrix (MTM). The matrix represents the probabilities of jumps between every pair of lattice nodes within a single timestep. The propagator for an arbitrary diffusion time can be calculated as the appropriate matrix power. For periodic geometries, the transition matrix needs to be defined only for a single unit cell. This makes MTM ideally suited for periodic systems.Both LPC and MTM are closely related to existing computational techniques: LPC, to combinatorial techniques; and MTM, to the Fokker-Planck master equation. The relationship between LPC, MTM and other computational techniques is briefly discussed in the paper. Both LPC and MTM perform favourably compared to Monte Carlo sampling, yielding highly accurate and almost noiseless restricted diffusion propagators. Initial tests indicate that their computational performance is comparable to that of finite element methods. Both LPC and MTM can be applied to complicated pore-space geometries with no analytic solution. We discuss the new methods in the context of diffusion propagator calculation in porous materials and model biological tissues.

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“…Similarly, Harkins et al [46] employed FEM analysis in diffusion calculations, but only to calculate apparent diffusion coefficients. Nordin et al developed a perturbation approach involving the use of mixed basis for calculating the spin-echo decay in the SGP-limit in restricted geometries [47]. Buhai et al [48] used finite elements to simulate electroosmotic flow.…”

Section: Introductionmentioning

confidence: 99%

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

Moroney

Stait‐Gardner

Ghadirian

et al. 2013

Journal of Magnetic Resonance

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A mixed basis approach in the SGP-limit

Cited by 6 publications

References 35 publications

Finite difference diagonalization to simulate nuclear magnetic resonance diffusion experiments in porous media

Finite difference diagonalization to simulate nuclear magnetic resonance diffusion experiments in porous media

Further development of discrete computational techniques for calculation of restricted diffusion propagators in porous media

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

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