An efficient eigenfunction approach to calculate spin-echo signals in heterogeneous porous media

Matias Nordin; Denis Grebenkov; Martin Nilsson Jacobi; Magnus Nydeń

doi:10.1016/j.micromeso.2013.02.055

An efficient eigenfunction approach to calculate spin-echo signals in heterogeneous porous media

Matias Nordin^*, Denis Grebenkov, Martin Nilsson Jacobi, Magnus Nydeń

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

An approximate method for solving the Bloch-Torrey equation by surface integrals is developed. The method presents a fast means for calculating pulsed-gradient spin-echo nuclear magnetic resonance signals in porous systems, and it is especially efficient when the surface-to-volume ratio is low. The number of operations for retrieving echo decays scale as O(k²), where k is the number of surface elements. The theory is numerically validated for pulsed-gradient spin-echo sequences on two-dimensional and three-dimensional examples.

Original language	English
Pages (from-to)	7-10
Number of pages	4
Journal	Microporous and Mesoporous Materials
Volume	178
DOIs	https://doi.org/10.1016/j.micromeso.2013.02.055
Publication status	Published - 15 Sept 2013
Externally published	Yes

Keywords

NMR
Diffusion
Laplace operator
Eigenvalues
Eigenfunctions

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10.1016/j.micromeso.2013.02.055

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abstract = "An approximate method for solving the Bloch-Torrey equation by surface integrals is developed. The method presents a fast means for calculating pulsed-gradient spin-echo nuclear magnetic resonance signals in porous systems, and it is especially efficient when the surface-to-volume ratio is low. The number of operations for retrieving echo decays scale as O(k2), where k is the number of surface elements. The theory is numerically validated for pulsed-gradient spin-echo sequences on two-dimensional and three-dimensional examples.",

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author = "Matias Nordin and Denis Grebenkov and Jacobi, {Martin Nilsson} and Magnus Nyde{\'n}",

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AU - Nordin, Matias

AU - Grebenkov, Denis

AU - Jacobi, Martin Nilsson

AU - Nydeń, Magnus

PY - 2013/9/15

Y1 - 2013/9/15

N2 - An approximate method for solving the Bloch-Torrey equation by surface integrals is developed. The method presents a fast means for calculating pulsed-gradient spin-echo nuclear magnetic resonance signals in porous systems, and it is especially efficient when the surface-to-volume ratio is low. The number of operations for retrieving echo decays scale as O(k2), where k is the number of surface elements. The theory is numerically validated for pulsed-gradient spin-echo sequences on two-dimensional and three-dimensional examples.

AB - An approximate method for solving the Bloch-Torrey equation by surface integrals is developed. The method presents a fast means for calculating pulsed-gradient spin-echo nuclear magnetic resonance signals in porous systems, and it is especially efficient when the surface-to-volume ratio is low. The number of operations for retrieving echo decays scale as O(k2), where k is the number of surface elements. The theory is numerically validated for pulsed-gradient spin-echo sequences on two-dimensional and three-dimensional examples.

KW - NMR

KW - Diffusion

KW - Laplace operator

KW - Eigenvalues

KW - Eigenfunctions

UR - http://www.scopus.com/inward/record.url?scp=84894904777&partnerID=8YFLogxK

U2 - 10.1016/j.micromeso.2013.02.055

DO - 10.1016/j.micromeso.2013.02.055

M3 - Article

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VL - 178

SP - 7

EP - 10

JO - Microporous and Mesoporous Materials

JF - Microporous and Mesoporous Materials

ER -

An efficient eigenfunction approach to calculate spin-echo signals in heterogeneous porous media

Abstract

Keywords

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