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Dynamics of local magnetization in the eigenbasis of the Bloch-Torrey operator
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Biomedical Engineering, Division of Biomedical Engineering. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Biomedical Engineering, Division of Biomedical Engineering. Linköping University, Faculty of Science & Engineering. Linköping University, Center for Medical Image Science and Visualization (CMIV).ORCID iD: 0000-0002-9091-4724
Linköping University, Department of Biomedical Engineering, Division of Biomedical Engineering. Linköping University, Faculty of Science & Engineering. Harvard Medical Sch, MA 02215 USA.
2017 (English)In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 146, no 12, 124201Article in journal (Refereed) Published
Abstract [en]

We consider diffusion within pores with general shapes in the presence of spatially linear magnetic field profiles. The evolution of local magnetization of the spin bearing particles can be described by the Bloch-Torrey equation. We study the diffusive process in the eigenbasis of the non-Hermitian Bloch-Torrey operator. It is possible to find expressions for some special temporal gradient waveforms employed to sensitize the nuclear magnetic resonance (NMR) signal to diffusion. For more general gradient waveforms, we derive an efficient numerical solution by introducing a novel matrix formalism. Compared to previous methods, this new approach requires a fewer number of eigenfunctions to achieve the same accuracy. This shows that these basis functions are better suited to the problem studied. The new framework could provide new important insights into the fundamentals of diffusion sensitization, which could further the development of the field of NMR. Published by AIP Publishing.

Place, publisher, year, edition, pages
AMER INST PHYSICS , 2017. Vol. 146, no 12, 124201
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-136576DOI: 10.1063/1.4978621ISI: 000397929300038PubMedID: 28388135OAI: oai:DiVA.org:liu-136576DiVA: diva2:1090305
Note

Funding Agencies|Swedish Foundation [AM13-0090]; Swedish Research Council CADICS Linneaus research environment; Swedish Research Council [2015-05356, 2016-04482]; Linkoping University Center for Industrial Information Technology (CENIIT); VINNOVA/ITEA3 [13031]; National Institutes of Health [P41EB015902]

Available from: 2017-04-24 Created: 2017-04-24 Last updated: 2017-04-24

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Herberthson, MagnusÖzarslan, EvrenKnutsson, HansWestin, Carl-Fredrik
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