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NMR measurements of anomalous diffusion reflect fractional order dynamics

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dc.contributor.author Magin, Richard L.
dc.contributor.author Baleanu, Dumitru
dc.date.accessioned 2022-07-29T13:25:57Z
dc.date.available 2022-07-29T13:25:57Z
dc.date.issued 2008-01-01
dc.identifier.citation Magin, Richard L.; Baleanu, Dumitru. "NMR measurements of anomalous diffusion reflect fractional order dynamics", ASME International Design Engineering Technical Conferences/Computers and Information in Engineering Conference, Las Vegas, NV, SEP 04-07, 2007. tr_TR
dc.identifier.uri http://hdl.handle.net/20.500.12416/5734
dc.description.abstract Diffusion weighted MRI is often used to detect and stage neurodegenerative, malignant and ischemic diseases. The correlation between developing pathology and localized diffusion measurements relies on the design of selective phase encoding pulses that alter the intensity of the acquired signal according to biophysical models of spin diffusion in tissue. The most common approach utilizes a bipolar or Stejskal-Tanner gradient pulse sequence to encode the apparent diffusion coefficient as an exponential, multi-exponential or stretched exponential function of experimentally-controlled parameters. Several studies have investigated the ability of the stretched exponential to provide an improved fit to diffusion-weighted imaging data. These results were recently analyzed by establishing a direct link between water diffusion, as measured using NMR, and fractal structural models of tissues. In this paper we suggest an alternative description for stretched exponential behavior that reflects fractional order dynamics of a generalized Bloch-Torrey equation in either space or time. Such generalizations are the basis for similar anomalous diffusion phenomena observed in optical spectroscopy, polymer dynamics and electrochemistry. Here we demonstrate a correspondence between the detected NMR signal and anomalous diffusional dynamics of water through the Riesz fractional order space derivative and the Caputo form of the fractional order Riemann-Liouville time derivative. tr_TR
dc.description.sponsorship ASME, Design & Engn Div; ASME, Comp & Informat Engn Div tr_TR
dc.language.iso eng tr_TR
dc.publisher ASME tr_TR
dc.rights info:eu-repo/semantics/closedAccess tr_TR
dc.subject Field-Gradient Spectroscopy tr_TR
dc.subject Fractal Networks tr_TR
dc.subject Strange Kinetics tr_TR
dc.subject Systems tr_TR
dc.subject Media tr_TR
dc.title NMR measurements of anomalous diffusion reflect fractional order dynamics tr_TR
dc.type conferenceObject tr_TR
dc.relation.journal ASME International Design Engineering Technical Conferences/Computers and Information in Engineering Conference tr_TR
dc.contributor.authorID 56389 tr_TR
dc.identifier.volume 5 tr_TR
dc.identifier.startpage 1197 tr_TR
dc.identifier.endpage 1203 tr_TR
dc.contributor.department Çankaya Üniversitesi, Fen-Edebiyat Fakültesi, Matematik Bölümü tr_TR


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