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Anomalous diffusion expressed through fractional order differential operators in the Bloch-Torrey equation

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dc.contributor.author Magin, Richard
dc.contributor.author Abdullah, Osama
dc.contributor.author Baleanu, Dumitru
dc.contributor.author Zhou, Xiaohong Joe
dc.date.accessioned 2016-04-27T10:59:53Z
dc.date.available 2016-04-27T10:59:53Z
dc.date.issued 2008-02
dc.identifier.citation Magin, R.L...et al. (2008). Anomalous diffusion expressed through fractional order differential operators in the Bloch-Torrey equation. Journal of Magnetic Resonance, 190(2), 255-270. http://dx.doi.org/10.1016/j.jmr.2007.11.007 tr_TR
dc.identifier.issn 1090-7807
dc.identifier.uri http://hdl.handle.net/20.500.12416/921
dc.description.abstract Diffusion weighted MRI is used clinically to detect and characterize neurodegenerative, malignant and ischemic diseases. The correlation between developing pathology and localized diffusion relies on d iffusi on -weighted pulse sequences to probe biophysical models of molecular diffusion-typically exp[-(bD)]-where D is the apparent diffusion coefficient (turn (2)/s) and b depends on the specific gradient pulse sequence parameters. Several recent studies have investigated the so-called anomalous diffusion stretched exponential model-exp[-(bD)(alpha)], where alpha is a measure of tissue complexity that can be derived from fractal models of tissue structure. In this paper we propose an alternative derivation for the stretched exponential model using fractional order space and time derivatives. First, we consider the case where the spatial Laplacian in the Bloch-Torrey equation is generalized to incorporate a fractional order Brownian model of diffusivity. Second, we consider the case where the time derivative in the Bloch-Torrey equation is replaced by a Riemann-Liouville fractional order time derivative expressed in the Caputo form. Both cases revert to the classical results for integer order operations. Fractional order dynamics derived for the first case were observed to fit the signal attenuation in diffusion-weighted images obtained from Sephadex gels, human articular cartilage and human brain. Future developments of this approach may be useful for classifying anomalous diffusion in tissues with developing pathology. (c) 2007 Elsevier Inc. All rights reserved tr_TR
dc.language.iso eng tr_TR
dc.publisher Academic Press INC Elsevier Science tr_TR
dc.relation.isversionof 10.1016/j.jmr.2007.11.007 tr_TR
dc.rights info:eu-repo/semantics/closedAccess
dc.subject Anomalous Diffusion tr_TR
dc.subject Bloch–Torrey Equation tr_TR
dc.subject Fractional Calculus tr_TR
dc.subject Diffusion-Weighted MRI tr_TR
dc.subject Stretched Exponential tr_TR
dc.title Anomalous diffusion expressed through fractional order differential operators in the Bloch-Torrey equation tr_TR
dc.type article tr_TR
dc.relation.journal Journal of Magnetic Resonance tr_TR
dc.identifier.volume 190 tr_TR
dc.identifier.issue 2 tr_TR
dc.identifier.startpage 255 tr_TR
dc.identifier.endpage 270 tr_TR
dc.contributor.department Çankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bilgisayar Bölümü tr_TR


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