Fractional order analysis of Sephadex gel structures: NMR measurements reflecting anomalous diffusion

Richard L. Magin, Belinda S. Akpa, Thomas Neuberger, Andrew G. Webb

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

Abstract

We report the appearance of anomalous water diffusion in hydrophilic Sephadex gels observed using pulse field gradient (PFG) nuclear magnetic resonance (NMR). The NMR diffusion data was collected using a Varian 14.1 Tesla imaging system with a home-built RF saddle coil. A fractional order analysis of the data was used to characterize heterogeneity in the gels for the dynamics of water diffusion in this restricted environment. Several recent studies of anomalous diffusion have used the stretched exponential function to model the decay of the NMR signal, i.e., exp[-(bD)α], where D is the apparent diffusion constant, b is determined the experimental conditions (gradient pulse separation, durations and strength), and α is a measure of structural complexity. In this work, we consider a different case where the spatial Laplacian in the Bloch-Torrey equation is generalized to a fractional order model of diffusivity via a complexity parameter, β, a space constant, μ, and a diffusion coefficient, D. This treatment reverts to the classical result for the integer order case. The fractional order decay model was fit to the diffusion-weighted signal attenuation for a range of b-values (0<b<4000smm-2). Throughout this range of b values, the parameters β, μ and D, were found to correlate with the porosity and tortuosity of the gel structure.

Original languageEnglish (US)
Pages (from-to)4581-4587
Number of pages7
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume16
Issue number12
DOIs
StatePublished - Dec 2011

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modeling and Simulation
  • Applied Mathematics

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