RT Journal Article ID 3b22a03c54bb13df A1 Magin, Richard A1 Ingo, Carson A1 Triplett, William A1 Colon-Perez, Louis A1 Mareci, Tom H. T1 Classification of Fractional Order Biomarkers for Anomalous Diffusion Using q-Space Entropy JF Critical Reviews™ in Biomedical Engineering JO CRB YR 2014 FD 2014-08-15 VO 42 IS 1 SP 63 OP 83 K1 diffusion K1 anomalous K1 entropy K1 q-space K1 fractional calculus K1 Mittag-Leffler function AB In this study, we applied continuous random walk theory (CTRW) to develop a new model that characterizes anomalous diffusion in magnetic resonance imaging experiments. Furthermore, we applied a classification scheme based on information theoretic a techniques to characterize the degree of heterogeneity and complexity in biological tissues. From a CTRW approach, the Fourier transform of the generalized solution to the diffusion equation comes in the form of the Mittag-Leffler function. In this solution form, the relative stochastic uncertainty in the diffusion process can be computed with spectral entropy. We interrogated both white and gray matter regions of a fixed rat brain with diffusion − weighted magnetic resonance imaging experiments up to 26,000 s/mm2 by independently weighting q and Δ. to investigate the effects on the diffusion phenomena. Our model fractional order parameters, α and β, and entropy measure, H(q, Δ), differentiated between tissue types and extracted differing information within a region of interest based on the type of diffusion experiment performed. By combining fractional order modeling and information theory, new and powerful biomarkers are available to characterize tissue microstructure and provide contextual information about the anatomical complexity. PB Begell House LK https://www.dl.begellhouse.com/journals/4b27cbfc562e21b8,5d2385320a8fec1d,3b22a03c54bb13df.html