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Critical Reviews™ in Biomedical Engineering
SJR: 0.207 SNIP: 0.376 CiteScore™: 0.79

ISSN Print: 0278-940X
ISSN Online: 1943-619X

Critical Reviews™ in Biomedical Engineering

DOI: 10.1615/CritRevBiomedEng.2014011027
pages 63-83

Classification of Fractional Order Biomarkers for Anomalous Diffusion Using q-Space Entropy

Richard L. Magin
Diagnostic Imaging System Group (DIS), Richard and Loan Hill Department of Bioengineering, University of Illinois at Chicago, 851 South Morgan Street, Chicago, IL 60607
Carson Ingo
C. J. Gorter Center for High Field MRI, Department of Radiology, Leiden University Medical Center, Leiden, NL
William Triplett
Advanced Magnetic Resonance Imaging and Spectroscopy Facility (AMRIS), McKnight Brain Institute, University of Florida, Gainesville, FL, USA 32610
Louis Colon-Perez
Advanced Magnetic Resonance Imaging and Spectroscopy Facility (AMRIS), McKnight Brain Institute, University of Florida, Gainesville, FL, USA 32610
Tom H. Mareci
Advanced Magnetic Resonance Imaging and Spectroscopy Facility (AMRIS), McKnight Brain Institute, University of Florida, Gainesville, FL, USA 32610

ABSTRACT

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.


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