Fractional order measures of anomalous diffusion in healthy aging of neural tissue

Carson Ingo, Richard L. Magin, Luis Colon-Perez, Thomas H. Mareci

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper we use fractional calculus to characterize diffusion in brain tissue by generalizing Fick's 2nd Law. This approach, rooted in the physics of the Continuous Time Random Walk (CTRW) Theory expresses separate measures of tissue complexity through the fractional order of the time derivative, α, and the space derivative, ß. We also calculate the entropy of the characteristic function of the probability distribution function (pdf) as a measure of the heterogeneity of the tissue. We applied this theory to the analysis of high-field (17.6 Tesla) diffusion-weighted MRI data to characterize the structural complexity of neural tissue. When interpreted in the context of anomalous diffusion, healthy aging in the normal rat brain is observed in both white matter (WM) and gray matter (GM).

Original languageEnglish (US)
Title of host publication2014 International Conference on Fractional Differentiation and Its Applications, ICFDA 2014
EditorsDumitru Baleanu, J.A. Tenreiro Machado
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781479925919
DOIs
StatePublished - Nov 25 2014
Event2014 International Conference on Fractional Differentiation and Its Applications, ICFDA 2014 - Catania, Italy
Duration: Jun 23 2014Jun 25 2014

Publication series

Name2014 International Conference on Fractional Differentiation and Its Applications, ICFDA 2014

Other

Other2014 International Conference on Fractional Differentiation and Its Applications, ICFDA 2014
CountryItaly
CityCatania
Period6/23/146/25/14

ASJC Scopus subject areas

  • Applied Mathematics
  • Modeling and Simulation
  • Numerical Analysis

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  • Cite this

    Ingo, C., Magin, R. L., Colon-Perez, L., & Mareci, T. H. (2014). Fractional order measures of anomalous diffusion in healthy aging of neural tissue. In D. Baleanu, & J. A. T. Machado (Eds.), 2014 International Conference on Fractional Differentiation and Its Applications, ICFDA 2014 [6967418] (2014 International Conference on Fractional Differentiation and Its Applications, ICFDA 2014). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICFDA.2014.6967418