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 contributionpeer-review

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
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 - 25 Nov 2014
Event2014 International Conference on Fractional Differentiation and Its Applications, ICFDA 2014 - Catania, Italy
Duration: 23 Jun 201425 Jun 2014

Publication series

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

Conference

Conference2014 International Conference on Fractional Differentiation and Its Applications, ICFDA 2014
Country/TerritoryItaly
CityCatania
Period23/06/1425/06/14

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