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

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

doi:10.1109/ICFDA.2014.6967418

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 proceeding › Conference contribution › peer-review

Abstract

In this paper we use fractional calculus to characterize diffusion in brain tissue by generalizing Fick's 2^nd 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 language	English
Title of host publication	2014 International Conference on Fractional Differentiation and Its Applications, ICFDA 2014
Editors	Dumitru Baleanu, J.A. Tenreiro Machado
Publisher	Institute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)	9781479925919
DOIs	https://doi.org/10.1109/ICFDA.2014.6967418
State	Published - 25 Nov 2014
Event	2014 International Conference on Fractional Differentiation and Its Applications, ICFDA 2014 - Catania, Italy Duration: 23 Jun 2014 → 25 Jun 2014

Publication series

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

Conference

Conference	2014 International Conference on Fractional Differentiation and Its Applications, ICFDA 2014
Country/Territory	Italy
City	Catania
Period	23/06/14 → 25/06/14

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10.1109/ICFDA.2014.6967418

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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

Ingo, Carson ; Magin, Richard L. ; Colon-Perez, Luis et al. / Fractional order measures of anomalous diffusion in healthy aging of neural tissue. 2014 International Conference on Fractional Differentiation and Its Applications, ICFDA 2014. editor / Dumitru Baleanu ; J.A. Tenreiro Machado. Institute of Electrical and Electronics Engineers Inc., 2014. (2014 International Conference on Fractional Differentiation and Its Applications, ICFDA 2014).

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title = "Fractional order measures of anomalous diffusion in healthy aging of neural tissue",

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).",

author = "Carson Ingo and Magin, {Richard L.} and Luis Colon-Perez and Mareci, {Thomas H.}",

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doi = "10.1109/ICFDA.2014.6967418",

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publisher = "Institute of Electrical and Electronics Engineers Inc.",

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Ingo, C, Magin, RL, Colon-Perez, L & Mareci, TH 2014, Fractional order measures of anomalous diffusion in healthy aging of neural tissue. in D Baleanu & JAT 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., 2014 International Conference on Fractional Differentiation and Its Applications, ICFDA 2014, Catania, Italy, 23/06/14. https://doi.org/10.1109/ICFDA.2014.6967418

Fractional order measures of anomalous diffusion in healthy aging of neural tissue. / Ingo, Carson; Magin, Richard L.; Colon-Perez, Luis et al.

2014 International Conference on Fractional Differentiation and Its Applications, ICFDA 2014. ed. / Dumitru Baleanu; J.A. Tenreiro Machado. Institute of Electrical and Electronics Engineers Inc., 2014. 6967418 (2014 International Conference on Fractional Differentiation and Its Applications, ICFDA 2014).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - 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).

AB - 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).

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BT - 2014 International Conference on Fractional Differentiation and Its Applications, ICFDA 2014

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Ingo C, Magin RL, Colon-Perez L, Mareci TH. Fractional order measures of anomalous diffusion in healthy aging of neural tissue. In Baleanu D, Machado JAT, editors, 2014 International Conference on Fractional Differentiation and Its Applications, ICFDA 2014. Institute of Electrical and Electronics Engineers Inc. 2014. 6967418. (2014 International Conference on Fractional Differentiation and Its Applications, ICFDA 2014). doi: 10.1109/ICFDA.2014.6967418

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

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