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Applicable Analysis
An International Journal
Volume 95, 2016 - Issue 5
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Articles

Homogenization of oxygen transport in biological tissues

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Pages 1013-1049 | Received 28 Feb 2015, Accepted 05 May 2015, Published online: 07 Jul 2015
 

Abstract

In this paper, we extend previous work on the mathematical modeling of oxygen transport in biological tissues. Specifically, we include in the modeling process the arterial and venous microstructure within the tissue by means of homogenization techniques. We focus on the two-layer tissue architecture investigated in [Matzavinos et al., PNAS; 2009;106:12091] in the context of abdominal tissue flaps that are commonly used for reconstructive surgery. We apply two-scale convergence methods and unfolding operator techniques to homogenize the developed microscopic model, which involves different unit cell geometries in the two distinct tissue layers (skin layer and fat tissue) to account for different arterial branching patterns.

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Notes

No potential conflict of interest was reported by the authors.

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