Homogenization of oxygen transport in biological tissues

Anastasios Matzavinos, Mariya Ptashnyk (Lead / Corresponding author)

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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.

Original languageEnglish
Pages (from-to)1013-1049
Number of pages37
JournalApplicable Analysis
Volume95
Issue number5
Early online date7 Jul 2015
DOIs
Publication statusPublished - 2016

Keywords

  • Arterial branching pattern
  • DIEP tissue flap
  • Homogenization
  • Oxygen transport
  • Reconstructive surgery
  • Thin domains
  • Tissue engineering
  • Two-scale convergence
  • Unfolding method

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