Homogenization of oxygen transport in biological tissues

TL;DR

This paper develops a homogenized mathematical model for oxygen transport in layered biological tissues, incorporating microvascular structures to better understand tissue oxygenation, especially in reconstructive surgery contexts.

Contribution

It introduces a homogenization approach that accounts for microvascular architecture in layered tissues, advancing previous models of oxygen transport.

Findings

Homogenized model accurately captures microvascular effects.

Different tissue layers modeled with distinct geometries.

Enhanced understanding of oxygen distribution in tissue layers.

Abstract

In this paper, we extend previous work on the mathematical modeling of oxygen transport in biological tissues (Matzavinos et al., 2009). 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., 2009) 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.