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.