  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.
