The introduction of complex internal geometries into flow problems increases greatly the required physical information and mathematical complexity. The purpose is to find morphological properties that are useful to construct a reductive model for the transport problem. Percolation theory is a mathematical tool that allows the prediction of morphological and transport properties for heterogeneous materials by the use of simple scaling laws. A continuous pathway of conductive sites that span the tumor is formed and transport takes place through the tumor. The tumor perfusion is considered to take place in a percolation-like cluster.
Fractal characteristics are determined for each two-dimensional cluster.
Invasion percolation, as a statistical growth process, is then used to monitor the perfusion front in the tumor. It is concluded that the blood perfusion in a 2D tumor vessel network has a fractal structure and that the evolution of the perfusion front can be characterized using invasion percolation. In addition, local fractal dimensions of tumor fragments might be correlated with the respective fragment hypoxic ratio, thus leading to a non-invasive mean of determining the tumor oxygenation.