Dynamic Contrast-Enhanced MRI and Fractal Characteristics of Percolation Clusters in Two-Dimensional Tumor Blood Perfusion

Abstract

Dynamic contrast-enhanced magnetic resonance imaging (DE-MRI) of the tumor blood pool is used to study tumor tissue perfusion. The results are then analyzed using percolation models. Percolation cluster geometry is depicted using the wash-in component of MRI contrast signal intensity. Fractal characteristics are determined for each two-dimensional cluster. The invasion percolation model is used to describe the evolution of the tumor perfusion front. Although tumor perfusion can be depicted rigorously only in three dimensions, two-dimensional cases are used to validate the methodology. It is concluded that the blood perfusion in a two-dimensional tumor vessel network has a fractal structure and that the evolution of the perfusion front can be characterized using invasion percolation. For all the cases studied, the front starts to grow from the periphery of the tumor (where the feeding vessel was assumed to lie) and continues to grow toward the center of the tumor, accounting for the well-documented perfused periphery and necrotic core of the tumor tissue.