The microvascular network of the pituitary gland: a model for the application of fractal geometry to the analysis of angioarchitecture and angiogenesis of brain tumors

In geometrical terms, tumor vascularity is an exemplary anatomical system that irregularly fills a three-dimensional Euclidean space. This physical characteristic, together with the highly variable vessel shapes and surfaces, leads to considerable spatial and temporal heterogeneity in the delivery of oxygen, nutrients and drugs, and the removal of metabolites. Although these biological features have now been well established, quantitative analyses of neovascularity in two-dimensional histological sections still fail to view tumor architecture in non-Euclidean terms, and this leads to errors in visually interpreting the same tumor, and discordant results from different laboratories. A review of the literature concerning the application of microvessel density (MVD) estimates, an Euclidean-based approach used to quantify vascularity in normal and neoplastic pituitary tissues, revealed some disagreements in the results and led us to discuss the limitations of the Euclidean quantification of vascularity. Consequently, we introduced fractal geometry as a better means of quantifying the microvasculature of normal pituitary glands and pituitary adenomas, and found that the use of the surface fractal dimension is more appropriate than MVD for analysing the vascular network of both. We propose extending the application of this model to the analysis of the angiogenesis and angioarchitecture of brain tumors.