Geometry of human vascular system: Is it an obstacle for quantifying antiangiogenic therapies?

It is now recognized that all human natural and diseased anatomic systems are characterized by irregular shapes and very complex behaviors. In geometrical terms, tumor vascularity (which is the result of a nonlinear dynamic process called angiogenesis) is an archetypal anatomic system that irregularly fills a 3-dimensional Euclidean space. This characteristic, together with the highly variable nature of 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 biologic features have been well established, the quantitative analysis of neovascularity in 2-dimensional histologic sections still fails to view its architecture as a non-Euclidean geometrical object, thus allowing errors in visual interpretation and discordant results concerning the same tumor from different laboratories. We discuss here the tumor-induced vascular system as a fractal object, and what changes this new way of observing may bring to the quantification of effective antiangiogenic therapies.