title: Geometry of human vascular system: is it an obstacle for quantifying antiangiogenic therapies?
abstract: 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.
authors.affiliation: Laboratories of Quantitative Medicine, Istituto Clinico Humanitas, IRCCS, Via Manzoni 56 20089 Rozzano, Milan, Italy. fabio.grizzi@humanitas.it
authors.forename: Fabio
authors.initials: F
authors.lastname: Grizzi
authors.forename: Piergiuseppe
authors.initials: P
authors.lastname: Colombo
authors.forename: Gianluigi
authors.initials: G
authors.lastname: Taverna
authors.forename: Maurizio
authors.initials: M
authors.lastname: Chiriva-Internati
authors.forename: Everardo
authors.initials: E
authors.lastname: Cobos
authors.forename: Pierpaolo
authors.initials: P
authors.lastname: Graziotti
authors.forename: Pier Carlo
authors.initials: PC
authors.lastname: Muzzio
authors.forename: Nicola
authors.initials: N
authors.lastname: Dioguardi
mesh_terms: D016222:Fibroblast Growth Factor 2 / Q000627:therapeutic use*; D017709:Fractals; D006801:Humans; D008954:Models, Biological; D009369:Neoplasms / Q000098:blood supply*; D009389:Neovascularization, Pathologic / Q000188:drug therapy* / Q000473:pathology*; D042461:Vascular Endothelial Growth Factor A / Q000627:therapeutic use*
chemical_list: D042461:Vascular Endothelial Growth Factor A; D016222:Fibroblast Growth Factor 2