Euclidean and fractal geometry of microvascular networks in normal and neoplastic pituitary tissue

Neurosurg Rev. 2008 Jul;31(3):271-81. doi: 10.1007/s10143-008-0127-7. Epub 2008 Mar 8.


In geometrical terms, tumour vascularity is an exemplary anatomical system that irregularly fills a three-dimensional Euclidean space. This physical characteristic and the highly variable shapes of the vessels lead to considerable spatial and temporal heterogeneity in the delivery of oxygen, nutrients and drugs, and the removal of metabolites. Although these biological characteristics are well known, quantitative analyses of newly formed vessels in two-dimensional histological sections still fail to view their architecture as a non-Euclidean geometrical entity, thus leading to errors in visual interpretation and discordant results from different laboratories concerning the same tumour. We here review the literature concerning microvessel density estimates (a Euclidean-based approach quantifying vascularity in normal and neoplastic pituitary tissues) and compare the results. We also discuss the limitations of Euclidean quantitative analyses of vascularity and the helpfulness of a fractal geometry-based approach as a better means of quantifying normal and neoplastic pituitary microvasculature.

Publication types

  • Review

MeSH terms

  • Adenoma / blood supply
  • Adenoma / pathology
  • Capillaries / anatomy & histology
  • Capillaries / pathology
  • Fractals*
  • Humans
  • Pituitary Gland / anatomy & histology*
  • Pituitary Gland / blood supply
  • Pituitary Gland / pathology*
  • Pituitary Neoplasms / blood supply
  • Pituitary Neoplasms / pathology*
  • Regional Blood Flow / physiology