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

Antonio Di Ieva*, Fabio Grizzi, Paolo Gaetani, Umberto Goglia, Manfred Tschabitscher, Pietro Mortini, Riccardo Rodriguez Y Baena

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review

24 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)271-280
Number of pages10
JournalNeurosurgical Review
Issue number3
Publication statusPublished - Jul 2008
Externally publishedYes


  • Adenoma
  • Complexity
  • Fractal geometry
  • Microvessel density
  • Pituitary
  • Vascularity


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