Many biological structures like vessels, membrains etc., at a suitable scale can be modelled as random sets having Hausdorff dimension lower than the relevant space in which they are observed. In particular, angiogenesis (i.e. the formation of blood vessels from an existing one) is a process under intensive study nowadays in Biomedicine, because of its relation with tumor growth. Generalized densities \'{a} la Dirac-Schwartz have been shown to provide a useful approach for the mathematical description of such processes. Here an introduction to this mathematical approach is provided, together with related statistical techniques, which may provide a quantitative description of the mean geometric characteristics of the studied phenomenon.
Stochastic geometry and statistics in the analysis and therapy of tumour growth and tumour-driven angiogenesis / V. Capasso, A. Micheletti. - In: ECMI NEWSLETTER. - ISSN 1013-9338. - 46:(2009 Oct), pp. 11-17.
Stochastic geometry and statistics in the analysis and therapy of tumour growth and tumour-driven angiogenesis
V. CapassoPrimo
;A. MichelettiUltimo
2009
Abstract
Many biological structures like vessels, membrains etc., at a suitable scale can be modelled as random sets having Hausdorff dimension lower than the relevant space in which they are observed. In particular, angiogenesis (i.e. the formation of blood vessels from an existing one) is a process under intensive study nowadays in Biomedicine, because of its relation with tumor growth. Generalized densities \'{a} la Dirac-Schwartz have been shown to provide a useful approach for the mathematical description of such processes. Here an introduction to this mathematical approach is provided, together with related statistical techniques, which may provide a quantitative description of the mean geometric characteristics of the studied phenomenon.Pubblicazioni consigliate
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