Quantitative evaluation and modeling of two-dimensional neovascular network complexity: the surface fractal dimension

doi:10.1186/1471-2407-5-14

BMC Cancer

Volume 5

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Grizzi F
Russo C
Colombo P
Franceschini B
Frezza EE
Cobos E
Chiriva-Internati M

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Russo C
Colombo P
Franceschini B
Frezza EE
Cobos E
Chiriva-Internati M
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Research article

Quantitative evaluation and modeling of two-dimensional neovascular network complexity: the surface fractal dimension

Fabio Grizzi¹^,2 , Carlo Russo¹^,2 , Piergiuseppe Colombo³ , Barbara Franceschini¹^,2 , Eldo E Frezza⁴ , Everardo Cobos⁵ and Maurizio Chiriva-Internati⁶

¹Scientific Direction, Istituto Clinico Humanitas, Via Manzoni 56 – 20089 Rozzano, Milan, Italy

²"Michele Rodriguez" Foundation-Institute for Quantitative Measures in Medicine, Via Ludovico Di Breme 79 – 20100 Milan Italy

³Department of Pathology, Istituto Clinico Humanitas, Via Manzoni 56 – 20089 Rozzano, Milan, Italy

⁴Department of Surgery, Texas Tech University Health Science Center and the Southwest Cancer Treatment and Research Center, 79430 Lubbock, Texas, USA

⁵Department of Internal Medicine, Texas Tech University Health Science Center and the Southwest Cancer Treatment and Research Center, 79430 Lubbock, Texas, USA

⁶Department of Microbiology and Immunology, Texas Tech University Health Science Center and the Southwest Cancer Treatment and Research Center, 79430 Lubbock, Texas, USA

author email corresponding author email

BMC Cancer 2005, 5:14doi:10.1186/1471-2407-5-14


Published:	8 February 2005

Abstract

Background

Modeling the complex development and growth of tumor angiogenesis using mathematics and biological data is a burgeoning area of cancer research. Architectural complexity is the main feature of every anatomical system, including organs, tissues, cells and sub-cellular entities. The vascular system is a complex network whose geometrical characteristics cannot be properly defined using the principles of Euclidean geometry, which is only capable of interpreting regular and smooth objects that are almost impossible to find in Nature. However, fractal geometry is a more powerful means of quantifying the spatial complexity of real objects.

Methods

This paper introduces the surface fractal dimension (D_s) as a numerical index of the two-dimensional (2-D) geometrical complexity of tumor vascular networks, and their behavior during computer-simulated changes in vessel density and distribution.

Results

We show that D_ssignificantly depends on the number of vessels and their pattern of distribution. This demonstrates that the quantitative evaluation of the 2-D geometrical complexity of tumor vascular systems can be useful not only to measure its complex architecture, but also to model its development and growth.

Conclusions

Studying the fractal properties of neovascularity induces reflections upon the real significance of the complex form of branched anatomical structures, in an attempt to define more appropriate methods of describing them quantitatively. This knowledge can be used to predict the aggressiveness of malignant tumors and design compounds that can halt the process of angiogenesis and influence tumor growth.