Quantitative evaluation and modeling of two-dimensional neovascular network complexity: the surface fractal dimension
<p>Abstract</p> <p>Background</p> <p>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 organ...
| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
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BMC
2005-02-01
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| Series: | BMC Cancer |
| Online Access: | http://www.biomedcentral.com/1471-2407/5/14 |
| _version_ | 1811284072946728960 |
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| author | Franceschini Barbara Colombo Piergiuseppe Russo Carlo Grizzi Fabio Frezza Eldo E Cobos Everardo Chiriva-Internati Maurizio |
| author_facet | Franceschini Barbara Colombo Piergiuseppe Russo Carlo Grizzi Fabio Frezza Eldo E Cobos Everardo Chiriva-Internati Maurizio |
| author_sort | Franceschini Barbara |
| collection | DOAJ |
| description | <p>Abstract</p> <p>Background</p> <p>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.</p> <p>Methods</p> <p>This paper introduces the <it>surface fractal dimension (D<sub><it>s</it></sub>) </it>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.</p> <p>Results</p> <p>We show that <it>D</it><sub><it>s </it></sub>significantly 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.</p> <p>Conclusions</p> <p>Studying the fractal properties of neovascularity induces reflections upon the real significance of the complex <it>form </it>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.</p> |
| first_indexed | 2024-04-13T02:23:07Z |
| format | Article |
| id | doaj.art-7a71a84740cf4d9fa87276ced39bf12b |
| institution | Directory Open Access Journal |
| issn | 1471-2407 |
| language | English |
| last_indexed | 2024-04-13T02:23:07Z |
| publishDate | 2005-02-01 |
| publisher | BMC |
| record_format | Article |
| series | BMC Cancer |
| spelling | doaj.art-7a71a84740cf4d9fa87276ced39bf12b2022-12-22T03:06:53ZengBMCBMC Cancer1471-24072005-02-01511410.1186/1471-2407-5-14Quantitative evaluation and modeling of two-dimensional neovascular network complexity: the surface fractal dimensionFranceschini BarbaraColombo PiergiuseppeRusso CarloGrizzi FabioFrezza Eldo ECobos EverardoChiriva-Internati Maurizio<p>Abstract</p> <p>Background</p> <p>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.</p> <p>Methods</p> <p>This paper introduces the <it>surface fractal dimension (D<sub><it>s</it></sub>) </it>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.</p> <p>Results</p> <p>We show that <it>D</it><sub><it>s </it></sub>significantly 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.</p> <p>Conclusions</p> <p>Studying the fractal properties of neovascularity induces reflections upon the real significance of the complex <it>form </it>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.</p>http://www.biomedcentral.com/1471-2407/5/14 |
| spellingShingle | Franceschini Barbara Colombo Piergiuseppe Russo Carlo Grizzi Fabio Frezza Eldo E Cobos Everardo Chiriva-Internati Maurizio Quantitative evaluation and modeling of two-dimensional neovascular network complexity: the surface fractal dimension BMC Cancer |
| title | Quantitative evaluation and modeling of two-dimensional neovascular network complexity: the surface fractal dimension |
| title_full | Quantitative evaluation and modeling of two-dimensional neovascular network complexity: the surface fractal dimension |
| title_fullStr | Quantitative evaluation and modeling of two-dimensional neovascular network complexity: the surface fractal dimension |
| title_full_unstemmed | Quantitative evaluation and modeling of two-dimensional neovascular network complexity: the surface fractal dimension |
| title_short | Quantitative evaluation and modeling of two-dimensional neovascular network complexity: the surface fractal dimension |
| title_sort | quantitative evaluation and modeling of two dimensional neovascular network complexity the surface fractal dimension |
| url | http://www.biomedcentral.com/1471-2407/5/14 |
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