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

This paper introduces the surface fractal dimension (Ds) 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.We show that Ds 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.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.The term "angiogenesis" defines the fundamental process of the development and growth of new blood vessels from the pre-existing vasculature, and is essential for reproduction, development and wound repair [1]. Under these conditions, it is highly regulated: i.e. "turned on" for brief periods of time (days) and then completely inhibited.The cyclic nature of the microvascular bed in the corpus luteum provides a unique experimental model for examining the discrete physiological steps of angiogenesis in the life cycle of endothelial cells which, together with pericytes (supportive vascular smooth muscle cells), carry all of the genetic information necessary to form tubes, branches and entire capillary networks.However, many human diseases (including solid tumors) are driven by persistently up-regulated angiogenesis [1]. In some non-malignant processes, such as pyogenic granuloma or keloid formation [2], angiogenesis is prolonged but still self-limited; however, this is not true of tumor angiogenesis which, once begun, contin