Biological Background and Motivation

Vasculogenesis, in vivo, is the formation of (major) blood vessels by cells (endothelial cells and angioblasts) while angiogenesis refers to the development of vascular structures which sprout out from existing vessels. The word angiogenesis was first used in 1935 to describe the formation of new blood vessels in the placenta. The motivation for the modelling in this chapter is to try and determine the key elements in the underlying mechanism involved in creating such patterned structures. Since in vivo studies are prone to a variety of sensitivity problems much of the experimental work in this area has been on in vitro (biological) model systems which avoid many of the experimental difficulties with in vivo systems. The development of in vitro angiogenesis (biological) models provides a controlled means for studying blood vessel formation (Folkman and Haudenschild 1980). The reasonable assumption is that, if the in vitro studies replicate the type of patterns observed in vivo, then these models provide information on the pattern formation mechanism which operates in vivo. The essentially planar network patterns we study in this chapter are more akin to vasculogenesis than angiogenesis which are distinctly three-dimensional.

Angiogenesis, and vessel formation in general, is of fundamental importance in wound healing, sustaining tumour growth, morphogenesis and so on. Vascularisation is necessary for the growth of solid cancer tumours. Folkman (1972), in what is now considered as possibly one of the most important papers in the solid tumour cancer field, hypothesized that if it were possible to inhibit neovascularization it might stop the growth of the tumour or at least contain its growth to a dormant mass of around 2 to 3 mm in diameter; see also Folkman's (1976) general article on vascularisation of tumours. He speculated that such antiangiogenesis could be the basis for a new form of cancer therapy. He presented some convincing evidence that the tumour produces a chemical, a tumour-angiogenesis factor, which induces neovascularisation. His work was almost totally ignored (even ridiculed) until the late 1990's when anti-angiogenesis factors, such as endostatin, an endogenous inhibitor of angiogenesis and tumor growth, and angiostatin were found (O'Reilly et al. 1997).1 Even thalidomide is having a come

1When the news broke in the world press in 1997 it was heralded as the holy grail of cancer therapy with numerous people making ever wilder predictions. After most of the rushed interviews and media hyperbole had subsided Folkman made the pertinent comment that 'If you are a mouse with cancer we can take good care of you.'

back: it has been shown to inhibit angiogenesis (D'Amato et al. 1994). Folkman (1972) concluded with a series of highly pertinent medical questions which suggest a variety of modelling challenges still of relevance, or rather of even more relevance in the light of recent findings.2 Folkman and Klagsbrun (1987) described some angiogenic factors that had been found in tumours. A particularly important aspect, from a cancer therapy point of view, is that antiangiogenic therapy does not induce acquired drug resistance in experimental cancer (Boehm et al. 1997) unlike chemotherapy which does induce drug resistance (see Chapter 11). Folkman's (1995) review article discusses some clinical applications of research on angiogenesis. The general article by Kerbel (1997) gives an overview of the newer developments while Sage (1997a) discusses several protein regulators of angiogenesis in particular, and in Sage (1997b) describes results on the role of the protein SPARC which suppresses tumourigenicity of human melanoma cancer cells. The field of anti-angiogenesis is now fast growing with an increasing number of areas where modelling could be of some considerable value.

After reading some of Folkman's early work in the early 1990's we initiated research into trying to model the biological processes involved in the network pattern observed in angiogenesis. Even without the cancer connection, it is, as we have noted, an important and challenging question. In this chapter we describe the application of the mechanochemical (although it is strictly just mechanical) theory to the patterning process. Although motivated by Folkman's ideas from the 1970's this application is directly related to experiments carried out by Sage and Vernon and their coworkers (Vernon et al. 1995). These experiments were also used for comparison between the theory and experiment (see below) and were the basis for most of the parameter estimates which are essential in any practical application of a model to a specific biological problem.

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