Tamtam Proceedings - lamsin

26 Habbal1. IntroductionAngiogenesis is the biological process by which networks of blood vessels are initiatedand proliferate towards a mature vasculature -local circulatory system-. At earlydevelopment and growth, angiogenesis is necessary to go from the embryonic vasculogenesisinto a complete and mature blood circulatory system. Moreover, angiogenesisplays an important role in wound healing and tissue repairing. But from other part, angiogenesisplays also a pathological role, being a fundamental step in the growth of cancertumors and in tumoral metastasis, the ability of tumor cells to develop in other places usingthe blood and lymphatic networks. Recently, oncologists have suggested that the useof inhibitors of angiogenesis, an approach that is often referred to as anti-angiogenesis,could prove effective in cancer treatment. Combined with directly curative drugs, antiangiogenicdrugs are intended to efficiently stop the expansion of tumoral mass, forcingthe tumor to dormancy or even regression.In the present work, we consider angiogenesis and anti-angiogenesis processes as resultingfrom a mathematical game between two players : activators of angiogenesis, willingto provide the tumor with an efficient feeding (and waste expelling) network of bloodvessels, and inhibitors, with a specific action on the tumor vasculature.From the activators viewpoint, the biological tissue surrounding the tumor, and locatedbetween close existing vessels and the tumor is seen as a porous medium, defined by itsporosity distribution. The latter is defined as a result of an interaction between activatorsand inhibitors. Activators would like to design the porosity in order to yield the minimalpressure drop. From the inhibitors viewpoint, the same biological medium is seen as alinear elastic continuum, defined by its material elasticity tensor. As for the porosity,the material properties are defined as a result of an interaction between activators andinhibitors. Inhibitors would like to design the material distribution in order to provide thematrix with the minimal mechanical compliance.2. Mathematical modelingObviously, solid tumor growth is not only a question of diffusion ; it should and infact it does include key factors from structural mechanics. Indeed, there are only a veryfew and quite recent contributions to this area. In Chaplain and Sleeman [3], elasticitytheory is used to describe tumor invasion. Jones et al. in [1] introduce a constitutivelaw that combines the stress-strain relation of linear elasticity with a growth term derivedby analogy with thermal expansion. Tumor spheroid growth is also studied with poroelasticitymodeling in [7] [5]. A more recent study by Araujo and McElwain addressinggrowth-induced stresses in tumors can be found in [4], the model presented highlights therole of various tissue properties in inducing vascular collapse phenomena observed insidetumors.TAMTAM –Tunis– 2005