Modeling Proteolytically Driven Tumor Lymphangiogenesis

With the exception of a limited number of sites in the body, primary tumors infrequently lead to the demise of cancer patients. Instead, mortality and a significant degree of morbidity result from the growth of secondary tumors in distant organs. Tumor survival, growth and dissemination are associated with the formation of both new blood vessels (angiogenesis) and new lymph vessels (lymphagenesis or lymphangiogenesis). Although intensive research in tumor angiogenesis has been going on for the past four decades, experimental results in tumor lymphangiogenesis began to appear only in the last 10 years. In this chapter we expand the models proposed by Friedman, Lolas and Pepper on tumor lymphangiogenesis mediated by proteolytically and un-proteolytically processed growth factors (Friedman and Lolas G, Math Models Methods Appl Sci 15(01):95-107, 2005; Pepper and Lolas G, Selected topics in cancer modeling: genesis, evolution, immune competition, and therapy. In: The lymphatic vascular system in lymphangiogenesis invasion and metastasis a mathematical approach. Birkhäuser Boston, Boston, pp 1-22, 2008). The variables represent different cell densities and growth factors concentrations, and where possible the parameters are estimated from experimental and clinical data. The results obtained from computational simulations carried out on the model equations produce dynamic heterogeneous ("anarchic") spatio-temporal solutions. More specifically, we observed coherent masses of tumor clusters migrating around and within the lymphatic network. Our findings are in line with recent experimental evidence that associate cluster formation with the minimization of cell loss favoring high local extracellular matrix proteolysis and thus protecting cancer invading cells from an immunological assault driven by the lymphatic network.