Abstract
It is well known that avascular tumours only grow to a limited size before metabolic demands are impeded due to the diffusion limit of oxygen and other nutrients. For continued growth the tumour switches to an angiogenic phenotype that induces sprouting of new blood vessels from the surrounding medium. Sprouting angiogenesis is the most widely studied aspect of neovascular growth and has been modelled from several mathematical points of view. In this paper we propose a new underlying theme, which unifies a number of the existing techniques employed to model angiogenesis. The basic formulation is in terms of stochastic differential equations. The ideas discussed have wide application, particularly in the validation of models of vessel cooption, vasculogenic mimicry and lymphangiogenesis.
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