We propose two models of vessel impairment in the process of tumour angiogenesis and we consider three types of treatment: standard chemotherapy, antiangiogenic treatment and a combined treatment. The models are based on the idea of Hahnfeldt et al. that the carrying capacity for any solid tumour depends on its vessel density. In the models proposed the carrying capacity also depends on the process of vessel impairment. In the first model a logistic type equation is used to describe the neoplastic...

We propose a model of vascular tumour growth, which generalises the well recognised model formulated by Hahnfeldt et al. in 1999. Our model is based on the same idea that the carrying capacity for any solid tumour depends on its vessel density but it also incorporates vasculature quality which may be lost during angiogenesis as recognised by Jain in 2005. In the model we assume that the loss of vessel quality affects the diffusion coefficient inside the tumour. We analyse basic mathematical properties...

Mathematical models prove valuable tools to study the proof-of-concept and underlying mechanisms of a tumour progression. They enable us to explore possible radio-, chemo- and various therapy combinations that until now have been only a promising hypothesis because of huge costs of their clinical studies. Here we present a family of mathematical models of tumour angiogenesis, which were successfully compared to biological data. In addition, after modifications they can describe the effect of anti-angiogenic...

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