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Tumour angiogenesis model with variable vessels’ effectiveness. (English) Zbl 1221.92051
Summary: We propose a model of vascular tumour growth, which generalises the well recognised model formulated by P. Hahnfeldt et al. [Cancer Res. 59, 4770-4775 (1999)]. Our model is based on the same idea that the carrying capacity for any solid tumour depends on its vessel density but also incorporates vasculature quality which may be lost during angiogenesis as recognised by R. K. Jain [Science 307, 58–62 (2005)]. In the model we assume that the loss of vessel quality affects the diffusion coefficient inside the tumour. We analyse basic mathematical properties of the proposed model and present some numerical simulations.

MSC:
92C50 Medical applications (general)
34A99 General theory for ordinary differential equations
37N25 Dynamical systems in biology
65C20 Probabilistic models, generic numerical methods in probability and statistics
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