## Tumour angiogenesis model with variable vessels' effectiveness

### Volume 38 / 2011

Applicationes Mathematicae 38 (2011), 33-49
MSC: Primary 92C50; Secondary 34A12.
DOI: 10.4064/am38-1-3

#### Abstract

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 of the proposed model and present some numerical simulations.