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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am38-1-3,
author = {Jan Poleszczuk and Iwona Skrzypczak},
title = {Tumour angiogenesis model with variable vessels' effectiveness},
journal = {Applicationes Mathematicae},
volume = {38},
year = {2011},
pages = {33-49},
zbl = {1221.92051},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am38-1-3}
}
Jan Poleszczuk; Iwona Skrzypczak. Tumour angiogenesis model with variable vessels' effectiveness. Applicationes Mathematicae, Tome 38 (2011) pp. 33-49. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am38-1-3/