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 cell dynamics, while in the second one we use the Gompertz type of growth. Simulations of solutions show that a vascular dormant state of the tumour can be reached in two different ways. In addition in each case efficiency of treatments is different.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am36-3-5,
author = {Jan Poleszczuk and Urszula Fory\'s},
title = {Angiogenesis process with vessel impairment for Gompertzian and logistic type of tumour growth},
journal = {Applicationes Mathematicae},
volume = {36},
year = {2009},
pages = {313-331},
zbl = {1184.92022},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am36-3-5}
}
Jan Poleszczuk; Urszula Foryś. Angiogenesis process with vessel impairment for Gompertzian and logistic type of tumour growth. Applicationes Mathematicae, Tome 36 (2009) pp. 313-331. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am36-3-5/