Angiogenesis process with vessel impairment for Gompertzian and logistic type of tumour growth

Jan Poleszczuk¹ ; Urszula Foryś¹

¹ Institute of Applied Mathematics and Mechanics Faculty of Mathematics, Informatics and Mechanics University of Warsaw Banacha 2 02-097 Warszawa, Poland

Applicationes Mathematicae, Tome 36 (2009) no. 3, pp. 313-331

Résumé

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.

Détail

DOI : 10.4064/am36-3-5

Keywords: propose models vessel impairment process tumour angiogenesis consider three types treatment standard chemotherapy antiangiogenic treatment combined treatment models based idea hahnfeldt carrying capacity solid tumour depends its vessel density models proposed carrying capacity depends process vessel impairment first model logistic type equation describe neoplastic cell dynamics while second gompertz type growth simulations solutions vascular dormant state tumour reached different ways addition each efficiency treatments different