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

• Autorzy: Jan Poleszczuk , Urszula Foryś
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 92C50: Medical applications (general)
• 34A34: Nonlinear equations and systems, general
• 34A12: Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2009
• Tom: 36
• Numer: 3
• Strony: 313-331

Daty

wydano

2009

Twórcy

autor

Jan Poleszczuk

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

autor

Urszula Foryś

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

Identyfikatory

DOI

10.4064/am36-3-5