Analysis of a delay differential equations modelling tumor growth with angiogenesis

Maja Szlenk, and Marek Bodnar. "Analysis of a delay differential equations modelling tumor growth with angiogenesis." Mathematica Applicanda 47.2 (2019): null. <http://eudml.org/doc/295478>.

@article{MajaSzlenk2019,
abstract = {Angiogenesis is a crucial process for the survival of cancer cells. Due to the rapid growth of the tumor, blood vessels delivering oxygen become insufficient, which leads to hypoxic regions inside the tumor and therefore death of the cells. Cancer cells deal with this problem by stimulating the growth of new vessels, thus providing the necessary amount of oxygen. The understanding of this process allowed to develop antiangiogenic therapy, which attack tumor vasculature instead of cells themselves. It is believed that effective treatment combines antiangiogenic factors with radio- and chemotherapy. Our aim is to construct a mathematical model describing this process, which would further allow to select optimal dosage. In this paper we propose a delay differential model of tumor growth and perform its preliminary analysis. We then introduce a method, which enables further study on this model. The results are illustrated by numerical simulations.},
author = {Maja Szlenk, Marek Bodnar},
journal = {Mathematica Applicanda},
keywords = {angiogenesis, VEGF, antiangiogenic treatment, delay differential equations, stability analysis},
language = {eng},
number = {2},
pages = {null},
title = {Analysis of a delay differential equations modelling tumor growth with angiogenesis},
url = {http://eudml.org/doc/295478},
volume = {47},
year = {2019},
}

TY - JOUR
AU - Maja Szlenk
AU - Marek Bodnar
TI - Analysis of a delay differential equations modelling tumor growth with angiogenesis
JO - Mathematica Applicanda
PY - 2019
VL - 47
IS - 2
SP - null
AB - Angiogenesis is a crucial process for the survival of cancer cells. Due to the rapid growth of the tumor, blood vessels delivering oxygen become insufficient, which leads to hypoxic regions inside the tumor and therefore death of the cells. Cancer cells deal with this problem by stimulating the growth of new vessels, thus providing the necessary amount of oxygen. The understanding of this process allowed to develop antiangiogenic therapy, which attack tumor vasculature instead of cells themselves. It is believed that effective treatment combines antiangiogenic factors with radio- and chemotherapy. Our aim is to construct a mathematical model describing this process, which would further allow to select optimal dosage. In this paper we propose a delay differential model of tumor growth and perform its preliminary analysis. We then introduce a method, which enables further study on this model. The results are illustrated by numerical simulations.
LA - eng
KW - angiogenesis, VEGF, antiangiogenic treatment, delay differential equations, stability analysis
UR - http://eudml.org/doc/295478
ER -