Mathematical and numerical analysis for a model of growing metastatic tumors

In cancer diseases, the appearance of metastases is a very pejorative forecast. Chemotherapies are systemic treatments which aim at the elimination of the micrometastases produced by a primitive tumour. The efficiency of chemotherapies closely depends on the protocols of administration. Mathematical...

Full description

Saved in:
Bibliographic Details
Published in:Mathematical biosciences 2009-03, Vol.218 (1), p.1-14
Main Authors: Barbolosi, Dominique, Benabdallah, Assia, Hubert, Florence, Verga, Federico
Format: Article
Language:English
Subjects:
Analysis of PDEs
Antineoplastic Agents - therapeutic use
Asymptotic behaviour
Cancer
Cell Growth Processes - physiology
Characteristic scheme
Humans
Life Sciences
Mathematics
Metastatic tumors
Models, Biological
Neoplasm Metastasis
Neoplasms - drug therapy
Neoplasms - pathology
Numerical Analysis
Semigroup approach
Von Foerster equation
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In cancer diseases, the appearance of metastases is a very pejorative forecast. Chemotherapies are systemic treatments which aim at the elimination of the micrometastases produced by a primitive tumour. The efficiency of chemotherapies closely depends on the protocols of administration. Mathematical modeling is an invaluable tool to help in evaluating the best treatment strategy. Iwata et al. [K. Iwata, K. Kawasaki, N. Shigesad, A dynamical model for the growth and size distribution of multiple metastatic tumors, J. Theor. Biol. 203 (2000) 177.] proposed a partial differential equation (PDE) that describes the metastatic evolution of an untreated tumour. In this article, we conducted a thorough mathematical analysis of this model. Particularly, we provide an explicit formula for the growth rate parameter, as well as a numerical resolution of this PDE. By increasing our understanding of the existing model, this work is crucial for further extension and refinement of the model. It settles down the framework necessary for the consideration of drugs administration effects on tumour development.
ISSN:0025-5564
1879-3134
DOI:10.1016/j.mbs.2008.11.008