May 21, 2015

A non-local model for cancer stem cells and the tumor growth paradox

BioRxiv : the Preprint Server for Biology
I BorsiThomas Hillen


The "tumor growth paradox" refers to the observation that incomplete treatment of cancers can enhance their growth. As shown here and elsewhere, the existence of cancer stem cells (CSC) can explain this effect. CSC are less sensitive to treatments, hence any stress applied to the tumor selects for CSC, thereby increasing the fitness of the tumor. In this paper we use a mathematical model to understand the role of CSC in the progression of cancer. Our model is a rather general system of integro-differential equations for tumor growth and tumor spread. Such a model has never been analysed, and we prove results on local and global existence of solutions, their uniqueness and their boundedness. We show numerically that this model exhibits the tumor growth paradox for all parameters tested. This effect becomes more relevant for small renewal rate of the CSC.

  • References
  • Citations


  • We're still populating references for this paper, please check back later.
  • References
  • Citations


  • This paper may not have been cited yet.

Mentioned in this Paper

Cancer Progression
Tumor Growth
Malignant Neoplasms
Cancer Stem Cells
Disease Progression

About this Paper

Related Feeds

BioRxiv & MedRxiv Preprints

BioRxiv and MedRxiv are the preprint servers for biology and health sciences respectively, operated by Cold Spring Harbor Laboratory. Here are the latest preprint articles (which are not peer-reviewed) from BioRxiv and MedRxiv.

Related Papers

Mathematical Medicine and Biology : a Journal of the IMA
I BorsiThomas Hillen
Mathematical Biosciences
A FasanoM Primicerio
Acta Biotheoretica
Angélique Perrillat-MercerotRémy Guillevin
Mathematical Biosciences and Engineering : MBE
Thierry ColinOlivier Saut
Proceedings of the National Academy of Sciences of the United States of America
W J Trjitzinsky
© 2020 Meta ULC. All rights reserved