Mathematical Models of Avascular Tumor Growth
- 1 January 2007
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Review
- Vol. 49 (2), 179-208
- https://doi.org/10.1137/s0036144504446291
Abstract
This review will outline a number of illustrative mathematical models describing the growth of avascular tumours. The aim of the review is to provide a relatively comprehensive list of existing models in this area and discuss several representative models in greater detail. In the latter part of the review, some possible future avenues of mathematical modelling of avascular tumour development are outlined together with a list of key questionsKeywords
This publication has 99 references indexed in Scilit:
- An error catastrophe in cancer?Journal of Theoretical Biology, 2004
- Model of the developing tumorigenic phenotype in mammalian cells and the roles of sustained stress and replicative senescenceJournal of Theoretical Biology, 2004
- A cellular automaton model for tumour growth in inhomogeneous environmentJournal of Theoretical Biology, 2003
- Intercellular Adhesion and Cancer Invasion: A Discrete Simulation Using the Extended Potts ModelJournal of Theoretical Biology, 2002
- The Different Effects of Apoptosis and DNA Repair on TumorigenesisJournal of Theoretical Biology, 2002
- A Biokinetic Model to Describe Consequences of Inhibition/Stimulation in DNA-Proofreading and Repair—1. Development of the ModelJournal of Theoretical Biology, 2001
- Simulated Brain Tumor Growth Dynamics Using a Three-Dimensional Cellular AutomatonJournal of Theoretical Biology, 2000
- On Rugged Shape of Skin Tumor (Basal Cell Carcinoma)Journal of Theoretical Biology, 1998
- Cellular and geometric control of tissue growth and mitotic instabilityJournal of Theoretical Biology, 1976
- On the growth and stability of cell cultures and solid tumorsJournal of Theoretical Biology, 1976