Computational and Mathematical Methods in Medicine
Volume 7 (2006), Issue 4, Pages 215-228

Solutions for the Cell Cycle in Cell Lines Derived from Human Tumors

Department of Mathematics, Boise State University, 1910 Boise University Drive, Boise, Idaho 83725, USA

Received 21 February 2006; Revised 2 August 2006; Accepted 10 August 2006

Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The goal of the paper is to compute efficiently solutions for model equations that have the potential to describe the growth of human tumor cells and their responses to radiotherapy or chemotherapy. The mathematical model involves four unknown functions of two independent variables: the time variable t and dimensionless relative DNA content x. The unknown functions can be thought of as the number density of cells and are solutions of a system of four partial differential equations. We construct solutions of the system, which allow us to observe the number density of cells for different t and x values. We present results of our experiments which simulate population kinetics of human cancer cells in vitro. Our results show a correspondence between predicted and experimental data.