## Abstract

A traditional model of the cell cycle has been used, with the addition of a resting (G//0) state from which cells could reenter the reproductive cycle. The model assumes that a growth regulatory substance regulates the transition of cells to and from the resting state. Other transitions between the phases of the cycle were modeled as a first order process. Cell loss is an important feature of growth kinetics, and has been represented by a general but tractable mathematical form. The resulting model forms a system of ordinary nonlinear differential equations. Analytic methods are employed first in the study of this system. Simplifying assumptions regarding cell loss give rise to special cases for which equilibrium solutions can be found. One special case, which assumes first order loss from all cell cycle phases at equal rates, is presented here. Simulation methods were used to further characterize the behavior of this model. Parameter values were chosen based on animal tumor cell cycle kinetic data, resulting in a set of 45 model simulations. Several tumor treatment protocols were simulated which illustrated the importance of the intrinsic growth rate and cell loss concepts.

Original language | English (US) |
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Pages (from-to) | 293-306 |

Number of pages | 14 |

Journal | Mathematical Biosciences |

Volume | 66 |

Issue number | 2 |

State | Published - Jan 1 1983 |

## ASJC Scopus subject areas

- Statistics and Probability
- Modeling and Simulation
- Biochemistry, Genetics and Molecular Biology(all)
- Immunology and Microbiology(all)
- Agricultural and Biological Sciences(all)
- Applied Mathematics