title: Quiescence as an explanation of Gompertzian tumor growth revisited.
abstract: Gompertz's empirical equation remains the most popular one in describing cancer cell population growth in a wide spectrum of bio-medical situations due to its good fit to data and simplicity. Many efforts were documented in the literature aimed at understanding the mechanisms that may support Gompertz's elegant model equation. One of the most convincing efforts was carried out by Gyllenberg and Webb. They divide the cancer cell population into the proliferative cells and the quiescent cells. In their two dimensional model, the dead cells are assumed to be removed from the tumor instantly. In this paper, we modify their model by keeping track of the dead cells remaining in the tumor. We perform mathematical and computational studies on this three dimensional model and compare the model dynamics to that of the model of Gyllenberg and Webb. Our mathematical findings suggest that if an avascular tumor grows according to our three-compartment model, then as the death rate of quiescent cells decreases to zero, the percentage of proliferative cells also approaches to zero. Moreover, a slow dying quiescent population will increase the size of the tumor. On the other hand, while the tumor size does not depend on the dead cell removal rate, its early and intermediate growth stages are very sensitive to it.
authors: Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia.
authors: E O
authors: EO
authors: Alzahrani
authors: Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia.
authors: Asim
authors: A
authors: Asiri
authors: Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia; Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt.
authors: M M
authors: MM
authors: El-Dessoky
authors: School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, USA. Electronic address: kuang@asu.edu.
authors: Y
authors: Y
authors: Kuang
mesh_terms: D016923:Cell Death / Q000502:physiology*; D006801:Humans; D008954:Models, Biological; D009369:Neoplasms / Q000473:pathology*
keywords: Proliferation; Quiescence; Stability; Steady state; Tumor model