Abstract
A model for normal and abnormal tissue growth is defined by a system of differential equations. The model consists of a proliferating compartment, which is characterized by a decreasing growth rate, and a nonproliferating one. The compartments are also parametrized by their death and transfer rates. A stability analysis of the system shows in a precise way how abnormal growth may result from a perturbation of the parameters leading to a change in an equilibrium of the tissue size.
Similar content being viewed by others
Literature
Barrett, J. C. 1966. “A Mathematical Model of the Mitotic Cycle and its Application to the Interpretation of Percentage Labeled Mitosis Date.”J. Natn. Cancer Inst.,37, 443–450.
Bronk, B. V. 1969. “On Radioactive Labeling of Proliferating Cells: the Graph of Labeled Mitosis.”J. Theor. Biol.,22, 468–492.
Deakin, M. A. B. 1970. “Gompertz Curves. Allometry and Embryogenesis.”Bull. Math. Biophys.,32, 445–452.
Fried, J. 1970. “A Mathematical Model to Aid in the Interpretation of Radioactive Tracer Data from Proliferating Cell Populations.”Math. Biosci.,8, 379–396.
Mendelsohn, M. L. and L. A. Dethlefson. 1968. “Tumour Growth and Cellular Kinetics.” InThe Proliferation and Spread of Neoplastic Cells. Baltimore: Williams & Wilkins Co.
Shock, N. W. and M. F. Morales. 1942. “A Fundamental Form for the Differential Equations of Colonial and Organism Growth.”Bull. Math. Biophys.,4, 63–71.
Simpson-Herren, L. and H. Lloyd. 1970. “Kinetic Parameters and Growth Curves for Experimental Tumor Systems.”Cancer Chemother. Rep.,51, 143–174.
Skipper, H. F. 1971. “Kinetics of Mammary Tumor Cell Growth and Implications for Therapy.”Cancer,28, 1479–1499.
Takahashi, M. 1966. “Theoretical Basis for Cell Cycle Analysis. I. Labeled Mitosis Wave Method.”J. Theor. Biol.,13, 202–211.
— 1968. “Theoretical Basis for Cell Cycle Analysis. II. Further Studies on Labeled Mitosis Wave Method.”J. Theor. Biol.,18, 195–209.
Trucco, E. and P. J. Brockwell. 1968. “Percentage Labeled Mitosis Curves in Exponentially Growing Cell Populations.”J. Theor. Biol. 20, 321–337.
Von Foerster, H. 1959. “Some Remarks on Changing Populations.” InThe Kinetics of Cellular Proliferation, Ed. F. Stohlman, Jr. New York: Grune & Stratton, Inc.
Quastler, H. and F. G. Sherman. 1959. “Cell Population Kinetics in the Intestinal Epithelium of the Mouse.”Exp. Cell Res.,17, 420–438.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Eisen, M., Schiller, J. Stability analysis of normal and neoplastic growth. Bltn Mathcal Biology 39, 597–605 (1977). https://doi.org/10.1007/BF02461205
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02461205