Solutions for the cell cycle in cell lines derived from human tumors

Computational and Mathematical Methods in Medicine

Volumn 7, Issue 4, 2006, Pages 215-228

  Zubik Kowal, B ^a  

^a BOISE STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CELL CULTURE; CHEMOTHERAPY; FUNCTIONS; TUMORS;

HUMAN CANCER CELLS; HUMAN TUMOR CELLS; HUMAN TUMORS; INDEPENDENT VARIABLES; MODEL EQUATIONS; NUMBER DENSITY; POPULATION KINETICS; TIME VARIABLE;

CELLS;

CELL DNA;

ACCURACY; ARTICLE; CANCER GROWTH; CELL CYCLE; CELL CYCLE G1 PHASE; CELL CYCLE G2 PHASE; CELL CYCLE M PHASE; CELL DENSITY; CELL POPULATION; CONTROLLED STUDY; DNA CONTENT; IN VITRO STUDY; INDEPENDENT VARIABLE; MATHEMATICAL MODEL; MATHEMATICAL VARIABLE; PREDICTION; SIMULATION; TUMOR CELL LINE;

EID: 34547428408     PISSN: 1748670X     EISSN: 17486718     Source Type: Journal    
DOI: 10.1080/10273660601017254     Document Type: Article

References (23)

1. Basse, B., Baguley, B. C., Marshall, E. S., Joseph, W. R., van Brunt, B., Wake, G. C. and Wall, D. J. N. (2003) A mathematical model for analysis of the cell cycle in cell lines derived from human tumours. Journal of Mathematical Biology, 47, pp. 295-312.
2. Hoffman, I. and Karsenti, E. (1994) The role of cdc25 in checkpoints and feedback controls in the eukaryotic cell cycle. Journal of Cell Science, 18, pp. 75-79.
3. Prescot, D. M. (1987) Cell reproduction. International Review of Cytology, 100, pp. 93-128.
4. Smith, J. A. and Martin, L. (1973) Do cells cycle?. Proceedings of the National Academy of Sciences USA, 70, pp. 1263-1267.
5. Watson, J. V. (1991) Tumour growth dynamics. British Medical Bulletin, 47, pp. 47-63.
6. Wilson, G. D., McNally, N. J., Dische, S., Saunders, M. I., Rochers, C. Des, Lewis, A. A. and Bennet, M. H. (1988) Measurement of cell kinetics in human tumours in vivo using bromodeoxyuridine incorporation and low cytometry. British Journal of Cancer, 58, pp. 423-431.
7. Bell, G. and Anderson, E. (1967) Cell growth and division. Mathematical model with applications to cell volume distributions in mammalian suspension cultures. Biophysics Journal, 7, pp. 329-351.
8. Diekmann, O., Heijmans, H. J. A. M. and Thieme, H. R. (1983) On the stability of the cell size distribution. Journal of Mathematical Biology, 19, pp. 227-248.
9. Diekmann, O. (1984) Growth, fission and the stable size distribution. Journal of Mathematical Biology, 18, pp. 135-148.
10. Hall, A. J. and Wake, G. C. (1989) A functional differential equation arising in the modelling of cell-growth. Journal of Australian Mathematical Society Series B, 30, pp. 424-435.
11. Hannsgen, K. B. and Tyson, J. J. (1985) Stability of the steady-state size distribution in a model of cell growth and division. Journal of Mathematical Biology, 22, pp. 293-301.
12. Montalenti, F., Sena, G., Cappella, P. and Ubezio, P. (1999) Simulating cancer-cell kinetics after treatment: Application to cisplatin on ovarian carcinoma. Physical Review E, 57:5, pp. 5877-5887.
13. Priori, L. and Ubezio, P. (1996) Mathematical modelling and computer simulation of cell synchrony. Methods in cell science, 18, pp. 83-91.
14. Rossa, B. (1995) Asynchronous exponential growth in a size structured cell population with quiescent compartment. Volume 2: Carcinogenesis and Cell & Tumor Growth of Arino et al., [1], pp. 183-200.
15. Sena, G., Onado, C., Cappella, P., Montalenti, F. and Ubezio, P. (1999) Measuring the complexity of cell cycle arrest and killing of drugs: kinetics of phase-specific effects induced by taxol. Cytometry, 37, pp. 113-124.
16. Sinko, S. and Streifer, W. (1967) A new model for age-size structure of a population. Ecology, 48, pp. 330-335.
17. Tyson, J. J. and Hannsgen, K. B. (1985) Global asymptotic stability of the cell size distribution in probabilistic models of the cell cycle. Journal of Mathematical Biology, pp. 61-68.
18. Ubezio, P. (1990) Cell cycle simulation for flow cytometry. Computer methods and programs in biomedicine. Section II. Systems and Programs, 31:3697, pp. 255-266.
19. van Leer, B. (1985) Upwind-difference methods for aerodynamic problems governed by the Euler equations. Large Scale Computations in Fluid Mechanics, pp. 327-336. American Mathematical Society
20. Basse, B., Baguley, B. C., Marshall, E. S., Joseph, W. R., van Brunt, B., Wake, G. C. and Wall, D. J. N. (2004) Modelling cell death in human tumour cell lines exposed to the anticancer drug paclitaxel. Journal of Mathematical Biology, 49, pp. 329-357.
21. Basse, B., Baguley, B. C., Marshall, E. S., Wake, G. C. and Wall, D. J. N. (2004) Modelling cell population growth with applications to cancer therapy in human tumour cell lines. Progress in Biophysics and Molecular Biology, 85, pp. 353-368.
22. Basse, B., Wake, G. C., Wall, D. J. N. and van Brunt, B. (2004) On a cell growth model for plankton. Mathematical Medicine and Biology: A Journal of the IMA, 21, pp. 49-61.
23. Basse, B., Baguley, B. C., Marshall, E. S., Wake, G. C. and Wall, D. J. N. (2005) Modelling the flow cytometric data obtained from unperturbed human tomour cell lines: Parameter fitting and comparison. Bulletin of Mathematical Biology, 67:4, pp. 815-830.