A stochastic model of tumor response to fractionated radiation: Limit theorems and rate of convergence

Mathematical Biosciences

Volumn 191, Issue 1, 2004, Pages 1-17

  Hanin, Leonid G ^a,b  

^a Nucl Eng Idaho State University   (United States)

^b UNIVERSITY OF ROCHESTER   (United States)

Author keywords

Clonogenic tumor cell; Fractionated irradiation; Generalized geometric distribution; Generalized negative binomial distribution; Iterated birth and death Markov process; Law of Rare Events; Limiting distribution; Poisson distribution

Indexed keywords

CELLS; HEALTH CARE; MARKOV PROCESSES; POPULATION STATISTICS; PROBABILITY; RANDOM PROCESSES; TUMORS;

MORTALITY RATE; RANDOM VARIABLES; TUMOR CELLS;

RADIATION EFFECTS;

POPULATION SIZE; STOCHASTICITY; TUMOR;

ARTICLE; CANCER SURVIVAL; CHEMICAL PARAMETERS; KINETICS; MATHEMATICAL MODEL; PROBABILITY; RADIATION DOSE FRACTIONATION; STOCHASTIC MODEL; THEORETICAL STUDY;

CELL SURVIVAL; CLONE CELLS; DOSE FRACTIONATION; HUMANS; MARKOV CHAINS; MODELS, BIOLOGICAL; NEOPLASMS; NUMERICAL ANALYSIS, COMPUTER-ASSISTED; POISSON DISTRIBUTION; RADIATION ONCOLOGY;

EID: 4143127682     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mbs.2004.04.003     Document Type: Article

References (20)

1. Tucker S.L., Thames H.D., Taylor J.M.G. How well is the probability of tumor cure after fractionated irradiation described by Poisson statistics? Radiat. Res. 124:1990;273
2. Yakovlev A.Y., Asselain B., Bardou V.-J., Fourquet A., Hoang T., Rochefordière A., Tsodikov A.D. A simple stochastic model of tumor recurrence and its application to data on premenopausal breast cancer. Asselain B., Boniface M., Duby C., Lopez C., Masson J.-P., Tranchefort J. Biométrie et Analyse de Données Spatio-Temporelles. vol. 12:1993;66 Société Française de Biométrie, ENSA, Rennes, France
3. Hanin L.G. Iterated birth and death process as a model of radiation cell survival. Math. Biosci. 169:2001;89
4. Hanin L.G., Zaider M., Yakovlev A.Y. Distribution of the number of clonogens surviving fractionated radiotherapy: a long-standing problem revisited. Int. J. Radiat. Biol. 77(2):2001;205
5. Zaider M., Zelefsky M.J., Hanin L.G., Tsodikov A.D., Yakovlev A.Y., Leibel S.A. A survival model for fractionated radiotherapy with an application to prostate cancer. Phys. Med. Biol. 46:2001;2745
6. Kendal W.S. A closed-form description of tumour control with fractionated radiotherapy and repopulation. Int. J. Radiat. Biol. 73:1998;207
7. Zaider M., Minerbo G.N. Tumor control probability: a formulation applicable to any protocol of dose delivery. Phys. Med. Biol. 45:2000;279
8. Okada S. Radiation Biochemistry. Cells. vol. 1:1970;Academic Press, New York
9. Weiss B.G. Perturbations in precursor incorporation into DNA of X-irradiated HeLA S3 cells. Radiat. Res. 48:1971;128
10. Mitchell J.B., Bedford J.S., Bailey S.M. Observations of the first postirradiation division of HeLa cells following continuous or fractionated exposure to γ rays. Radiat. Res. 80:1979;186
11. Tucker S.L., Taylor J.M.G. Improved models of tumour cure. Int. J. Radiat. Biol. 70:1996;539
12. Klein M., Bartoszyński R. Estimation of growth and metastatic rates of primary breast cancer. Arino O., Axelrod D.E., Kimmel M. Mathematical Population Dynamics. 1991;397 Marcel Dekker, New York
13. Tucker S.L. Modeling the probability of tumor cure after fractionated radiotherapy. Horn M.A., Simonett G., Webb G. Mathematical Models in Medical and Health Sciences. 1999;1 Vanderbilt University, Nashville
14. Taylor H.M., Karlin S. An Introduction to Stochastic Modeling. 3rd Ed.:1998;Academic Press, San Diego, CA
15. Harris T.E. The Theory of Branching Processes. 1963;Springer, Berlin
16. Karlin S. A First Course In Stochastic Processes. 1966;Academic Press, New York, London
17. Kendall D.G. On the generalized "birth and death" process. Ann. Math. Stat. 19:1948;1
18. Athreya K.B., Ney P.E. Branching Processes. 1972;Springer, New York
19. Asmussen S., Hering H. Branching Processes. 1983;Birkhäuser, Boston
20. Hall E.J. Radiobiology for the Radiologist. 4th Ed.:1994;Lippincott-Raven