From cell population models to tumor control probability: Including cell cycle effects

Acta Oncologica

Volumn 49, Issue 8, 2010, Pages 1315-1323

  Hillen, Thomas ^a   De Vries, Gerda ^a   Gong, Jiafen ^a   Finlay, Chris ^a  

^a UNIVERSITY OF ALBERTA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CANCER RADIOTHERAPY; CELL CYCLE; CELL POPULATION; CELL PROLIFERATION; CELL SURVIVAL; PRIORITY JOURNAL; PROBABILITY SAMPLE; PROSTATE CANCER; STATISTICAL CONCEPTS; TUMOR CONTROL PROBABILITY; TUMOR MODEL;

CELL CYCLE; CELL LINE, TUMOR; CELL SURVIVAL; DOSE-RESPONSE RELATIONSHIP, RADIATION; HUMANS; MALE; MATHEMATICAL COMPUTING; MODELS, STATISTICAL; NEOPLASTIC STEM CELLS; POISSON DISTRIBUTION; PROBABILITY; PROSTATIC NEOPLASMS; RADIOTHERAPY DOSAGE; RADIOTHERAPY PLANNING, COMPUTER-ASSISTED; STOCHASTIC PROCESSES;

EID: 77958184147     PISSN: 0284186X     EISSN: 1651226X     Source Type: Journal    
DOI: 10.3109/02841861003631487     Document Type: Article

References (39)

1. Munro TR, Gilbert CW. The relation between tumor lethal doses and the radiosensitivity of tumour cells. Br J Radiol 1961;34:246-51.
2. Masunaga S, Ono K, Akuta K, Akaboshi M, Abe M, Ando K, et al. The radiosensitivity of quiescent cell populations in murine solid tumors in irradiation with fast neutrons. Int J Radiat Oncol Biol Phys 1994;29:239-42. (Pubitemid 24166525)
3. Prescott DM, Flexer AS. Cancer: The misguided cell. Massachusetts: Sinauer Assoc. Inc.; 1982.
4. Lea DE. Actions of radiation on living cells. 2nd ed. New York: Cambridge University Press; 1955.
5. Chadwick KH, Leenhouts HP. The molecular theory of radiation biology. Berlin: Springer-Verlag; 1981.
6. Tobias CA, Blakeley EA, Ngo F Q H, Yang T C H. The repairmisrepair model of cell survival. In RE Meyn and HR Withers, editors. Radiation Biology and Cancer Research. New York: Raven Press; 1980. pp. 195-230.
7. Curtis SB. Lethal and potentially lethal lesions induced by radiation-a unified repair model. Radiation Res 1986;106:252-71.
8. Dale RG. Time-dependent tumor repopulation factors in linear-quadratic equations-Implications for treatment strategies. Radiother Oncol 1989;15:371-82.
9. Kellerer AM, Rossi HH. The theory of dual radiation action. Curr Top Radiat Res Q 1972;8:85-158.
10. Sachs RK, Hahnfeld P, Brenner DJ. The link between low-LET dose-response relations and the underlying kinetics of damage production/repair/misrepair. Int J Radiat Biol 1997;72:351-74.
11. Fowler JF. The linear-quadratic formula and progress in fractionated radiotherapy. Br J Radiol 1989;62:679-94.
12. Travis EL, Tucker SL. Isoeffect models and fractionated radiation-therapy. Int J Radiat Oncol Biol Phys 1987;13:283-7.
13. Maciejewski B, Withers HR, Taylor J M G, Hliniak A. Dose fractionation and regeneration in radiotherapy for cancer of the oral cavity and oropharynx-Tumor dose-response and repopulation. Int J Radiat Oncol Biol Phys 1989;16:7831-43.
14. Thames HD, Bentzen SM, Turesson I, Overgaard M, Vandenbogaert W. Time-dose factors in radiotherapy-a review of the human data. Radiother Oncol 1990;19:219-35.
15. Withers HR, Taylor J M G, Maciejewski B. The hazard of accelerated tumor clonogen repopulation during radiotherapy. Acta Oncol 1988;27:131-46.
16. Yaes RJ. Linear-quadratic model isoeffect relations for proliferating tumor-cells for treatment with multiple fractions per day. Int J Radiat Oncol Biol Phys 1989;17:901-5.
17. Tucker SL, Thames HD, Taylor J M G. How well is the probability of tumor cure after fractionated-irradiation described by poisson statistics. Radiat Res 1990;124:273-82.
18. Yakovlev AY. Comments on the distribution of clonogens in irradiated tumors. Radiat Res 1993;134:117-20.
19. Hanin LG. A stochastic model of tumor response to fractionated radiation: Limit theorems and rate of convergence. Math Biosci 2004;91:1-17.
20. Hanin LG, Zaider M, Yakovlev AY. Distribution of the number of clonogens surviving fractionated radiotherapy: A long-standing problem revisited. Int J Radiat Biol 2001;77:205-13.
21. Kendal WS. A closed-form description of tumour control with fractionated radiotherapy and repopulation. Int J Radiat Biol 1998;73:207-10.
22. Stavrev P, Weldon M, Warkentin B, Stavreva N, Fallone BG. Radiation damage, repopulation and cell recovery analysis of in vitro tumour cell megacolony culture data using a non-Poissonian cell repopulation TCP model. Phys Med Biol 2005;50:3053-61.
23. Zaider M, Minerbo GN. Tumour control probability: A formulation applicable to any temporal protocol of dose delivery. Phys Med Biol 2000;45:279-93.
24. Dawson A, Hillen T. Derivation of the tumour control prabability (TCP) from a cell cycle model. Comput Math Method Med 2006;7:121-42.
25. Yurtseven O. Effects of the cell cycle on the tumor control probability (TCP) in radiation treatment and comparison of treatment protocols. M. Sc. Thesis, University of Alberta. 2006.
26. Villasana M, Radunskaya A. A delay differential equation model for tumor growth. J Math Biol 2003;47:270-94.
27. Swanson KR, True LD, Lin DW, Buhler KR, Vessella R, Murray JD. A quantitative model for the dynamics of serum prostate-specific antigens as a marker for cancerous growth. Am J Pathol 2001;158:2195-9.
28. Basse B, Baguley BC, Marshall ES, Joseph WR, van Brunt B, Wake G, et al. A mathematical model for analysis of the cell cycle in human tumour. J Math Biol 2002;47:295-312.
29. Carlson DJ, Stewart RD, Li XA, Jennings K, Wang JZ, Guerrero M. Comparison of in vitro and in vivo α/β ratios for prostate cancer. Phys Med Biol 2004;49:4477-91.
30. Stavrev P, Stavevra N, Niemerko A, Gotein M. Generalization of a model of tissue response to radiation based on the idea of functional subunits and binomial statistics. Phys Med Biol 2001;46:1501-18.
31. 50 for different individual TCP and NTCP models. Phys Med Biol 2002;47:3591-601.
32. Stavreva NA, Stavrev PV, Warkentin B, Fallone BG. Investigating the effect of cell repopulation on the tumor response to fractionated external radiotherapy. Med Phys 2003;30:735-42.
33. Liu W, Hillen T, Freedman HI. A mathematical model for M-phase specific chemotherapy including the G0-Phase and immuno-response. Math Biosci Eng 2007;4:239-59.
34. Novak B, Toth A, Csikasz-Nagy A, Gyorffy B, Tyson JJ, Nasmyth K. Finishing the cell cycle. J Theor Biol 1999;199:223-33.
35. Webb G, Grabosch A. Asynchronous exponential growth in transition probability models of the cell cycle. SIAM J Math Anal 1987;18:897-907.
36. Maler A, Lutscher F. Cell cycle times and the tumor control probability. J Math Med Biol 2009 (in press).
37. Usher JR. Mathematical derivation of optimal uniform treatment schedules for the fractionated irradiation of human tumors. Math Biosci 1980;49:157-84.
38. McAneney A, O'Rourke S F C. Inverstigation of various growth mechanisms of solid tumor growth within the linear-quadratic model for radiotherapy. Phys Med Biol 2006;52:1039-54.
39. Gong J, Hillen T. Optimal cancer radiotherapy treatment schedules under cumulative radiation effect constraint (in preparation).