Delay differential equations and the dose-time dependence of early radiotherapy reactions

Medical Physics

Volumn 33, Issue 9, 2006, Pages 3526-3540

  Fenwick, John D ^a  

^a CLATTERBRIDGE CENTRE FOR ONCOLOGY   (United Kingdom)

Author keywords

Acute reaction; Delay differential equation; Dose time; Early reaction; Radiotherapy

Indexed keywords

DIFFERENTIAL EQUATIONS; RADIOTHERAPY; STEM CELLS; TISSUE;

ACUTE REACTION; DELAY DIFFERENTIAL EQUATIONS; DIFFERENTIAL MODELS; DOSE TIME; EARLY REACTION; FIRST-ORDER DELAY DIFFERENTIAL EQUATIONS; FRACTIONATION SCHEDULES; TOTAL RADIATION DOSE;

RADIATION EFFECTS;

ARTICLE; CELL COUNT; CELL PROLIFERATION; PRIORITY JOURNAL; RADIATION DOSE; RADIATION DOSE FRACTIONATION; STEM CELL; TISSUE INJURY;

ANIMALIA;

EID: 33745507901     PISSN: 00942405     EISSN: None     Source Type: Journal    
DOI: 10.1118/1.2241995     Document Type: Article

References (62)

1. F. A. Stewart and A. J. van der Kogel, "Proliferative and cellular organization of normal tissues," in Basic Clinical Radiobiology, 3rd ed., edited by G. G. Steel (Hodder, London, 2002) Chap. 3.
2. J. H. A. M. Kaanders, A. J. van der Kogel, and K. K. Ang, "Altered fractionation: limited by mucosal reactions?" Radiother. Oncol. 50, 247-260 (1998).
3. J. E. Moulder and J. J. Fischer, "Radiation reaction of rat skin - the role of the number of fractions and the overall treatment time," Cancer 37, 2762-2767 (1976).
4. E. van Rongen and H. B. Kal, "Acute reactions in rat feet exposed to multiple fractions of X-rays per day," Radiother. Oncol. 2, 141-150 (1984).
5. K. K. Ang, F.-X. Xu, L. Vanuytsel, and E. van der Schueren, "Repopulation kinetics in irradiated mouse lip mucosa: the relative importance of treatment protraction and time distribution of irradiations," Radiat. Res. 101, 162-169 (1985).
6. J. Denekamp, M. M. Ball and J. F. Fowler, "Recovery and repopulation in mouse skin as a function of time after X-irradiation," Radiat. Res. 37, 361-370 (1969).
7. J. Denekamp, "Changes in the rate of repopulation during multifraction irradiation of mouse skin," Br. J. Radiol. 46, 381-387 (1973).
8. J. F. Fowler, J. Denekamp, C. Delapeyre, S. R. Harris and P. W. Sheldon, "Skin reactions in mice after multifraction X-irradiation," Int. J. Radiat. Biol. Relat. Stud. Phys. Chem. Med. 25, 213-223 (1974).
9. R. W. Tsang, M. C. Joiner, A. Rojas, and H. Johns, "Repopulation in murine skin after X-ray treatments with multiple fractions per day," Radiat. Res. 125, 163-172 (1991).
10. G. J. M. J. van den Aardweg, J. W. Hopewell, and R. H. Simmonds, "Repair and recovery in the epithelial and vascular connective tissues of pig skin after irradiation," Radiother. Oncol. 11, 73-82 (1988).
11. M. Rezvani, J. W. Hopewell, G. M. Morris, D. Wilding, E. Whitehouse, M. E. C. Robbins, and M. J. F. Cortina-Borja, "Repair, repopulation and cell cycle redistribution in rat foot skin," Radiother. Oncol. 46, 193-199 (1998).
12. J. W. Hopewell, J. Nyman, and I. Turesson, "Time factor for acute tissue reactions following fractionated irradiation: a balance between repopulation and enhanced radiosensitivity," Int. J. Radiat. Biol. 79, 513-524 (2003).
13. W. Dörr and J. Kummermehr, "Accelerated repopulation of mouse tongue epithelium during fractionated irradiations or following single doses," Radiother. Oncol. 17, 249-259 (1990).
14. W. Dörr and J. Kummermehr, "Increased radiation tolerance of mouse tongue epithelium after local conditioning," Int. J. Radiat. Biol. 61, 369-379 (1992).
15. W. Dörr, A. Breitner, and J. Kummermehr, "Capacity and kinetics of SLD repair in mouse tongue epithelium," Radiother. Oncol. 27, 36-45 (1993).
16. W. Dörr, H. Emmendörfer, E. Haide, and J. Kummermehr, "The proliferative equivalent of 'accelerated repopulation' in mouse oral mucosa," Int. J. Radiat. Biol. 66, 157-167 (1994).
17. W. Dörr, "Repopulation in mouse oral mucosa: treatment splits," Radiother. Oncol. 33, 139-147 (1994).
18. W. Dörr and M. Weber-Frisch, "Repopulation response of mouse oral mucosa during unconventional radiotherapy protocols," Radiother. Oncol. 37, 230-236 (1995).
19. W. Dörr and M. Weber-Frisch, "Effect of changing weekly dose on accelerated repopulation during fractionated irradiation of mouse tongue mucosa," Int. J. Radiat. Biol. 67, 577-585 (1995).
20. W. Dörr, K. Brankovic, and B. Hartmann, "Repopulation in mouse oral mucosa: changes in the effect of dose fractionation," Int. J. Radiat. Biol. 76, 383-390 (2000).
21. A. Shirazi, K. Liu, and K. R. Trott, "Epidermal morphology, cell proliferation and repopulation in mouse skin during daily fractionated irradiation," Int. J. Radiat. Biol. 68, 215-221 (1995).
22. W. Dörr, "Three A's of repopulation during fractionated irradiation of squamous epithelia: Asymmetry loss, Acceleration of stem-cell divisions and Abortive divisions," Int. J. Radiat. Biol. 72, 635-643 (1997).
23. J. F. Fowler, P. M. Harari, F. Leborgne, and J. H. Leborgne, "Acute radiation reactions in oral and pharyngeal mucosa: tolerable levels in altered fractionation schedules," Radiother. Oncol. 69, 161-168 (2003).
24. E. L. Travis and S. L. Tucker, "Isoeffect models and fractionated radiotherapy," Int. J. Radiat. Oncol., Biol., Phys. 13, 283-287 (1987).
25. J. F. Fowler, "The linear-quadratic formula and progress in fractionated radiotherapy: A review," Br. J. Radiol. 62, 679-694 (1989).
26. W. Dörr, C. S. Hamilton, T. Boyd, B. Reed and J. W. Denham, "Radiation-induced changes in cellularity and proliferation in human oral mucosa," Int. J. Radiat. Oncol., Biol., Phys. 52, 911-917 (2002).
27. G. M. Morris, "Review article: Effects of radiation on the cell proliferation kinetics of epithelial tissues - therapeutic implications," Br. J. Radiol. 69, 795-803 (1996).
28. G. H. Fletcher, W. S. MacComb, and R. J. Shalek, Radiation Therapy in the Management of the Oral Cavity and Oropharynx (Thomas, Springfield, MO, 1962), p. 51.
29. W. Dörr and M. N. Obeyesekere, "A mathematical model for cell density and proliferation in squamous epithelium after single-dose irradiation," Int. J. Radiat. Biol. 77, 497-505 (2001).
30. J. W. Denham, Q. J. Walker, D. S. Lamb, C. S. Hamilton, P. C. O'Brien, N. A. Spry, A. Hindley, M. Poulsen, M. O'Brien, and L. Tripcony, "Mucosal regeneration during radiotherapy," Radiother. Oncol. 41, 109-118 (1996).
31. J. W. Denham and T. Kron, "Extinction of the weakest," Int. J. Radiat. Oncol., Biol., Phys. 51, 807-819 (2001).
32. N. MacDonald, Biological Delay Systems: Linear Stability Theory (Cambridge University Press, Cambridge, UK, 1989).
33. J. D. Murray, Mathematical Biology I: An Introduction, 3rd ed. (Springer-Verlag, New York, 2002), Chaps. 1-3.
34. A. Beuter, L. Glass, M. C. Mackey, and M. S. Titcombe (eds.), Nonlinear Dynamics in Physiology and Medicine (Springer-Verlag, New York, 2003), Chaps. 1-3, 8.
35. J. D. Farmer, "Chaotic attractors of an infinite-dimensional dynamical system," Physica D 4, 366-393 (1982).
36. G. G. Steel, "Cell survival as a determinant of tumour response," in Basic Clinical Radiobiology, 3rd ed., edited by G. G. Steel (Hodder, London, 2002), Chap. 6.
37. S. M. Bentzen and M. Baumann, "The linear-quadratic model in clinical practice," in Basic Clinical Radiobiology, edited by G. G. Steel (Hodder, London, 2002) Chap., 13.
38. T. E. Wheldon, Mathematical Models in Cancer Research (IOP, Bristol, UK, 1988), Chap. 8.
39. T. E. Wheldon, Mathematical Models in Cancer Research (IOP, Bristol, UK, 1988), Chap. 5.
40. N. R. Drapper and H. Smith, Applied Regression Analysis, 2nd ed. (Wiley, New York, 1981).
41. J. O. Rawlings, Applied Regression Analysis: A Research Tool (Wadsworth and Brooks, Belmont CA, 1988), Chap. 10.
42. F. J. Keller, W. E. Gettys, and M. J. Skove, Physics Classical and Modern, 2nd ed. (McGraw-Hill, New York, 1993), Chap. 14.
43. J. O. Archambeau and G. W. Bennett, "Quantification of Morphologic, Cytologic and Kinetic Parameters of Unirradiated Swine Skin: A Histological Model," Radiat. Res. 98, 254-273 (1984).
44. G. M. Morris and J. W. Hopewell, "Cell population kinetics in pig epidermis: further studies," Cell Tissue Kinet. 20, 161-169 (1987).
45. D. Barthel, B. Matthé, C. S. Potten, G. Owen, and M. Loeffler, "Proliferation in murine epidermis after minor mechanical stimulation Part 2. Alterations in keratinocyte fluxes," Cell Prolif 33, 247-259 (2000).
46. G. M. Morris, G. J. M. J. van den Aardweg, R. Hamlet, E. Whitehouse, J. W. Hopewell, H. Franke, and M. Loeffler, "Age-related changes in the cell kinetics of rat foot epidermis," Cell Tissue Kinet. 23, 113-123 (1990).
47. G. M. Morris, W. Landuyt, E. Whitehouse, L. Vanuytsel, and J. W. Hopewell, "Radiation response of mouse lip mucosal epithelium: a cell kinetic study," Int. J. Radiat. Biol. 63, 509-517 (1993).
48. C. S. Potten, D. Booth, N. J. Cragg, G. L. Tudor, J. A. O'Shea, D. Appleton, D. Barthel, T. G. Gerike, F. A. Meineke, M. Loeffler, and C. Booth, "Cell kinetic studies in the murine ventral tongue epithelium: thymidine metabolism studies and circadian rhythm determination," Cell Prolif 35(Suppl. 1), 1-15 (2002).
49. W. Dörr and J. Kummermehr, "Proliferation kinetics of mouse tongue epithelium under normal conditions and following single dose irradiation," Virchows Arch. B 60, 287-294 (1991).
50. B. Maciejewski, K. Skladowski, B. Pilecki, J. M. G. Taylor, R. H. Withers, L. Miszczyk, A. Zajusz, and R Suwinski, "Randomized clinical trial on accelerated 7 days per week fractionation in radiotherapy for head and neck cancer. Preliminary report on acute toxicity," Radiother. Oncol. 40, 137-145 (1996).
51. K. Skladowski, B Maciejewski, M. Golen, B. Pilecki, W. Przeorek, and R. Tarnawski, "Randomized clinical trial on 7-day-continuous accelerated irradiation (CAIR) of head and neck cancer - report on 3-years tumour control and normal tissue toxicity," Radiother. Oncol. 55, 101-110 (2000).
52. R. Tarnawski, J. Fowler, K. Skladowski, A. Świerniak, R. Suwiński, B. Maciejewski, and A. Wygoda, "How fast is repopulation of tumor cells during the treatment gap?," Int. J. Radiat. Oncol., Biol., Phys. 54, 229-236 (2002).
53. S. Pabst, K. Spekl, and W. Dörr, "Changes in the effect of dose fractionation during daily fractionated irradiation: studies in mouse oral mucosa," Int. J. Radiat. Oncol., Biol., Phys. 58, 485-492 (2004).
54. I. Turesson and H. D. Thames, "Repair capacity and kinetics of human skin during fractionated radiotherapy: Erythema, desquamation, and telangiectasia after 3 and 5 years's follow-up," Radiother. Oncol. 15, 169-188 (1989).
55. P. M. Harari, "Adding dose escalation to accelerated hyperfractionation for head and neck cancer: 76 Gy in 5 weeks," Semin. Radiat. Oncol. 2, 58-61 (1992).
56. C. H. J. Terhaard, H. B. Kal, and G.-J. Hordijk, "Why to start the concomitant boost in accelerated radiotherapy for advanced laryngeal cancer in week 3," Int. J. Radiat. Oncol., Biol., Phys. 62, 62-69 (2005).
57. G. P. Delaney, R. J. Fisher, R. J. Smee, C. Kook, and M. B. Barton, "Split-course accelerated therapy in head and neck cancer: an analysis of toxicity," Int. J. Radiat. Oncol., Biol., Phys. 32, 763-768 (1995).
58. T. D. Nguyen, X. Panis, M. Legros, and D. Froissart, " Hyperfractionated radiotherapy in advanced squamous cell carcinoma of the head and neck," Int. J. Radiat. Oncol., Biol., Phys. 9, 393-395 (1983).
59. M. Villasana and A. Radunskaya, "A delay differential equation model for tumor growth," J. Math. Biol. 47, 270-294 (2003).
60. E. A. Gaffney, "The application of mathematical modelling to aspects of adjuvant chemotherapy scheduling," J. Math. Biol. 48, 375-422 (2004).
61. F. J. Keller, W. E. Gettys, and Skove M. J., Physics Classical and Modern (2nd edition - McGraw-Hill, New York, U.S.A., 1993), Chap. 14.
62. W. H. Press, S. A. Teulovsky, W. T. Vetterling, and B. P. Flannery Numerical Recipes in C: The Art of Scientific Computing (2nd edition - Cambridge University Press, Cambridge, U. K., 1992).