A generalized linear-quadratic model for radiosurgery, stereotactic body radiation therapy, and high-dose rate brachytherapy

Science Translational Medicine

Volumn 2, Issue 39, 2010, Pages

  Wang, Jian Z ^a   Huang, Zhibin ^a   Lo, Simon S ^a   Yuh, William T C ^a   Mayr, Nina A ^a  

^a OHIO STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANIMAL CELL; ARTICLE; BRACHYTHERAPY; CELL SURVIVAL; CHO CELL; CONTROLLED STUDY; DOSIMETRY; GENERALIZED LINEAR QUADRATIC MODEL; MATHEMATICAL MODEL; MOUSE; NONHUMAN; PRIORITY JOURNAL; RADIATION DOSE FRACTIONATION; RADIATION RESPONSE; RADIOLOGICAL PARAMETERS; STEREOTACTIC BODY RADIATION THERAPY; STEREOTACTIC RADIOSURGERY; ANIMAL; METHODOLOGY; PNEUMONIA; RADIOSURGERY; STATISTICAL MODEL;

ANIMALS; BRACHYTHERAPY; DOSE-RESPONSE RELATIONSHIP, RADIATION; LINEAR MODELS; MICE; PNEUMONIA; RADIOSURGERY;

EID: 77955623159     PISSN: 19466234     EISSN: 19466242     Source Type: Journal    
DOI: 10.1126/scitranslmed.3000864     Document Type: Article

References (57)

1. D. E. Lea, D. G. Catcheside, The mechanism of the induction by radiation of chromosome aberrations in Tradescantia. J. Genet. 44, 216-245 (1942).
2. D. E. Lea, Actions of Radiations on Living Cells (Cambridge Univ. Press, Cambridge, 1947).
3. A. M. Kellerer, H. H. Rossi, The theory of dual radiation action. Curr. Top. Radiat. Res. Q. 8, 85-158 (1972).
4. G. W. Barendsen, Dose fractionation, dose rate and iso-effect relationships for normal tissue responses. Int. J. Radiat. Oncol. Biol. Phys. 8, 1981-1997 (1982).
5. R. G. Dale, The application of the linear-quadratic dose-effect equation to fractionated and protracted radiotherapy. Br. J. Radiol. 58, 515-528 (1985).
6. H. D. Thames, An 'incomplete-repair' model for survival after fractionated and continuous irradiations. Int. J. Radiat. Biol. Relat. Stud. Phys. Chem. Med. 47, 319-339 (1985).
7. J. F. Fowler, The linear-quadratic formula and progress in fractionated radiotherapy. Br. J. Radiol. 62, 679-694 (1989).
8. R. K. Sachs, P. Hahnfeld, D. J. Brenner, The link between low-LET dose-response relations and the underlying kinetics of damage production/repair/misrepair. Int. J. Radiat. Biol. 72, 351-374 (1997).
9. D. J. Brenner, E. J. Hall, Conditions for the equivalence of continuous to pulsed low dose rate brachytherapy. Int. J. Radiat. Oncol. Biol. Phys. 20, 181-190 (1991).
10. R. G. Dale, Radiobiological assessment of permanent implants using tumour repopulation factors in the linear-quadratic model. Br. J. Radiol. 62, 241-244 (1989).
11. B. Jones, M. Cominos, R. G. Dale, Application of biological effective dose (BED) to estimate the duration of symptomatic relief and repopulation dose equivalent in palliative radiotherapy and chemotherapy. Int. J. Radiat. Oncol. Biol. Phys. 55, 736-742 (2003).
12. D. J. Brenner, L. R. Hlatky, P. J. Hahnfeldt, E. J. Hall, R. K. Sachs, A convenient extension of the linear-quadratic model to include redistribution and reoxygenation. Int. J. Radiat. Oncol. Biol. Phys. 32, 379-390 (1995).
13. B. Jones, R. G. Dale, A. M. Gaya, Linear quadratic modeling of increased late normal-tissue effects in special clinical situations. Int. J. Radiat. Oncol. Biol. Phys. 64, 948-953 (2006).
14. J. F. Fowler, Rapid repopulation in radiotherapy: A debate on mechanism. The phantom of tumor treatment - continually rapid proliferation unmasked. Radiother. Oncol. 22, 156-158 (1991).
15. E. Shaw, C. Scott, L. Souhami, R.Dinapoli, R. Kline, J. Loeffler, N. Farnan, Single dose radiosurgical treatment of recurrent previously irradiated primary brain tumors and brain metastases: Final report of RTOG protocol 90-05. Int. J. Radiat. Oncol. Biol. Phys. 47, 291-298 (2000).
16. S. S. Lo, A. J. Fakiris, L. Papiez, R. Abdulrahman, R. C. McGarry, M. A. Henderson, J. A. Forquer, D. Hoopes, R. D. Timmerman, Stereotactic body radiation therapy for early-stage non-small-cell lung cancer. Expert Rev. Anticancer Ther. 8, 87-98 (2008).
17. S. S. Lo, H. R. Cardenes, B. S. Teh, A. J. Fakiris, M. A. Henderson, L. Papiez, R. C. McGarry, J. Z. Wang, K. Li, N. A. Mayr, R. D. Timmerman, Stereotactic body radiation therapy for nonpulmonary primary tumors. Expert Rev. Anticancer Ther. 8, 1939-1951 (2008).
18. S. S. Lo, A. J. Fakiris, B. S. Teh, H. R. Cardenes, M. A. Henderson, J. A. Forquer, L. Papiez, R. C. McGarry, J. Z. Wang, K. Li, N. A. Mayr, R. D. Timmerman, Stereotactic body radiation therapy for oligometastases. Expert Rev. Anticancer Ther. 9, 621-635 (2009).
19. S. S. Lo, A. J. Fakiris, E. L. Chang, N. A. Mayr, J. Z. Wang, L. Papiez, B. S. Teh, R. C. McGarry, H. R. Cardenes, R. D. Timmerman, Stereotactic body radiation therapy: A novel treatment modality. Nat. Rev. Clin. Oncol. 7, 44-54 (2010).
20. L. Liu, D. A. Bassano, S. C. Prasad, S. S. Hahn, C. T. Chung, The linear-quadratic model and fractionated stereotactic radiotherapy. Int. J. Radiat. Oncol. Biol. Phys. 57, 827-832 (2003).
21. J. F. Fowler, The radiobiology of prostate cancer including new aspects of fractionated radiotherapy. Acta Oncol. 44, 265-276 (2005).
22. H. A. Gay, C. H. Sibata, R. R. Allison, B. Jeremic, Isodose-based methodology for minimizing the morbidity and mortality of thoracic hypofractionated radiotherapy. Radiother. Oncol. 91, 369-378 (2009).
23. L. B. Marks, Extrapolating hypofractionated radiation schemes from radiosurgery data: Regarding Hall et al., IJROBP 21:819-824; 1991 and Hall and Brenner, IJROBP 25:381-385; 1993. Int. J. Radiat. Oncol. Biol. Phys. 32, 274-276 (1995).
24. M. Guerrero, X. A. Li, Extending the linear-quadratic model for large fraction doses pertinent to stereotactic radiotherapy. Phys. Med. Biol. 49, 4825-4835 (2004).
25. J. Z. Wang, N. A. Mayr, W. T. C. Yuh, A generalized linear-quadratic formula for high-doserate brachytherapy and radiosurgery. Int. J. Radiat. Oncol. Biol. Phys. 69, S619-S620 (2007).
26. C. Park, L. Papiez, S. Zhang, M. Story, R. D. Timmerman, Universal survival curve and single fraction equivalent dose: Useful tools in understanding potency of ablative radiotherapy. Int. J. Radiat. Oncol. Biol. Phys. 70, 847-852 (2008).
27. M. Astrahan, Some implications of linear-quadratic-linear radiation dose-response with regard to hypofractionation. Med. Phys. 35, 4161-4172 (2008).
28. M. C. Joiner, Quantifying cell kill and cell survival. In Basic Clinical Radiobiology, M. C. Joiner, A. J. van der Kogel, Eds. (Hodder Arnold, London, ed. 4, 2009), pp. 41-55.
29. L. M. Garcia, D. E. Wilkins, G. P. Raaphorst, α/β ratio: A dose range dependence study. Int. J. Radiat. Oncol. Biol. Phys. 67, 587-593 (2007).
30. C. Zhang, N. A. Mayr, S. S. Lo, L. Lu, K. Li, J. Z. Wang, The α/β ratio: Dose-range dependent or model limitation? Int. J. Radiat. Oncol. Biol. Phys. 75, S610 (2009).
31. E. J. Hall, Radiobiology for the Radiologist (Lippincott Williams and Wilkins, Philadelphia, ed. 5, 2000).
32. M. C. Joiner, Models of radiation cell killing, in Basic Clinical Radiobiology, G. G. Steel, Ed. (Oxford Univ. Press, London, ed. 3, 2002), pp. 64-70.
33. M. Krämer, W. K. Weyrather, M. Scholz, The increased biological effectiveness of heavy charged particles: From radiobiology to treatment planning. Technol. Cancer Res. Treat. 2, 427-436 (2003).
34. S. B. Curtis, Lethal and potentially lethal lesions induced by radiation - a unified repair model. Radiat. Res. 106, 252-270 (1986).
35. F. W. McKenna, S. Ahmad, Fitting techniques of cell survival curves in high-dose region for use in stereotactic body radiation therapy. Phys. Med. Biol. 54, 1593-1608 (2009).
36. M. Carlone, D. Wilkins, P. Raaphorst, The modified linear-quadratic model of Guerrero and Li can be derived from a mechanistic basis and exhibits linear-quadratic-linear behaviour. Phys. Med. Biol. 50, L9-L13 (2005).
37. B. D. Kavanagh, F. Newman, Toward a unified survival curve: In regard to Park et al. (Int J Radiat Oncol Biol Phys 2008;70:847-852) and Krueger et al. (Int J Radiat Oncol Biol Phys 2007;69:1262-1271). Int. J. Radiat. Oncol. Biol. Phys. 71, 958-959 (2008).
38. M. Astrahan, BED calculations for fractions of very high dose: In regard to Park et al. (Int J Radiat Oncol Biol Phys 2007;69:S623-S624). Int. J. Radiat. Oncol. Biol. Phys. 71, 963 (2008).
39. J. F. Fowler, Linear quadratics is alive and well: In regard to Park et al. (Int J Radiat Oncol Biol Phys 2008;70:847-852). Int. J. Radiat. Oncol. Biol. Phys. 72, 957 (2008).
40. F. McKenna, S. Ahmad, Toward a unified survival curve: In regard to Kavanagh and Newman (Int J Radiat Oncol Biol Phys 2008;71:958-959) and Park et al. (Int J Radiat Oncol Biol Phys 2008;70:847-852). Int. J. Radiat. Oncol. Biol. Phys. 73, 640 (2009).
41. J. P. Kirkpatrick, J. J. Meyer, L. B. Marks, The linear-quadratic model is inappropriate to model high dose per fraction effects in radiosurgery. Semin. Radiat. Oncol. 18, 240-243 (2008).
42. D. J. Brenner, The linear-quadratic model is an appropriate methodology for determining isoeffective doses at large doses per fraction. Semin. Radiat. Oncol. 18, 234-239 (2008).
43. J. P. Kirkpatrick, D. J. Brenner, C. G. Orton, The linear-quadratic model is inappropriate to model high dose per fraction effects in radiosurgery. Med. Phys. 36, 3381-3384 (2009).
44. J. Z. Wang, X. A. Li, W. D. D'Souza, R. D. Stewart, Impact of prolonged fraction delivery times on tumor control: A note of caution for intensity-modulated radiation therapy (IMRT). Int. J. Radiat. Oncol. Biol. Phys. 57, 543-552 (2003).
45. M. A. Manning, R. D. Zwicker, D. W. Arthur, M. Arnfield, Biologic treatment planning for high-dose-rate brachytherapy. Int. J. Radiat. Oncol. Biol. Phys. 49, 839-845 (2001).
46. M. M. Elkind, H. Sutton, X-ray damage and recovery in mammalian cells in culture. Nature 184, 1293-1295 (1959).
47. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Confidence limits on estimated model parameters, in Numerical Recipes in C (Cambridge Univ. Press, Cambridge, ed. 2, 2002) pp. 689-699.
48. V. Vegesna, H. R. Withers, H. D. Thames Jr., K. Mason, Multifraction radiation response of mouse lung. Int. J. Radiat. Biol. Relat. Stud. Phys. Chem. Med. 47, 413-422 (1985).
49. H. D. Thames Jr., H. R. Withers, L. J. Peters, Tissue repair capacity and repair kinetics deduced from multifractionated or continuous irradiation regimens with incomplete repair. Br. J. Cancer Suppl. 6, 263-269 (1984).
50. E. van Rongen, E. L. Travis, H. D. Thames Jr., Repair rate in mouse lung after clinically relevant radiation doses per fraction. Radiat. Res. 141, 74-78 (1995).
51. E. van Rongen, H. D. Thames Jr., E. L. Travis, Recovery from radiation damage in mouse lung: Interpretation in terms of two rates of repair. Radiat. Res. 133, 225-233 (1993).
52. J. F. Fowler, C. A. Whitsed, M. C. Joiner, Repair kinetics in mouse lung: A fast component at 1.1 Gy per fraction. Int. J. Radiat. Biol. 56, 335-353 (1989).
53. V. Vegesna, H. R. Withers, J. M. Taylor, Repair kinetics of mouse lung. Radiother. Oncol. 15, 115-123 (1989).
54. C. S. Parkins, C. A. Whitsed, J. F. Fowler, Repair kinetics in mouse lung after multiple X-ray fractions per day. Int. J. Radiat. Biol. 54, 429-443 (1988).
55. E. L. Travis, H. D. Thames, T. L. Watkins, I. Kiss, The kinetics of repair in mouse lung after fractionated irradiation. Int. J. Radiat. Biol. Relat. Stud. Phys. Chem. Med. 52, 903-919 (1987).
56. T. T. Puck, P. I. Marcus, Action of x-rays on mammalian cells. J. Exp. Med. 103, 653-666 (1956).
57. In memoriam: Colleagues, students, postdoctoral fellows, residents, trainees, friends, and family mourn the loss of Dr. Jian Z. Wang, director of Ohio State University's Tumor Response Modeling Laboratory. Dr. Wang passed away unexpectedly in June 2010.We are deeply grateful for having had the opportunity to work with him and will do our best to carry on his work. Funding: Ohio Cancer Research Associates. Author contributions: J.Z.W. designed and performed the study, wrote the paper, and was responsible for the entire study. Z.H., S.S.L., W.T.C.Y., and N.A.M. participated in the design and interpretation of the study, and in drafting and revising the paper. Z.H. participated in the data analysis of the study. Competing interests: The authors declare that they have no competing interests.