Seminars in Radiation Oncology
Volume 18, Issue 4 , Pages 234-239 , October 2008

The Linear-Quadratic Model Is an Appropriate Methodology for Determining Isoeffective Doses at Large Doses Per Fraction

  • David J. Brenner, PhD, DSc

      Affiliations

    • Corresponding Author InformationAddress reprint requests to David J. Brenner, PhD, Center for Radiological Research, Columbia University Medical Center, 630 West 168th Street, New York, NY 10032

References 

  1. Fowler JF. The linear-quadratic formula and progress in fractionated radiotherapy. Br J Radiol. 1989;62:679–694
  2. Thames HD, Hendry JH. Fractionation in Radiotherapy. New York: Taylor & Francis; 1987;
  3. Dale RG. The application of the linear-quadratic dose-effect equation to fractionated and protracted radiotherapy. Br J Radiol. 1985;58:515–528
  4. Lea DE. Actions of Radiation on Living Cells. Cambridge: University Press; 1946;
  5. 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;72:351–374
  6. Ellis F. Is NSD-TDF useful to radiotherapy?. Int J Radiat Oncol Biol Phys. 1985;11:1685–1697
  7. Turesson I, Notter G. Skin reaction as a biological parameter for prospective studies of different dose schedules with the CRE formula. Bull Cancer. 1976;63:11–26
  8. Bates TD, Peters LJ. Dangers of the clinical use of the NSD formula for small fraction numbers. Br J Radiol. 1975;48:773
  9. Peters LJ, Withers HR. Morbidity from large dose fractions in radiotherapy. Br J Radiol. 1980;53:170–171
  10. Gerweck LE, Zaidi ST, Zietman A. Multivariate determinants of radiocurability (I: Prediction of single fraction tumor control doses). Int J Radiat Oncol Biol Phys. 1994;29:57–66
  11. Brown M, Bristow R, Glazer P, et al. Comment on “tumor response to radiotherapy regulated by endothelial cell apoptosis” (II). Science. 2003;302:1894
  12. Preston RJ. Mechanisms of induction of specific chromosomal alterations. Basic Life Sci. 1990;53:329–336
  13. Wlodek D, Hittelman WN. The relationship of DNA and chromosome damage to survival of synchronized X-irradiated L5178Y cells. II. Repair Radiat Res. 1988;115:566–575
  14. Savage JR. A brief survey of aberration origin theories. Mutat Res. 1998;404:139–147
  15. Lea DE, Catcheside DG. The mechanism of the induction by radiation of chromosome aberrations in tradescantia. J Genet. 1942;44:216–245
  16. Kellerer AM, Rossi HH. The theory of dual radiation action. Curr Top Radiat Res. 1972;8:85–158
  17. Thames HD. An ‘incomplete-repair’ model for survival after fractionated and continuous irradiations. Int J Radiat Biol. 1985;47:319–339
  18. Brenner DJ, Huang Y, Hall EJ. Fractionated high dose-rate versus low dose-rate regimens for intracavitary brachytherapy of the cervix: Equivalent regimens for combined brachytherapy and external irradiation. Int J Radiat Oncol Biol Phys. 1991;21:1415–1423
  19. Fowler JF, Ritter MA, Chappell RJ, et al. What hypofractionated protocols should be tested for prostate cancer?. Int J Radiat Oncol Biol Phys. 2003;56:1093–1104
  20. Prevost JB, Voet P, Hoogeman M, et al. Four-dimensional stereotactic radiotherapy for early stage non-small cell lung cancer: A comparative planning study. Technol Cancer Res Treat. 2008;7:27–34
  21. Brenner DJ, Martel MK, Hall EJ. Fractionated regimens for stereotactic radiotherapy of recurrent tumors in the brain. Int J Radiat Oncol Biol Phys. 1991;21:819–824
  22. Bartkowiak D, Hogner S, Nothdurft W, et al. Cell cycle and growth response of CHO cells to X-irradiation: Threshold-free repair at low doses. Int J Radiat Oncol Biol Phys. 2001;50:221–227
  23. Garcia LM, Leblanc J, Wilkins D, et al. Fitting the linear-quadratic model to detailed data sets for different dose ranges. Phys Med Biol. 2006;51:2813–2823
  24. Barendsen GW. Dose fractionation, dose rate and iso-effect relationships for normal tissue responses. Int J Radiat Oncol Biol Phys. 1982;8:1981–1997
  25. van der Kogel AJ. Chronic effects of neutrons and charged particles on spinal cord, lung, and rectum. Radiat Res Suppl. 1985;8:S208–S216
  26. Douglas BG, Fowler JF. The effect of multiple small doses of x rays on skin reactions in the mouse and a basic interpretation. Radiat Res. 1976;66:401–426
  27. Peck JW, Gibbs FA. Mechanical assay of consequential and primary late radiation effects in murine small intestine: Alpha/beta analysis. Radiat Res. 1994;138:272–281
  28. Taylor JM, Kim DK. The poor statistical properties of the Fe-plot. Int J Radiat Biol. 1989;56:161–167
  29. de Boer RW. The use of the D versus dD plot to estimate the alpha/beta ratio from iso-effect radiation damage data. Radiother Oncol. 1988;11:361–367
  30. Tucker SL. Tests for the fit of the linear-quadratic model to radiation isoeffect data. Int J Radiat Oncol Biol Phys. 1984;10:1933–1939
  31. Ling CC, Chen CH, Fuks Z. An equation for the dose response of radiation-induced apoptosis: Possible incorporation with the LQ model. Radiother Oncol. 1994;33:17–22
  32. Brenner DJ, Hlatky LR, Hahnfeldt PJ, et al. The linear-quadratic model and most other common radiobiological models result in similar predictions of time-dose relationships. Radiat Res. 1998;150:83–91
  33. Curtis SB. Lethal and potentially lethal lesions induced by radiation—A unified repair model. Radiat Res. 1986;106:252–270
  34. Hawkins RB. A microdosimetric-kinetic model of cell death from exposure to ionizing radiation of any LET, with experimental and clinical applications. Int J Radiat Biol. 1996;69:739–755
  35. Obaturov GM, Moiseenko VV, Filimonov AS. Model of mammalian cell reproductive death (I. Basic assumptions and general equations). Radiat Environ Biophys. 1993;32:285–294
  36. Tobias CA. The repair-misrepair model in radiobiology: Comparison to other models. Radiat Res Suppl. 1985;8:S77–S95
  37. Zaider M. There is no mechanistic basis for the use of the linear-quadratic expression in cellular survival analysis. Med Phys. 1998;25:791–792
  38. Sachs RK, Brenner DJ. The mechanistic basis of the linear-quadratic formalism. Med Phys. 1998;25:2071–2073
  39. Kiefer J. A repair fixation model. In:  Kiefer J editors. Quantitative Mathematical Models in Radiation Biology. New York: Springer-Verlag; 1988;
  40. Haynes RH. The interpretation of microbial inactivation and recovery phenomena. Radiat Res Suppl. 1966;6:1–29
  41. Laurie J, Orr JS, Foster CJ. Repair processes and cell survival. Br J Radiol. 1972;45:362–368
  42. Reddy NM, Mayer PJ, Lange CS. The saturated repair kinetics of Chinese hamster V79 cells suggests a damage accumulation–interaction model of cell killing. Radiat Res. 1990;121:304–311
  43. Sontag W. A cell survival model with saturable repair after irradiation. Radiat Environ Biophys. 1987;26:63–79
  44. Ward JF, Limoli CL, Calabro-Jones PM, et al. An examination of the repair saturation hypothesis for describing shouldered survival curves. Radiat Res. 1991;127:90–96
  45. Kiefer J, Lobrich M. The repair fixation model, general aspects and the influence of radiation quality. In:  Chadwick KH,  Moschini G,  Varma M editor. Biophysical Modelling of Radiation Effects. New York: Adam Hilger Press; 1992;p. 211–218
  46. Brenner DJ, Hall EJ. Fractionation and protraction for radiotherapy of prostate carcinoma. Int J Radiat Oncol Biol Phys. 1999;43:1095–1101
  47. Duchesne GM, Peters LJ. What is the α/β ratio for prostate cancer? (Rationale for hypofractionated high-dose-rate brachytherapy). Int J Radiat Oncol Biol Phys. 1999;44:747–748
  48. Miles EF, Lee WR. Hypofractionation for prostate cancer: A critical review. Semin Radiat Oncol. 2008;18:41–47
  49. Haustermans K, Withers HR. The biological basis of fractionation. Rays. 2004;29:231–236
  50. Brenner DJ, Hlatky LR, Hahnfeldt PJ, et al. A convenient extension of the linear-quadratic model to include redistribution and reoxygenation. Int J Radiat Oncol Biol Phys. 1995;32:379–390
  51. Travis EL, Tucker SL. Isoeffect models and fractionated radiation therapy. Int J Radiat Oncol Biol Phys. 1987;13:283–287
  52. Whitehead AN. Introduction to mathematics. In: New York: H. Holt; 1911;p. 27

 Supported by NIH grants U19 AI-067773 and P41 RR-11623.

PII: S1053-4296(08)00033-7

doi: 10.1016/j.semradonc.2008.04.004

Seminars in Radiation Oncology
Volume 18, Issue 4 , Pages 234-239 , October 2008

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