Research progress on linear quadratic and biological equivalent dose models for high-dose-per-fraction radiotherapy
Zhu Jian, Yue Chenxi, Yin Yong, Li Baosheng, Yang Bo
Department of Radiation Oncology Physic and Technology, Shandong Cancer Hospital and Institute, Ji′nan 250117,China (Zhu J,Yin Y);School of Informatics, University of Linyi, Linyi 276000,China (Yang B);Shandong Provincial Key Laboratory of Network Based Intelligent Computing, University of Ji′nan,Ji′nan 250022,China (Yue CX,Yang B);Shandong Province Medical Imaging and Radiation Engineering Technology Research Center, Ji′nan 250117,China (Zhu J,Yin Y,Li BS)
Abstract：The linear quadratic (LQ) model and deduced biological equivalent dose (BED) model are widely applied in the radiobiological studies and the mathematic models of radiation oncology in clinical practice. However, the LQ model cannot accurately fit the experimental and clinical data in the high-dose region under the high-dose-per-fraction treatment mode. To resolve this issue, researchers have made modifications to the LQ models since 2008. In the paper, first, the theoretical basis and the application scope of LQ and BED models were introduced and the debate on whether LQ model is applicable to the high-dose-per-fraction radiotherapy was reviewed. Second, five modified models were introduced in two categories and their characteristics were summarized. Finally, current research situation and existing problems of radiotherapy using biological equivalent dose (BED) models were briefly summarized and the development trend of models was predicted.
Zhu Jian,Yue Chenxi,Yin Yong et al. Research progress on linear quadratic and biological equivalent dose models for high-dose-per-fraction radiotherapy[J]. Chinese Journal of Radiation Oncology, 2018, 27(9): 859-863.
[1] Fowler JF.The linear-quadratic formula and progress in fractionated radiotherapy[J].Brit J Radiol,1989,62(740):679-694.DOI:10.1259/0007-1285-62-740-679. [2] Astrahan M.Some implications of linear-quadratic-linear radiation dose-response with regard to hypofractionation[J].Med Phys,2008,35(35):4161-4172.DOI:10.1118/1.2969065. [3] Fowler JF.Rapid repopulation in radiotherapy:a debate on mechanism. The phantom of tumor treatment—continually rapid proliferation unmasked[J].Radiother Oncol,1991,22(3):156-158.DOI:10.1016/0167-8140(91)90017-B. [4] Timmerman R,McGarry R,Papiez L,et al. Initial Report of a Prospective phase Ⅱ trial of stereotactic body radiation therapy for patients with medically inoperable stage Ⅰ non-small cell lung cancer[J].Int J Radiat Oncol,2005,63(2):S99-S99. DOI:org/10.1016/j.ijrobp.2005.07.170. [5] Rusthoven KE,Kavanagh BD,Burri SH,et al. Multi-institutional phase Ⅰ/Ⅱ trial of stereotactic body radiation therapy for lung metastases[J].J Clin Oncol,2009,27(10):1579-1584.DOI:10.1200/JCO.2008.19.6386. [6] King CR,Brooks JD,Gill H,et al. Stereotactic body radiotherapy for localized prostate cancer:interim results of a prospective phase Ⅱ clinical trial[J].Int J Radiat Oncol,2009,73(4):1043-1048.DOI:org/10.1016/j.ijrobp.2008.05.059. [7] 冯炎.分割放疗中剂量、时间因素的生物学基础[J].中华放射肿瘤学杂志,1995(2):4-8. Feng Y.Biological basis of dose and time factors in fractionated radiotherapy[J].Chin J Radiat Oncol,1995(2):4-8. [8] Lea DE,Catcheside DG.The mechanism of the induction by radiation of chromosome aberrations in tradescantia[J].J Genetics,1942,44(2):216-245. [9] Lea DE.Action of radiation on living cells[J].Am J Med Genet A,1955,229(6):709.DOI:10.1097/00000441-195506000-00022. [10] Kellerer AM,Rossi HH.The theory of dual radiation action[J].Cur Top Radiat Res,1974(1):85-158. [11] Kellerer AM,Rossi HH.A generalized formulation of dual radiation action[J].Radiat Res,1978,178(2):AV204. [12] Barendsen GW.Dose fractionation,dose rate and iso-effect relationships for normal tissue responses[J].Int J Radiat Oncol,1982,8(11):1981-1997. [13] 冯炎,何少琴,刘泰福.线性二次模型及其临床意义[J].中国放射肿瘤学,1988(3):65-69. Feng Y,He SQ,Liu TF.Linear quadratic model and its clinical significance[J].Chin Radiat Oncol,1988(3):65-69. [14] Fowler JF,Tomadasu I,Dasu A.Is the α/β ratio for prostate tumours really low and does it vary with the level of risk at diagnosis?[J].Anticancer Res,2013,33(3):1009-1011. [15] Withers HR,Withers HR.Biologic basis for altered fractionation schemes. Cancer 55,2086-2095[J].Cancer,1985,55(9 Suppl):2086-2095.DOI:10.1002/1097-0142(19850501)55:9+<2086::AID-CNCR2820551409>3.0.CO;2-1. [16] Kelsey CA, Heintz PH, Chambers GD, et al. Radiation biology of medical imaging[M].NY:John Wiley& Sons,2013. [17] Elkind MM,Sutton H.X-ray damage and recovery in mammalian cells in culture[J].Nature,1959,184(4695):1293-1295. [18] 冯炎,刘泰福,郑秀英,等.小鼠小肠隐窝细胞不同剂量率照射生物效应研究[J].中国放射肿瘤学,1991(2):41-44. Feng Y,Liu TF,Zheng XY,et al. Biological effects of different dose rates on mouse intestinal crypt cells[J].Chin Radiat Oncol,1991(2):41-44. [19] 冯炎,刘泰福,桑梅仙,等.分割放射中小肠上皮细胞亚致死性损伤修复的特点[J].复旦学报(医学版),1991(1):23-26. Feng Y,Liu TF,Sang MX,et al. Characteristics of sublethal injury repair of intestinal epithelial cells in segmented radiation[J].Fudan Univ J (Med Sci),1991(1):23-26. [20] 谭榜宪,张有望,胡超苏,等.鼻咽癌常规分割放疗中的时间剂量效应关系[J].中华放射肿瘤学杂志,1998,7(1):41-45. Tan BX,Zhang YW,Hu CS,et al. Time dose effect relationship in conventional fractionated radiotherapy for nasopharyngeal carcinoma[J].Chin J Radiat Oncol,1998,7(1):41-45. [21] 李夏东,吴稚冰,马胜林,等.放射生物LQ线性二次模型的数理基础及临床意义[J].中国医学物理学杂志,2012,29(1):3188-3193. Li XD,Wu ZB,Ma SL,et al. Mathematical basis and clinical significance of radiological biological LQ linear two time model[J].Chin J Med Phys,2012,29(1):3188-3193. [22] Chang JY,Senan S,Paul MA,et al. Stereotactic ablative radiotherapy versus lobectomy for operable stage Ⅰ non-small-cell lung cancer:a pooled analysis of two randomised trials[J].Lancet Oncol,2015,16(6):630.DOI:org/10.1016/S1470-2045(15)70168-3. [23] Kirkpatrick JP,Meyer JJ,Marks LB.The linear-quadratic model is inappropriate to model high dose per fraction effects in radiosurgery[J].Semin Radiat Oncol,2008,18(4):3381-3384.DOI:10.1016/j.semradonc.2008.04.005. [24] Brenner DJ.Point:the linear-quadratic model is an appropriate methodology for determining iso-effective doses at large doses per fraction[J].Semin Radiat Oncol,2008,18(4):234.DOI:10.1016/j.semradonc.2008.04.004. [25] Leith JT,Cook S,Chougule P,et al. Intrinsic and extrinsic characteristics of human tumors relevant to radiosurgery:comparative cellular radiosensitivity and hypoxic percentages[J].Acta Neurochir Suppl,1994,62(62):18-27. [26] Kocher M,Treuer H,Voges J,et al. Computer simulation of cytotoxic and vascular effects of radiosurgery in solid and necrotic brain metastases[J].Radiother Oncol,2000,54(2):149.DOI:org/10.1016/S0167-8140(99)00168-1. [27] Park C,Papiez L,Zhang S,et al. Universal survival curve and single fraction equivalent dose:useful tools in understanding potency of ablative radiotherapy[J].Int J Radiat Oncol,2008,70(3):847-852.DOI:10.1016/j.ijrobp.2008.12.001. [28] Elkind MM,Whitmore GF.The radiobiology of cultured mammalian cells[M].New York:Gordon& Breach,1967. [29] Kavanagh BD,Newman F.Toward a unified survival curve:in regard to Park et al (IntJ Radiat Oncol Biol Phys,2008,70:847-852) and Krueger et al (Int J Radiat Oncol Biol Phys,2007,69:1262-1271)[J].Int J Radiat Oncol,2008,71(3):958-959.DOI:10.1016/j.ijrobp.2008.03.016. [30] Haynes RH.The interpretation of microbial inactivation and recovery phenomena[J].Radiat Res,1966,6(1):Suppl 6:1. [31] Wang JZ,Huang Z,Lo SS,et al. A generalized linear-quadratic model for radiosurgery,stereotactic body radiation therapy,and high-dose rate brachytherapy[J].Sci Transl Med,2010,2(39):39ra48.DOI:10.1126/scitranslmed.3000864.
2018, Vol. 27 
