title: Estimation of cell response in fractionation radiotherapy using different methods derived from linear quadratic model.
abstract: BACKGROUND
  The aim of this study was to use various theoretical methods derived from the Linear Quadratic (LQ) model to calculate the effects of number of subfractions, time intervals between subfractions, dose per subfraction, and overall fraction time on the cells' survival. Comparison of the results with experimental outcomes of melanoma and breast adenocarcinoma cells was also performed. Finally, the best matched method with experimental outcomes is introduced as the most accurate method in predicting the cell response.
  
  
  METHODS
  The most widely used theoretical methods in the literature, presented by Keall et al., Brenner, and Mu et al., were used to calculate the cells' survival following radiotherapy with different treatment schemes. The overall treatment times were ranged from 15 to 240 minutes. To investigate the effects of number of subfractions and dose per subfraction, the cells' survival after different treatment delivery scenarios were calculated through fixed overall treatment times of 30, 60 and 240 minutes. The experimental tests were done for dose of 4 Gy. The results were compared with those of the theoretical outcomes.
  
  
  RESULTS
  The most affective parameter on the cells' survival was the overall treatment time. However, the number of subfractions per fractions was another effecting parameter in the theoretical models. This parameter showed no significant effect on the cells' survival in experimental schemes. The variations in number of subfractions per each fraction showed different results on the cells' survival, calculated by Keall et al. and Brenner methods (P<0.05).
  
  
  CONCLUSIONS
  Mu et al. method can predict the cells' survival following fractionation radiotherapy more accurately than the other models. Using Mu et al. method, as an accurate and simple method to predict the cell response after fractionation radiotherapy, is suggested for clinical applications.
authors.affiliation: Department of Medical Physics, Faculty of Medicine, Hamadan University of Medical Sciences, Hamadan, Iran.
authors.forename: Safoora
authors.initials: S
authors.lastname: Nikzad
authors.affiliation: Department of Medical Physics, Tarbiat Modares University, Tehran, Iran.
authors.forename: Bijan
authors.initials: B
authors.lastname: Hashemi
authors.affiliation: Department of Medical Physics, School of Medicine, Sabzevar University of Medical Sciences, Sabzevar, Iran.
authors.forename: Golshan
authors.initials: G
authors.lastname: Mahmoudi
authors.affiliation: Department of Medical Physics and Medical Engineering & Medical Student's Research Center, School of Medicine, Isfahan University of Medical Sciences, Isfahan, Iran; Department of Medical Radiation Engineering, Faculty of Advanced Sciences & Technologies, Isfahan University, Isfahan, Iran.
authors.forename: Milad
authors.initials: M
authors.lastname: Baradaran-Ghahfarokhi
keywords: dose per fraction; fractionation radiotherapy; linear quadratic model; number of fractions; survival
references.citation: Radiother Oncol. 2010 Jun;95(3):261-8
references.pmid: 20363041
references.citation: Radiat Res. 1978 Dec;76(3):510-21
references.pmid: 569880
references.citation: Australas Phys Eng Sci Med. 2001 Sep;24(3):132-46
references.pmid: 11764395
references.citation: Int J Radiat Biol. 1990 Jan;57(1):127-42
references.pmid: 1967284
references.citation: Int J Radiat Oncol Biol Phys. 2004 May 1;59(1):242-9
references.pmid: 15093921
references.citation: Radiat Oncol. 2012 Jan 03;7:1
references.pmid: 22214341
references.citation: Phys Med. 2014 Dec;30(8):867-70
references.pmid: 25022453
references.citation: Int J Radiat Oncol Biol Phys. 2004 Aug 1;59(5):1484-90
references.pmid: 15275736
references.citation: Int J Radiat Oncol Biol Phys. 1996 Jul 1;35(4):721-30
references.pmid: 8690638
references.citation: Int J Radiat Oncol Biol Phys. 1985 Jul;11(7):1367-73
references.pmid: 4008293
references.citation: Eur J Clin Chem Clin Biochem. 1995 Nov;33(11):813-23
references.pmid: 8620058
references.citation: Radiother Oncol. 2003 Aug;68(2):181-7
references.pmid: 12972314
references.citation: J Biomed Phys Eng. 2013 Jun 01;3(2):29-36
references.pmid: 25505745
references.citation: Cancer Res. 1990 Mar 1;50(5):1392-6
references.pmid: 2302704
references.citation: Int J Radiat Oncol Biol Phys. 2010 Dec 1;78(5):1541-7
references.pmid: 21092834
references.citation: Semin Radiat Oncol. 2008 Oct;18(4):234-9
references.pmid: 18725109
references.citation: Int J Radiat Biol Relat Stud Phys Chem Med. 1985 Mar;47(3):319-39
references.pmid: 3872284
references.citation: Int J Radiat Oncol Biol Phys. 2008 Aug 1;71(5):1547-52
references.pmid: 18495369
references.citation: Int J Radiat Oncol Biol Phys. 2003 Oct 1;57(2):543-52
references.pmid: 12957268
references.citation: Radiat Oncol. 2011 Jan 12;6:4
references.pmid: 21226899
references.citation: Radiat Res. 1993 Jan;133(1):41-51
references.pmid: 8434112
references.citation: Med Phys. 2000 May;27(5):948-59
references.pmid: 10841397
references.citation: Int J Med Sci. 2012;9(3):193-9
references.pmid: 22408567
references.citation: J Math Biol. 2009 Apr;58(4-5):799-817
references.pmid: 18825382
references.citation: Int J Radiat Oncol Biol Phys. 1999 Aug 1;45(1):187-91
references.pmid: 10477023
references.citation: Int J Radiat Oncol Biol Phys. 2005 Nov 1;63(3):892-900
references.pmid: 16199319
references.citation: Nat Rev Cancer. 2011 Apr;11(4):239-53
references.pmid: 21430696