Monte Carlo role in radiobiological modelling of radiotherapy outcomes

Physics in Medicine and Biology

Volumn 57, Issue 11, 2012, Pages

  El Naqa, Issam ^a   Pater, Piotr ^a   Seuntjens, Jan ^a  

^a Department of Oncology   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

BIOLOGICAL INTERACTIONS; CLINICAL TRIAL; ESSENTIAL COMPONENT; LIVING TISSUES; MONTE CARLO; NEW PROTOCOL; NORMAL TISSUE COMPLICATION PROBABILITIES; PARTICLE TRACKS; RADIATION TRANSPORT; RADIATION-INDUCED EFFECTS; RADIOTHERAPY TREATMENT PLANNING; STOCHASTIC NATURE; TECHNIQUES USED; TREATMENT PLANNING; TUMOUR CONTROL PROBABILITIES; TUMOUR GROWTH;

CHEMICAL ANALYSIS; ESTIMATION; QUALITY CONTROL; RADIOTHERAPY; RISK PERCEPTION; TRANSMISSION CONTROL PROTOCOL; TUMORS;

MONTE CARLO METHODS;

BIOLOGICAL MODEL; HUMAN; METHODOLOGY; MONTE CARLO METHOD; RADIATION INJURY; RADIOBIOLOGY; RADIOTHERAPY; REVIEW; TREATMENT OUTCOME;

HUMANS; MODELS, BIOLOGICAL; MONTE CARLO METHOD; RADIATION INJURIES; RADIOBIOLOGY; RADIOTHERAPY; TREATMENT OUTCOME;

EID: 84861152856     PISSN: 00319155     EISSN: 13616560     Source Type: Journal    
DOI: 10.1088/0031-9155/57/11/R75     Document Type: Review

References (127)

1. Agostinelli S et al 2003 GEANT4-a simulation toolkit Nucl. Instrum. Methods A 506 250303
2. Allison J et al 2006 GEANT4 developments and applications IEEE Trans. Nucl. Sci. 53 2708
3. Alloni D, Campa A, Friedland W, Mariotti L and Ottolenghi A 2012 Track structure, radiation quality and initial radiobiological events: considerations based on the PARTRAC code experience Int. J. Radiat. Biol. 88 7786
4. Armstrong K, Weber B, Ubel P A, Peters N, Holmes J and Schwartz J S 2005 Individualized survival curves improve satisfaction with cancer risk management decisions in women with BRCA1/2 mutations J. Clin. Oncol. 23 931928
5. Begg A C, Stewart F A and Vens C 2011 Strategies to improve radiotherapy with targeted drugs Nat. Rev. Cancer 11 23953
6. Berger M, Seltzer S, Wang R and Schechter A 1993 Elastic Scattering of Electrons and Positrons by Atoms: Database ELAST (Gaithersburg, MD: U.S. Department of Commerce) Report NISTIR 5166
7. Berger M and Wang R 1988 Monte Carlo Transport of Electrons and Photons ed T M Jenkins (New York: Plenum) pp 2156
8. Bernal M A, Dealmeida C E, David M and Pires E 2011 Estimation of the RBE of mammography-quality beams using a combination of a Monte Carlo code with a B-DNA geometrical model Phys. Med. Biol. 56 7393403
9. Blanco A I, Chao K S, El Naqa I, Franklin G E, Zakarian K, Vicic M and Deasy J O 2005 Dose-volume modeling of salivary function in patients with head-and-neck cancer receiving radiotherapy Int. J. Radiat. Oncol. Biol. Phys. 62 105569 (Pubitemid 40884418)
10. Booth J T and Zavgorodni S F 2001 The effects of radiotherapy treatment uncertainties on the delivered dose distribution and tumour control probability Australas. Phys. Eng. Sci. Med. 24 718 (Pubitemid 32691240)
11. Borkenstein K, Levegrun S and Peschke P 2004 Modeling and computer simulations of tumor growth and tumor response to radiotherapy Radiat. Res. 162 7183 (Pubitemid 39044721)
12. Bouzy B and Helmstetter B 2003 Advances in Computer Games 10: Many Games, Many Challenges ed H van den Herik (Boston, MA: Kluwer) pp 15974
13. Bradley J, Deasy J O, Bentzen S and El Naqa I 2004a Dosimetric correlates for acute esophagitis in patients treated with radiotherapy for lung carcinoma Int. J. Radiat. Oncol. Biol. Phys. 58 110613 (Pubitemid 38314792)
14. Bradley J, Deasy J O, Bentzen S and El-Naqa I 2004b Dosimetric correlates for acute esophagitis in patients treated with radiotherapy for lung carcinoma Int. J. Radiat. Oncol. Biol. Phys. 58 110613 (Pubitemid 38314792)
15. Bradley J D, Hope A, El Naqa I, Apte A, Lindsay P E, Bosch W, Matthews J, Sause W, Graham M V and Deasy J O 2007 A nomogram to predict radiation pneumonitis, derived from a combined analysis of RTOG 9311 and institutional data Int. J. Radiat. Oncol. Biol. Phys. 69 98592 (Pubitemid 47625854)
16. Brahme A 1999 Optimized radiation therapy based on radiobiological objectives Semin. Radiat. Oncol. 9 3547 (Pubitemid 29096022)
17. Buffa F M and Nahum A E 2000 Monte Carlo dose calculations and radiobiological modelling: analysis of the effect of the statistical noise of the dose distribution on the probability of tumour control Phys. Med. Biol. 45 300923
18. Carlson D J, Stewart R D, Semenenko V A and Sandison G A 2008 Combined use of Monte Carlo DNA damage simulations and deterministic repair models to examine putative mechanisms of cell killing Radiat. Res. 169 44759 (Pubitemid 351620043)
19. Casciari J J, Sotirchos S V and Sutherland R M 1992 Mathematical-modeling of microenvironment and growth in Emt6/Ro multicellular tumor spheroids Cell Prolif. 25 122
20. Champion C, Incerti S, Aouchiche H and Oubaziz D 2009 A free-parameter theoretical model for describing the electron elastic scattering in water in the GEANT4 toolkit Radiat. Phys. Chem. 78 74550
21. Chetty I J et al 2007 Report of the AAPM Task Group No. 105: Issues associated with clinical implementation of Monte Carlo-based photon and electron external beam treatment planning Med. Phys. 34 481853 (Pubitemid 350197721)
22. Choi N, Baumann M, Flentjie M, Kellokumpu-Lehtinen P, Senan S, Zamboglou N and Kosmidis P 2001 Predictive factors in radiotherapy for non-small cell lung cancer: present status Lung Cancer 31 4356 (Pubitemid 32012602)
23. Cucinotta F A, Nikjoo H, O'Neill P and Goodhead D T 2000 Kinetics of DSB rejoining and formation of simple chromosome exchange aberrations Int. J. Radiat. Biol. 76 146374
24. Deasy J O and El Naqa I 2008 Image-based modeling of normal tissue complication probability for radiation therapy Cancer Treat. Res. 139 21556
25. Deasy J O, Niemierko A, Herbert D, Yan D, Jackson A, Ten Haken R K, Langer M and Sapareto S 2002 Methodological issues in radiation dose-volume outcome analyses: summary of a joint AAPM/NIH workshop Med. Phys. 29 210927
26. Deisboeck T S, Wang Z, Macklin P and Cristini V 2011 Multiscale cancer modeling Annu. Rev. Biomed. Eng. 13 12755
27. Dingfelder M, Hantke D, Inokuti M and Paretzke H G 1999 Electron inelastic-scattering cross sections in liquid water Radiat. Phys. Chem. 53 118
28. Dingfelder M, Ritchie R H, Turner J E, Friedland W, Paretzke H G and Hamm R N 2008 Comparisons of calculations with PARTRAC and NOREC: transport of electrons in liquid water Radiat. Res. 169 58494 (Pubitemid 351671524)
29. Diot Q, Kavanagh B, Timmerman R and Miften M 2012 Biological-based optimization and volumetric modulated arc therapy delivery for stereotactic body radiation therapy Med. Phys. 39 23745
30. Drasdo D 1998 Dynamical Networks in Physics and Biology at the Frontier of Physics and Biology ed D Beysens and G Forgacs (Berlin: Springer) pp 17185
31. Drasdo D, Kree R and McCaskill J S 1995 Monte Carlo approach to tissue-cell populations Phys. Rev. E 52 663557
32. Eckhardt R 1987 Stan Ulam, John von Neumann, and the Monte Carlo method Los Alamos Sci. 15 13143
33. El Naqa I 2012 Machine learning methods for predicting tumor response in lung cancer Wiley Interdiscip. Rev.: Data Min. Knowl. Discov. 2 17381
34. El Naqa I, Bradley J, Blanco A I, Lindsay P E, Vicic M, Hope A and Deasy J O 2006a Multivariable modeling of radiotherapy outcomes, including dose-volume and clinical factors Int. J. Radiat. Oncol. Biol. Phys. 64 127586
35. El Naqa I, Bradley J D, Lindsay P E, Blanco A I, Vicic M, Hope A J and Deasy J O 2006b Multi-variable modeling of radiotherapy outcomes including dose-volume and clinical factors Int. J. Radiat. Oncol. Biol. Phys. 64 127586
36. El Naqa I, Bradley J D, Lindsay P E, Hope A J and Deasy J O 2009 Predicting radiotherapy outcomes using statistical learning techniques Phys. Med. Biol. 54 S930
37. El Naqa I, Deasy J O, Mu Y, Huang E, Hope A J, Lindsay P E, Apte A, Alaly J and Bradley J D 2010 Datamining approaches for modeling tumor control probability Acta Oncol. 49 136373
38. El Naqa I, Suneja G, Lindsay P E, Hope A J, Alaly J R, Vicic M, Bradley J D, Apte A and Deasy J O 2006c Dose response explorer: an integrated open-source tool for exploring and modelling radiotherapy dose-volume outcome relationships Phys. Med. Biol. 51 571935 (Pubitemid 46217664)
39. Emfietzoglou D, Karava K, Papamichael G and Moscovitch M 2003 Monte Carlo simulation of the energy loss of low-energy electrons in liquid water Phys. Med. Biol. 48 235571 (Pubitemid 37020983)
40. Emfietzoglou D, Papamichael G, Kostarelos K and Moscovitch M 2000 A Monte Carlo track structure code for electrons (similar to 10 eV10 keV) and protons (similar to 0.310 MeV) in water: partitioning of energy and collision events Phys. Med. Biol. 45 317194
41. Fertil B and Malaise E 1985 Intrinsic radiosensitivity of human cell lines is correlated with radioresponsiveness of human tumors: analysis of 101 published survival curves Int. J. Radiat. Oncol. Biol. Phys. 11 1699707 (Pubitemid 15233633)
42. Fraass B A and Moran J M 2012 Quality, technology and outcomes: evolution and evaluation of new treatments and/or new technology Semin. Radiat. Oncol. 22 310
43. Francis Z, Villagrasa C and Clairand I 2011 Simulation of DNA damage clustering after proton irradiation using an adapted DBSCAN algorithm Comput. Methods Programs Biomed. 101 26570
44. Friedland W, Dingfelder M, Kundrat P and Jacob P 2011a Track structures, DNA targets and radiation effects in the biophysical Monte Carlo simulation code PARTRAC Mutat. Res. 711 2840
45. Friedland W, Jacob P and Kundrat P 2010 Stochastic simulation of DNA double-strand break repair by non-homologous end joining based on track structure calculations Radiat. Res. 173 67788
46. Friedland W, Jacob P and Kundrat P 2011b Mechanistic simulation of radiation damage to DNA and its repair: on the track towards systems radiation biology modelling Radiat. Prot. Dosim. 143 5428
47. Friedland W, Paretzke H, Ballarini F, Ottolenghi A, Kreth G and Cremer C 2008 First steps towards systems radiation biology studies concerned with DNA and chromosome structure within living cells Radiat. Environ. Biophys. 47 4961
48. Fu X L, Zhu X Z, Shi D R, Xiu L Z, Wang L J, Zhao S, Qian H, Lu H F, Xiang Y B and Jiang G L 1999 Study of prognostic predictors for non-small cell lung cancer Lung Cancer 23 14352 (Pubitemid 29123884)
49. Goitein M 1987 Evaluation of Treatment Planning for Particle Beam Radiotherapy ed S Zink (Bethesda, MD: National Cancer Institute)
50. Goodhead D T 1994 Initial events in the cellular effects of ionizing-radiations - clustered damage in DNA Int. J. Radiat. Biol. 65 717 (Pubitemid 24063524)
51. Guirado D and Ruiz de Almodovar J M 2003 Prediction of normal tissue response and individualization of doses in radiotherapy Phys. Med. Biol. 48 321323 (Pubitemid 37258364)
52. Gulliford S L, Webb S, Rowbottom C G, Corne D W and Dearnaley D P 2004 Use of artificial neural networks to predict biological outcomes for patients receiving radical radiotherapy of the prostate Radiother. Oncol. 71 312 (Pubitemid 38452896)
53. Hall E J 1994 Radiobiology for the Radiologist (Philadelphia, PA: Lippincott)
54. Hall E J and Giaccia A J 2006 Radiobiology for the Radiologist (Philadelphia, PA: Lippincott Williams & Wilkins)
55. Halperin E C, Perez C A and Brady L W 2008 Perez and Brady's Principles and Practice of Radiation Oncology (Philadelphia, PA: Kluwer/Lippincott Williams & Wilkins)
56. Harriss-Phillips W M, Bezak E and Yeoh E K 2011 Monte Carlo radiotherapy simulations of accelerated repopulation and reoxygenation for hypoxic head and neck cancer Br. J. Radiol. 84 90318
57. Hope A J, Lindsay P E, El Naqa I, Bradley J D, Alaly J, Vicic M, Purdy J A and Deasy J O 2006 Radiation pneumonitis risk based on clinical, dosimetric, and location related factors Int. J. Radiat. Oncol. Biol. Phys. 65 11224
58. Hope A J, Lindsay P E, El Naqa I, Bradley J D, Vicic M and Deasy J O 2005 Clinical, dosimetric, and location-related factors to predict local control in non-small cell lung cancer ASTRO 47th Annu. Meeting (Denver, CO,) p S231
59. Huang E X, Bradley J D, El Naqa I, Hope A J, Lindsay P E, Bosch W R, Matthews J W, Sause W T, Graham M V and Deasy J O 2012 Modeling the risk of radiation-induced acute esophagitis for Combined Washington University and RTOG Trial 9311 lung cancer patients Int. J. Radiat. Oncol. Biol. Phys. 82 16749
60. Huang E X, Hope A J, Lindsay P E, Trovo M, El Naqa I, Deasy J O and Bradley J D 2011 Heart irradiation as a risk factor for radiation pneumonitis Acta Oncol. 50 5160
61. ICRU 1983 Microdosimetry ICRU (Bethesda, MD: International Commission of Radiation Units and Measurements (ICRU))
62. Incerti S et al 2010 Comparison of GEANT4 very low energy cross section models with experimental data in water Med. Phys. 37 4692708
63. Joiner M and van der Kogel A 2009 Basic Clinical Radiobiology (London: Hodder Arnold)
64. Kawrakow I 2004 The effect of Monte Carlo statistical uncertainties on the evaluation of dose distributions in radiation treatment planning Phys. Med. Biol. 49 154956 (Pubitemid 38578503)
65. Keall P J, Siebers J V, Jeraj R and Mohan R 2000 The effect of dose calculation uncertainty on the evaluation of radiotherapy plans Med. Phys. 27 47884 (Pubitemid 30171796)
66. Kreipl M S, Friedland W and Paretzke H G 2009 Time- and space-resolved Monte Carlo study of water radiolysis for photon, electron and ion irradiation Radiat. Environ. Biophys. 48 1120
67. Kutcher G J and Burman C 1989 Calculation of complication probability factors for nonuniform normal tissue irradiation: the effective volume method Int. J. Radial. Biol. 16 162330 (Pubitemid 19154353)
68. Lehnert S 2008 Biomolecular Action of Ionizing Radiation (New York: Taylor and Francis)
69. Levegrun S, Jackson A, Zelefsky M J, Skwarchuk M W, Venkatraman E S, Schlegel W, Fuks Z, Leibel S A and Ling C C 2001 Fitting tumor control probability models to biopsy outcome after three-dimensional conformal radiation therapy of prostate cancer: pitfalls in deducing radiobiologic parameters for tumors from clinical data Int. J. Radiat. Oncol. Biol. Phys. 51 106480 (Pubitemid 33026439)
70. Li X A 2011 Adaptive Radiation Therapy (Boca Raton, FL: Taylor and Francis)
71. Lindsay P E, El Naqa I, Hope A J, Vicic M, Cui J, Bradley J D and Deasy J O 2007 Retrospective Monte Carlo dose calculations with limited beam weight information Med. Phys. 34 33446 (Pubitemid 46035255)
72. Lyman J T 1985 Complication probability as assessed from dose-volume histogram Radiat. Res. Suppl. 8 139
73. Marcu L, van Doorn T and Olver I 2004 Modelling of post-irradiation accelerated repopulation in squamous cell carcinomas Phys. Med. Biol. 49 376779 (Pubitemid 39206456)
74. Marks L B 2002 Dosimetric predictors of radiation-induced lung injury Int. J. Radiat. Oncol. Biol. Phys. 54 3136 (Pubitemid 35286792)
75. McMahon S J, Butterworth K T, McGarry C K, Trainor C, O'Sullivan J M, Hounsell A R and Prise K M 2012 A computational model of cellular response to modulated radiation fields Int. J. Radiat. Oncol. Biol. Phys. (at press)
76. Michalik V 1993 Energy deposition clusters in nanometer regions of changed-particle tracks Radiat. Res. 134 26570 (Pubitemid 23209248)
77. Moiseenko V, Kron T and Van Dyk J 2004 Biologically-based treatment plan optimization: a systematic comparison of NTCP models for tomotherapy treatment plans Proc. 14th Int. Conf. on the Use of Computers in Radiation Therapy (Seoul, Korea,)
78. Munley M T, Lo J Y, Sibley G S, Bentel G C, Anscher M S and Marks L B 1999 A neural network to predict symptomatic lung injury Phys. Med. Biol. 44 22419 (Pubitemid 29424384)
79. Niemierko 1999 A generalized concept of equivalent uniform dose (EUD) Med. Phys. 26 1101
80. Niemierko A and Goitein M 1993 Modeling of normal tissue response to radiation: the critical volume model Int. J. Radiat. Oncol. Biol. Phys. 25 13545 (Pubitemid 23029785)
81. Nikjoo H, O'Neill P, Wilson W E and Goodhead D T 2001 Computational approach for determining the spectrum of DNA damage induced by ionizing radiation Radiat. Res. 156 57783 (Pubitemid 33027531)
82. Nikjoo H, Uehara S, Emfietzoglou D and Cucinotta F A 2006 Track-structure codes in radiation research Radiat. Meas. 41 105274 (Pubitemid 44792451)
83. Nikjoo H, Uehara S, Wilson W E, Hoshi M and Goodhead D T 1998 Track structure in radiation biology: theory and applications Int. J. Radiat. Biol. 73 35564 (Pubitemid 28202107)
84. Oh J H, Craft J, Al Lozi R, Vaidya M, Meng Y, Deasy J O, Bradley J D and El Naqa I 2011 A Bayesian network approach for modeling local failure in lung cancer Phys. Med. Biol. 56 163551
85. Paretzke H G, Turner J E, Hamm R N, Ritchie R H and Wright H A 1991 Spatial distributions of inelastic events produced by electrons in gaseous and liquid water Radiat. Res. 127 1219
86. Partridge M 2008 A radiation damage repair model for normal tissues Phys. Med. Biol. 53 3595608 (Pubitemid 352020043)
87. Ploquin N, Kay I, Rangel-Baltazar A, Lau H and Dunscombe P 2006 A comparison of techniques for simulating set-up error and uncertainty in head and neck IMRT Med. Phys. 33 32139 (Pubitemid 44327422)
88. Ritchie R, Hamm R, Turner J, Wright H and Bolch W 1991 Physical and Chemical Mechanisms in Molecular Radiation Biology ed M Varma (New York: Plenum) pp 99135
89. Rogers D W 2006 Fifty years of Monte Carlo simulations for medical physics Phys. Med. Biol. 51 R287301
90. Roose T, Chapman S J and Maini P K 2007 Mathematical models of avascular tumor growth SIAM Rev. 49 179208 (Pubitemid 46888016)
91. Sanchez-Nieto B and Nahum A E 2000 Bioplan: software for the biological evaluation of radiotherapy treatment plans Med. Dosim. 25 716 (Pubitemid 30336646)
92. Seltzer S M 1988 Monte Carlo Transport of Electrons and Photons ed T M Jenkins (New York: Plenum) pp 81114
93. Semenenko V A and Stewart R D 2004 A fast Monte Carlo algorithm to simulate the spectrum of DNA damages formed by ionizing radiation Radiat. Res. 161 4517 (Pubitemid 40754242)
94. Semenenko V A, Turner J E and Borak T B 2003 NOREC, a Monte Carlo code for simulating electron tracks in liquid water Radiat. Environ. Biophys. 42 2137 (Pubitemid 37518065)
95. Seuntjens J and Rogers D W 2009 Clinical Dosimetry Measurements in Radiotherapy ed D W Rogers and J E Cygler (Madison, WI: Medical Physics Publishing) pp 14780
96. Spezi E and Lewis G 2008 An overview of Monte Carlo treatment planning for radiotherapy Radiat. Prot. Dosim. 131 1239
97. Stamatakos G S, Antipas V P, Uzunoglu N K and Dale R G 2006 A four-dimensional computer simulation model of the in vivo response to radiotherapy of glioblastoma multiforme: studies on the effect of clonogenic cell density Br. J. Radiol. 79 389400 (Pubitemid 43676342)
98. Stamatakos G S, Dionysiou D D, Zacharaki E I, Mouravliansky N A, Nikita K S and Uzunoglu N K 2002 In silico radiation oncology: combining novel simulation algorithms with current visualization techniques Proc. IEEE 90 176477
99. Stathakis S, Li J and Ma C C 2007 Monte Carlo determination of radiation-induced cancer risks for prostate patients undergoing intensity-modulated radiation therapy J. Appl. Clin. Med. Phys. 8 2685
100. Stavrev P, Stavreva N, Niemierko A and Goitein M 2001 Generalization of a model of tissue response to radiation based on the idea of functional subunits and binomial statistics Phys. Med. Biol. 46 150118 (Pubitemid 32440201)
101. Steel G G 2002 Basic Clinical Radiobiology (London, New York: Arnold; Oxford University Press)
102. Stewart R D, Yu V K, Georgakilas A G, Koumenis C, Park J H and Carlson D J 2011 Effects of radiation quality and oxygen on clustered DNA lesions and cell death Radiat. Res. 176 587602
103. Stroian G, Martens C, Souhami L, Collins D L and Seuntjens J 2008 Local correlation between Monte-Carlo dose and radiation-induced fibrosis in lung cancer patients Int. J. Radiat. Oncol. Biol. Phys. 70 92130 (Pubitemid 351199723)
104. Su M, Miftena M, Whiddon C, Sun X, Light K and Marks L 2005 An artificial neural network for predicting the incidence of radiation pneumonitis Med. Phys. 32 31825 (Pubitemid 40322310)
105. Taleei R, Weinfeld M and Nikjoo H 2011 A kinetic model of single-strand annealing for the repair of DNA double-strand breaks Radiat. Prot. Dosim. 143 1915
106. Thomson R M and Kawrakow I 2011 On the Monte Carlo simulation of electron transport in the sub-1 keV energy range Med. Phys. 38 45314
107. Titz B and Jeraj R 2008 An imaging-based tumour growth and treatment response model: investigating the effect of tumour oxygenation on radiation therapy response Phys. Med. Biol. 53 447188
108. Toburen L H 2012 Challenges in Monte Carlo track structure modelling Int. J. Radiat. Biol. 0 19
109. Tucker S L, Cheung R, Dong L, Liu H H, Thames H D, Huang E H, Kuban D and Mohan R 2004 Dose-volume response analyses of late rectal bleeding after radiotherapy for prostate cancer Int. J. Radiat. Oncol. Biol. Phys. 59 35365 (Pubitemid 38622586)
110. Tuckwell W, Bezak E, Yeoh E and Marcu L 2008 Efficient Monte Carlo modelling of individual tumour cell propagation for hypoxic head and neck cancer Phys. Med. Biol. 53 4489507
111. Turner J E, Magee J L, Wright H A, Chatterjee A, Hamm R N and Ritchie R H 1983 Physical and chemical development of electron tracks in liquid water Radiat. Res. 96 43749 (Pubitemid 14183172)
112. Uehara S, Nikjoo H and Goodhead D T 1993a Cross-sections for water vapour for the Monte Carlo electron track structure code from 10 eV to the MeV region Phys. Med. Biol. 38 1841
113. Uehara S, Nikjoo H and Goodhead D T 1993b Cross-sections for water-vapor for the Monte-Carlo electron track structure code from 10-Ev to the MeV region Phys. Med. Biol. 38 184158 (Pubitemid 24026131)
114. Vaidya M, Creach K M, Frye J, Dehdashti F, Bradley J D and El Naqa I 2012 Combined PET/CT image characteristics for radiotherapy tumor response in lung cancer Radiother. Oncol. 102 23945
115. Verhaegen F and Reniers B 2004 Microdosimetric analysis of various mammography spectra: lineal energy distributions and ionization cluster analysis Radiat. Res. 162 5929 (Pubitemid 39600549)
116. Villagrasa C, Francis Z and Incerti S 2011 Physical models implemented in the GEANT4-DNA extension of the GEANT-4 toolkit for calculating initial radiation damage at the molecular level Radiat. Prot. Dosim. 143 2148
117. Wang C K 2010 The progress of radiobiological models in modern radiotherapy with emphasis on the uncertainty issue Mutat. Res. 704 17581
118. Ward J F 1994 The complexity of DNA-DamageRelevance to biological consequences Int. J. Radiat. Biol. 66 42732
119. Warkentin B, Stavrev P, Stavreva N A and Fallone B G 2005 Limitations of a TCP model incorporating population heterogeneity Phys. Med. Biol. 50 357188 (Pubitemid 41019097)
120. Watanabe R and Nikjoo H 2002 Modelling the effect of incorporated halogenated pyrimidine on radiation-induced DNA strand breaks Int. J. Radiat. Biol. 78 95366 (Pubitemid 35333030)
121. Webb S 2001 The Physics of Three-Dimensional Radiation Therapy: Conformal Radiotherapy, Radiosurgery, and Treatment Planning (Bristol: Institute of Physics Publishing)
122. Webb S and Nahum A E 1993 A model for calculating tumour control probability in radiotherapy including the effects of inhomogeneous distributions of dose and clonogenic cell density Phys. Med. Biol. 38 65366 (Pubitemid 23188329)
123. Weinstein M C, Toy E L, Sandberg E A, Neumann P J, Evans J S, Kuntz K M, Graham J D and Hammitt J K 2001 Modeling for health care and other policy decisions: uses, roles, and validity Value Health 4 34861 (Pubitemid 32946233)
124. Wodarz D and Komarova N L 2008 Computational Biology of Cancer: Lecture notes and Mathematical Modeling (Hackensack, NJ: World Scientific)
125. Zagars G K, Schultheiss T E and Peters L J 1987 Inter-tumor heterogeneity and radiation dose-control curves Radiother. Oncol. 8 35361 (Pubitemid 17115581)
126. Zaider M and Minerbo G N 2000 Tumour control probability: a formulation applicable to any temporal protocol of dose delivery Phys. Med. Biol. 45 27993 (Pubitemid 30096764)
127. Zhang L, Wang Z, Sagotsky J A and Deisboeck T S 2009 Multiscale agent-based cancer modeling J. Math. Biol. 58 54559