Radiobiological impact of dose calculation algorithms on biologically optimized IMRT lung stereotactic body radiation therapy plans
© Liang et al. 2016
Received: 15 May 2015
Accepted: 22 December 2015
Published: 22 January 2016
The aim of this study is to evaluate the radiobiological impact of Acuros XB (AXB) vs. Anisotropic Analytic Algorithm (AAA) dose calculation algorithms in combined dose-volume and biological optimized IMRT plans of SBRT treatments for non-small-cell lung cancer (NSCLC) patients.
Twenty eight patients with NSCLC previously treated SBRT were re-planned using Varian Eclipse (V11) with combined dose-volume and biological optimization IMRT sliding window technique. The total dose prescribed to the PTV was 60 Gy with 12 Gy per fraction. The plans were initially optimized using AAA algorithm, and then were recomputed using AXB using the same MUs and MLC files to compare with the dose distribution of the original plans and assess the radiobiological as well as dosimetric impact of the two different dose algorithms. The Poisson Linear-Quadatric (PLQ) and Lyman-Kutcher-Burman (LKB) models were used for estimating the tumor control probability (TCP) and normal tissue complication probability (NTCP), respectively. The influence of the model parameter uncertainties on the TCP differences and the NTCP differences between AAA and AXB plans were studied by applying different sets of published model parameters. Patients were grouped into peripheral and centrally-located tumors to evaluate the impact of tumor location.
PTV dose was lower in the re-calculated AXB plans, as compared to AAA plans. The median differences of PTV(D95%) were 1.7 Gy (range: 0.3, 6.5 Gy) and 1.0 Gy (range: 0.6, 4.4 Gy) for peripheral tumors and centrally-located tumors, respectively. The median differences of PTV(mean) were 0.4 Gy (range: 0.0, 1.9 Gy) and 0.9 Gy (range: 0.0, 4.3 Gy) for peripheral tumors and centrally-located tumors, respectively. TCP was also found lower in AXB-recalculated plans compared with the AAA plans. The median (range) of the TCP differences for 30 month local control were 1.6 % (0.3 %, 5.8 %) for peripheral tumors and 1.3 % (0.5 %, 3.4 %) for centrally located tumors. The lower TCP is associated with the lower PTV coverage in AXB-recalculated plans. No obvious trend was observed between the calculation-resulted TCP differences and tumor size or location. AAA and AXB yield very similar NTCP on lung pneumonitis according to the LKB model estimation in the present study.
AAA apparently overestimates the PTV dose; the magnitude of resulting difference in calculated TCP was up to 5.8 % in our study. AAA and AXB yield very similar NTCP on lung pneumonitis based on the LKB model parameter sets we used in the present study.
The goal of radiation therapy is to optimize therapeutic ratios by delivering tumoricidal doses to targets while maximally sparing organs-at-risk (OARs). Mostly, the quality of a radiation treatment plan is judged by isodose distribution and dose-volume-histograms (DVH). Typically the biological outcomes in terms of tumor control and normal tissue complication are not estimated when evaluating a plan. Significant progress and contributions to our understanding and modeling of volume effects for both normal and tumor tissues started in the 1980s with the advent of modern three dimensional treatment planning techniques. Models for estimating the tumor control probability(TCP) and normal-tissue complication probabilities (NTCP) were proposed in the late 1980s [1–8]. Even though dose-volume techniques are a mainstay of current clinical treatment planning optimization, biological optimization using complication probability models in intensity modulated radiotherapy (IMRT) planning has shown potential for reducing radiation-induced toxicity [9–11]. The current study used combined biological optimization and dose-volume optimization to take advantage of using radiobiological models and at the same time also keep the “important” dose-volume characteristics. The report of AAPM Task Group 166  recommends that dose-volume constraints and the biologic optimization function be used together for optimization.
In 2005, Eclipse TPS released the Analytical Anisotropic Algorithm (AAA) . AAA is a convolution–superposition-based photon beam dose computation algorithm. This algorithm was quickly and widely adopted for clinical use. More recently, Varian Eclipse TPS implemented another dose calculation algorithm, Acuros XB Advanced Dose Calculation (AXB), which uses a deterministic grid-based Boltzmann equation solver (GBBS or the discrete ordinates method). The GBBS [14, 15] explicitly solves the linear Boltzmann transport equation (LBTE), which is the governing equation that describes the macroscopic behavior of ionizing particles (neutrons, photons, electrons, etc) as they travel through and interact with matter. The GBBS then iteratively solves the radiation transport problem within specified volumes to compute radiation doses. AXB was first published by Vassiliev et al.  and has been considered to be similar to classic Monte Carlo methods for accurate modeling of dose deposition in heterogeneous media [16–18].
Among the numerous studies comparing the dosimetric differences between plans calculated with conventional algorithms (pencil beam type and convolution-superposition type) vs. with advanced algorithms (Monte Carlo type and GBBS type) [19–26], lung SBRT has been shown as the treatment where the differences due to dose algorithms are among the most significant, hence necessitating the adoption of the more advanced algorithms. This is due to the low density lung tissue and the high risk of normal tissue toxicity in hypofractionated treatments like SBRT. Compared with the very large dosimetric differences found between pencil beam type algorithms and advanced algorithms, smaller differences were seen between convolution-superposition typealgorithms such as AAA and advanced algorithms. Improved accuracy with advanced algorithms was always observed and deemed necessary in some cases. Pertaining to the two dose algorithms investigated, studies [19, 20] have illustrated that AXB is more accurate in modelling the radiation transportation and dose deposition in the patient. However, those studies were focused purely on dosimetric comparisons between AAA and AXB algorithms. The impact of these two algorithms on biological indices has not been thoroughly studied. To date, the radiobiological impact of AAA and AXB dose computation algorithms on lung tumor treatment plans, where the impact of dose algorithms would be prominent due to the low density lung tissue, has not been published. Furthermore, planning techniques in the existing literature investigating dosimetric differences between the conventional and advanced dose algorithms on lung SBRT were predominantly based on physical dose volume constraints. In this paper, we have retrospectively planned 28 stereotactic body radiation therapy (SBRT) non-small-cell lung cancer (NSCLC) patients using combined dose-volume optimization and biological optimization provided by a Varian Eclipse (Varian Medical Systems, Palo Alto, CA) planning system (V11). Dose computation was performed alternatingly with AAA (V11) and AXB (V11) algorithms on these plans optimized with AAA. The tumor control probability (TCP) and normal tissue complication probability (NTCP) on normal lung tissue (pneumonitis ≥ 2) from AAA and AXB plans were evaluated using the Eclipse biological evaluation module (V1.4).
Materials and methods
This study was approved by the University of Arkansas Medical Science Institutional Review Board (FWA00001119).
Median age (range, yrs)
Tumor position, peripheral/central
Median PTV size (range, cc)
45.6 (15.3, 107.3)
Dose-volume cost function parameters used in this study
Dose-volume cost function parameters
Physical Dose (Gy)
Biological cost function parameters used in this study
Biological NTCP-LKB model parameters
Pneumonit-is Grade ≥ 2
Esophagitis Grade ≥ 2
Biological NTCP-PLQ model parameters
Normal tissue dose criteria for evaluation of SBRT lung plans
Max point dose (Gy)
Max critical volume above threshold
Threshold dose (Gy)
Bilateral Lung - ITV
The Poisson Linear-Quadatric (PLQ) model was used for estimating the tumor control probability. The PLQ model  is derived from the linear-quadratic cell survival model using the Poisson distribution:
Where D is the cumulative dose and d is the dose of a single fraction.
Where v i is the partial volume with absorbed dose EQD 2,i and n is the dose-weighting factor, which defines the risks associated with partial organ volume uniform irradiation.
In the present study, the NTCP values for lung pneumonitis grade ≥ 2 were calculated using the LKB model. Several studies have reported estimates of the model parameters obtained from different clinical studies. A study from Burman et al.  was based on treatment plans in which no density correction was performed. Later, Seppenwoolde et al.  and Kwa et. al  presented difference model parameters obtained from density corrected treatment plans. We applied these three sets of model parameters in this study to investigate the influence of the model parameter uncertainty on NTCP. In addition, we also studied the influence of α/β ratios by applying two different α/β ratios for normal lung tissue; 1.3 Gy from the recent study of Scheenstra et al.  and 3 Gy as the standard normal tissue value.
Results and discussion
Comparison of total physical doses totarget volume calculated using AAA and AXB for peripheral and centrally-located tumor patients
Target (dose metric)
Median dose (range) in Gy
63.7 (62.3, 67.9)
63.9 (60.5, 68.1)
62.9 (61.7, 65.0)
62.2 (60.5, 64.5)
66.0 (63.7, 73.2)
67.0 (64.1, 75.5)
55.2 (51.2, 57.1)
51.3 (37.6, 56.1)
64.7 (63.6, 73.1)
64.1 (61.1, 69.3)
59.0 (55.6, 59.4)
63.5 (62.8, 67.2)
62.6 (61.0, 66.0)
66.9 (64.8, 86.9)
67.5 (63.9, 84.4)
53.1 (45.1, 57.0)
50.4 (42.3, 53.6)
Median and range of NTCP on lungpneumonitis grade ≥ 2 for peripheral and centrally-located tumor patients with three different sets of LKB model parameters and two different α/β ratios
0.7 (0.2, 5.3)
0.7 (0.1, 5.2)
1.8 (0.2, 18.7)
1.7 (0.2, 18.5)
2.5 (0.8, 6.0)
2.4 (0.8, 6.1)
4.6 (0.9, 23.8)
4.4 (0.9, 23.6)
2.1 (0.8, 5.8)
2.1 (0.7, 5.7)
Seppenwoolde  α/β = 3Gy
3.1 (0.8, 13.9)
3.0 (0.8, 13.8)
0.2 (0.0, 7.0)
0.2 (0.0, 15.9)
1.5 (0.0, 72.0)
1.2 (0.0, 71.2)
The mean lung dose (MLD) has been widely used as a simple and effective metric for probability of pneumonitis . In the present study, we have studied the relationship between the ΔNTCP and the MLD difference between AAA and AXB plans (ΔMLD). No obvious trend was observed. We also studied the correlation between the ΔNTCP and the PTV size with all three LKB model parameter sets and with two different α/β ratios. No correlation was observed.
Although we could not find published literature to make direct comparisons against our current study on SBRT lung plans, it is relevant to mention previous studies on the influence of dose calculation algorithms on the predicted TCP and NTCP values [31, 43, 44], these studies revealed some potential differences in TCP/NTCP values depending on the calculation algorithm used. Nielsen et al.  showed an estimated NTCP value for pneumonitis that varied 4 % across the six investigated dose algorithms. Bufacchi et al.  reported that the NTCP value from AAA-calculated plans was lower than that from pencil beam-calculated plans in most treated sites. Petillion et al.  reported lower TCP and NTCP predictions when using advanced algorithms. Since our fractionation scheme and studied algorithms were much different from these published works, direct comparison cannot be meaningfully made between our findings and their results. The radiobiological indices impact of AAA and ABX dose computation algorithms were published by Rana et al.  and Padmanaban et al. . The study of Rana et al concluded that both AAA and AXB predicted comparable NTCP and TCP values for low-risk prostate cancer plans. However, in Padmanaban et al. study on esophagus cancer, where it also involves complex tissue heterogeneities, a difference in TCP between 1.2 % and 3.1 % was found. The study of Petillion et al.  reported a 0.3 % lower TCP on breast in AXB plans compared with AAA plans.
It should be stated that there are large uncertainties in the biological models used and its associated parameters.The published TCP/NTCP model parameters that we used were obtained from studies that used different treatment techniques and dose algorithms from the present study. This would introduce some uncertainties too. In addition, some studies have suggested that the LQ model may overestimate the radiobiological effect at the dose level commonly used in SBRT . Conversely, results from our group and others suggests that the LQ model may actually underestimate the cell killing expected at higher SBRT doses if a significant amount of vascular damage and indirect cell death occurs [48, 49]. Whatever the case, it certainly seems appropriate to only treat the findings of the current study as a relative comparison between the different dose calculation algorithms rather than studying the absolute expected values. There is likely a lot more biological information that could be added to the model to make it more truly a biological optimization and evaluation. As more clinical data are collected, it may help in the formulation of methods to predict biophysical response and result in more accurate predictions of TCP and NTCP.
In this study, AXB-recalculated plans yielded lower TCP than the AAA-calculated plans. The lower TCP is associated with the lower PTV coverage in AXB-calculated plans. The maximum 11.9 Gy EQD 2 dose of ΔD95% in our patient cohort corresponds to up to 5.8 % ΔTCP for 30 months local control.AAA-calculated and AXB-recalculated plans yield very similar NTCP values. The above conclusion stays valid when different sets of published lung NTCP model parameters were used. No correlation was observed between the ΔTCP/ΔNTCP and the PTV size or location.
Ethics approval and consent to participate
This study was approved by the University of Arkansas Medical Science Institutional Review Board (FWA00001119).
Consent to publish
We acknowledge financial support by University of Nebraska Medical Center for funding Open Access Publishing.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
- Lyman JT. Complication probability as assessed from dose-volume histograms. Radiat Res. 1985;104 Suppl. 8:S13–9.Google Scholar
- Lyman JT, Wolbarst AB. Optimization of radiation therapy, III: A method of assessing complication probabilities from dose-volume histograms. Int J Radiat OncolBiol Phys. 1987;13:103–9.View ArticleGoogle Scholar
- Kutcher GJ, Burman C. Calculation of complication probability factors for non-uniform normal tissue irradiation: the effective volume method. Int J Radiat OncolBiol Phys. 1989;16:1623–30.View ArticleGoogle Scholar
- Burman C, Kutcher GJ, Emami B, Goitein M. Fitting of normal tissue tolerance data to an analytic fuction. Int J Radiat Oncol Biol Phys. 1991;21(1):123–35.View ArticlePubMedGoogle Scholar
- Kutcher GJ, Burman C, Brewster L, Gotein M, Mohan R. Histogram reduction method for Calculation complication probabilities for three dimensional treatment evaluation. Int J Radiat Oncol Biol Phys. 1991;21(1):137–46.View ArticlePubMedGoogle Scholar
- Källman P, Agren A, Brahme A. Tumour and normal tissue responses to fractionated non-uniform dose delivery. Int J Radiat Biol. 1992;62(2):249–62.View ArticlePubMedGoogle Scholar
- Schultheiss TE, Orten CG. Models in radiotherapy: definition of decision criteria. Med Phys. 1985;12(2):183–7.View ArticlePubMedGoogle Scholar
- Morrill SM, Lane RG, Jacobson G, Rosen II. Treatment planning optimization using constrained simulated annealing. Phys Med Biol. 1991;36(10):1341–61.View ArticlePubMedGoogle Scholar
- Qi XS, Semenenko VA, Li XA. Improved critical structure sparing with biologically based IMRT optimization. Med Phys. 2009;36(5):1790–9.View ArticlePubMedGoogle Scholar
- Das S. A role for biological optimization within the current treatment planning paradigm. Med Phys. 2009;36(10):4672–82.View ArticlePubMedGoogle Scholar
- Doit Q, Kavanagh B, Timmerman R, Miften M. Biological-based optimization and volumetric modulated arc therapy delivery for stereotactic body radiation therapy. Med Phys. 2012;39(1):237–45.View ArticleGoogle Scholar
- Allen Li X, Alber M, Deasy JO, Jackson A, Ken Jee KW, Marks LB, et al. The use and QA of biologically related models for treatment planning: short report of the TG-166 of the therapy physics committee of the AAPM. Med Phys. 2012;39(3):1386–409.View ArticlePubMedGoogle Scholar
- Ulmer W, Pyyry J, Kaissl W. A 3D photon superposition/convolution algorithm and its foundation on results of Monte Carlo calculations. Phys Med Biol. 2005;50(8):1767–90.View ArticlePubMedGoogle Scholar
- Lewis EE, Miller WF. Computational Methods of Neutron Transport. New York: Wiley; 1984.Google Scholar
- Ahnesjö A, Aspradakis MM. Dose calculations for external photon beams in radiotherapy. Phys Med Biol. 1999;44(11):R99–155.View ArticlePubMedGoogle Scholar
- Vassiliev ON, Wareing TA, McGhee J, Failla G, Salehpour MR, Mourtada F. Validation of a new grid-based Boltzmann equation solver for dose calculation in radiotherapy with photon beams. Phys Med Biol. 2010;55(3):581–98.View ArticlePubMedGoogle Scholar
- Bush K, Gagne IM, Zavgorodni S, Ansbacher W, Beckham W. Dosimetric validation of Acuros XB with Monte Carlo methods for photon dose calculations. Med Phys. 2011;38(4):2208–21.View ArticlePubMedGoogle Scholar
- Fogliata A, Nicolini G, Clivio A, Vanetti E, Mancosu P, Cozzi L. Dosimetric validation of the Acuros XB Advanced Dose Calculation algorithm: fundamental characterization in water. Phys Med Biol. 2011;56(6):1879–904.View ArticlePubMedGoogle Scholar
- Kan MW, Leung LH, Yu PK. Verification and dosimetric impact of Acuros XB algorithm on intensity modulated stereotactic radiotherapy for locally persistent nasopharyngeal carcinoma. Med Phys. 2012;39(8):4705–14.View ArticlePubMedGoogle Scholar
- Han T, Mikell JK, Salehpour M, Mourtada F. Dosimetric comparison of Acuros XB deterministic radiation transport method with Monte Carlo and model-based convolution methods in heterogeneous media. Med Phys. 2011;38(5):2651–64.PubMed CentralView ArticlePubMedGoogle Scholar
- Moiseenko V, Liu M, Bergman AM, Gill B, Kristensen S, Teke T, et al. Monte Carlo calculation of dose distribution in early stage NSCLC patients planned for accelerated hypofractionated radiation therapy in the NCIC-BR25 protocol. Phys Med Biol. 2010;55(3):723–33.View ArticlePubMedGoogle Scholar
- Elmpt WV, Ollers M, Velders M, Poels K, Mijnheer B, Ruysscher DD, et al. Transition from a simple to a more advanced dose calculation algorithm for radiotherapy of non-small cell lung cancer (NSCLC): implications for clinical implementation in an individualized dose-escalation protocol. Radio Ther Oncol. 2008;88(3):326–34.View ArticleGoogle Scholar
- Vanderstraeten B, Reynaert N, Paelinck L, Madani I, De Wagter C, De Gersem W, et al. Accuracy of patient dose calculation for lung IMRT: A comparison of Monte Carlo, convolution/superposition, and pencil beam computations. Med Phys. 2006;33(9):3149–58.View ArticlePubMedGoogle Scholar
- Fogliata A, Nicolini G, Clivio A, Vanetti E, Cozzi L. Critical appraisal of Acuros XB and Anisotropic Analytic Algorithm dose calculation in advanced non-small-cell lung cancer treatments. Int J Radiat Oncol Biol Phys. 2012;83(5):1587–95.View ArticlePubMedGoogle Scholar
- Rana S, Rogers K, Pokharel S, Cheng C. Evaluation of Acuros XB algorithm based on RTOG 0813 dosimetric criteria for SBRT lung treatment with RapidArc. J Appl Clin Med Phys. 2014;15(1):4474.PubMedGoogle Scholar
- Kroon PS, Hol S, Essers M. Dosimetric accuracy and clinical quality of Acuros XB and AAA dose calculation algorithm for stereotactic and conventional lung volumetric modulated arc therapy plans. Radiat Oncol. 2013;8:149.PubMed CentralView ArticlePubMedGoogle Scholar
- Timmerman R, McGarry R, Yiannoutsos C, Papiez L, Tudor K, DeLuca J, et al. Excessive toxicity when treating central tumors in a phase II study of stereotactic body radiation therapy for medically inoperable early-stage lung cancer. J Clin Oncol. 2006;24(30):4833–9.View ArticlePubMedGoogle Scholar
- Seamless Phase I/II Study of Stereotactic Lung Radiotherapy (SBRT) for Early Stage, Centrally Located, Non-Small Cell Lung Cancer (NSCLC) in Medically Inoperable Patients. https://www.rtog.org/ClinicalTrials/ProtocolTable/StudyDetails.aspx?study=0813. Accessed date: 6 Aug 2015.
- Mutter RW, Liu F, Abreu A, Yorke E, Jackson A, Rosenzweig KE. Dose-volume parameters predict for the development of chest wall pain after stereotactic body radiation for lung cancer. Int J Radiat Oncol Biol Phys. 2012;82(5):1783–90.PubMed CentralView ArticlePubMedGoogle Scholar
- Joiner MC, Bentzen SM. Time-dose relationships: the linear-quadratic approach. In: Steel GG, editor. Basic clinical radiobiology. London: Edward Arnold; 2002.Google Scholar
- Petillion S, Swinnen A, Defraene G, Verhoeven K, Weltens C, Van den Heuvel F. The photon dose calculation algorithm used in breast radiotherapy has significant impact on the parameters of radiobiological models. J Appl Clin Med Phys. 2014;15(4):4853.PubMedGoogle Scholar
- Willner J, Baier K, Caragiani E, Tschammler A, Flentje M. Dose, volume, and tumor control prediction in primary radiotherapy of non-small-cell lung cancer. Int J Radiat Oncol Biol Phys. 2002;52(2):382–9.View ArticlePubMedGoogle Scholar
- Martel MK, Ten Haken RK, Hazuka MB, Kessler ML, Strawderman M, Turrisi AT, et al. Estimation of tumor control probability model parameters from 3-D dose distributions of non-small cell lung cancer patients. Lung Cancer. 1999;24(1):31–7.View ArticlePubMedGoogle Scholar
- Guckenberger M, Wulf J, Mueller G, Krieger T, Baier K, Gabor M, et al. Dose-response relationship for image-guided stereotactic body radiotherapy of pulmonary tumors: relevance of 4D dose calculation. Int J Radiat Oncol Biol Phys. 2009;74(1):47–54.View ArticlePubMedGoogle Scholar
- Niemierko A. A generalized concept of equivalent uniform dose (EUD). Med Phys. 1999;26:1100.Google Scholar
- Seppenwoolde Y, Lebesque JV, de Jaeger K, Belderbos JS, Boersma LJ, Schilstra C, et al. Comparing different NTCP models that predict the incidence of radiation pneumonitis. Normal tissue complication probability. Int J Radiat Oncol Biol Phys. 2003;55(3):724–35.View ArticlePubMedGoogle Scholar
- Kwa SL, Lebesque JV, Theuws JC, Marks LB, Munley MT, Bentel G, et al. Radiation pneumonitis as a function of mean lung dose: an analysis of pooled data of 540 patients. Int J Radiat Oncol Biol Phys. 1998;42(1):1–9.View ArticlePubMedGoogle Scholar
- Scheenstra AE, Rossi MM, Belderbos JS, Damen EM, Lebesque JV, Sonke JJ. Alpha/beta ratio for normal lung tissue as estimated from lung cancer patients treated with stereotactic body and conventionally fractionated radiation therapy. Int J Radiat Oncol Biol Phys. 2014;88(1):224–8.View ArticlePubMedGoogle Scholar
- KruskalHK WWA. Use of ranks in one-criterion variance analysis. J Am Stat Assoc. 1952;47(260):583–621.View ArticleGoogle Scholar
- Sikora M, Muzik J, Söhn M, Weinmann M, Alber M, Monte Carlo V. pencil beam based optimization of stereotactic lung IMRT. Radiat Oncol. 2009;12(4):64.View ArticleGoogle Scholar
- Guckenberger M, Wilbert J, Krieger T, Richter A, Baier K, Meyer J, et al. Four-dimensional treatment planning for stereotactic body radiotherapy. Int J Radiat Oncol Biol Phys. 2007;69(1):276–85.View ArticlePubMedGoogle Scholar
- Marks LB, Bentzen SM, Deasy JO, Kong FM, Bradley JD, Vogelius IS, et al. Radiation dose-volume effects in the lung. Int J Radiat Oncol Biol Phys. 2010;76(3 Suppl):s70–6.PubMed CentralView ArticlePubMedGoogle Scholar
- Nielsen TB, Wieslander E, Fogliata A, Nielsen M, Hansen O, Brink C. Influence of dose calculation algorithms on the predicted dose distribution and NTCP values for NSCLC patients. Med Phys. 2011;38(5):2412–8.View ArticlePubMedGoogle Scholar
- Bufacchi A, Nardiello B, Capparella R, Begnozzi L. Clinical implications in the use of the PBC algorithm versus the AAA by comparison of different NTCP models/parameters. Radiat Oncol. 2013;8(1):164.PubMed CentralView ArticlePubMedGoogle Scholar
- Rana S, Rogers K. Radiobiological impact of Acuros XB dose calculation algorithm on low-risk prostate cancer treatment plans created by RapidArc technique. Austral-Asian J Cancer. 2012;11(4):261–9.Google Scholar
- Padmanaban S, Warren S, Walsh A, Partridge M, Hawkins MA. Comparison of Acuros (AXB) and Anisotropic Analytical Algorithm (AAA) for dose calculation in treatment of oesophageal cancer: effects on modelling tumour control probability. Radiat Oncol. 2014;9:286.PubMed CentralView ArticlePubMedGoogle Scholar
- Park C, Papiez L, Zhang S, Story M, Timmerman RD. Universal survival curve and single fraction equivalent dose: useful tools in understanding potency of ablative radiotherapy. Int J Rad Onc Biol Phys. 2008;70(3):847–52.View ArticleGoogle Scholar
- Park HJ, Griffin RJ, Hui S, Levitt SH, Song CW. Radiation-induced vascular damage in tumors: implications of vascular damage in ablative hypofractionated radiotherapy (SBRT and SRS). Radiat Res. 2012;177(3):311–27.View ArticlePubMedGoogle Scholar
- Song CW, Cho LC, Yuan J, Dusenbery KE, Griffin RJ, Levitt SH. Radiobiology of stereotactic body radiation therapy/stereotactic radiosurgery and the linear-quadratic model. Int J Radiat OncolBiol Phys. 2013;87(1):18–9.View ArticleGoogle Scholar
- Chapet O, Kong FM, Lee JS, Hayman JA, Ten Haken RK. Normal tissue complication probability modeling for acute esophagitis in patients treated with conformal radiation therapy for non-small cell lung cancer. Radiother Oncol. 2005;77(2):176–81.View ArticlePubMedGoogle Scholar
- Martel MK, Sahijdak WM, Ten Haken RK, Kessler ML, Turrisi AT. Fraction size and dose parameters related to the incidence of pericardial effusions. Int J Radiat Oncol Biol Phys. 1998;40(1):155–61.View ArticlePubMedGoogle Scholar
- AgrenCronqvist AK, Källman P, Turesson I, Brahme A. Volume and heterogeneity dependence of the dose-response relationship for head and neck tumours. Acta Oncol. 1995;34(6):851–60.View ArticleGoogle Scholar