

ORIGINAL ARTICLE 

Year : 2020  Volume
: 16
 Issue : 6  Page : 13231330 

Ipsilateral lung normal tissue complication probability parameters for different dose calculation algorithms in radiotherapy of breast cancer
Nasim Kavousi^{1}, Hassan Ali Nedaie^{2}, Somayeh Gholami^{2}, Mahbod Esfahani^{3}, Sajad Shafiekhani^{4}, Mohssen Hassani^{4}
^{1} Department of Medical Physic,Faculty of Medicine, Mashhad University of Medical Sciences, Mashhad, Iran ^{2} Radiation Oncology Research Center, Cancer Institute; Department of Medical Physics and Medical Engineering, Faculty of Medicine, Tehran University of Medical Sciences, Tehran, Iran ^{3} Radiation Oncology Research Center, Cancer Institute, Tehran University of Medical Sciences, Tehran, Iran ^{4} Department of Medical Physics and Medical Engineering, Faculty of Medicine, Tehran University of Medical Sciences, Tehran, Iran
Date of Submission  22Dec2019 
Date of Decision  07Apr2020 
Date of Acceptance  18Jun2020 
Date of Web Publication  18Dec2020 
Correspondence Address: Somayeh Gholami Radiation Oncology Research Center, Cancer Institute, Tehran University of Medical Sciences, Keshavarz Blvd., Poursina Ave., Tehran 141556447 Iran
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/jcrt.JCRT_1149_19
Purpose: Different dose calculation algorithms (DCAs) predict different dose distributions for the same treatment. Awareness of optimal model parameters is vital for estimating normal tissue complication probability (NTCP) for different algorithms. The aim is to determine the NTCP parameter values for different DCAs in leftsided breast radiotherapy, using the LymanKutcherBurman (LKB) model. Materials and Methods: First, the methodology recommended by International Atomic Energy Agency TECDOC 1583 was used to establish the accuracy of dose calculations of different DCAs including: Monte Carlo (MC) and collapsed cone algorithms implemented in Monaco, pencil beam convolution (PBC) and analytical anisotropic algorithm (AAA) implemented in Eclipse, and superposition and Clarkson algorithms implemented in PCRT3D treatment planning systems (TPSs). Then, treatment planning of 15 patients with leftsided breast cancer was performed by the mentioned DCAs and NTCP of the leftlung normal tissue were calculated for each patient individually, using the LKB model. For the PB algorithm, the NTCP parameters were taken from previously published values and new model parameters obtained for each DCA, using the iterative least squares methods. Results: For all cases and DCAs, NTCP computation with the same model parameters resulted in >15% deviation in NTCP values. The new NTCP model parameters were classified according to the algorithm type. Thus, the discrepancy of NTCP computations was reduced up to 5% after utilizing adjusted model parameters. Conclusions: This paper confirms that the NTCP values for a given treatment type are different for the different DCAs. Thus, it is essential to introduce appropriate NTCP parameter values according to DCA adopted in TPS, to obtain a more precise estimation of lung NTCP. Hence, new parameter values, classified according to the DCAs, must be determined before introducing NTCP estimation in clinical practice.
Keywords: Dose calculation algorithm, ipsilateral lung normal tissue, LymanKutcherBurman model, normal tissue complication probability
How to cite this article: Kavousi N, Nedaie HA, Gholami S, Esfahani M, Shafiekhani S, Hassani M. Ipsilateral lung normal tissue complication probability parameters for different dose calculation algorithms in radiotherapy of breast cancer. J Can Res Ther 2020;16:132330 
How to cite this URL: Kavousi N, Nedaie HA, Gholami S, Esfahani M, Shafiekhani S, Hassani M. Ipsilateral lung normal tissue complication probability parameters for different dose calculation algorithms in radiotherapy of breast cancer. J Can Res Ther [serial online] 2020 [cited 2022 Jan 24];16:132330. Available from: https://www.cancerjournal.net/text.asp?2020/16/6/1323/303888 
> Introduction   
The aim of radiation therapy (RT) is to achieve a balance of maximization target dose with simultaneous minimization of the risk of complications in the tumor surrounding normal tissues.^{[1]} The most commonly used and available standards for evaluating radiotherapy treatment plans are based on the dosevolume histogram (DVH). DVH calculates physical dose distributions related to a structure volume.^{[2]} Recently, predicting normal tissue complication probabilities (NTCP) were recommended as substitutes of DVH.^{[3]} The application of biological index in the treatment plan evaluation can improve clinical outcomes. The biological indices, for example, tumor control probabilities (TCP) and NTCP, are important indicators in choosing appropriate treatment planning.^{[4],[5]}
In the late 1980s, several mathematical models have been developed to estimate the TCP and NTCP based on input parameters estimated from the analysis of clinical data.^{[4],[6],[7],[8],[9],[10],[11],[12]}
Numerous mathematical NTCP models such as LymanKutcherBurman (LKB), relative seriality, equivalent uniform dose (EUD) models, were proposed, validated, and started to be gradually implemented in the clinic as a plan evaluation tool.^{[6],[8],[13]} The LKB model is a widely used method for predicting NTCP and comparing radiotherapy treatment plans using biologically index.^{[3],[14],[15]} Emami et al.^{[16]} and Burman et al.^{[4]} were among the first who conducted a comprehensive study of radiation tolerance for normal tissues. The initial therapeutic judgments have been made according to their estimated model parameters. These parameter sets were obtained without considering tissue inhomogeneity which might lead to notable risks in predicting NTCP. Therefore, updating these estimates is an imperative issue. In the past, 3D dose calculations and following that the description of the NTCP and TCP were performed assuming the patient's body as water.^{[17],[18],[19],[20]} The basic limitation of these calculation algorithms is that they do not take into account the lateral electron scatters in the heterogeneous area.^{[21]} Furthermore, a number of studies have evaluated the impact of tissue inhomogeneity on dose calculations for lung cancer. It was concluded that the tissue inhomogeneity has a considerable impact on the dose calculation and is a challengeable issue for accurate dose computation in the RT of lung cancer.^{[17],[22],[23]}
In the past few years, several experimental studies have investigated the dose calculation accuracy particularly in lung heterogeneity.^{[18],[19]}
Recently, more advanced algorithms^{[24],[25],[26]} including the AAA, collapsed cone (CC), superposition (SP), and Monte Carlo (MC) methods became available in some commercial treatment planning systems (TPSs), which account for lateral electron transport.
By changing the algorithm type, under the same conditions (such as the same patient positioning, gantry rotation, and size of the field) dose distributions will differ. Consequently, conflicting and inaccurate NTCP values may be obtained.^{[27]} Thus, due to the appearance of different and more sophisticated dose calculation algorithms (DCAs) and the complexity of quantifying clinical outcomes of dose calculations, the value of the model parameters stays controversial.^{[25],[26],[28]} Therefore, optimal algorithmspecific model parameters for normal tissues need to be estimated. Recent studies on NTCP parameters suggest that different correctionbased DCAs (e.g., PB and pencil beam convolution [PBC]) can make analogous NTCP values,^{[28]} but this has not been confirmed and further research is needed to this effect. In spite of efforts and optimization of NTCP models in several studies, the accuracy of the obtained parameters yet needs to be verified to make them applicable in clinical judgment.^{[20],[29]}
For RT treatment of breast cancer, both threedimensional conformal radiotherapy (3DCRT) and intensitymodulated radiation therapy (IMRT) methods were adopted in the clinics.^{[30]} However, still in most cancer institutes around the world, the 3DCRT technique is preferred instead of the IMRT in the treatment of breast cancer.^{[31]} Besides, due to the high prevalence of this disease and presence a portion of the lung within the therapeutic field, it is vital that we introduce appropriate model parameters using dosimetry and clinical data of patients with breast cancer treated with the 3DCRT technique improve the quality of life in these patients. In this study, the LKB model parameters of the PB algorithm were considered as reference values based on the published clinical studies of pneumonitis. Then, we calculated optimal parameters for different DCAs and radiation pneumonitis of ipsilateral lung normal tissue in patients with leftsided breast cancer, by adopting a mathematical optimization method.
> Materials and Methods   
The flow chart of the process of this project is shown in [Figure 1]. The details would be described in the following subsections.
Treatment planning systems and dose calculations
For dose calculations, we considered PBC, and analytical anisotropic algorithm (AAA) in Eclipse™ v13 TPS (Varian, Palo Alto, California, USA), PB, MC, and CC in Monaco^{®} v5.10 TPS (CMS, Elekta, Crawley, UK), SP, and Clarkson algorithms in PCRT3D v6.0.2 TPS (TécnicasRadiofísicas, Zaragoza, Spain).
The accuracy of the treatment planning systems dose computation algorithms
The accuracy of the TPS dose computation algorithms at the presence of inhomogeneities such as lung has been validated using a CIRS semianthropomorphic phantom according to clinical tests proposed by IAEA TECDOC 1583^{[32]} [Figure 2]. In addition, a summary definition of tests is shown in [Table 1].  Figure 2: (a) A view of 002 LFC CIRS Thorax phantom. (b) Position of measurement points in CIRS thorax phantom
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 Table 1: Description of tests for checking the treatment planning system algorithms accuracy
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Treatment planning for leftsided breast cancer patients
In this study, we randomly selected 15 leftsided breast cancer patients (Group 1), all of whom were treated with conservative tangential technique. All the patients were scanned with computed tomography (CT) simulation GE (General Electric, USA). CT scans were performed at 3mm slice spacing. All the organs at risk (OARs) such as lung, heart, spinal cord, and thyroid, as well as planning target volumes (PTV) were individually contoured on the CT data set by the radiation oncologist. Treatment planning was performed based on a 3D conformal technique for all patients. All plans consisted of two tangential fields, toward the breast [Figure 3] and dose distributions were calculated using a 6 MV Xray linear accelerator machine (Elekta Compact 6 MV). The prescribed dose at the ICRU Reference Point was set at 50 Gy in 25 fractions, and the plans were performed using CT imaging of the thorax with a 2 mm dose calculation grid. Dose variations were kept between +7% and 5% in the PTV, and the treated volume was enclosed by the 47.5 Gy (=95% of the 50 Gy) isodose surface.^{[33]} Each plan was assessed for dose heterogeneity, target coverage, and conformity and dose limits of OARs.  Figure 3: View a treatment planning for a sample patient with left side breast cancer, using two tangential fields
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Normal lung tissue complication probability
The cumulative DVHs with 1Gy dose bins were calculated from the 3D dose distributions. These DVHs were converted to the differential DVHs (according to Gay's method),^{[34]} then the (Di, Vi) data pairs were obtained from the differential DVHs of each radiotherapy plan. A MATLAB (7.9.0 Math Works, Natick, MA) script was developed to calculate leftlung NTCP for each breast cancer patient, according to the model which was originally proposed by LKB.^{[8]} Radiationinduced pneumonitis was selected as the critical endpoint of lung NTCP. Equations (1–3) were considered for the NTCP calculations.^{[35]}
Whereas t depends on the slope m and the TD50 value
Where;
EUD is the EUD that can be applied to both tumors and normal tissues. It is calculated using the following formula:^{[36]}
Here, “TD_{50}” is the dose for a complication rate of 50%. The “m” is the slope of the doseresponse curve and parameter “n” describes the volume dependence of the target tissue. The Di is the dose given to a subvolume, v_{i}. The radiobiological parameters for the LKB model were obtained from three different studies, and were then utilized to calculate NTCP. [Table 2] shows the model parameters suggested by several studies.  Table 2: Summary of normal tissue complication probability modeling studies about normal lung tissue complications
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EUD and NTCP were computed by the parameters as reported previously. In the published studies and this work, the parameters were extracted on DVHs of the same breast cancer treatment and ipsilateral lung volume.
Optimization method for adjusting model parameters
Due to the difference in the accuracy of doses in different DCAs, the determination of the new NTCP parameters is necessary. The method for adjusting model parameters was implemented in a MATLAB program. The iterative least squares methods were used to derive new optimal NTCP model parameters for all algorithms. We aimed to find a minimum of an unconstrained multivariable function using a nonlinear programming solver. It is optimal to minimize f (x) function ?, where, f (x) is the cost function that returns a scalar and x is the vector of NTCP parameters, which leads to the same NTCP, in conjunction with the DVH of the other algorithm, as the published model parameters and the DVH from the PB calculation. For each DCA, model parameters were obtained according to the following steps:
 For each patient, NTCP values were calculated based on PB dose calculation and model parameters. The PB algorithm was selected as a reference for radiation lung pneumonitis, due to the availability of its parameters based on published clinical data.^{[28]} Parameters for PB calculations are estimated from analysis of clinical data for doseresponse relationships. These NTCP values will be referred to as PB NTCP
 For the same treatment planning feature, the dose distributions were recalculated for each investigated algorithm
 From each DCA (e.g., CC), NTCP values (CCbased) were calculated as a function of NTCP model parameters, which were subsequently used to minimize the cost function as the squared difference between PBbased NTCP and CCbased NTCP (Equation 4). With the present data, it is necessary to keep one model parameter fixed (“n”). The NTCP values for the i'th patient are named NTCP_{PBi} and NTCP_{CCi} for the PB and CC algorithms, respectively.
Where “N” is the number of patients, “x” is the parameters vector, “m” is the slope of the doseresponse curve, and “T” is the transpose symbol. Furthermore, we estimated the uncertainty of values of the new optimal model parameters distribution of the difference of NTCP_{PB}  NTCP_{CC}, σ^{2} according to Brink suggestion:^{[27]}
Validation of new model parameters
The aim was to validate the accuracy of the acquired new model parameters. A total of 10 new patients (Group 2) with leftsided breast cancer were randomly chosen from recently treated clinical cases. Treatment plannings were performed for these patients, using different DCAs and then NTCP values were calculated employing new parameters (calculated in the previous step). The computed NTCP values for the corresponding algorithms were compared.
Statistical analysis
Ttest procedure was run to estimate the significance of the NTCP value in Statistical Product and Service Solutions (SPSS) (IBM CO, New York, USA). The significance level was set at P < 0.05.
> Results   
Calculated dose differences
Deviations for each acceptance test, related dosimetric points, and their sum, were calculated for all studied DCAs. The result shows that the sum of the deviations did not exceed the critical value. Despite that, some algorithms indicated deviations outside the critical value in one or two dosimetric points of a specific test. In Clarkson and PBC algorithms, results showed 5% and 4% deviations out of critical value. The SP, AAA, and CC algorithms showed 0.9%, 3%, and 1% deviations out of agreement criteria, while in the MC algorithm, these values were <1%. DVHs of the ipsilateral lung for the studied DCAs were compared, for each pair of patients [Figure 4]. The result showed a higher volume in the lower doses for the advanced algorithm in comparison with the PB algorithm. It can be observed in the graphs below that lower dosages correspond to larger volumes in all the patients.  Figure 4: Cumulative dose volume histogram for the radiated lung (left lung) in one patient calculated with the pencil beam and collapsed cone, Monte Carlo, AAA, pencil beam convolution, superposition, and Clarkson algorithms
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Normal tissue complication probability for ipsilateral lung using the same model parameter
The average dose received by the clinical target volume was between =95% and <100% of the prescribed dose and PTV completely covered with the 95% isodose. [Table 3] represents the NTCP values, predicting radiationinduced pneumonitis for ipsilateral lung as an endpoint. Table 3shows that ipsilateral lung NTCPs are significantly different (P < 0.05), for different DCAs while using the same radiobiological parameters according to PB NTCP. This difference between NTCPs value from different algorithms can reach a value of >15%.  Table 3: Average normal tissue complication probability values calculated for different dose calculation algorithms
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NTCP curve is computed and plotted upon the different values of EUD for different DCAs as shown in [Figure 5]. [Figure 5] displays the NTCP diagram changes due to a change of DCA from PB (reference) to PBC, AAA, SP, CC, MC, and Clarkson algorithms.  Figure 5: Normal tissue complication probability values plotted against equivalent uniform dose for different algorithms. The line shows the normal tissue complication probability curve for different DACs, the model parameters were considered from Rancati et al. study^{[28]} for ipsilateral normal lung tissue complication
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A shift of the curve was observed that is imperative to generate the same NTCP value for DCAscalculated DVHs as for the reference PBcalculated DVH. As we can see in this figure, there are slight absolute variations in NTCP values at the bottom of the diagram, and the NTCP values rose by increasing EUD in all patients.
Model parameter optimization
[Table 4] shows a summary of the optimal NTCP model parameters for ipsilateral lung, which were obtained from the optimization method in the present study and a comparison with other published reports. The volumeeffect parameter, n = 0.91 was kept fixed to simplify calculations according to the Seppenwoolde et al. recommendation.^{[36]}  Table 4: Normal tissue complication probability parameter values for different dose calculation algorithms
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In addition, NTCP calculated values for different DCAs for the first group of 15 leftsided breast cancer patients with the new parameters (obtained from the optimization method), were presented in [Table 3] inside the parenthesis.
Validation of the new normal tissue complication probability model parameters
Results for validation of new NTCP model parameters for the #10 leftsided breast cancer patients (Group 2) are shown in [Table 5]. There were nonsignificant differences (P > 0.05) for NTCP values of the ipsilateral lung of each case compared to the calculation algorithms.  Table 5: Normal tissue complication probability values for the #10 new leftsided breast cancer patients (group 2) using optimal model parameters
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> Discussion   
The accurate model parameters are needed to incorporate biological index in a clinical decisionmaking process (e.g., NTCP presented by the LKB model). In the present study, we first compared available algorithms, which demonstrate that DCAs' accuracy is imperative for the inhomogeneous environment such as the lung. Then, we have derived optimal LKB model parameters for AAA, PBC, MC, CC, SP, and Clarkson algorithms, based on the PB algorithm as a reference [Table 4]. The LKB model parameters used to calculate the NTCP value for the PB calculations were obtained from Rancati et al.^{[29]} (ipsilateral lung): which was a study of breast cancer radiotherapy and NTCP model parameters were estimated from analysis of clinical data for doseresponse relationships.
Accuracy of dose calculation algorithms
Several studies have investigated the accuracy of DCAs for external beam radiotherapy.^{[17],[18],[19],[37]} All dose calculations of this study include tissue density inhomogeneity correction in computation. In some of them (e.g. PB, PBC, and Clarkson), the changes in lateral transport of electrons are not modeled and calculations systematically overestimate the local dose, >10%^{[20]} in the inhomogeneous regions such as lung. Instead, the MC is regarded as a highaccuracy algorithm and is widely used as a benchmark algorithm to evaluate other DCAs. The correctness of SP and CC computations (as a modelbased algorithm)^{[38],[39],[40],[41],[42]} was adjacent to the results of MC algorithm while it requires much less processing time. The AAA algorithm is a convolution SP model that^{[43],[44]} separate modeling for photons (primary and scattered), and electrons using spatially variant convolution scatter kernels.
Radiobiological parameter adjustment for normal tissue complication probability
The results presented in this study show >15% discrepancies in estimating NTCP value in the same patient for different DCAs [Table 3]. It was revealed that the new DCAs with lung heterogeneity correction influenced the DVHs and NTCP values.^{[4],[6],[27],[28]} This discrepancy can be due to the difference in calculated DVH and the radiobiological model parameters. The magnitude of this effect depends on the DCA, beam quality, and lung density. This result highlights the necessity of deriving new specific model parameters. By replacing a simple DCA (e.g., PB, PBC, and Clarkson) with an advanced algorithm (e.g., CC, AAA, SP, and MC), computation of the NTCP with un adapted model parameters leads to lower NTCP values. Our findings are consistent with previous studies. Petillion et al.^{[45]} have also reported lower NTCP value when using advanced algorithms. However, in some cases in Eclipse and Monaco, TPSs, AAA and MC yielded higher NTCP value compared to PBC, and CC calculations, respectively. Correctionbased algorithms do not clearly account for electron transfer, and lead to overestimating the dose in lung tissue, and affecting the NTCP computations.^{[28]} The parameters for PB and PBC algorithms showed a low variation. Thus, identical NTCP model parameters are recommended for both PB and PBC algorithms for NTCP estimation while other algorithms need an alteration in the NTCP model parameters (the volumeeffect parameter, n, was kept fixed at 0.91). Hedin and Bäck^{[28]} previously studied 10 breast cancer patients and determined specific model parameters for CC, AAA, and PBC DCAs concerning different grades of pneumonitis. New optimal model parameters for CC, AAA, and PBC DCAs in our study are in the same range of Hedin's studies with 5.63%, 4.84%, and 2.71% difference in parameter TD50, and 2.15%, 1.84%, and 1.50% difference in parameter m, respectively. The difference in parameter value compared to this study may be due to the smaller patient population, and the more specific endpoint. In addition to that, we have obtained new model parameters for Clarkson, SP, and MC DCAs. In a study by Nielsen et al.,^{[46]} the differences in calculated dose distributions and NTCP values of six different DCAs for nonsmall cell lung cancer patients were investigated. The authors found that for fixed values of parameters, the changes in NTCP can be up to 45%.^{[46]} It is therefore important when working with NTCP models in treatment planning to use NTCP parameter values related to the selected calculation method.^{[27],[28],[46]} The results obtained in our study are consistent with Nielsen et al.^{[46]} reports. Some factors may cause differences between planned and delivered dose, which are caused by setup errors, errors in organ contouring, dose calculation, specific model parameters, and dose delivery leading to uncertainty in NTCP calculations. In addition, the NTCP value is greatly influenced by the radiobiological model parameters as confirmed by other studies.^{[27],[28]} The difference between the dose distributions of the studied algorithms yields significant differences even >10% in the NTCP values for the same type of treatment plan and model parameters.^{[28]} The NTCP value obtained in another group of patients using new parameters are in accordance with the initial group of patients, which can lend support to the idea that the results are valid beyond the patient populations. However, further research is needed on the radiobiological parameters and their relationship with DCA. The application of the inaccurate parameter may lead to notable errors in the estimation of NTCP. Accordingly, the optimization of the NTCP model and radiobiological parameters for each radiation oncology department might be imperative to avoid the overestimation/underestimation of the NTCP values. It must be noted that the idea of establishing optimal parameters values has a much broader applicability region than just for breast and lung patients. In general, the parameters determined in this study are authentic only for breast cancer treatment and results depend highly on the treatment modalities. However, the subject stated in this study is a general problem. Furthermore, it is recommended that tumor control probability (TCP) calculations be performed in future studies. However, the TCP index should be maximized.
> Conclusions   
In this study, it was shown that NTCP values depend significantly on the choice of radiobiological parameters and both of them are affected when the calculation algorithm is changed. The radiobiological index can play a vital role in treatment planning optimization. However, uncertainty on model parameters value may influence treatment outcomes and patient safety. It is crucial to use NTCP parameter sets based on DCAs and treatment techniques; thus, it is essential to modify and gain strong model parameter values.
Acknowledgment
This research was supported by Tehran University of Medical Sciences as a master thesis number of 33446.
Financial support and sponsorship
Nil.
Conflicts of interest
There are no conflicts of interest.
> References   
1.  Brady LW, Wazer DE, Perez CA. Perez & Brady's Principles and Practice of Radiation Oncology. Philadelphia: Lippincott Williams & Wilkins; 2013. 
2.  Lyman JT, Wolbarst AB. Optimization of radiation therapy, IV: A dosevolume histogram reduction algorithm. Int J Radia Oncol Biol Physics 1989;17:4336. 
3.  Warkentin B, Stavrev P, Stavreva N, Field C, Fallone BG. A TCP NTCP estimation module using DVHs and known radiobiological models and parameter sets. J Appl Clin Med Phys 2004;5:5063. 
4.  Burman C, Kutcher G, Emami B, Goitein M. Fitting of normal tissue tolerance data to an analytic function. Int J Radia Oncol Biol Physics 1991;21:12335. 
5.  Shahzadeh S, Gholami S, Aghamiri SM, Mahani H, Nabavi M, Kalantari F. Evaluation of normal lung tissue complication probability in gated and conventional radiotherapy using the 4D XCAT digital phantom. Comput Biol Med 2018;97:219. 
6.  Lyman JT. Complication probability as assessed from dosevolume histograms. Radia Res 1985;104:S139. 
7.  Lyman JT, Wolbarst AB. Optimization of radiation therapy, III: A method of assessing complication probabilities from dosevolume histograms. Int J Radia Oncol Biol Physics 1987;13:1039. 
8.  Kutcher GJ, Burman C. Calculation of complication probability factors for nonuniform normal tissue irradiation: The effective volume method Gerald. Int J Radia Oncol Biol Physics 1989;16:162330. 
9.  Kutcher G, Burman C, Brewster L, Goitein M, Mohan R. Histogram reduction method for calculating complication probabilities for threedimensional treatment planning evaluations. Int J Radia Oncol Biol Physics 1991;21:13746. 
10.  Källman P, Ågren A, Brahme A. Tumour and normal tissue responses to fractionated nonuniform dose delivery. Int J Radia Biol 1992;62:24962. 
11.  Schultheiss TE, Orton CG. Models in radiotherapy: Definition of decision criteria. Med Phys 1985;12:1837. 
12.  Morrill S, Lane R, Jacobson G, Rosen I. Treatment planning optimization using constrained simulated annealing. Physics Med Biol 1991;36:1341. 
13.  Niemierko A. A generalized concept of equivalent uniform dose (EUD). Med Phys 1999;26:1100. 
14.  SanchezNieto B, Nahum A. BIOPLAN: Software for the biological evaluation of radiotherapy treatment plans. Med Dosimetry 2000;25:716. 
15.  Miften MM, Das SK, Su M, Marks LB. A dose volume based tool for evaluating and ranking IMRT treatment plans. J Appl Clin Med Phys 2004;5:114. 
16.  Emami B, Lyman J, Brown A, Cola L, Goitein M, Munzenrider J, et al. Tolerance of normal tissue to therapeutic irradiation. Int J Radia Oncol Biol Phys 1991;21:10922. 
17.  Narabayashi M, Mizowaki T, Matsuo Y, Nakamura M, Takayama K, Norihisa Y, et al. Dosimetric evaluation of the impacts of different heterogeneity correction algorithms on target doses in stereotactic body radiation therapy for lung tumors. J Radiat Res 2012;53:77784. 
18.  Knöös T, Wieslander E, Cozzi L, Brink C, Fogliata A, Albers D, et al. Comparison of dose calculation algorithms for treatment planning in external photon beam therapy for clinical situations. Phys Med Biol 2006;51:5785. 
19.  Fogliata A, Vanetti E, Albers D, Brink C, Clivio A, Knöös T, et al. On the dosimetric behaviour of photon dose calculation algorithms in the presence of simple geometric heterogeneities: Comparison with Monte Carlo calculations. Phys Med Biol 2007;52:1363. 
20.  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 Radia Oncol Biol Physics 1998;42:19. 
21.  Engelsman M, Damen EM, Koken PW, van 't Veld AA, van Ingen KM, Mijnheer BJ. Impact of simple tissue inhomogeneity correction algorithms on conformal radiotherapy of lung tumours. Radiother Oncol 2001;60:299309. 
22.  Gray A, Oliver LD, Johnston PN. The accuracy of the pencil beam convolution and anisotropic analytical algorithms in predicting the dose effects due to attenuation from immobilization devices and large air gaps. Med Phys 2009;36:318191. 
23.  Rana S, Pokharel S. Verification of dose calculation algorithms in a multilayer heterogeneous phantom using films. Gulf J Oncol 2013;1:63. 
24.  Gershkevitsh E, Schmidt R, Velez G, Miller D, Korf E, Yip F, et al. Dosimetric verification of radiotherapy treatment planning systems: Results of IAEA pilot study. Radiother Oncol 2008;89:33846. 
25.  Maes D, Saini J, Zeng J, Rengan R, Wong T, Bowen SR. Advanced proton beam dosimetry part II: Monte Carlo vs. pencil beambased planning for lung cancer. Transl Lung Cancer Res 2018;7:114. 
26.  Saini J, Traneus E, Maes D, Regmi R, Bowen SR, Bloch C, et al. Advanced proton beam dosimetry part I: Review and performance evaluation of dose calculation algorithms. Transl Lung Cancer Res 2018;7:1719. 
27.  Brink C, Berg M, Nielsen M. Sensitivity of NTCP parameter values against a change of dose calculation algorithm. Med Phys 2007;34:357986. 
28.  Hedin E, Bäck A. Influence of different dose calculation algorithms on the estimate of NTCP for lung complications. J Appl Clin Med Phys 2013;14:12739. 
29.  Rancati T, Wennberg B, Lind P, Svane G, Gagliardi G. Early clinical and radiological pulmonary complications following breast cancer radiation therapy: NTCP fit with four different models. Radiother Oncol 2007;82:30816. 
30.  Mock U, Georg D, Bogner J, Auberger T, Pötter R. Treatment planning comparison of conventional, 3D conformal, and intensitymodulated photon (IMRT) and proton therapy for paranasal sinus carcinoma. Int J Radia Oncol Biol Phys 2004;58:14754. 
31.  Beckham WA, Popescu CC, Patenaude VV, Wai ES, Olivotto IA. Is multibeam IMRT better than standard treatment for patients with leftsided breast cancer? Int J Radia Oncol Biol Phys 2007;69:91824. 
32.  TecDoc I. 1583: Commissioning of Radiotherapy Treatment Planning Systems: Testing for Typical External Beam Treatment Techniques. Vienna: International Atomic Energy Agency; 2008. 
33.  Stroom JC, Heijmen BJ. Geometrical uncertainties, radiotherapy planning margins, and the ICRU62 report. Radiother Oncol 2002;64:7583. 
34.  Gay HA, Niemierko A. A free program for calculating EUDbased NTCP and TCP in external beam radiotherapy. Phys Med 2007;23:11525. 
35.  Martel MK, Ten Haken RK, Hazuka MB, Turrisi AT, Fraass BA, Lichter AS. Dosevolume histogram and 3D treatment planning evaluation of patients with pneumonitis. Int J Radia Oncol Biol Phys 1994;28:57581. 
36.  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. Int J Radia Oncol Biol Phys 2003;55:72435. 
37.  Kavousi N, Nedaie HA, Gholami S, Esfahani M. Evaluation of dose calculation algorithms accuracy for eclipse, PCRT3D, and monaco treatment planning systems using IAEA TPS commissioning tests in a Heterogeneous Phantom. Iran J Med Phys 2019;16:286. 
38.  Boyer A, Mok E. A photon dose distribution model employing convolution calculations. Med Phys 1985;12:16977. 
39.  Mackie T, Scrimger J, Battista J. A convolution method of calculating dose for 15MVxrays. Med Phys 1985;12:18896. 
40.  Mohan R, Chui C, Lidofsky L. Differential pencil beam dose computation model for photons. Med Phys 1986;13:6473. 
41.  Ahnesjö A. Collapsed cone convolution of radiant energy for photon dose calculation in heterogeneous media. Med Phys 1989;16:57792. 
42.  Fogliata A, Nicolini G, Vanetti E, Clivio A, Cozzi L. Dosimetric validation of the anisotropic analytical algorithm for photon dose calculation: Fundamental characterization in water. Phys Med Biol 2006;51:1421. 
43.  Ulmer W, Kaissl W. The inverse problem of a Gaussian convolution and its application to the finite size of the measurement chambers/detectors in photon and proton dosimetry Phys Med Biol 2003;48:707. 
44.  Sievinen J, Ulmer W, Kaissl W. AAA Photon dose Calculation Model in Eclipse. Palo Alto (CA). Varian Med Syst 2005;118:2894. 
45.  Petillion S, Swinnen A, Defraene G, Verhoeven K, Weltens C, den Heuvel FV. The photon dose calculation algorithm used in breast radiotherapy has significant impact on the parameters of radiobiological models. J Appl Clin Med Phys 2014;15:25969. 
46.  Nielsen TB, Wieslander E, Fogliata A, Nielsen M, Hansen O, Brink C. Influence of dose calculation algorithms on the predicted dose distributions and NTCP values for NSCLC patients. Med Phys 2011;38:24128. 
[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5]
[Table 1], [Table 2], [Table 3], [Table 4], [Table 5]
