

ORIGINAL ARTICLE 

Year : 2017  Volume
: 13
 Issue : 3  Page : 501509 

Evaluation of the accuracy of various dose calculation algorithms of a commercial treatment planning system in the presence of hip prosthesis and comparison with Monte Carlo
Kheirollah Mohammadi^{1}, Mohsen Hassani^{2}, Mahdi Ghorbani^{3}, Bagher Farhood^{4}, Courtney Knaup^{5}
^{1} Department of Physics, MalekAshtar University of Technology, Tehran, Iran ^{2} Department of Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran ^{3} Department of Biomedical Engineering and Medical Physics, Faculty of Medicine, Shahid Beheshti University of Medical Sciences, Tehran, Iran ^{4} Department of Medical Physics and Biomedical Engineering, Faculty of Medicine, Tehran University of Medical Sciences, Tehran, Iran ^{5} Comprehensive Cancer Centers of Nevada, Las Vegas, Nevada, USA
Date of Web Publication  31Aug2017 
Correspondence Address: Kheirollah Mohammadi Department of Physics, Malek.Ashtar University of Technology, Tehran Iran
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/09731482.204903
Purpose: High atomic number elements are commonly used in a hip prosthesis which can cause uncertainty in accurate dose calculations in radiation therapy. The aim of this study is to assess the accuracy of the three various algorithms of ISOgray treatment planning system in the presence of hip prosthesis by Monte Carlo (MC). Materials and Methods: A MC model of Siemens PRIMUS linear accelerator has been built and verified by the measured data of the different algorithms of ISOgray treatment planning systems (TPS) in 6 and 15 MV photon beam energies. Two types of hip prosthesis have been used: stainless steel and titanium. The accuracy of mentioned dose calculation algorithms in the presence of hip prosthesis was evaluated. Results: There were 24.78%, 27.68%, and 27.72% errors in fast Fourier transform (FFT) Convolution, collapsed cone (CC), and superposition in 6 MV photon beam and 26.45%, 30.45%, and 28.63% in 15 MV photon beam for titanium type, respectively. However, there were 32.84%, 35.89%, and 35.57% in 6 MV photon beam and 38.81%, 47.31%, and 39.91% errors in 15 MV photon beam in steel type, respectively. In addition, the ISOgray TPS algorithms are not able to predict the dose enhancement and reduction at the proximal and distal prosthesis interfaces, respectively. Conclusions: Hip prosthesis creates a considerable disturbance in dose distribution which cannot be predicted accurately by the FFT convolution, CC, and superposition algorithms. It is recommended to use of MCbased TPS for the treatment fields including the hip prosthesis.
Keywords: Dose calculation algorithm, hip prosthesis, Monte Carlo, radiotherapy, treatment planning system
How to cite this article: Mohammadi K, Hassani M, Ghorbani M, Farhood B, Knaup C. Evaluation of the accuracy of various dose calculation algorithms of a commercial treatment planning system in the presence of hip prosthesis and comparison with Monte Carlo. J Can Res Ther 2017;13:5019 
How to cite this URL: Mohammadi K, Hassani M, Ghorbani M, Farhood B, Knaup C. Evaluation of the accuracy of various dose calculation algorithms of a commercial treatment planning system in the presence of hip prosthesis and comparison with Monte Carlo. J Can Res Ther [serial online] 2017 [cited 2020 Jun 4];13:5019. Available from: http://www.cancerjournal.net/text.asp?2017/13/3/501/204903 
> Introduction   
Recently, patients undergoing radiation therapy of the pelvic region constitutes a significant portion of all the patients treated with radiation therapy. During the past several decades, worldwide, the number of people with implanted hip prostheses has increased.^{[1],[2]} According to the report of Task Group No. 63 of the American Association of Physicists in Medicine, 1%–4% of radiation therapy patients have prosthetic. These devices are commonly made from high atomic number (highZ) elements (highZ materials are defined as a material with an atomic number higher than cortical bone).^{[3]} Hip prostheses are made from cobaltchromemolybdenum (CoCrMo) alloys because they are considered to have the best balance of corrosion resistance, mechanical strength, and resistance to fatigue. However, both stainless steel and titanium hip prostheses are also available, and the vast majority of artificial hips in clinical use are made from these materials.^{[4],[5],[6],[7],[8]}
For radiation therapy treatment planning of patients with bilateral or unilateral implants, two main challenges exist. First, the hip implant made from a highZ material generates significant artifacts in the computed tomography (CT) images that have a vital role in radiation therapy dose calculation.^{[9],[10]} Second, the presence of highZ material generates a considerable attenuation to the beam down range of the implant, which effects the dose distribution in that region. Furthermore, there is a dose peak upstream from the material surface due to radiation backscatter from the implant.^{[2]} In other words, treatment planning in the presence of a hip prosthesis is difficult owing to the effects of prosthesis on dose distribution. In threedimensional (3D) treatment planning, CT images are applied. Although CT is able to provide detailed information about the densities of the internal structures and their geometries in most clinical condition, metallic implants generate artifacts.^{[1]} They also cause significant beamhardening artifacts, CT number errors and produce partial image loss, and geometry error in the CT images. These artifacts cause considerable dose calculation errors in computerized treatment planning systems (TPSs).^{[11]} In addition, the limitations of the TPSs in modeling the charged particle generation and photon scattering from various materials will result to significant errors in their dose calculations.^{[3],[4],[12],[13],[14],[15],[16],[17]}
Knowledge about the prosthesis material may be unavailable, or the actual geometry may deviate from the supposed one. These points will result in an increase in dose to atrisk organs or considerable under or overdosage of the tumor. Therefore, potentially creating problems for the patient and compromise tumor control.^{[18]}
Application of Monte Carlo (MC) methods in dose calculation for treatment planning has shown that this method can be applied as a benchmarking implement to verify the other dose calculation algorithms.^{[1],[16],[19],[20],[21],[22],[23],[24]}
There are numerous studies, which have been carried out in the field of comparison of the results of MC simulations/measurement with the calculations commercial TPSs on dose perturbation produced by prostheses in radiation therapy.^{[4],[19],[25],[26]} Some of these studies are reviewed here: Çatli and Tanir,^{[25]} in an experimental and MC study, have evaluated Eclipse TPS for effects on dose distribution in the presence of hip prostheses. They showed that when a highZ material is applied in prosthesis; large dose changes can exist due to the radiation scattering from the prosthesis. The variance in dose observed in the study depended on material type, atomic number, and density as well as photon energy. The dose perturbation effect of hip prostheses was considerable and could not be predicted accurately by the pencil beam convolution (PBC) method. The results showed that for accurate dose calculation, a MCbased TPS should be used in patients with hip prostheses.
Keall et al.^{[4]} investigated the capability of different dose calculation algorithms to obtain accurate treatment plans in the case of highZ implants. In their study, dose distributions in phantom and patient geometries with highZ prostheses were calculated using MC, pencil beam (PB), superposition, and heterogeneity correction algorithms. The results indicated that treatment plans calculated with superposition have similar isodose curves, tumor control probability, normal tissue complication probability, and dosevolume histograms as the MC plan. On the other hand, treatment plans calculated with either no heterogeneity correction or PB methods varied significantly from the MC plans.
Ojala et al.^{[26]} evaluated the accuracy of the Acuros XB (AXB) algorithm in volumetric modulated arc therapy technique by MC simulations. In their study, the calculated dose distribution by AXB algorithm was compared to the MC simulation to assess the accuracy of the AXB algorithm in clinical situations. The agreement between AXB algorithm and MC model was very good in the vicinity, inside of the implant and elsewhere. The results verified the accuracy of the AXB algorithm for patient treatment planning with beams traversing through a highZ material.
Wieslander and Knöös^{[19]} carried out a study on dose perturbation in the presence of metallic implants (treatment planning system versus MC simulations). They used two algorithms, i.e., PB and the collapsed cone (CC) for 6 and 18 MV photon beam. The CC algorithm showed overall a better agreement with MC simulations than the PB algorithm. Finally, they recommended to use the CC algorithm to achieve the more accurate dose calculation for both tissues adjacent to the implants and for the planning target volume when the beams are set up to pass through implants.
Although there are various investigations on different TPSs and calculation algorithms, to the best of our knowledge, there is not any investigation on the accuracy of dose calculation of ISOgray treatment planning system in the presence of hip prostheses. In the present study, the accuracy of different dose calculation algorithms; fastFourier transform (FFT) convolution, CC convolution (CCC), and superposition convolution of ISOgray treatment planning system are evaluated in the presence of hip prosthesis by MC simulation.
> Materials and Methods   
Monte Carlo simulation of Siemens PRIMUS linear accelerator
In the present study, a MCNPX (version 2.6.0) radiation transport MC code was used to simulate a Siemens PRIMUS medical linear accelerator (Siemens AG, Erlangen, Germany). This code allows the development of a 3D model of the treatment head of a linear accelerator and dose calculation in various materials and complex geometries.^{[27]} The 6 MV and 15 MV photon modes of a Siemens PRIMUS linear accelerator were simulated based on the geometry information from the manufacturer. The main components of the linear accelerator's head for 6 and 15 MV photon modes are target, primary collimator, absorber (15 MV), flattening filter, photon dose chamber, as well as Y and X jaws. A water phantom of 32 cm × 32 cm × 40 cm in dimensions was defined and positioned under the treatment head at a source to surface distance (SSD) of 100 cm. In the simulations for percentage depth dose (PDD) in 6 and 15 MV, a cylinder was defined with 0.5 cm in radius (for 10 × 10 field sizes) to fulfill depth dose calculation for different depths of the water phantom. The cylinder axis was assumed to be on the beams central axis. The cylinder was then divided into small cells, with 2 mm in height that named scoring cells. To calculate beam profiles in 6 and 15 MV photon, we used 51 cubic scoring cells as the main axes of scoring cells were perpendicular to the central axis of the beam and dimension of them are 0.2 cm × 1 cm × 1 cm. The cubes were positioned at 5 cm depth of the water phantom, for 10 × 10 field size. The energy cutoffs for electrons and photons were set to 0.5 and 0.01 MeV, respectively, in the simulations for PDD and profiles calculations and all input files by *F8 tally were run for 2 × 10^{9} particle histories. The statistical uncertainties were <1.4% in all energies.
To verify our simulation data, we have compared our MC results with the corresponding measured values using gamma function method. Measurements were performed on a Siemens PRIMUS medical linear accelerator with 6 and 15 MV nominal photon energy. Dosimetry was performed using PTWFreiburg Mephysto Export V.6.0 at Radiotherapy Department of Sadra Center (Qom, Iran).
In gamma function method, if gamma value is between 0 and 1, it is considered a pass. On the other hand, values exceeding 1 are considered to as fail.^{[28]}
Gamma function criteria that are typically used are 3% for dose difference (DD) and 3 mm for distance to agreement (DTA).^{[29],[30],[31],[32]} However, other combinations have been used in the clinic.^{[28],[33],[34]} Most of the available gamma function software compares twodimensional dose distributions, but we needed a software capable of comparing onedimensional relative dose distributions with respect to our PDD and dose profile data. Special gamma function software has been prepared by DOSIsoft Company (Cachan, France). The software (Gamma_index.exe) is working under Gnuplot software environment (version: 4.4 patch level 3, Geeknet Inc., Fairfax, VA). In the present study, in calculation for gamma function, we have used DD and DTA criteria equal to 3% and 3 mm, respectively.
Treatment planning systems dose calculation algorithms
ISOgray TPS employs three algorithms to calculate dose distribution in 3D space. These algorithms are FFT convolution, CCC, and superposition convolution that categorize the modelbased algorithm that widely used in commercial radiotherapy TPSs. The calculation modelbased algorithm has two methods for calculating dose: one representing the energy imparted to the medium by the interactions of primary photons called total energy released per unit mass (TERMA) and another one representing the energy deposited about a primary photon interaction site, the kernel. The dose at any point can be calculated from the convolution of the TERMA with the kernel. To account for tissue heterogeneities in a patient, kernel is scaled by radiological distances which are calculated from the material densities defined by CT images.^{[12]} Therefore, density of material, quality of CT image, and existence CT artifacts including beam hardening and metal artifacts arising from highdensity materials such as prosthesis can affect the accuracy of TPSs.
In this study, we used two hip prostheses: stainless steel and titanium. The stainless steel was modeled as a cube with 3 cm × 3 cm × 7 cm in dimensions, and with a density of 6.45 g/cm^{3} as well as titanium as a cylinder with 18 cm in length, 1.5 cm in radius, and with a density of 4.48 g/cm^{3}. A water phantom of 30 cm × 30 cm × 30 cm in dimensions was used. Moreover, stainless steel and titanium “implants” were placed horizontally at a depth of 5 cm of that so that their longitudinal axis was perpendicular to the axis of the phantom.
The hip prosthesis phantoms were scanned on a CT scanner (Neusoft 16 slice). The axial mode was chosen to acquire 5 mm thick slices, with 5 mm separation, and all scans consisted of 24 images with 512 × 512 pixels. These images were entered into the ISOgray TPS, and dose values along the central axis were calculated by different algorithms within and after the prosthesis. It is notable that these calculations were performed in field size 10 cm × 10 cm, SSD of 100 cm, and energy 6 MV and 15 MV for 100 cGy in the surface of water phantom.
Monte Carlo dose calculation
For MC simulations, a water phantom of 50 cm × 50 cm × 50 cm in dimensions defined and was positioned under the treatment head (6 and 15 MV) at a SSD of 100 cm. Secondary collimators were set to create a field size of 10 cm × 10 cm on the phantom surface. The stainless steel (cube with 3 cm × 3 cm × 7 cm in dimensions and ρ = 6.45 g/cm^{3}) and titanium (cylinder with 18 cm in length, 1.5 cm in radius cm^{3}, and ρ = 4.48 g/cm^{3}) implants were simulated at a depth of 5 cm in a water phantom. The elemental compounds of the two hip prostheses are listed in [Table 1].^{[35]} The dose values on the central axis of the beam were calculated for these types of input files. Each prosthesis material was studied by a separate input file. In this case, *F8 tally was utilized for calculation of photon dose in depths ranging from 0 to 25 cm. Energy cutoff for both electrons and photons was set at 0.5 and 0.01 MeV, respectively. The input files used for calculation of photon dose were run for 2 × 10^{9} particles and the MC errors in the tally cells did not exceed 2.77%.  Table 1: Elemental composition (percentage fraction by weight) and mass density (ρ) of the hip prostheses materials used in this study
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Analysis of the results
For analysis of the results, TECDOC 1540^{[36]} and TRS 430^{[37]} protocols were used. These protocols include detailed information on quality assurance of TPSs. According to these protocols, the difference between the TPS dose calculation algorithms and the MC calculated dose is defined following:
δ (%), D_{TPS} and D_{MC} are a percent error, the calculated dose by TPS and the simulated dose by MC, respectively.
The backscattered dose perturbation factor (BSDF) at the entrance side of the highZ material can be calculated using BSDF = D_{i}/D_{h}, which D_{i} and D_{h} are the doses with and without the prosthesis, respectively.
> Results   
Validations of the Monte Carlo model
PDD values that were obtained by MC simulations and measurements for 6 and 15 MV photon beams are plotted in [Figure 1]a and [Figure 1]b, respectively. The data in the figure are related to 10 cm × 10 cm field size and SSD = 100 cm. As it was mentioned previously, comparisons of the simulation data of Siemens PRIMUS medical linear accelerator and measurement data were based on gamma function calculations. The data gamma function values applied for PDD comparisons have been plotted in [Figure 2]. Gamma calculations were performed using DD and DTA of 3% and 3 mm, respectively. According to the gamma data in [Figure 2], there are few points with gamma values greater than unity, which is interpreted as disagreement or fail at these points, are 2 and 0 points for 6 and 15 MV photon beams, respectively.  Figure 1: Percent depth dose values for 6 MV (a) and 15 MV (b) photon beam calculated by Monte Carlo code versus measurement data for 10 cm × 10 cm field size and source to surface distance = 100
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 Figure 2: Gamma function results for percentage depth dose values for 6 MV (a) and 15 MV (b) in 10 cm × 10 cm field size. Dose difference and distance to agreement criteria were set as 3% and 3 mm in the gamma calculations, respectively
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Dose profile values that were obtained by MC simulations and measurements for 6 and 15 MV photon beams are plotted in [Figure 3]. The data in the figures are related to 10 cm × 10 cm field size, SSD = 100 cm, and depth of 5 cm.  Figure 3: Dose profile data for 6 MV (a) and 15 MV (b) photon beam calculated by Monte Carlo code versus measurement data 10 cm × 10 cm field size, depth of 5 cm, and source to surface distance = 100
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The gamma function results of dose profile for 6 and 15 MV photon beams plotted in [Figure 4]. Gamma calculations were performed using DD and DTA limits of 3% and 3 mm, respectively. According to the gamma data in [Figure 4], there are several points of gamma values greater than unity. The number of points with gamma index of greater than unity is 9 and 6 points for 6 and 15 MV photon beams, respectively.  Figure 4: Gamma function results for dose profile data for 6 MV (a) and 15 MV (b) in 10 cm × 10 cm field size and depth of 5 cm. Dose difference and distance to agreement criteria were set as 3% and 3 mm in the gamma calculations, respectively
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Monte Carlo and treatment planning systems calculations for hip prostheses
In this section, the results of the calculations by various dose calculation algorithms of ISOgray TPS, in the presence of hip prosthesis along the beam's central axis of Siemens PRIMUS 6 and 15 MV photons was compared to data of MC simulations. The data presented are related to 10 cm × 10 cm, field size, and SSD = 100 cm in TPS algorithms and MC simulations. For TPS calculation, the prescribed dose was 100 cGy in the surface of water phantom. Furthermore, the hip prosthesis was placed at a depth of 5 cm in the water phantom. As it was mentioned previously, comparisons of the TPScalculated and MCsimulated data were expressed as percent error that has mentioned in Formula 1.
The PDD curves obtained from various dose calculation algorithms of ISOgray TPS (FFT convolution, collapsed cone, and superposition) and MC simulation in the presence of stainless steel and titanium for 6 and 15 MV photon beam are shown in [Figure 5]a,[Figure 5]b,[Figure 5]c,[Figure 5]d, respectively. For better comparison, PDD curve of the homogeneous water phantom was included in all figures.  Figure 5: Comparison of the dose reduction resulting from various dose calculation algorithms of ISOgray TPS and Monte Carlo simulation in the presence of the prostheses for source to surface distance = 100 cm, field size of 10 × 10 cm^{2}.(a) titanium6 MV; (b) stainless steel6 MV; (c) titanium15 MV; (d) stainless steel15 MV
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The MC simulation predicts dose intensification at the surface of the prosthesis which arises from backscattered electrons and photons of the prosthesis surface. The BSDFs at the entrance side of the highZ implants were calculated. The magnitude and the extent of this factor were calculated by comparing it to the homogeneous water phantom depthdose values and are shown in [Table 2]. It is seen that the BSDF is dependent on density and energy and is higher for the steel implant in 15 MV (1.14), and the extent of perturbation is about 5 mm, falling off rapidly with distance from the interface. The results are in accordance with the results of Gullane, in which comparable results for titanium and stainless steel were found for a 6 MV photon beam.^{[38]}  Table 2: Backscattered dose perturbation factor versus distance from interface for different implants
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According to MC simulation data, in proximal edge of the prosthesis, there is a maximum secondary dose (rebuildup) that it is due increased mass scattering power of the prosthesis relative to that of water. The dose perturbation at the downstream interface is the effect of the forward scattering electrons from the prosthesis material and the penetration depth of the electrons in the water. The extension of this rebuildup depends on the beam energy more than the prosthesis density.
Neither of the TPS algorithms predict the backscatter interface and rebuildup region behind the prostheses.
[Figure 6] displays the relative error (100 × [D_{TPS}− D_{MC}]/D_{MC}) of these PDD curves of MC and various algorithms of ISOgray TPS.  Figure 6: The relative errors (100× [D_{TPS}− D_{MC}])/D_{MC}) by various dose calculation algorithms of ISOgray treatment planning systems in the presence of the prosthesis. (a) Titanium6 MV; (b) stainless steel6 MV; (c) titanium15 MV; (d) stainless steel15 MV
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The results show that in 6 MV photon beam and in region after hip prostheses (>6.5 cm), using the calculations of FFT convolution, CC, and superposition can cause 24.78% (range: 18.17%–29.14%), 27.68% (range: 24.18%–30.72%), and 27.72% (range: 25.01%–30.41%) overdosage in the titanium and 32.84% (range: 25.26%–32.45%), 35.89% (range: 31.75%–39.58%). and 35.57% (range: 32.15%–39.11%) in stainless steel, respectively. In 15 MV photon beam, DDs were typically 26.45% (range: 18.68%–32.19%), 30.45% (range: 21.27%–36.16%), and 28.63% (range: 20.51%–33.11%) for titanium and 38.81% (range: 29.69%–46.77%), 47.31% (range: 33.41%–55.13%), and 39.91% (range: 30.58%–45.84%) for stainless steel, respectively. It is evident that the magnitude of error for TPS calculations increases with the density of the implants. This is more obvious in highenergy photon beam. It can be seen that the difference between the two methods is less for titanium and steel in 6 MV photon beam and remains approximately constant.
Comparison between FFT convolution, CC, and superposition algorithm indicated that FFT convolution algorithm shows more accuracy than other algorithms down range of prosthesis (>6.5 cm, <10 cm) and these differences between algorithms is less at greater depth (>10 cm) of prostheses.
> Discussion   
In the present study, the accuracy of various dose calculation algorithms of ISOgray TPS including FFT convolution, CC, and superposition in the presence of hip prosthesis (stainless still and titanium) has been evaluated using 6 and 15 MV photon beams by MC. The accuracy of the dose calculation algorithms in the vicinity of hip prosthesis materials is proportional to the complexity of physical process modeling. At the border surface of two media (hip prosthesis and body tissue), the FFT convolution, CC, andsuperposition algorithms have limitations in dose calculation. The mentioned TPS algorithms cannot predict overdose from backscatter radiation on the edge of prostheses due to their dense materials, unlike simulation calculations.
The maximum underdosage of TPS algorithms was observed up to 7 mm above the surface between dense material and water which occurred in steel in 15 MV photon beam (BSDF = 1.14), this value decreases with atomic number and beam energy. Increasing the dose at the border of prosthesis and other media can be significant and may increase the probability of necrosis in bone and soft tissue. An improvement of the kernels could be generated in different media as suggested by Papanikolaou and Mackie^{[39],[40]} and the corrections of Sauer.^{[41]}
The rebuildup region which occurs behind the implant is more visible for lowdensity material (Titanium) and high energy photon beam (15 MV); this is in a conflict with the results of Sung Lin et al.^{[11]} None of the TPS algorithms cannot predict rebuildup in the shadow of the prostheses.
In 6 MV photon beam, the average error of the FFT convolution, CC, and superposition was 24.78%, 27.68%, and 27.72% in the titanium and 32.84%, 35.89%, and 35.57% in stainless steel, respectively. In 15 MV photon beam, the average error was 26.45%, 30.45%, and 28.63% in titanium and 38.81%, 47.31%, and 39.91% in stainless steel, respectively.
Ojala et al.^{[26]} showed that there were small deviations in dose distributions calculated by the AXB algorithm, on average within 2.5%, when compared to the MC model and measurements. The performance was considered acceptable which verifies the accuracy of the AXB algorithm for patient plans with beams passing highZ material. In addition, they showed that the use of the anisotropic analytic algorithm is not encouraged because of increased error in dose distributions in the vicinity of and downstream from the prosthesis due to inaccurate modeling of the backscatter and beam attenuation in the prosthesis, respectively. In another study, Wieslander and Knöös^{[19]} demonstrated that for CC algorithm at 6 cm beyond the cavities of different steel alloys, TiAlV, Ti, and CoCrMo, the calculated dose by CC algorithm was within −0.8%–7.3% for 18 MV and −2.2%–5.2% for 6 MV compared to MC. For TiAlV and Ti, the calculated dose by PB algorithm was within 4%–6% beyond the cavity for both energies of 6 and 18 MV. In addition, for the CoCrMo cavity and the two steel cavities, the calculated dose by PB algorithm was within 4%–15% for 6 MV beam depending on the depth beyond the cavity. Finally, they concluded that the difference in dose between PB and MC in the highZ cavity is due to both drawbacks of the PB algorithm and differences in elemental composition between the highZ media and water. In another study, Lloyd and Ansbacher^{[42]} concluded that AXB algorithm is a beneficial dose calculation tool for treatments with highZ materials, as its accuracy is equal to MC, yet fast enough for clinical application. Lin et al.^{[11]} showed that scattered radiation from highZ materials is significant and could not be predicted precisely in ADAC TPS. Ding and Yu^{[1]} found that CADPLAN TPS is inaccurate in calculating doses for beams traversing a highZ material, as this TPS notably underestimated the attenuation of hip prostheses because of its limitation in assigning the electron density of the prostheses. Catli and Tanir^{[25]} demonstrated that the dose perturbation effect of hip prostheses was considerable and could not be predicted accurately by the PBC algorithm for hip prostheses. Their findings showed that for accurate dose calculation, the MCbased TPS should be applied in patients with hip prosthesis. It is notable that because of the use of different algorithms and TPSs in the abovementioned studies^{[1],[11],[19],[25],[26],[42]} and the present study, the DDs between TPS and MC simulation at various distances from highZ materials in these studies cannot be compared precisely with each other.
The CT numbers of ISOgray TPS correspond to an electron density ratio of 2.90 in titanium and 3.1 in steel, which is lower than the electron density ratio of titanium (3.78) and steel (4.2) in MC simulation. These differences in electron density cause photoelectric and Compton interactions to decrease, as higher dose after the prostheses predicted.
This study shows that the uncertainties arisen by TPS can clinically cause uncertainties in received dose by the patients, and therefore, a reasonable correction must be considered in treatment plans. In addition, in the heterogeneous media with high density, the MCbased TPS should be used.
In the present study, a standard phantom was used in the calculations. An anthropomorphic phantom such as RANDO phantom contains geometries and material compositions which are more similar to the human body. It is obvious that application of a standard phantom instead of anthropomorphic phantom causes some restrictions to compare our results with actual human body. As a subject for future study, evaluation of the accuracy of the algorithms applied in this study and dose calculation in anthropomorphic phantom will be interesting.
> Conclusions   
The accuracy of ISOgray TPS algorithms including FFT convolution, CC, and superposition in the presence of hip prostheses was studied using the MC method for 6 and 15 MV photon beams.
We found that the ISOgray algorithms lack precision in dose calculation when passing through a highdensity material. Comparison of the MC and algorithms results showed that uncertainty of TPS algorithms increases with photon energy and density of hip prostheses. In addition, TPS algorithms cannot predict increased dose arising from backscatter and rebuildup in surface and shadow of the hip prostheses. The problems such as artifacts in images and inaccuracy in dose calculations by TPS algorithms may introduce errors in the delivered dose to lesion and received dose by OARs such as bladder, rectum, prostate, and uterus in a patient with hip prostheses. Our study recommends the use of the MCbased TPS for accurate dose calculation in the presence of a hip prosthesis.
Acknowledgment
The authors would like to thank MalekAshtar University of Technology, Cancer Institute of Tehran University of Medical Sciences and Sadra Radiotherapy Center staffs who helped to carrying out this project.
Financial support and sponsorship
MalekAshtar University staffs and radiation physics department staffs (Cancer Institute, Tehran University of Medical Sciences) have financially supported the work, and this is stated in the acknowledgment section of the article.
Conflicts of interest
There are no conflicts of interest.
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[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6]
[Table 1], [Table 2]
