Dosimetric verification of lung phantom calculated by collapsed cone convolution: A Monte Carlo and experimental evaluation

Abstract

OBJECTIVE:

To evaluate the dose calculation accuracy in the Prowess Panther treatment planning system (TPS) using the collapsed cone convolution (CCC) algorithm.

METHODS:

The BEAMnrc Monte Carlo (MC) package was used to predict the dose distribution of photon beams produced by the Oncor^® linear accelerator (linac). The MC model of an 18 MV photon beam was verified by measurement using a p-type diode dosimeter. Percent depth dose (PDD) and dose profiles were used for comparison based on three field sizes: 5×5, 10×10, and 20×20cm². The accuracy of the CCC dosimetry was also evaluated using a plan composed of a simple parallel-opposed field (11×16cm²) in a lung phantom comprised of four tissue simulating media namely, lung, soft tissue, bone and spinal cord. The CCC dose calculation accuracy was evaluated by MC simulation and measurements according to the dose difference and 3D gamma analysis. Gamma analysis was carried out through comparison of the Monte Carlo simulation and the TPS calculated dose.

RESULTS:

Compared to the dosimetric results measured by the Farmer chamber, the CCC algorithm underestimated dose in the planning target volume (PTV), right lung and lung-tissue interface regions by about –0.11%, –1.6 %, and –2.9%, respectively. Moreover, the CCC algorithm underestimated the dose at the PTV, right lung and lung-tissue interface regions in the order of –0.34%, –0.4% and –3.5%, respectively, when compared to the MC simulation. Gamma analysis results showed that the passing rates within the PTV and heterogeneous region were above 59% and 76%. For the right lung and spinal cord, the passing rates were above 80% for all gamma criteria.

CONCLUSIONS:

This study demonstrates that the CCC algorithm has potential to calculate dose with sufficient accuracy for 3D conformal radiotherapy within the thorax where a significant amount of tissue heterogeneity exists.

Keywords

Monte Carlo treatment planning collapsed cone convolution 3D conformal radiotherapy

1 Introduction

Globally, lung cancer is the main leading cause of cancer-related death and the most frequently diagnosed cancer among males and females [1]. A variety of treatment options exist for lung cancer such as surgery, chemotherapy, radiotherapy and brachytherapy [2]. Among them, radiotherapy is a common modality of treatment for patients who have lung cancer. The goal of radiotherapy is to eradicate or control the cancerous tissues while minimizing toxicity to normal tissue [3]. As a result, treatment planning systems (TPSs) are used to calculate and optimize dose distribution in radiotherapy. Dose calculation algorithms can generally be classified into correction based, model based and Monte-Carlo based algorithms. Model based algorithms have traditionally offered the most suitable balance between accuracy and processing time and thus are most commonly implemented in computerized treatment planning systems. There are two prevalent model based algorithms: collapsed cone convolution (CCC) and Anisotropic Analytical Algorithm (AAA) [4]. The accuracy of the dose calculation directly affects the quality and reliability of radiotherapy treatment planning. Accurate dose calculation at the border between two media such as a bone-tissue or lung-tissue interface remains a challenge for most treatment planning systems. Due to the presence of tissues with different electron densities, electronic disequilibrium occurs in these regions which can be difficult to model leading to dosimetric inaccuracies [5, 6]. The ability of model based algorithms to accurately predict dose at tissue interfaces has been evaluated by many authors [7 –11]. For instance, Han et al. [12] investigated the dosimetric accuracy of the CCC and AAA algorithms for IMRT and VMAT treatment techniques using a head-and-neck phantom. They reported dosimetric errors for CCC and AAA algorithms on the order of 11% and 4.5% at lung-tissue interfaces, respectively. Other studies have shown a close relationship between dosimetric deviations and dose-response using tumor control probability (TCP) and normal tissue complication probability (NTCP) curves. A difference in dose of 5% might lead to a TCP change of 10% to 20% with even larger effects on the NTCP [5 , 14]. Therefore, accurate dose calculation is essential to the efficacy of radiation therapy.

Currently, Monte Carlo (MC) algorithms are viewed as the gold standard for dose calculation in radiotherapy because they simulate all physical interactions that contribute to dose deposition [15, 16]. It has been used by many authors to benchmark the accuracy of dose calculation algorithms [7 , 17–20]. Although comparisons of MC calculations with the CCC algorithm in various TPSs are reported elsewhere, few studies have been devoted to the benchmarking of the CCC algorithm as implemented in the Prowess Panther TPS with MC code (BEAMnrc/DOSXYZnrc) and measurements [21]. In addition, a few studies have focused on the commissioning of BEAMnrc code for the Oncor ^® linear accelerator (linac) (Siemens AG, Munich, Germany) [22, 23]. In order to address these issues, the motivation of this work is to conduct a new study to better evaluate the dose calculation accuracy of the CCC algorithm implementation in the Prowess Panther TPS for 3-dimensional conformal therapy. To this end, this work sets out to satisfy the following objectives namely, (1) commissioning of the BEAMnrc code for an 18 MV photon produced by Siemens Oncor^® linac treatment head by using data measured under simplified beam conditions, and (2) evaluating of the dose calculation accuracy of the CCC algorithm with respect to measurements and MC simulation in a heterogeneous thorax phantom.

2 Materials and methods

2.1 Linac modelling

The BEAMnrc MC code (version 2017) [24] was used to simulate an 18 MV photon beam produced by the Siemens Oncor^® linac treatment head situated at the Shahid Ramezanzadeh Radiation On-cology Center in Yazd, Iran. A detailed geometry was provided by the manufacturer in order to accomplish this. The following component modules were used in this study: target, primary collimator, flattening filter, ion chamber, mirror, and jaws on the X and Y coordinates. Three open field sizes of 5×5, 10×10 and 20×20 cm² with a varying number of histories in the range of 4×10⁷ to 1×10⁸ were used for simulations using a 125,000 cm³ cube of water.

Phase space files were created with the scoring plane located at the top of the virtual water phantom surface at an SSD of 100 cm. In all simulations the AP and AE parameters, which are the low-energy thresholds for the production of secondary bremsstrahlung photons and knock-on electrons were set to 0.521 and 0.001 MeV, respectively. Photon and electron cut off energies were set to 0.5 and 0.001 MeV, respectively. A Bremsstrahlung splitting technique was used to achieve a much better efficiency with a splitting number of 1000.

2.2 Dose calculation in the water phantom

The stored phase space files were then used as a source input for the calculation of dose in a homogeneous water phantom using DOSXYZnrc [25]. The water phantom dimensions were 50×50×50 cm³ with a grid resolution of 0.5×0.5×0.2 cm³. After dose was calculated, the code produced 3Ddose files which report the dose per incident particle in each voxel of the phantom. The 3Ddose files were then used to obtain depth-dose curves and cross-plane profiles at a 10 cm depth using an in-house MATLAB^® (R2016a; Mathworks, Natick, MA, USA) script. For these simulations, the number of histories was set to 5×10⁹ and ECUT and PCUT parameters were set to 0.5 MeV and 0.001 MeV, respectively.

2.3 Experimental measurements

All measurements were made by using a p-type photon diode field detector (PFD, IBA dosimetry, Louvain-La-Neuve, Belgium) for an 18 MV photon beam on a Siemens Oncor^® (Siemens AG, Germany) linac. A water tank (Scanditronix-Wellhofer, RFA-300 Water Phantom), with dimensions of 50 × 50 × 50 cm³ was used. Depth-dose and cross plane dose profiles at 10 cm were obtained experimentally for three open field sizes of 5×5, 10×10 and 20×20 cm². In order to benchmark the MC model of Oncor linac’s head, the depth-dose and dose profiles curves of MC method were compared with those of the experimental measurements.

2.4 Heterogeneous thorax phantom

This study used the Behyaar Thorax phantom (Behyaar Sanaat sepahan, Esfahan, Iran) (Fig. 1). The phantom is elliptical in shape (356 mm wide×210 mm height×240 mm long) and represents an average human torso in proportion, density and two-dimensional structure. The phantom body is made of solid water, lung and bone sections containing 8 holes to hold interchangeable rod inserts for an ionization chamber. The phantom includes a set of four reference plugs with well-defined electron and physical densities simulating soft tissue, spinal cord, lung and bone.

Fig.1

Behyaar thorax phantom.

2.5 Treatment planning and dose measurement

Computed Tomography (CT) scans of the thorax phantom were acquired using a Siemens Somatom CT scanner (Siemens AG Germany). The CT DICOM images were transferred to the Prowess Panther TPS (Prowess Inc. Concord, CA, USA). The CT images were obtained using 130 kVp, 24.8 mAs and a 5 mm slice thickness. Structure contouring was performed using the Prowess Panther TPS. The dose grid resolution was set to 0.65×0.65×0. 5 cm³ resulting in a dose matrix of 70×70×83 voxels.

For all dose computations and measurements, the 18 MV X-ray beam from Siemens Oncor^® medical linac and an isocentric setup were used. The plan was designed with parallel-opposed fields and an isocenter placed within the left lung. The right lung, bone and spinal cord were delineated as separate ROIs. The fields were set up obliquely using gantry angles of 344° and 158°. The prescription was set to 200 cGy at isocenter. The dose distribution, as calculated using the CCC algorithm is shown in the Fig. 2 [26].

Fig.2

Static 11×16cm² plan from prowess panther: dose calculation (a) axial, (b) coronal and (c) sagittal.

After plan completion, The treatment plan was delivered several times to the thorax phantom and point dose measurements were made by using a 0.65cc FC-65 G Farmer type ionization chamber (Scanditronix Wellhofer AB, Sweden) with an electrometer (dose1, Scanditronix Wellhofer AB, Sweden) as seen in Fig. 3. Measurements were repeated twice at each location. Dose measurements were performed based on the recommendations outlined in IAEA TRS 398 [27].

Fig.3

Anthropomorphic Phantom with measurement locations, a: Left lung, b: Lung-tissue interface, c: spinal region, d: Right lung.

2.6 CT based phantom dose calculations

The BEAMnrc Monte Carlo code was used for simulating the Oncor^® linear accelerator. A model of an 18 MV photon beam with two parallel-opposed fields of 11×16 cm² was simulated. The number of histories taken within the phantom for all treatment fields was set to 5×10⁷. ECUT and PCUT parameters were chosen to be 0.521 and 0.001 MeV, respectively Directional Bremsstrahlung splitting(DBS) variance reduction was used with a splitting number of 1000 [28]. A phase space file was scored below the jaws for two 11×16 cm² fields and included 1.3×10⁸ particles.

In the next step of the simulation, the phase space file was imported to the DOSXYZnrc code and the phantom dicom images were converted to a Monte Carlo geometry using a program called CTCREATE which was used to convert the patient’s CT data to the desired dimensions, material types, and mass densities [25]. The voxel size for EGS phantom was set to 0.65×0.65×0.5cm³ to match with the dose grid resolution of the TPS and dimensions of the chamber. The dimensions of the phantom was roughly 70×70×83 cm³. To achieve an excellent uncertainty the number of history was set to 5×10⁹

After the simulation completed, DOSXYZnrc produced a 3Ddose file which uses units of dose per incident particle (Gy per electron) in the calculation voxel of phantom. The simulated results were then converted to absolute dose according to the method proposed by Popsecu et al. [29]. Generally, in the head of linac, monitor chambers are used to measure output of the linear accelerator. Dose deposited in the monitor chamber results from both the primary beam and backscatter from components of the linac head. In our simulations, backscatter radiation was accounted for using a backscatter factor. The calculated dose from MC simulations were converted to the absolute dose using the following equations: $D_{xyz, abs} = D_{xyz} \frac{(D_{ch}^{forward} + D_{ch (10 \times 10)}^{back})}{D_{ch}^{forward} + D_{ch}^{back}} \frac{D_{xyz, abs}^{cal}}{D_{xyz}^{cal}} MU$ (1) $BSF = \frac{(D_{ch}^{forward} + D_{ch (10 \times 10)}^{back})}{D_{ch}^{forward} + D_{ch}^{back}}$ (2) where D_xyz is the dose per incident history along the beam central axis deposited in a prescribed voxel, D_ch is the dose per incident history accumulated in the monitor chamber, $D_{ch}^{forward}$ is the dose contribution from the primary beam interacting with the monitor chamber, $D_{ch}^{back}$ is the dose contribution from the beam interaction with collimator, $D_{xyz}^{cal}$ is the normalized dose at the calibration point of a clinical accelerator and $D_{xyz, abs}^{cal}$ is the absolute dose at the calibration point (x, y, z) in the phantom. In our center, megavoltage photon beams are calibrated at 10×10 cm² field size, 100 cm SSD and 10 cm depth. Therefore the same setup was used for obtaining the dose at the calibration point using simulation. Finally, the TPS dose and 3Ddose data were imported into CERR [21] to facilitate gamma analysis.

2.7 Data Comparison

To evaluate the dose produced by the MC model of the linac a 1D Gamma analysis was performed using an open source MATLAB^® based software [30]. For all depth dose and cross-plane profiles, using PFD measurement as a reference. Distance to agreement (DTA) and dose difference (DD) criteria were set to 3 mm and 3%. The TPS dosimetric performance was evaluated against MC simulations and measurements by calculating the dose difference as follows: $DD (%) = \frac{D_{cal} - D_{MC}}{D_{ref}} * 100$ (3)

$DD (%) = \frac{D_{cal} - D_{measu}}{D_{ref}} * 100$ (4) where D_cal, D_MC and D_measu are point doses calculated by the TPS, MC simulations and measurements, respectively and D_ref is the reference dose which set according to the prescribed dose (200 cGy) for treatment planning.

TPS dose distributions were quantitatively evaluated in comparison with Monte Carlo code using dose volume histograms and gamma index analysis [31]. In terms of gamma evaluation, the dose distribution of the Monte Carlo simulation and TPS were both used as a reference and evaluated dose separately. In this study, the gamma index (γ) criteria of 2% /2 mm, 3% /3 mm and 5% /5 mm were used in which a γ<1 indicates that points pass the criteria and γ>1 represents a failure. The gamma score represents the percentage of voxels that pass these criteria. A dose threshold of 5% of the evaluated maximum dose was used in the analysis.

3 Results

3.1 Tuning of Monte Carlo parameters

For the current study, parameters were determined based on trial and error. Monte Carlo benchmarking of the 18 MV photon beam was performed and the acceptable agreements between the Monte Carlo method and experimental measurements were found for an incident electron beam with a mean energy of 14.2 MeV and Gaussian energy distribution (FWHM) of 0.08 cm. The focal spot size was 0.08 cm (FWHM) in the cross-line and in-line directions with a mean angular spread of 0.8°. For this energy, the statistical uncertainty of the MC calculations for depth dose profile ranged from below 1% within the buildup region to 0.6% after the buildup region and for the lateral dose profiles ranged from 0.4% within the high dose region to 1% beyond the penumbra. In Fig. 4, depth dose and lateral profiles are shown for 5×5, 10×10 and 20×20 cm² field sizes. The depth dose and dose profile data were normalized to the maximum dose at a nominal depth of 3 cm along the central axis. Figure 4 shows the results of the gamma analysis with a criterion of 3% /3 mm. As seen in this figure, a passing gamma value is found for all depths and distances from the central axis.

Fig.4

Comparison of measured and simulated depth doses and dose profile curve and Gamma index at 18 MV. Left: depth dose distribution for (a) 5×5, (c) 10×10 and (e) 20×20 cm² filed size with SSD 100 cm. the depth dose data were normalized to maximum dose at depth of 3 cm. Right: dose profile curves for (b) 5×5, (d) 10×10 and (f) 20×20 cm² field size at depth of 10 cm. Dose profile data were normalized to the central dose. Gamma index analysis (black lines) with % 3/3 mm criteria for the comparison of MC simulated and measurements. Left (a, c, e) gamma curves for depth dose curve at 5×5, 10×10 and 20×20 cm² field size. Right (b, d, f) gamma curves for dose profile curves of 5×5, 10×10 and 20×20 cm² field size.

3.2 Absolute dose comparison using CT-based data

Clinical conventional plans were calculated and experimentally measured in the chest region of the Behyaar phantom. Measurements were performed using an FC 65 G Farmer chamber. The Prowess Panther (CCC algorithm) software was used to calculate point doses for each chamber location, and these results were compared with the measured doses. This is summarized in Table 1. The dose difference (% dd) was obtained from the difference between the measured and calculated doses divided by the reference dose (200 cGy). The results have shown that the TPS dose for the parallel opposed pair treatment technique has an acceptable agreement with the Farmer chamber measurements in the lung region. The maximum difference was less than 3% for the 18-MV photon beam.

Table 1
Comparison the CCCS and Farmer chamber absolute doses for a clinical simple plan delivered on the CT-based data of the Behyaar thorax phantom

No regions 18 MV

CCC(cGy) Farmer (cGy) dd

1 left lung(PTV) 201.01 201.034 –0.11%

2 right Lung 0 3.23 –1.6%

3 Lung-tissue interface 208.39 214.3 –2.9%

4 Spinal Cord 13.42 12.6 0.7%

No	regions	18 MV
1	left lung(PTV)	201.01	201.034	–0.11%
2	right Lung	0	3.23	–1.6%
3	Lung-tissue interface	208.39	214.3	–2.9%
4	Spinal Cord	13.42	12.6	0.7%

In this work, the TPS results were also compared to MC doses calculated using the same plan and geometry. Table 2 lists percentage differences in dose between the MC and the CCC data in the chest region of the Behyaar thorax phantom for an 18-MV photon beam. The maximum difference for all treatment plans was less than 3%. In Table 3, the dose difference between MC and the Farmer chamber measurements showed a maximum difference of 1%.

Table 2

Comparison between CCC and EGSnrc absolute doses for a clinical simple plan delivered on the CT-based data of the Behyaar thorax phantom

No	regions	18 MV
		CCC (cGy)	EGSnrc (cGy)	dd
1	left lung(PTV)	201.01	201.71±1.35%	–0.34%
2	right Lung	0	2.82±0.29%	–0.4%
3	Lung-tissue interface	208.39	215.46±0.94%	–3.5%
4	Spinal Cord	13.42	11.57±0.32%	0.93%

Table 3

Comparison between Farmer chamber and EGSnrc absolute doses for a clinical simple plan delivered on the CT-based data of the Behyaar thorax phantom

No	regions	18 MV
		EGSnrc (cGy)	Farmer (cGy)	dd
1	left lung(PTV)	201.71±1.35%	201.034	0.33%
2	right Lung	2.82±0.29%	3.23	0.58%
3	Lung-tissue interface	215.6±0.94%	214.3	0.61%
4	Spinal Cord	11.57±0.32%	12.6	–0.52 %

3.3 3D Gamma analysis

Figure 5 (a)-(c) shows 3D gamma distributions in which dose difference and distance to agreement criteria of 2% /2 mm, 3% /3 mm and 5% /5 mm were used. From the dose volume histogram (DVH), as shown in Fig. 6, the differences between mean doses were 0.7%, 0.33%, 2.3% and 17% for PTV, right lung, lung-tissue interface and spinal cord respectively. Table 4 shows the 3D gamma passing rates in each structure for our conformal plan. It demonstrates that as the criteria increase, the number of points that pass the gamma criterion increases significantly as expected. The passing rates for the PTV were 59%, 82.96% and 97.52 % for 2% /2 mm, 3% /3 mm and 5% /5 mm criteria, respectively. The passing rates within the right lung increased from 83.06 % for 2% /2 mm to 88.53% for 3% /3 mm and 93.17 % for the 5% /5 mm criteria. Furthermore, the passing rates for the interfaces were 76.97 %, 77.35% and 78.67% for 2% /2 mm, 3% /3 mm and 5% /5 mm criteria, respectively. Additionally the passing rates within the spinal cord were improved from 83.08 for 2% /2 mm to 88.56% for the 3% /3 mm and 93.17% for the 5% /5 mm criteria, respectively.

Fig.5

3D gamma index distributions with (a) 2% /2 mm, (b) 3% /3 mm and 5% /5 mm criteria.1.

Fig.6

Dose volume histograms in each structure for thoracic conformal plan.

Table 4

3D gamma passing rates in each structure for a thorax conformal plan

Structures	Criteria
	2% /2mm	3% /3mm	5% /5mm
PTV	59	82.96	97.52
Right lung	83.06	87.53	93.67
Lung-tissue interface	76.97	77.35	78.67
Spinal cord	83.08	88.56	93.17

4 Discussion

In this study, the CCC algorithm in the Prowess Panther TPS was evaluated using MC simulations and experimental measurements. As seen in Table 1, compared with Farmer chamber measurements, the CCC algorithm underestimated the dose in the PTV, right lung and lung-tissue interface and overestimated dose in the spinal cord region. Furthermore, in Table 2, CCC results were compared with EGSnrc results and found to underestimate dose for all points shown in the Fig. 2. All Monte Carlo dose calculations were closer to the Farmer measurements than the CCC calculations (Table 3). A potential source of uncertainty in this study was the statistical uncertainty of the MC simulations and its influence on the dose distribution. In this study, the number of histories for both simulations in the water and heterogeneous phantoms were set in order to achieve uncertainty of less than 1% which has been recommended by AAPM TG 105 [32]. The values of this uncertainty in all voxels of the phantom was less than 1%. Other sources of uncertainty were recorded during point dose measurement in the phantom. These uncertainties directly affected the Farmer chamber reading. The most important of them were temperature-pressure effect (ρ_PT), polarity effect (ρ_pol) and recombination effect (ρ_ion). The ρ_PT is the temperature–pressure correction which corrects the disagreement between standard environmental conditions in which the chamber has been calibrated and the user’s environmental conditions. This value was measured about 1.143. The correction factor due to the polarity effect ρ_pol which corrects the response of an ionization chamber for the effect of a change in polarity of the polarizing voltage applied to the chamber. ρ_pol was measured about 1.0002. There is no recommended value for ρ_pol but it is recommended that the difference between the ionization currents measured at positive and negative polarizing potential should be less than 0.5% for any radiation beam quality [33]. In the present study, all charges were measured at two bias voltages (±300 v) and differences between measured charges of positive and negative polarizing potential were 0.19%.

The uncertainty due to charge recombination during measurement was corrected using an ion recombination correction factor ρ_ion. The ρ_ion was also measured to be about 1.003 which is less than the 1.05 value limit recommended by the AAPM TG 51 for reference class ionization chambers [34]. A further potential source of uncertainty was also measured during experimental setup of phantom. According to the AAPM recommendation, this source of uncertainty can result to an overall uncertainty of 2.5% [5]. During setup of measurements, the phantom was fixed and a Farmer chamber inserted into it without any movement. Therefore movement during treatment is assumed to be negligible.

In the present study the CCC algorithm was able to calculate dose within the PTV region within 1 % (Tables 1, 2). Similar results have reported by other authors. Knoos [35] et al. evaluated the CCC algorithm against a MC simulation and found an agreement in the lung region by about 1.5% for large field sizes (11×10 cm²). However in the present study the CCC algorithm had a better agreement with our MC simulation and Farmer chamber measurements. The origin of dose errors in low density regions can be largely attributed to electronic disequilibrium making dose calculation quite challenging here. This effect has been studied by Caccia et al. [36] and Metcalfe et al. [37]. As described by Metcalfe et al., electronic disequilibrium increases when considering smaller field sizes and higher photon energies. Han et al. [12] reported that the CCC and AAA algorithms overestimate dose by about 4.6% and 11.6 % respectively in the lung region compared to MC and Acuros XB (AXB) algorithms. The AXB dose prediction was comparable with that of MC and dose differences were less than 2% for all evaluated voxels. AXB, as expected was much closer to the MC results than model-based algorithms such as the CCC and AAA because it is a significantly more detailed model compared to convolution algorithms. While model based algorithms use precomputed dose deposition kernels, AXB, like MC algorithms, more directly models and solves physical interactions of radiation using the radiation-transport problem. It accurately models not only the primary photon source using beam source and ray trace method but also the scattered photon fluence and scattered electron fluence. For the scattered photon and electron fluence, it also utilizes the linear base Boltzmann transform equations to create a ray trace scattered particle distribution at each voxel in a 3D patient CT image [38]. Compared with these results, in the present study subtle dose differences (less than 1%) were found between the CCC, MC and measurements for a target in the lung region. It should be mentioned that these different conclusions may be due to the differences in accelerator modelling (Varian, Elekta or Oncor), phantom design (slab phantom versus thorax phantom) and measurement modalities [39].

Another important consideration in association with treatment planning in radiotherapy is dose calculation inside heterogeneous media where electronic disequilibrium creates large deviations from measured and simulated values. In the present study, these effects were seen for lung-tissue interface below the PTV (Fig. 3, point b), which is comparable to what is seen in the literature. Carasco et al. [40] found that the CCC algorithm predicted a higher dose within heterogeneities by 3 to 5% which was more pronounced for higher energy photon beams and smaller field sizes and whose results agree more closely with our own. As described in this paper, these discrepancies were due to the fact that the CCC algorithm does not model the buildup region when entering from low density to high density regions. Moreover, Chow et al. [9] reported that the CCC algorithm uses a density scaling method that does not completely account primary electron transport at deeper depths. Since electrons become scattered at increasingly larger angles, this leads to an underestimation in dose when electrons travel from a high to low density media and vice versa in which density scaling assumes that electrons travel in a homogeneous medium when considering electron backscatter.

Furthermore, Davidson et al. [41] concluded that the CCC algorithm accounts for lateral scatter and electron transport in the lung-tumor interface and the peripheral lung dose. Zaman et al. [42] have shown that the AAA systematically underestimates (–5%) the dose at the lung-bone interface, especially for small fields while AXB calculations (–1%) were in good agreement with MC. They reported that this underestimation is probably due to the loss of electronic equilibrium at this interface and effects of attenuation and scattering close to the bone that are not fully taken into account by the AAA. As a beam reaches the lung-bone interface, the dose build is more prominent for the AAA as compared with MC, and could be attributed to the backscattered electrons from the bone. Compared to the PDD calculated by MC, the build-up and a subsequent build-down in bone was more accurately calculated by AXB as opposed to the AAA. A steeper buildup occurs within bone due to its high density increasing the compton cross section as reported by Shoaib et al. [21]. They previously evaluated the CCC algorithm in the Prowess TPS and reported that the CCC algorithm underestimates dose for small fields, while it overestimates dose for larger field sizes such as 15×15 and 20×20 cm² which is comparable with the results of the present study.

The dose underestimation calculated out of field by the TPS is well known and in the present study, the magnitude of dose differences were less than 2% satisfying ICRU and AAPM [5] recommendations for computed dose distributions. Two sources of out-of-field dose are leakage and phantom scattered radiation. Leakage radiation and head scatter is created through various interactions in the linac head contributing to the total dose of out of field and phantom scatter is generated during photon interaction with patient body.

Since this study used open photon fields in the treatment planning, the dose differences were not found to be significant. The modelling of the out-of-field doses under these conditions gave results showing a good agreement between the CCC algorithm and measurements. For more complex delivery techniques such as IMRT and VMAT, the agreement between the TPS and measurement is diminished as a more precise beam model is needed. These effects were reported by Van den Heuvel et al. [43] where the out-of-field dose is correctly predicted by the CCC algorithm in an open photon field geometry, while the algorithm underestimated the dose when using more complex techniques such as IMRT and VMAT. Similar assessments of the out-of-field doses were carried out by Howell et al. [44] and their results showed that the AAA algorithm underestimated the out-of-field dose by an average of 40% over the range of distances. It is well known that when the distance from the central beam axis increases, the magnitude of dose differences also increases. However, in comparison with 3D-CRT, complex delivery techniques such as IMRT and VMAT generally used more MUs to achieve the same amount of dose, and thus there is an expected increase in the patient and collimator scatter. This is important for normal tissues with high radiosensitivity that are positioned out of field. Although we did not compare our results with those attained using an IMRT plan, larger field sizes increase the patient scatter leading to lower dose per MU in 3D-CRT. Wang et al. [45] reported that the uncertainty of calculated out-of-field dose profiles between the AAA and MC was depth dependent and less than 1% in a water phantom. They also found similar results for patients when using IMRT and VMAT techniques. In comparison with their results, our study revealed similar dose differences.

Table 4 and Fig. 5 show the final results for gamma analyses. Greater than 59% of the evaluated points for the MC and TPS dose distributions show γ<1. The passing rate within the PTV increases when going from a gamma criteria of 2% /2 mm to 5% /5 mm. The low pass rates in the PTV for the 2% /2 mm criterion is due to incorrect modelling of electron transport in low density regions and around interfaces. As described by Tomioma et al. and Madani et al. [46, 47], the model based algorithms (AAA) experience a great challenge when they are faced with low density regions and cannot accurately model secondary electron transport. The passing rates within the right lung increased from 83.06 % for 2% /2 mm to 87.53% for 3% /3 mm and 93.17 % for the 5% /5 mm criteria, respectively. The primary loss of dosimetric accuracy for the right lung is due to incorrect modelling of lateral electron transport out of field [48]. Furthermore, the passing rates for the lung-tissue interface were 76.97 %, 77.35% and 78.67% for 2% /2 mm, 3% /3 mm and 5% /5 mm criteria, respectively. The passing rates within the spinal cord were improved from 83.08 for 2% /2 mm to 88.56% for 3% /3 mm and 93.17% for 5% /5 mm criteria. These results can be explained due to electron disequilibrium near the lung-tissue and bone-tissue interfaces which strongly depend on field size and beam energy, as described by Wang et al. [49].

5 Conclusion

The collapsed cone convolution algorithm is an advanced algorithm which is implemented in the Prowess Panther TPS. This study compares the accuracy of dose calculations using the collapsed cone convolution algorithm with a Monte Carlo simulation and Farmer chamber measurements in a thorax phantom. The CCC algorithm provided adequate dose accuracy within heterogeneous interfaces when surrounded by regions of low density such as lung. Maximum dose differences seen in the PTV and the spinal cord region were less than 5% satisfying ICRU report number 50 recommendations for dose calculation accuracy a radiotherapy treatment planning. The results of gamma analysis showed a passing rate higher than 59% for all criteria. Since the present study has focused on the thorax phantom using 3D-CRT, further evaluations of the CCC algorithm will be performed on real patient CT data and using both 3D-CRT as well as IMRT.

Footnotes

Acknowledgments

The authors wish to thank: Dr Frederic Tessier, Dr Blake Walters at NRCC for their useful advice and Dr Bruce Faddegon and Dr Mojtaba Hossieni for their invaluable help. This work was supported by Shahid Sadoughi University of Medical Sciences. All measurements and calculations were carried out at Shahid Ramazan Zadeh Radiotherapy Center, Yazd, Iran. Therefore, the authors express their sincere gratitude to the above center for their technical assistance.

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No	regions	18 MV
		CCC(cGy)	Farmer (cGy)	dd
1	left lung(PTV)	201.01	201.034	–0.11%
2	right Lung	0	3.23	–1.6%
3	Lung-tissue interface	208.39	214.3	–2.9%
4	Spinal Cord	13.42	12.6	0.7%