Comparison of four commercial dose calculation algorithms in different evaluation tests

Abstract

Background:

Accurate and fast dose calculation is crucial in modern radiation therapy. Four dose calculation algorithms (AAA, AXB, CCC, and MC) are available in Varian Eclipse and RaySearch Laboratories RayStation Treatment Planning Systems (TPSs).

Objectives:

This study aims to evaluate and compare dosimetric accuracy of the four dose calculation algorithms applying to homogeneous and heterogeneous media, VMAT plans (based on AAPM TG-119 test cases), and the surface and buildup regions.

Methods:

The four algorithms are assessed in homogeneous (IAEA-TECDOCE 1540) and heterogeneous (IAEA-TECDOC 1583) media. Dosimetric evaluation accuracy for VMAT plans is then analyzed, along with the evaluation of the accuracy of algorithms applying to the surface and buildup regions.

Results:

Tests conducted in homogeneous media revealed that all algorithms exhibit dose deviations within 5% for various conditions, with pass rates exceeding 95% based on recommended tolerances. Additionally, the tests conducted in heterogeneous media demonstrate high pass rates for all algorithms, with a 100% pass rate observed for 6 MV and mostly 100% pass rate for 15 MV, except for CCC, which achieves a pass rate of 94%. The results of gamma index pass rate (GIPR) for dose calculation algorithms in IMRT fields show that GIPR (3% /3 mm) for all four algorithms in all evaluated tests based on TG119, are greater than 97%. The results of the algorithm testing for the accuracy of superficial dose reveal variations in dose differences, ranging from –11.9% to 7.03% for 15 MV and –9.5% to 3.3% for 6 MV, respectively. It is noteworthy that the AXB and MC algorithms demonstrate relatively lower discrepancies compared to the other algorithms.

Conclusions:

This study shows that generally, two dose calculation algorithms (AXB and MC) that calculate dose in medium have better accuracy than other two dose calculation algorithms (CCC and AAA) that calculate dose to water.

Keywords

Treatment Planning System (TPS)Anisotropic Analytical Algorithm (AAA)Acuros (AXB)collapsed cone convolution (CCC)Monte Carlo (MC).

1 Introduction

The accurate and fast calculation of the dose distribution in patient plans is one of the most crucial processes in modern radiation therapy [1]. Dose delivery uncertainties of around 5% can influence the therapeutic window through which treatment is delivered, leading to reduced Tumor Control Probability (TCP) and/or increased Normal Tissue Complication Probabilities (NTCP). Therefore, based on recommendations from ICRU report 24, the overall dose uncertainty should be kept less than 5% [2]. The availability of model based, and commercial Monte Carlo (MC) dose calculation algorithms have the potential to reduce the dose uncertainty resulting from the treatment planning process [3]. Dose calculation algorithms can be categorized in terms of the medium of radiation transport and dose calculation. The physical properties of the medium for radiation transport and dose calculation are handled differently in different treatment planning systems [4]. There are three separate quantities used to specify the dose:

Dose to medium, as implemented in some Superposition/Convolution (S/C) algorithms (including Monaco, Oncentra, and Pinnacle), the Grid Based Boltzmann Solver (GBBS; Acuros AXB), and most Monte Carlo (MC) algorithms (including precision, iPlan, Monaco, and RaySearch): dose to medium-in medium, D_m,m [5].

Dose to water with variable electron density, as implemented in some S/C (including Xio and RaySearch), as well as in the Anisotropic Analytical Algorithm (AAA), Pencil Beam (PB) algorithms, and one Monte Carlo (MC) implementation (ViewRay): dose to water-in-water, D_w,w [5].

Dose to water converted from dose to medium using post processing. This is implemented commonly with stopping power ratios (as in some MC) as the dose to a small Bragg-Gray cavity of water surrounded by the medium: dose to water-in-medium, D_w,m [5].

As with all dose calculation algorithms, before their introduction into clinical practice, careful validation of dose calculations against measurement is required [3]. IAEA and AAPM suggest treatment simulation tests with acceptability criteria for beam models in the treatment planning systems (TPS) to assess the agreement with measured data. These publications allocate different tolerances to specific zones within the data, such as high dose, low dose, and high dose gradient sections found in the buildup or penumbra regions of beam data. They also address specific tests and tolerance levels in heterogeneous media, as well as tests for evaluating the accuracy of intensity modulated radiation therapy algorithms in fields [6 –9].

Despite the existing literature on reviewing and comparing commercial dose calculation algorithms in different TPSs for various evaluation tests [10 –12], there is still a lack of comprehensive studies that encompass a wide range of tests to facilitate direct comparisons and reveal the strengths and weaknesses of each algorithm. Furthermore, limited research explores different algorithms utilizing diverse types of dose calculations and using the same measured beam data for beam configuration, which is essential for unbiased and independent comparisons of their performance.

This study evaluates four commonly used dose calculation algorithms in clinical practice. The evaluation is conducted using the same measured beam data in one setting which includes all percentage depth-doses (PDDs), profiles and output factors, across various beam configurations within the Varian Eclipse and RaySearch Laboratories RayStation TPSs. By employing consistent measured beam data, the study aims to eliminate the performance dependency of the algorithms on the quality of imported measured beam data. Moreover, special attention is given to evaluating the accuracy of the Monte Carlo dose calculation algorithm within the RayStation TPS, an area that has received limited attention in existing literature. The findings of this study will provide valuable and comprehensive insights and serve as a reference for assessing the accuracy of dose calculation algorithms. Ultimately, this study aims to enhance our understanding of the strengths and weaknesses associated with various dose calculation algorithms, enabling meaningful comparisons between them.

In this study after modelling all algorithms based on vendor guidelines for each TPS, comprehensive comparison tests for all four algorithms were carried out. These tests included the algorithm’s accuracy:

In homogenous medium based on IAEA-TECDOC 1540 [8].

For calculation percentage depth dose and beam profiles.

In heterogeneous medium based on IAEA-TECDOC 1583 [9].

For intensity modulated fields based on AAPM task group report 119 (TG119) [6].

In surface and buildup region.

2 Materials and methods

2.1 Dose calculation algorithms

Four dose calculation algorithms, which are commercially available in two different TPS, were included in this study.

Eclipse (version 16.1) - Varian Medical Systems, Palo Alto, USA

AAA: Anisotropic Analytical Algorithm

AXB: Acuros XB

RayStation (version 10B) - RaySearch Laboratories AB, Stockholm, Sweden

CCC: Collapsed Cone Convolution

MC: Monte Carlo

Both Eclipse and RayStation were chosen for the study based on their extensive utilization in clinical practice and their robust treatment planning capabilities. A key factor in their selection was the availability of two types of dose calculation algorithms: D_w,w and D_m,m. This enabled a comprehensive evaluation of their performance and accuracy, providing valuable insights into the strengths and limitations of each algorithm.

2.1 2.1.a. Eclipse ’ ‘TPS’s dose calculation algorithms

AAA: The Anisotropic Analytic Algorithm is based on a multiple source model and poly-energetic pencil beam scaled in three dimensions specified in water. It is still based on the pencil beam (PB) kernel, but for increased dosimetric accuracy in heterogeneous media, lateral scatter is handled in a more refined manner than traditional PB algorithms. In this algorithm, all materials are considered as water of varying density, therefore, calculate dose-to-water in water, D_w . w. Consequently, because this algorithm does not inherently map from water to tissue, this step needs to be done manually by numerically adjusting the calibration reference dose in the TPS as “dose to muscle.” This manual conversion reports an approximate dose to tissue within the patient [13, 14]. AAA is an algorithm based on a multiple source, a model and a poly-energetic pencil beam determined in water and scaled in three dimensions.

AXB: The Acuros XB incorporates a sophisticated technique to solve the Linear Boltzmann Transport Equation (LBTE) and directly accounts for the effect of heterogeneities in patient dose calculation. The Boltzmann Transport Equation (BTE) is the governing equation describing the initial macroscopic behavior of radiation particles (neutrons, photons, electron, etc.) as they travel through and interact with matter. Next step is the calculation of the electron fluence spectrum in each voxel and the electron fluence depending on energy, is multiplied by the restricted electron stopping power for the material at that voxel, integrated over the electron spectrum and divided by the mass density at the point of calculation to get the dose. AXB supports two dose-reporting options: dose to water in water D_w . w and dose to medium in medium D_m . m. When D_m . m is calculated, the energy dependent response function based on the material properties of that voxel is used and for D_w . w, the energy dependent fluence-to-dose response function based on water is used [15]. In this study, D_m . m was calculated for all tests by AXB.

2.2 2.1.b. RayStation ’ ‘TPS’s dose calculation algorithms

CCC: The Collapsed Cone Convolution algorithm calculates the dose by means of the collapsed cone convolution/superposition (CS) methods [16, 17]. The main idea behind this method is to consider the primary photon transport separately from the secondary transport of photons and electrons that are created in the primary photon interaction. The dose is computed from energy fluence in two steps: Initially ray tracing of primary radiation through the medium considering inhomogeneity for determining TERMA (total energy released per unit mass) distribution. Secondly, superposition of the point spread kernel, collapsed cone in radial rays in spherical coordinate system considering inhomogeneity of the medium. This algorithm calculates dose-to-water, D_w . w .

MC: The RayStation photon Monte Carlo dose algorithm is a class II condensed history implementation with a dual virtual source model identical to the model used in the RayStation collapsed cone dose algorithm to model the LINAC head [18]_. The in-patient Monte Carlo transport is implemented directly on GPU for faster calculation and the physics behind is heavily inspired by EGSnrc [19], which is an extensively validated general purpose Monte Carlo method for electron and photon transport. The similarity was demonstrated in a poster by Tamm which reported > 95% 2% /2 mm gamma pass rates for heterogeneous geometries from 0.5 MeV to 20 MeV in comparison to doses computed by DOSXYZnrc, an EGSnrc user code to compute dose in rectilinear voxels [20]. The RayStation Monte Carlo implementation begins at the patient surface. The dose is calculated by tracing photons, electrons and positrons inside the patient and accumulating the deposited dose (dose to medium, average in voxel). For photons, Compton Scattering, Photoelectric absorption and Pair Production are simulated as separate events with cross sections compiled from elemental cross sections from the NIST XCOM database [18].

A short summary of the evaluated dose calculation algorithms in the study has been provided in Table 1.

Table 1
Summary of the Evaluated Four Dose Calculation Algorithms in the Study. (AXB: Acuros XB, AAA: An nisotropic analytic algorithm, CCC: Collapsed Cone Convolution and MC: Monte Carlo)

Algorithm TPS Dose Calculation Type Additional Features

AAA Eclipse Dose to Water (D_w . w) Based on a multiple source model and poly-energetic pencil beam scaled in three dimensions specified in water.

AXB Eclipse Dose to Medium (D_m . m) Incorporates the solution of the Linear Boltzmann Transport Equation (LBTE) and directly accounts for the effect of heterogeneities in patient dose calculation.

CCC RayStation Dose to Water (D_w . w) Utilizes the collapsed cone convolution/superposition (CS) methods for dose calculation.

MC RayStation Dose to Medium (D_m . m) Implements a photon Monte Carlo dose algorithm using a class II condensed history implementation. Simulates Compton Scattering, Photoelectric absorption, and Pair Production.

Algorithm	TPS	Dose Calculation Type	Additional Features
AAA	Eclipse	Dose to Water (D_w . w)	Based on a multiple source model and poly-energetic pencil beam scaled in three dimensions specified in water.
AXB	Eclipse	Dose to Medium (D_m . m)	Incorporates the solution of the Linear Boltzmann Transport Equation (LBTE) and directly accounts for the effect of heterogeneities in patient dose calculation.
CCC	RayStation	Dose to Water (D_w . w)	Utilizes the collapsed cone convolution/superposition (CS) methods for dose calculation.
MC	RayStation	Dose to Medium (D_m . m)	Implements a photon Monte Carlo dose algorithm using a class II condensed history implementation. Simulates Compton Scattering, Photoelectric absorption, and Pair Production.

This study used the same measured data including PDDs, profiles and output factors for modelling and commissioning of all four mentioned algorithms. A dose voxel grid calculation size of 0.1 cm³ was used for dose calculation for all algorithms in all the measurement tests in this study. An uncertainty of 0.5% was selected for dose calculation by MC dose calculation algorithm in all measurement tests in this study. In both TPS, a 50 cm long cubic phantom made of virtual water was used for all point doses, percentage depth dose (PDD) and beam profile calculation in homogenous medium by all algorithms. All measurements in the homogenous medium in this study were carried out using a PTW BEAMSCAN (PTW, Freiburg, Germany) water tank. Varian IX linear accelerator with the Millennium MLC120 (Varian, Palo Alto) with nominal 6 MV and 15 MV flattened beams used for all tests of this study.

2.2 Comparison Tests

2.2.2.1 2.2.a. Algorithms accuracy comparison in homogenous media based on IAEA-TECDOC 1540

The IAEA has developed TECDOC-1540 [8], which provides specific acceptance tests for dose calculation algorithms of TPS. The proposed tests are divided into three categories: the type tests, the site tests, and the optional tests. A summary of all dosimetric tests specified in TECDOC-1540 is given in Table 2. All tests 1–12 are type tests, tests 1–9 are site tests and tests 10–12 are optional. In the present study, all tests without the presence of inhomogeneity have been performed (all the tests were performed except test 8).

Table 2
Summary of all external beam calculation tests proposed in the IAEA-TECDOC-1540 and Sample criteria of acceptability for external beam TPS calculations Summary of all external beam calculation tests proposed in the IAEA-TECDOC-1540 and Sample criteria of acceptability for external beam TPS calculations

Test No. Short description of the test Position of chamber Equation for evaluation Tolerance (%)

1a Square field, 5×5 Outside beam edges (2) 3

inside beam edges (1) 2

1b Square field, 10×10 Outside beam edges (2) 3

inside beam edges (1) 2

1c Square field, 25×25 Outside beam edges (2) 3

inside beam edges (1) 2

2a Rectangular field, 5×25 Outside beam edges (2) 3

inside beam edges (1) 2

2b Rectangular field, 25×5 Outside beam edges (2) 3

inside beam edges (1) 2

3 Square field, 10×10, SSD = 85 Outside beam edges (2) 3

inside beam edges (1) 2

4 Square field, 9×9 wedge Outside beam edges (1) 3

inside beam edges (1) 3

5 Square field, 16×16, central block Outside beam edges (3) 3

inside beam edges (1) 3

6 Square field, 10×10, off-axis Outside beam edges (2) 4

inside beam edges (1) 3

7 Square field, 16×16, blocked to L-shaped field (irregular field) Outside beam edges (3) 3

inside beam edges (1) 3

9 Square field, 10×10, oblique incidence Outside beam edges (1) 3

inside beam edges (1) 3

10a Square field, 10×10, half phantom (“missing tissue”) Outside beam edges (1) 3

inside beam edges (1) 3

10b Square field, 20×20, half phantom (“missing tissue”) Outside beam edges (1) 3

inside beam edges (1) 3

11a Asymmetric field, 15×15; geometric radiation field center at:7.5,0; 0, 7.5; 7.5,7.5 Outside beam edges (1) 3

inside beam edges (1) 3

12 Asymmetrically wedged field, 15×15; geometric radiation field center at:±7.5,0; 0,7.5;±7.5,7.5 Outside beam edges (1) 4

inside beam edges (1) 3

Test No.	Short description of the test	Position of chamber	Equation for evaluation	Tolerance (%)
1a	Square field, 5×5	Outside beam edges	(2)	3
		inside beam edges	(1)	2
1b	Square field, 10×10	Outside beam edges	(2)	3
		inside beam edges	(1)	2
1c	Square field, 25×25	Outside beam edges	(2)	3
		inside beam edges	(1)	2
2a	Rectangular field, 5×25	Outside beam edges	(2)	3
		inside beam edges	(1)	2
2b	Rectangular field, 25×5	Outside beam edges	(2)	3
		inside beam edges	(1)	2
3	Square field, 10×10, SSD = 85	Outside beam edges	(2)	3
		inside beam edges	(1)	2
4	Square field, 9×9 wedge	Outside beam edges	(1)	3
		inside beam edges	(1)	3
5	Square field, 16×16, central block	Outside beam edges	(3)	3
		inside beam edges	(1)	3
6	Square field, 10×10, off-axis	Outside beam edges	(2)	4
		inside beam edges	(1)	3
7	Square field, 16×16, blocked to L-shaped field (irregular field)	Outside beam edges	(3)	3
		inside beam edges	(1)	3
9	Square field, 10×10, oblique incidence	Outside beam edges	(1)	3
		inside beam edges	(1)	3
10a	Square field, 10×10, half phantom (“missing tissue”)	Outside beam edges	(1)	3
		inside beam edges	(1)	3
10b	Square field, 20×20, half phantom (“missing tissue”)	Outside beam edges	(1)	3
		inside beam edges	(1)	3
11a	Asymmetric field, 15×15; geometric radiation field center at:7.5,0; 0, 7.5; 7.5,7.5	Outside beam edges	(1)	3
		inside beam edges	(1)	3
12	Asymmetrically wedged field, 15×15; geometric radiation field center at:±7.5,0; 0,7.5;±7.5,7.5	Outside beam edges	(1)	4
		inside beam edges	(1)	3

For all tests summarized in Table 2, the measurements are given in Excel spreadsheets. Three different approaches [8] have been used in these sheets to evaluate TPS calculations and the measurements:

Relative Difference (RD_meas): Dose difference between calculated dose by TPS (D_cal) and measured dose in the same point (D_meas) normalized to the measured dose (D_meas). ${RD}_{meas} [%] = 100 \times (D_{cal} - D_{meas}) / D_{meas}$ (1)

Relative Normalized Difference for open central axis fields (RND_open . cax): Dose difference between the dose calculated by the TPS in an open central axis field (D_cal . open) and the measured dose in the same point (D_{meas . open}) normalized to the measured dose of the central axis of an open field in the same depth (D_meas,_open . cax). ${RND}_{open . cax} [%] = 100 \times (D_{cal . open} - D_{meas . open}) / D_{meas, open . cax}$ (2)

Relative Normalized Difference for blocked central axis fields (RND_{blocked . cax}): Dose difference between the dose calculated by the TPS in a blocked central axis field (D_{cal . blocked}) and the measured dose at the same point (D_{meas . blocked}) normalized to the measured dose in an open field for the same depth (D_meas,open). ${RND}_{blocked . cax} [%] = 100 \times (D_{cal . blocked} - D_{meas . blocked}) / D_{meas, open . cax}$ (3)

where, D_meas represents the dose value measured by the PTW semi-flex ionization chamber 31002 (PTW, Freiburg, Germany) using the PTW BEAMSCAN (PTW, Freiburg, Germany) water tank.

The recommended equations for the comparison of measured and calculated data and the acceptability criteria are also given in Table 2.

2.2.2.2 2.2.b Algorithms accuracy comparison for the calculation of PDDs and beam profiles

PDD and beam profile measurements were acquired with a PTW pinpoint chamber 31022 (PTW, Freiburg, Germany) for 6 MV and 15 MV photon beam energies. The dosimetric data was acquired for fields sizes: 1×1 cm², 2×2 cm², 3×3 cm², 4×4 cm², 10×10 cm² and 20×20 cm², which were all defined by jaws. Also, beam data was measured for two MLC defined fields of 1×1 cm² and 2×2 cm². The accuracy of jaw and leaf calibration was verified through a short profile scan proceeding. All measurements were taken at 100 cm source to surface distance (SSD) with a 1 mm measurement step size in the scan direction, except for the 40×40 cm² diagonal profiles that were made at an SSD of 90 cm and had a step size of 5 mm across the central 20 cm of the field. All beam profiles were measured at 10 cm depth. The PDD scanning was performed starting from 300 mm depth to 0 mm depth in the upward direction throughout the phantom to avoid water turbulence. As a reference detector for PDD and beam profile measurements for field sizes 2×2 cm² and 4×4 cm², the PTW T-REF plane-parallel transmission chamber (PTW, Freiburg, Germany) was used. For larger field sizes, the PTW semi-flex ionization chamber 31002 (PTW, Freiburg, Germany) was used as the reference detector.

2.2.2.3 2.2.c. Algorithm accuracy comparison in heterogeneous mediums based on IAEA-TECDOC 1583

The procedures for IAEA-TECDOC-1583 tests [9] are based on the CIRS thorax phantom (CIRS Model 002LFC). The CIRS thorax phantom (Fig. 1.a) is elliptical (30 cm long×30 cm wide×20 cm thick) and represents an average human torso in proportion, density, and three-dimensional structures. The phantom has soft tissue, lung, and bone sections with holes to hold interchangeable rod inserts. This phantom is the phantom equipped with a set of five calibrated electron density reference plugs, as shown in Table 3. The measurements in this study were performed for both 6 MV and 15 MV beams by placing a 31013 Farmer 0.6cc ionization chamber (PTW, Freiburg, Germany) into the different holes in the phantom.

Fig. 1

a. Thorax Phantom (CIRS Model 002LFC). b. Labelling of holes and the recommended arrangement of the certified electron density reference plugs for the CT scan. Plug 1-water equivalent, plug 2- muscle substitute, plug 3 –syringe filled with water, plug 4 - adipose substitute, plug 5 - water equivalent, plug 6 - lung substitute, plug 7 - should be empty to represent air, plugs 8 & 9 - lung substitutes, plug 10- bone substitute.

Table 3

Characteristics of calibrated electron density reference plugs

Plug material\Plug characteristic	Density (g/cm3)	Electron density per cc ×10²³	Electron density relative to water
Lung	0.21	0.69	0.207
Bone	1.6	5.03	1.506
Dense bone	2.17	6.7	2.005
Muscle	1.06	3.48	1.042
Adipose	0.96	3.17	0.949

The holes in the phantom are labelled to identify the locations of the points of measurement within the phantom, thus enabling the comparison of the TPS calculations and the measured values. The recommended labelling of the holes and the recommended arrangement of the calibrated electron density reference plugs during CT scan are given in Fig. 1.b.

All the tests in this part of the study were performed based on the dosimetric tests proposed in Table A (1–12) of TECDOC-1583 [9]. To evaluate the measured and TPS calculated values, the following equation was used to determine the Relative Difference (RD_ref): ${RD}_{ref} [%] = 100 \times (D_{cal} - D_{meas}) / D_{meas, ref}$ (4) where D_meas,ref is the dose value measured at the reference point. This reference point is a point that is expected to have received 2 Gy (dose per fraction for each test) and is specified for each test case.

2.2.2.4 2.2.d Algorithm accuracy comparison for intensity modulated fields based on TG 119

The purpose of this part of the study was to compare the dose calculation algorithms used for volumetric modulated arc therapy (VMAT) plans for the AAPM TG-119 test cases [6]. Four structure sets and computed tomography (CT) images were downloaded from the AAPM website (www.aapm.org) and imported into the Eclipse and RayStation TPS. These were the structures of Multi-Target (a), Mock Prostate (b), Mock Head-and-Neck (c), and C-shape (d) and are shown in Fig. 2.

Fig. 2

AAPM TG-119 structure sets [reference12]. Multi-Target (a), Mock Prostate (b), Mock Head-and-Neck (c), and C-shape (d).

The VMAT dose distributions of each optimized fluence map for these cases (each case uses two complete arcs) were calculated using the AAA, AXB, CCC and MC algorithms for the 6 MV photon beam generated by a Varian IX linear accelerator. The 15 MV photon beam is generally not preferred for VMAT due to its lower modulation and potential neutron contamination [21], which is not observed with the 6 MV beam. Therefore, we solely considered the 6 MV beam in this test of our study and did not include the evaluation of the 15 MV beam. All parameters, dose prescriptions, and planning objectives followed the TG-119 guidelines. The dose calculation and dose optimization grid size were set at 0.25cm³ subsequently, the calculated dose distributions for each algorithm was converted and recalculated onto the ArcCheck phantom, (Model 1220, Sun Nuclear, Melbourne, FL). The ArcCheck is a cylindrical PMMA phantom with a three-dimensional array of 1386 diode detectors, arranged in a spiral pattern with 10 mm sensor spacing. In the final step, each dose distribution was recalculated for the ArcCheck in each TPS and compared with the ArcChack measured dose distribution using the gamma (γ) evaluation algorithm.

2.2.2.5 2.2.e Algorithm accuracy comparison in surface and buildup region

Roos Chamber 34001 parallel-plate ionization chamber (PTW, Freiburg, Germany) was used for surface and buildup region dose measurements for 6 MV and 15 MV photon beams. The shift of the effective point of measurement of the Roos chamber is Δz = (0.4±0.1) mm downstream from the front surface of its sensitive air volume, also fixed plane separation of this chamber is 2 mm. A set of water equivalent RW3 slab phantoms (SP34, PTW Freiburg, Freiburg, Germany) with physical density of 1.045 gcm^-3 was used for open field irradiation. The effective measurement point of the chamber was defined by using water equivalent depth (WED) values in the buildup region. Surface and buildup region dose measurements were carried out with a Roos chamber for 10×10 field size at 0, 1, 2, 3, 4, 5, 10 and 15 mm phantom depths for 6 MV photon beam and same depths plus 30 mm phantom depth for 15 MV Photon beam. Irradiations were made using a Varian IX linear accelerator with 6 MV photon energy in a fixed SSD of 100 cm by delivering 100MU. To obtain the percentage depth doses (PDDs), the measured doses were then normalized to the dose at 15 mm phantom depth for 6 MV photon beam and 30 mm phantom depth for 15 MV photon beam where were accepted the dose maximum depths. The overdoses obtained from Roos chamber were corrected by applying Gerbi’s method to PDDs [22]. The measured dose values at the phantom depths were used for interpolation calculations to obtain the doses at 0.07 mm WED (0.067 mm phantom depth).

CT images of the same set of phantoms that used for Roos chamber measurements was acquired by using Siemense Big Bore CT (Siemens Healthineers, Forchheim, Germany) with a 2 mm of slice thickness. These images were then sent to the TPSs for surface and buildup region dose calculations of 10×10 field size by AAA, AXB, CCC and MC dose calculation algorithms for the 6 MV and 15MVphoton beams.

3 Results

3.1 Algorithms accuracy comparison in homogenous media base IAEA-TECDOC 1540

For the 6 MV and 15 MV beam models, dose deviations under reference conditions (Field size:10×10, SSD:100, Depth:10) were 0.4% and 0.3% for AAA, 0.5% and 0.4% for AXB, 0.1% and 0.5% for the CCC, 0.4% and 0.3 for MC algorithms respectively. All dose differences in reference condition were less than or equal to 0.5%.

For the 6 MV and 15 MV beam models, mean dose difference in the high-dose regions at different depths and off-axis positions, with one parameter changed from reference conditions were 0.8±1% and 0.6±1.2% for AAA, 0.9±1.2% and 0.7±1% for AXB, 0.5±1.1% and 1±1% for the CCC, 0.8±1.1% and 0.8±1% for MC algorithms. All dose deviations in these positions were less than or equal to 2%.

For the 6 MV and 15 MV beam models, mean dose deviations in fields with multiple parameter changes (e.g., an off-axis measurement in the presence of a wedge etc. . . .) were 1±1.6% and 1.6±3.2% for AAA, 1±1.6% and 1.7±1.7% for AXB, 0.7±1.2% and 1.6±3.2% for the CCC, 0.9±1.5% and 1.4±2.7% for MC algorithms respectively. All dose deviations in these positions were less than or equal to 5%.

For the 6 MV and 15 MV beam models, total percentage pass rate base tolerances recommended by TEC-DOC 1540 presented in Table 2, were 97.8% and 95.2% for AAA, 98.8% and 96% for AXB, 97.1% and 95.1% for CCC, 98.9% and 97% for MC algorithms respectively. All dose calculation algorithms had more than 95% pass rates. Figure 3 and Fig. 4 show the mean dose differences of 6 MV and 15 MV for all tests, as shown in Table 2.

Fig. 3

Mean dose difference of 6 MV for AXB: Acuros XB, AAA: An anisotropic analytic algorithm, CCC: Collapsed Cone convolution and MC: Monte Carlo.

Fig. 4

Mean dose difference of 15 MV for AXB: Acuros XB, AAA: An anisotropic analytic algorithm, CCC: Collapsed Cone convolution and MC: Monte Carlo.

3.2 Algorithms accuracy comparison for the calculation of PDDs and beam profiles

The measured PDDs and beam profile values for 6 MV and 15 MV photon energies were compared with the TPS calculated 6 MV and 15 MV beam profiles (Fig. 5) and PDD (Fig. 6) values for each dose calculation algorithms (AAA, AXB, CCC and MC) using global gamma [21]. Base recommendation of Medical Physics Practice Guideline 5.a (MPPG 5.a) [24], the unite in gamma error measure when the distance to agreement (DTA) of less than or equal to 1 mm and a dose difference (DD) of less than or equal to 2% were used. The gamma index pass rate (GIPR), i.e., the percentage of points with γ(2% /1 mm) less than one, was recorded for global dose region. The fraction of points passing the gamma criteria is evaluated over reference points with doses higher than 10% of maximum dose. Table 4 shows GIPR result for AAA, AXB, CCC and MC.

Fig. 5

Comparison of measured vs calculated profiles for fields sizes: 1×1 cm², 2×2 cm², 3×3 cm², 4×4 cm², 10×10 cm^2, 20×20 cm² and 40×40 cm² diagonal which were all defined by jaws at 10 cm depth, 100 cm SSD. a) 6 MV beam profiles b) 15 MV beam profiles. (AXB: Acuros XB, AAA: An anisotropic analytic algorithm, CCC: Collapsed Cone convolution and MC: Monte Carlo).

Fig. 6

Comparison of measured vs calculated PDDs for fields sizes: 1×1 cm², 2×2 cm², 3×3 cm², 4×4 cm², 10×10 cm² and 20×20 cm² which were all defined by jaws at 10 cm depth, 100 cm SSD. a) 6 MV beam profiles b) 15 MV beam profiles. (AXB: Acuros XB, AAA: An anisotropic analytic algorithm, CCC: Collapsed Cone convolution and MC: Monte Carlo).

Table 4

Global index pass rate result (GIPR) of 6Mv and 15 MV for AXB: Acuros XB, AAA: An anisotropic analytic algorithm, CCC: Collapsed Cone Convolution and MC: Monte Carlo

Field size(cm)	GIPR (2% /1 mm)%
	AAA				AXB				CCC				MC
	PDD		Profile		PDD		Profile		PDD		Profile		PDD		Profile
	6MV	15MV	6MV	15MV	6MV	15MV	6MV	15MV	6MV	15MV	6MV	15MV	6MV	15MV	6MV	15MV
1×1 (MLC)	98.3	98	100	100	98.3	98.2	100	100	97.5	98.2	99.1	98.8	97.4	98.3	99.1	98.9
2×2 (MLC)	98.2	98	100	100	98	98.2	100	100	97.7	98.1	99.2	99	97.8	98	99.3	98.9
1×1 (jaws)	98.8	98.5	100	100	99.3	98.5	100	100	98.6	98.8	99.3	99	98.7	98.6	99.2	99.1
2×2 (jaws)	100	98.5	100	100	99.8	98.6	100	100	99.5	98.2	99.4	99.2	99.6	98.4	99.4	99.3
3×3 (jaws)	99.5	99.2	100	100	99.3	99.5	100	100	99	100	99.3	99.3	99.1	99.3	99.4	99.4
4×4 (jaws)	100	99	100	100	99.2	99.1	100	100	99.1	99.5	99.5	99.4	99.4	99.5	99.4	99.4
10×10 (jaws)	100	99.8	100	100	99.2	99.8	100	100	99	99.5	99.5	99.2	99.8	99.5	99.4	99.3
20×20 (jaws)	100	100	99.2	98.5	99.4	99.8	98.3	99.5	98.5	100	99.5	98.4	99	99.1	99.4	98.9
40×40	–	–	95.3	95.9	–	–	95.1	96.2	–	–	96.4	97.6	–	–	96.7	97.4

The γ evaluation of the calculated PDDs and Profiles by dose calculation algorithms and measured PDDs and beam profiles indicate very similar results with no significant differences being seen between evaluated algorithms. The average overall gamma pass rate was greater than 98% for all algorithms and for both energies.

For the 6 MV and 15 MV PDD models, average gamma pass rates were 99.3±1.01% and 98.8±1.2% for AAA, 99.1±1.0 and 99.0±0.8% for AXB, 98.6±1.1% and 99.0±0.9% for CCC, 98.8±1.4% and 98.7±0.7% for MC algorithms respectively. For the 6 MV and 15 MV beam profile models, gamma pass rates were 99.3±4.0 and 99.3±3.4% for AAA, 99.2±4.1% and 99.2±4.3% for AXB, 99.02±0.48% and 98.87±0.47% for CCC, 99.05±0.6% and 98.89±0.58% for MC algorithms respectively.

3.3 Algorithm accuracy comparison in heterogeneous mediums based on IAEA-TECDOC 1583

The differences in the results between measurements, calculations and agreement criteria related to each test for AAA, AXB, CCC and MC algorithms at 6 MV and 15 MV energies are shown in Fig. 7. For the 6 MV all algorithms had a 100% pass rate, also for 15 MV just CCC had 94% pass rate, and other algorithms had 100 pass rates. In water equivalent material behind lung for 6 MV (case4, point5), MC (0.0%), AXB and CCC (both with –0.5%) and AAA (1.2%) had the best accuracy respectively. For 15 MV at the same point MC, AXB and CCC all had –0.7% accuracy and AAA had 1.3% accuracy.

Fig. 7

Percentage dose difference of 6Mv and 15MV for AXB: Acuros XB, AAA: An anisotropic analytic algorithm, CCC: Collapsed Cone convolution and MC: Monte Carlo in CIRS heterogeneous phantom. The green region within the graph space indicates the acceptable tolerance level for each test performed and red region indicates that measurements are greater than the acceptable percentage difference.

In central axis of the beam for lung material (case4, point 6) for 6 MV, AXB (0.0%), AAA (–0.5%), MC (–0.7%) and CCC (1%) had the best accuracy respectively. For 15 MV at the same point AAA (0.1%), CCC (0.5%), and AXB and MC (both with 0.6%) had the best accuracy respectively. For the beam off axis in lung material (case 5, point 7) CCC (0.6%), AXB (–0.7%), AAA (–1.4) and MC (1.9%) had the best accuracy respectively. For 15 MV in the same point AXB (0.7%), MC (1.3%), AAA (–1.4) and CCC (1.7%) had the best accuracy respectively.

In the central axis of the beam for bone material (case1, point 10) AAA (–1.2%), AXB (–1.7%), CCC (–2.0 %) and MC (–2.3) had the best accuracy respectively. For 15 MV in the same point AAA, CCC and MC (all with –2.4%) and AXB (with –3.0%) had the best accuracy respectively. For the beam off axis in bone material (case 6, point 10) AXB (–0.2%), AAA (–0.7), MC (0.8%) and CCC (0.9%) had the best accuracy respectively. For 15 MV at the same point MC (0.0%), CCC (0.1%) and AAA and AXB (both with –0.3%) had the best accuracy respectively.

3.4 Algorithm accuracy comparison for intensity modulated fields based on TG 119

GIPRs value for each dose calculation algorithm for five different plans based on TG119 [6] was compared with the dose distributions measured by the ArcCheck during treatment delivery is summarized in Table 5. Average GIPR (3% /3 mm) were 98.14 for AAA, 98.64 for AXB, 97.42 for CCC and 98.3 for MC. In addition, Average GIPRs (2% /2 mm) were 94.5±2.5% for AAA, 96.14±1.04% for AXB, 92.82±1.68% for CCC and 94.7±1.7% for MC.

Table 5
Volumetric modulated arc therapy (VMAT) gamma index passing rate (GIPR) with of 2% /2 mm and 2% /2 mm criteria for AXB: Acuros XB, AAA: An anisotropic analytic algorithm, CCC: Collapsed Cone Convolution and MC: Monte Carlo

Test \ Dose Calculation Algorithms

AAA AXB CCC MC

GIPR (2% /2 mm)% GIPR (3% /3 mm)% GIPR (2% /2 mm)% GIPR (3% /3 mm)% GIPR (2% /2 mm)% GIPR (3% /3 mm)% GIPR (2% /2 mm)% GIPR (3% /3 mm)%

Multi target 93.5 97.9 95.1 98.8 93.0 97.5 93.8 98.2

Prostate 95.2 98.5 95.6 99.1 94.5 97.8 94.9 99.1

Head/Neck 96.8 97.4 96.9 99.3 94.5 97.5 93.1 99.2

C shape(easy) 94 97.8 96.5 98.1 91.9 97.2 93.4 97.8

C shape(hard) 93 99.1 96.6 97.9 90.2 97.1 97.8 97.2

Test \ Dose Calculation Algorithms
Multi target	93.5	97.9	95.1	98.8	93.0	97.5	93.8	98.2
Prostate	95.2	98.5	95.6	99.1	94.5	97.8	94.9	99.1
Head/Neck	96.8	97.4	96.9	99.3	94.5	97.5	93.1	99.2
C shape(easy)	94	97.8	96.5	98.1	91.9	97.2	93.4	97.8
C shape(hard)	93	99.1	96.6	97.9	90.2	97.1	97.8	97.2

3.5 Algorithm accuracy comparison in surface and buildup region

The measured percentage depth doses at the surface and buildup regions for 6 MV and 15 MV photon beams using the Roos parallel-plate ionization chamber are given in Table 6. Also calculated dose by AAA, AXB, CCC and MC dose calculation algorithms at 6 MV and 15 MV photon beams for same measured depths summarized in Table 6. The mean average dose difference for first 5 mm depth between calculated and measured dose of 6 MV photon beam were –9.5%, 3.3%, –8.4% and 1.9% for AAA, AXB, CCC and MC dose calculation algorithms respectively. Mean average dose difference for first 5 mm depth between calculated and measured dose of 15 MV photon beam were –11.9%, 7.03%, –10.6% and 5.2% for AAA, AXB, CCC and MC dose calculation algorithms respectively.

Table 6
Percentage depth doses (PDDs) obtained with a Ross chamber and calculated dose by AXB: Acuros XB, AAA: A nisotropic analytic algorithm, CCC: Collapsed Cone Convolution and MC: Monte Carlo for same depth in a water equivalent RW3 phantom using 6 MV photon beams for 10×10 field size at SSD = 100 cm (WED: Water Equivalent Depth)

Phantom PDD (%)

depth(mm) Measurement (Roos) AAA AXB CCC MC

6MV 15MV 6MV 15MV 6MV 15MV 6MV 15MV 6MV 15MV

0.0 16.11 12.65 11.2 7.04 18.52 15.89 11.71 7.80 17.58 14.80

0.067 (0.07 WED) 19.89 15.05 16.01 12.05 21.56 16.95 16.98 12.75 20.85 16.10

1 44.54 32.98 38.98 27.95 46.85 35.52 39.02 28.05 45.35 34.99

2 61.78 42.59 53.45 37.95 63.12 45.21 54.23 38.14 62.35 44.52

3 71.33 53.51 66.89 48.80 73.11 56.61 67.12 49.24 72.54 55.51

4 76.44 57.25 72.02 53.35 78.93 60.25 73.11 53.98 76.99 59.62

5 86.66 63.35 83.25 58.21 89.14 66.21 85.10 58.95 87.2 65.53

15 100 92.59 100 87.92 100 94.22 100 88.25 100 92.35

30 – 100 – 100 100 100 100

Phantom	PDD (%)
0.0	16.11	12.65	11.2	7.04	18.52	15.89	11.71	7.80	17.58	14.80
0.067 (0.07 WED)	19.89	15.05	16.01	12.05	21.56	16.95	16.98	12.75	20.85	16.10
1	44.54	32.98	38.98	27.95	46.85	35.52	39.02	28.05	45.35	34.99
2	61.78	42.59	53.45	37.95	63.12	45.21	54.23	38.14	62.35	44.52
3	71.33	53.51	66.89	48.80	73.11	56.61	67.12	49.24	72.54	55.51
4	76.44	57.25	72.02	53.35	78.93	60.25	73.11	53.98	76.99	59.62
5	86.66	63.35	83.25	58.21	89.14	66.21	85.10	58.95	87.2	65.53
15	100	92.59	100	87.92	100	94.22	100	88.25	100	92.35
30	–	100	–	100		100		100		100

To obtain the dose at 0.07 mm water depth, which is representing surface dose [23], an interpolation calculation was made by comparing the PDD data to a four-order polynomial fit of Roos chamber measurements in the buildup region (Table 6). Mean average dose difference for 0.07 mm water depth between calculated and measured dose of 6 MV photon beam were –19.5.1%, 8.3%, –14.8% and 4.8% for AAA, AXB, CCC and MC dose calculation algorithms respectively. Mean average dose difference for 0.07 mm water depth between calculated and measured dose of 15 MV photon beam were –19.01%, 11.3%, –15.2% and 7% for AAA, AXB, CCC and MC dose calculation algorithms respectively.

3.6 Comparison of dose calculation algorithms based on performance in the tests of study

Table 7 provides a comparison of four dose calculation algorithms based on their performance scores in passing the tests of this study. Each algorithm was assigned a score ranging from 4 to 1, with 4 being the best score and 1 representing the lowest score. The scores were determined based on the algorithms’ performance in the specific tests conducted.

Table 7
Comparison of Dose Calculation Algorithms Based on Test’s Scores. Each algorithm was assigned a score ranging from 4 to 1, with 4 being the best score and 1 representing the lowest score. Since test 3.4 was only performed for the 6 MV beam, no values were available for the 15 MV beam, and “N/A” was indicated in the table. (AXB: Acuros XB, AAA: An nisotropic analytic algorithm, CCC: Collapsed Cone Convolution and MC: Monte Carlo)

Test AAA AXB CCC MC

6MV 15MV 6MV 15MV 6MV 15MV 6MV 15MV

Test 3.1 1 1 2 4 4 2 3 3

Test 3.2 4 4 3 3 1 1 2 2

Test 3.3 2 1 4 3 1 2 3 4

Test 3.4 2 N/A 4 N/A 1 N/A 3 N/A

Test 3.5 1 1 3 3 2 2 4 4

Total Score 10 7 16 13 9 7 15 13

Test	AAA	AXB	CCC	MC
Test 3.1	1	1	2	4	4	2	3	3
Test 3.2	4	4	3	3	1	1	2	2
Test 3.3	2	1	4	3	1	2	3	4
Test 3.4	2	N/A	4	N/A	1	N/A	3	N/A
Test 3.5	1	1	3	3	2	2	4	4
Total Score	10	7	16	13	9	7	15	13

Table 7 have provided a clear illustration of the performance of each algorithm across multiple tests. The total score serves as a comprehensive measure of their overall performance. It is important to highlight that for 6 MV photons, the AXB and MC algorithms demonstrated the highest total scores of 16 and 15, respectively. Following closely behind, AAA and CCC achieved scores of 10 and 9, respectively. Similarly, for 15 MV photons, the evaluation yielded total scores of 13 for both MC and AXB, while AAA and CCC obtained scores of 7. These results underscore the differing performance levels of the algorithms and underscore the significant superior performance of AXB and MC, both of which are D_m,m type dose calculation algorithms, in comparison to AAA and CCC, which are D_w . w type dose calculation algorithms (p-value is lower than 0.05).

4 Discussion

The dose calculation algorithm commissioning process for each TPS has three steps: 1) data entry, 2) calculation of the beam model, and 3) verification of the beam model [24 –26]. Before the data is entered into the TPS for beam modelling, it is re-evaluated for potential processing errors (e.g., smoothing, mirroring etc.). For CCC and MC beam modelling in the RayStation TPS, after entering measured data and selecting the machine data from the machine template library, the next step is beaming modelling and user does this part. In the beam modelling, the Medical Physicist (MP) follows the vendor instructions and adjusts the source sizes, off-axis softening and beam profile corrections by using measured data: depth dose curves, in-plane and cross-plane profiles and output factors [18]. In the Eclipse TPS, the data required to calculate the beam model comes from a combination of data entered manually by the user (e.g., beam geometry, output factors, depth dose curves, beam profiles, flattening filter material) and data retrieved from a machine data library (step.1 of the dose calculation algorithm commissioning in Eclipse and RayStation is exactly same) [18, 26]. After data entry, in step 2, the Eclipse TPS independently from the user (opposite of Ray station, where the user carries out the beam modelling) tries to fit the beam model parameters to match the input measured beam profiles and depth dose curves [26]. In both TPSs and all algorithms, the TPS allows the user to evaluate the agreement between the calculated and measured curves for all input beam profiles and depth-dose curves [18, 26].

The final step of dose calculation algorithm commissioning is beaming model verification and the results of this step can be used for comparison dose calculation algorithms accuracy. Based on the recommendations of MPPG 5.a [24] basic validation testing in homogeneous media should be completed prior to testing algorithms in heterogeneous media and for IMRT fields. With the performance evaluation of each algorithm in homogenous media, the MP can be sure of how accurate the beam modelling is.

In this study, two types of evaluations of homogenous media were carried out. In the first type of evaluation, point dose measurements were comprised and validated for dose calculation algorithms based on IAEA-TECDOC 1540 [8]. The results of this part of the study showed good agreement between measured and calculated doses by all the algorithms in homogeneous media for; symmetric open, asymmetric open, wedged fields, open fields with different SSD and different radiation beam angles. For the 6 MV and 15 MV beam models in all algorithms, the total percentage pass rate was more than 95% with results not showing any significant differences between algorithms. This was based on using tolerances recommended by TEC-DOC 1540 [8]. Looking at the percentage pass rate, the scoring of dose calculation algorithms for both 6 MV and 15 MV can be taken as follows (from best to worst): MC(D_m,m), AXB(D_m,m), AAA(D_w,w), CCC(D_w,w). In this test, both algorithms that calculated D_m,m showed better results in comparison to algorithms those calculating D_w,w.

In the second type of evaluation in homogenous media, PDDs and beam profiles were comprised and validated for the four dose calculation algorithms (AAA, AXB, MC and CCC). Results of this part of the study showed average gamma pass rates of greater than 98% (gamma criteria 2% /1 mm) for all algorithms when comparing measured and computed PDDs and profiles. Based on gamma pass rates (gamma criteria 2% /1 mm) for PDDs, the scoring of dose calculation algorithms for both 6 MV and 15 MV can be taken as follows (from best to worst): AAA (Eclipse TPS), AXB (Eclipse TPS), CCC (Ray Station TPS), MC (Ray Station TPS). The scoring for beam profiles could be as follows (from best to worst): AAA (Eclipse TPS), AXB (Eclipse TPS), MC (Ray Station TPS), CCC (Ray Station TPS). The worst gamma pass rate for PDDs and profiles in all algorithms was seen in the penumbra region of the fields for profiles and in the buildup regions for PDDs in all investigated field sizes. This observation is in line with work carried out previously by other authors [27 –31]. In addition, the PDD-s and profiles result of this part of the study does not show any significant differences between 1×1 cm² and 2×2 cm² field size created by MLC when compared to the same field sizes created by jaws alone for all evaluated algorithms. The results of this part of the study also showed Eclipse dose calculation algorithms where beam modeling is almost independent from the user gave better results when compared to RayStation dose calculation algorithms, where the modeling was carried out by the user. The results of evaluating the performance of all algorithms (AAA, AXB, CCC and MC) in homogenous media (e.g. water) showed that the generated beam models for 6 MV and 15 MV were excellent as per recommended reference guidelines [8, 24].

The performance of algorithms in heterogeneous media were compared according to TECDOC1583 [9]. Results of this part of the study showed that all algorithms had 100% pass rates for both 6 MV and 15 MV energies except CCC for test 4 (point 10). Test 4 (point10) evaluates an algorithms performance in a four-field box in bone type material. The CCC of the RayStation TPS under-estimated the dose relative to measurements by 3.9%. For the same test, deviation between measurement and calculated dose for the other algorithms were –1.5% for AAA and –2.7% for AXB and MC. Upon observing the mean percentage dose difference between measured and calculated doses in lung heterogeneities for 6 MV, the scoring is as follows (from best to worst): AXB (0.87%), CCC (1.07%), MC (1.3%) and AAA (1.42%). The scoring for 15 MV in lung is as follows (from best to worst): AXB (0.72%), MC (1.15%), AAA (1.05%) and CCC (1.8%). The deviations presented here were in line with the findings of other studies.31–37 Upon observing the mean percentage dose difference between measured and calculated dose in bone heterogeneities for 6 MV, the scoring is as follows (from best to worst): MC (1.23%), AXB (1.36%) AAA (1.36%) and CCC (1.4%). The scoring for 15 MV in bone is as follows (from best to worst): MC (0.6%), AXB (1.25%), CCC (1.1%), and AAA (1.8%). The deviations presented here were also in line with the findings of other conducted studies [33 –39]. Dose deviations reported in this study were consistent with other studies where algorithms were compared to measurements in heterogeneous media: mean deviations were reported smaller than 3% for AAA [32 , 35], 1.1% for AXB [33, 37], 2.1% for MC [33 , 38] and 2.5% for CCC [33 –39].

The results of GIPR for dose calculation algorithms in IMRT fields showed that GIPR (3% /3 mm) for all the algorithms (AAA, AXB, CCC and MC) in all evaluated tests based on TG119,6 were greater than 97% (no significant difference seen). By changing the GIPR from 3% /3 mm to 2% /2 mm a better evaluation of the dose calculation algorithm performance can be obtained as some problems may be hidden in GIPR (3% /3 mm). Looking at the average gamma pass rates (2% /2 mm) for VMAT fields based on TG119, the scoring of dose calculation algorithms can be taken as follows (from best to worst): AXB (96.14% ±1.04%), MC (94.7±1.7%), AAA (94.5% ±2.5%), CCC (92.82% ±1.68%). This is in agreement with Zhengwen Shen et al (2022), who showed the gamma pass rate values for intensity modulated fields obtained with AAA and AXB were 95.6±1.9% and 96.2±1.7% respectively, with 3% /2 mm criteria [40].

The Eclipse dose calculation algorithms (AXB and AAA) had better results in comparison to the RayStation dose calculation algorithms (MC and CCC). This can be due to less uncertainty in penumbra positions (for profiles) and build up regions (for PDD) for AXB and AAA compared to MC and CCC. Although uncertainty in penumbra position and build up are generally small, when moving from simple fields to IMRT and VMAT, such uncertainty is combined with in-field uncertainty and uncertainty in the penumbra and buildup shape; this combination either can averaged out or can become magnified depending on the plan. In the case of magnification, this uncertainty can contribute a significant portion of the in-field dose. Although MLC beam model fine-tuning for IMRT/VMAT can be effective on this part of the study, it is outside the scope of this study (MLC modeling of all algorithms in this study performed using recommendations of vendor).

Due to the skin toxicity in radiotherapy, accuracy of the buildup region dose calculation, especially within the initial 5 mm depth, has a great importance. Thus, the surface and buildup region calculation accuracy of AAA, AXB, CCC and MC algorithm were checked by comparing the calculated and measured dose values. Result of comparison showed for both photon beams energy (6 MV and 15 MV), D_w,w type algorithms underestimated surface dose and D_m,m type dose calculation algorithms overestimated build up region dose. The scoring of dose calculation algorithms for both 6 MV and 15 MV can be taken as follows (from best to worst): MC(D_m,m), AXB (D_m,m), CCC (D_w,w) and AAA(D_w,w).

Also in this study, PDD values were investigated at the depth of 0.07 mm, which was suggested for surface dose measurements by ICRU Report [23]. The scoring of dose calculation algorithms for both 6 MV and 15 MV in surface depth recommended by ICRU can be taken as follows (from best to worst): MC(D_m,m), AXB (D_m,m), CCC (D_w,w) and AAA(D_w,w).

Ying Cao et al. [41] evaluate the superficial dose calculation accuracy of four commonly used algorithms in commercially available TPS by film measurements. They reported the superiority of MC over AXB and superiority of AXB over AAA which is in line with the result of our study.

5 Conclusion

The modeling and dosimetric accuracy of AAA and AXB of Eclipse (version 16.1) TPS and MC & CCC of RayStation (version 10.B) TPS were investigated for 6 MV and 15 MV flattened beams for a Varian CLINIC-IX linear accelerator. Testing in homogeneous media and in heterogeneous geometries has demonstrated a high level of agreement between measurements and calculations for both TPSs. The result of this study showed that generally, dose calculation algorithms that calculate dose in medium (AXB and MC) have better accuracy than dose calculation algorithms that calculate dose to water (CCC and AAA) in heterogeneous media. The same general results for algorithms were also seen when comparing GIPRs for intensity modulated fields. Also results of our study showed that D_m,m dose calculation algorithms (MC and AXB) performed better calculation accuracy of the superficial dose in compare AAA and CCC which are dose calculation algorithms that calculate dose in water. The AXB dose calculation algorithm in the Eclipse TPS and the MC dose calculation algorithm in the RayStation TPS are optional dose calculation algorithms that customers can purchase from the vender. As such, if that option is viable for customers, it is better to purchase those algorithms.

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Test \ Dose Calculation Algorithms
	AAA		AXB		CCC		MC
	GIPR (2% /2 mm)%	GIPR (3% /3 mm)%	GIPR (2% /2 mm)%	GIPR (3% /3 mm)%	GIPR (2% /2 mm)%	GIPR (3% /3 mm)%	GIPR (2% /2 mm)%	GIPR (3% /3 mm)%
Multi target	93.5	97.9	95.1	98.8	93.0	97.5	93.8	98.2
Prostate	95.2	98.5	95.6	99.1	94.5	97.8	94.9	99.1
Head/Neck	96.8	97.4	96.9	99.3	94.5	97.5	93.1	99.2
C shape(easy)	94	97.8	96.5	98.1	91.9	97.2	93.4	97.8
C shape(hard)	93	99.1	96.6	97.9	90.2	97.1	97.8	97.2

Phantom	PDD (%)
depth(mm)	Measurement (Roos)		AAA		AXB		CCC		MC
	6MV	15MV	6MV	15MV	6MV	15MV	6MV	15MV	6MV	15MV
0.0	16.11	12.65	11.2	7.04	18.52	15.89	11.71	7.80	17.58	14.80
0.067 (0.07 WED)	19.89	15.05	16.01	12.05	21.56	16.95	16.98	12.75	20.85	16.10
1	44.54	32.98	38.98	27.95	46.85	35.52	39.02	28.05	45.35	34.99
2	61.78	42.59	53.45	37.95	63.12	45.21	54.23	38.14	62.35	44.52
3	71.33	53.51	66.89	48.80	73.11	56.61	67.12	49.24	72.54	55.51
4	76.44	57.25	72.02	53.35	78.93	60.25	73.11	53.98	76.99	59.62
5	86.66	63.35	83.25	58.21	89.14	66.21	85.10	58.95	87.2	65.53
15	100	92.59	100	87.92	100	94.22	100	88.25	100	92.35
30	–	100	–	100		100		100		100