PRIMO Monte Carlo Simulation and One-dimensional Gamma Index Analysis as a Tool to Validate Experimentally Measured Beam Data and Treatment Planning System Calculated Dose Distribution

Abstract

Purpose:

The purpose of this study was to validate experimentally measured beam data, and treatment planning system (TPS) calculated volumetric modulated arc therapy (VMAT) three-dimensional (3D) dose distribution using PRIMO Monte Carlo (MC) simulation and one-dimensional (1D) gamma index analysis.

Materials and Methods:

The PRIMO code simulates the percentage depth dose (PDD) and beam profiles across varying field sizes in water phantoms, which were then compared with the ion chamber-measured beam characteristics using 1D gamma analysis. For the VMAT 3D dose distribution, the computed tomography scan of the anthropomorphic pelvis phantom was used for dose calculation and simulation in Eclipse TPS and PRIMO, respectively. Then, the doses of the target and organ at risk were compared with 1D gamma index analysis.

Results:

The results show that the PDD passed the 1D gamma index above 95% of all evaluated points at 2%/2 mm criteria. There was no significant difference between the mean values of measured and MC-simulated PDD at all field sizes. The results were statistically significant as P < 0.05. For beam profile at a 10 cm depth along in-line (in-plane) and cross-line (cross-plane) directions, above 95% of all the evaluated points passed the 1D gamma index at 3%/3 mm. The matching of dose volume histogram (DVH) of TPS calculated and PRIMO simulated DVH passed 2%/2 mm and 3%/3 mm gamma index passing criteria.

Conclusions:

Based on this study’s findings, PRIMO MC simulation can validate experimentally measured medical linear accelerator beam data and TPS 3D dose distribution with acceptable agreement using 1D gamma analysis.

INTRODUCTION

Monte Carlo (MC) simulation is a powerful computational technique that leverages random sampling to estimate outcomes for complex problems. In the field of radiotherapy, it plays a crucial role in accurately calculating absorbed doses and treatment planning. It is widely regarded as the “golden standard” method due to its ability to simulate the interactions of radiation with matter in a detailed and realistic manner.[1,2,3,4,5,6,7,8]

Several MC simulation codes are utilized extensively in radiotherapy for various applications. Each of these codes, such as Geant4 (Geometry ANd Tracking 4),[9] MC N-Particle (MCNP),[10] Electron Gamma Shower-National Research Council,[11] FLUKA,[12] TOPAS,[13] and PENELOPE,[14] has distinct strengths and capabilities. The choice of which code to use depends on specific simulation requirements and the expertise of the user. For instance, Geant4 is known for its robustness in modeling complex geometries and particle transport, whereas MCNP is often favored for its versatility in handling different types of particles and materials.

PRIMO is a notable example in this context, integrating components from PENELOPE 2011, PENEASY, dose planning method, and PENEASYLINAC into a unified graphical user interface (GUI).[15] This integration makes PRIMO particularly user-friendly, allowing practitioners to conduct MC simulations efficiently within a single environment. Moreover, PRIMO is available as open-access software, which means it can be used freely by researchers and clinicians alike.

The objective of this study in radiotherapy is to validate experimentally measured dosimetric parameters against MC simulations. This validation helps ensure the accuracy and reliability of simulations in predicting radiation doses and treatment outcomes. By comparing experimental data with simulation results from PRIMO, researchers can assess the effectiveness of the simulation in replicating real-world scenarios and make informed decisions regarding treatment planning and optimization.

In summary, MC simulation, facilitated by software like PRIMO, represents a cornerstone in modern radiotherapy for its ability to provide precise and detailed dose calculations.

MATERIALS AND METHODS

For this study, Varian Trilogy medical linear accelerator (LINAC) was chosen for the experimental measurement and simulation. It has a millennium 120 multi-leaf collimator with 6 megavolts (MV) and 15 MV photon energies. It also has electron beams of energies 6 million electron volts (MeV), 9 MeV, 12 MeV, 15 MeV, and 18 MeV, respectively. Only photon energy of 6MV was used for the dosimetric measurement and MC simulation for various field sizes.

Monte Carlo simulation

The simulations were performed through the PRIMO code (Version: 0.3.64.1814, 64-bit) a software created by Rodriguez et al., Brualla et al., specifically designed to simulate clinical LINACs, and predict absorbed dose distributions within water phantoms and computed tomography (CT) scans.[15,16] This tool is easy to use with a simple GUI, and it uses a computer system based on the PENELOPE MC code. It is incorporated with various LINAC head models of both Varian and Elekta medical systems with the option to choose either electron or photon beam. In this study, the Varian Clinac 2300 LINAC head model was used for the simulation as Varian Trilogy has this configuration.[17]

A water phantom of dimension 40 cm × 40 cm × 40 cm was created in PRIMO with bin size of 2 mm × 2 mm × 2 mm for percentage depth dose (PDD) and beam profile simulations and DICOM CT image, structures, and plan of the anthropomorphic pelvis phantom from the Eclipse treatment planning system (TPS) were used for volumetric modulated arc therapy (VMAT) three-dimensional (3D) dose simulations in it. All the simulations were run for 1 × 10⁸ particle histories in an Intel (R) Core (TM) i5-8250U CPU @ 1.60GHz, 1.80 GHz, 8GB RAM, 4 core, 8 threads processor system.

Experimental measurements

The experimental measurements of PDD and beam profiles were carried out with IBA Blue phantom and CC13 cylindrical ion chamber (IC) for all field sizes and 10 cm depth for beam profile, matching the parameters used in simulations. For 3D dose distribution, the Varian Eclipse TPS (Version:11.0, Varian Medical Systems, Palo Alto, CA, USA) was used to calculate the dose in anthropomorphic pelvis phantom CT images. The measured and calculated PDD and beam profiles were compared for one-dimensional (1D) gamma index using a python programming.

Gamma index

The gamma index is a quantitative metric commonly used in radiotherapy to assess the agreement between the measured and calculated dose distributions. It provides a comprehensive evaluation of both dose distribution and spatial agreement by comparing corresponding points in the calculated and measured dose distributions. The gamma index is calculated by considering both dose difference and distance-to-agreement criteria. The formula for the gamma index is typically expressed as:[18,19,20]

γ(r_m) = min{Γ(r_m,r_c}Ɐ(r_c),

which is the minimum value of Γ.

It is expressed as:

and it is the generalized Euclidean distance in the renormalized dose and distance space with

where rm and rc are the position of the measured dose (Dm) and calculated dose (Dc) respectively, and ΔD (%) and Δd (mm) are the percentage dose difference and distance-to- agreement (DTA) criteria respectively.

The pass–fail criteria become

Figure 1 shows the schematic diagram for calculating gamma. The circle or ellipse defines the pass and fail criteria. When the measured line is inside this circle or ellipse, then the gamma test passes otherwise, the test fails.

Figure 1.

One-dimensional gamma analysis search ellipsoid on the two curves of either percentage depth dose or beam profile of experimentally measured data and PRIMO Monte Carlo simulated data. MC: Monte Carlo

Statistical analysis

The results of this study were analyzed with Pearson’s correlation coefficients and one-way ANOVA for the significance of the results.

RESULTS

The comparison of PDD for flattening filtered 6 MV photon beam of various field sizes simulated by PRIMO and measured by ion chamber are shown in Figure 2 and Table 1 with their corresponding 1D gamma index at 2%/2 mm passing criteria. From Table 1, it was observed that the mean values of measured PDD and calculated PDD are nearly the same. These results are statistically significant as P < 0.05. The 1D gamma index pass percentages at 1%/1 mm and 2%/2 mm are also tabulated in Table 1. At 2% dose difference and 2 mm distance to agreement passing criteria, all the PDDs of all field sizes pass with 95% and above. Similarly, the comparisons of measured and MC calculated radiation beam profile along in-plane (in-line), and cross-plane (crossline) for small to large field sizes were analyzed [Figure 3] and tabulated in Table 2. Here, in Figure 3, the measured and calculated composite beam profiles, each for field sizes 5 cm × 5 cm, 10 cm × 10 cm^, and 30 cm × 30 cm^, along with the 1D gamma index, were shown. Gamma index was evaluated at different resolution such as 1%/1 mm, 2%/2 mm, and 3%/3 mm. It was observed that, for the beam profile, the 1D gamma index at 3% dose difference and 3 mm distance to agreement passed 95% and above of all the evaluated points, as illustrated in Table 2. At high resolution, 1%/1 mm and 2%/2 mm, the average passing percentage was lower than 95%.

Figure 2.

Comparison of measured and Monte Carlo simulated percentage depth dose for different field sizes with the gamma index at 2%/2 mm passing criteria. PDD: Percentage depth dose

Table 1.

Comparison of Monte Carlo simulated and measured ion chamber percentage depth dose percentage depth dose for different field sizes

	Mean of PDD	SD	Difference of mean PDD	Maximum difference	P	Gamma - 1%/1 mm (%)	Gamma - 2%/2 mm (%)
Field size 30 cm × 30 cm
IC	58.69	22.52	0.25	4.68	0.000004	98.03	100
MC	58.93	22.71
Field size 25 cm × 25 cm
IC	58.04	22.75	0.54	14.29	0.000000	95.39	100
MC	57.49	22.82
Field size 20 cm × 20 cm
IC	57.11	23.08	0.66	6.02	0.000000	68.42	100
MC	57.78	23.46
Field size 15 cm × 15 cm
IC	55.85	23.55	1.51	14.40	0.000000	13.16	95.39
MC	54.34	23.57
Field size 10 cm × 10 cm
IC	53.92	24.16	0.53	12.29	0.000000	88.82	100
MC	53.40	24.47
Field size 5 cm × 5 cm
IC	51.06	24.77	1.15	16.41	0.000000	33.55	100
MC	49.91	25.09

IC: Ion chamber, PDD: Percentage depth dose, MC: Monte Carlo, SD: Standard deviation

Figure 3.

Comparison of measured and Monte Carlo simulated cross-line and in-line beam profile at 10 cm depth for different field sizes with the gamma index at 3% and 3 mm passing criteria

Table 2.

Percentage of evaluated points passing the different gamma index passing criteria for measured ion chamber and calculated Monte Carlo beam profiles

Radiation beam profile	30 cm × 30 cm				10 cm × 10 cm				5 cm × 5 cm
	In-plane (%)		Cross-plane (%)		In-plane (%)		Cross-plane (%)		In-plane (%)		Cross-plane (%)
	IC	MC	IC	MC	IC	MC	IC	MC	IC	MC	IC	MC
Gamma - 1%/1 mm	54.05		44.86		42.42		72.06		70.59		41.18
Gamma - 2%/2 mm	87.57		82.16		74.24		94.12		97.06		79.41
Gamma - 3%/3 mm	96.76		96.76		96.97		98.53		100		100

IC: Ion chamber, MC: Monte Carlo

For the CT-based VMAT 3D dose distribution comparison between TPS and PRIMO code, the dose-color-wash [Figure 4a and b], respective dose volume histogram (DVH) [Figure 4c and d], and composite DVH of the planning target volume (PTV) with gamma index [Figure 4e] are shown. Table 3 shows the comparison of the maximum (Max), mean, and minimum (Min.) dose in the PTV and various organs at risk with the gamma index passing percentage at 1%/1 mm, 2%/2 mm, and 3%/3 mm. The gamma analysis at these criteria reveals high agreement between the TPS calculation and MC simulations dose distribution, with high pass percentages [Table 3]. The TPS PTV mean, max, and min doses were 40.61 Gy, 43.03 Gy, and 35.24 Gy, while that of MC simulation were 39.04 Gy, 44.93 Gy, and 29.04 Gy with their respective 2 σ (2 standard deviation), respectively [Table 3]. For the bladder, the TPS mean, max, and min doses were 16.85 Gy, 41.96 Gy, and 1.74 Gy, while that of MC simulation were 17.06 Gy, 41.74 Gy, and 2.03 Gy with their respective 2 σ, respectively [Table 3]. For the rectum, the TPS mean, max, and min doses were 23.18 Gy, 41.23 Gy, and 3.51 Gy, while that of MC simulation were 22.02 Gy, 42.12 Gy, and 2.27 Gy with their respective 2 σ, respectively [Table 3]. For the left femur, the TPS mean, max, and min doses were 7.78 Gy, 14.32 Gy, and 3.50 Gy, while that of MC simulation were 7.28 Gy, 13.85 Gy, and 2.14 Gy, with their respective 2 σ, respectively [Table 3]. Moreover, for the right femur, the TPS mean, max, and min doses were 9.07 Gy, 17.95 Gy, and 3.93 Gy, while that of MC simulation were 8.65 Gy, 16.90 Gy, and 3.31 Gy with their respective 2 σ, respectively [Table 3].

Figure 4.

Treatment planning system calculated (a), and PRIMO Monte Carlo simulated (b) dose dose-color-wash along with their respective dose volume histogram (c and d) and Gamma calculation for planning target volume (e). PTV: Planning target volume, MC: Monte Carlo, TPS: Treatment planning system, DVH: Dose-volume histogram

Table 3.

Computed tomography-based three-dimensional dosimetric comparison of planning target volume, and organ at risks of the anthropomorphic pelvis phantom from treatment planning system and Monte Carlo simulation

Structures	PRIMO MC dose (Gy)			Eclipse TPS dose (Gy)			Gamma index pass percentage
	Mean (2σ)	Maximum (2σ)	Minimum (2σ)	Mean	Maximum	Minimum	1%/1 mm	2%/2 mm	3%/3 mm
PTV	39.04 (2.64)	44.93 (2.88)	29.04 (2.44)	40.61	43.03	35.24	92.84	95.51	97.14
Bladder	17.06 (1.81)	41.74 (2.92)	2.03 (0.82)	16.85	41.96	1.74	100	100	100
Rectum	22.02 (1.89)	42.12 (2.77)	2.27 (1.02)	23.18	41.23	3.51	46.62	100	100
Left femur	7.28 (1.07)	13.85 (1.45)	2.14 (0.97)	7.78	14.32	3.50	91.67	100	100
Right femur	8.65 (1.26)	16.90 (1.49)	3.31 (1.15)	9.07	17.95	3.93	91.05	98.95	100

PTV: Planning target volume, MC: Monte Carlo, TPS: Treatment planning system

In Table 4, there is statistical comparison of bladder and rectum volume cover by various dose levels (V₄₀, V₃₅, V₃₀, V₂₅, V₂₀, V₁₅, V₁₀, and V₅). There is a high correlation between the dose predicted by PRIMO MC simulation and the dose from TPS. The 2-tailed Pearson’s correlation coefficients (r) were 0.9992 for the bladder and 0.9964 for the rectum. These results are statistically significant as P < 0.05 for both the organs.

Table 4.

Percentage dose volume of bladder and rectum encompassed by various dose in the anthropomorphic pelvis phantom from treatment planning system and Monte Carlo simulation with statistics

Dose- volume	TPS bladder volume (%)	MC bladder volume (%)	Difference	Statistical comparison	TPS rectum volume (%)	MC rectum volume (%)	Difference	Statistical comparison
V40	3.50	2.40	1.10	Pearson’s correlation (two-tailed): r=0.9992; P=0.0000	1.58	0.30	1.28	Pearson’s correlation (two-tailed): r=0.9964; P=0.0000
V35	8.21	9.40	1.19		13.58	11.00	2.58
V30	12.96	14.50	1.54		23.95	21.50	2.45
V25	20.54	22	1.46		44.67	35.30	9.37
V20	31.87	33.8	1.93		68.56	63.60	4.96
V15	48.32	48.9	0.58		78.60	77.30	1.30
V10	69.1	68.2	0.90		84.88	85.70	0.82
V5	91.98	89.2	2.78		95.35	92.30	3.05

MC: Monte Carlo, TPS: Treatment planning system

DISCUSSIONS

The presented data outline a comparative analysis of PDD and radiation beam profile measurements for various field sizes using ion chamber (IC) measurements and MC simulation methods. It also compared target dose (Gy) values obtained from TPS calculations with the MC simulations. For the largest field size of 30 cm × 30 cm, the mean PDD values for IC and MC are nearly the same, with a small difference of 0.25 and a maximum difference of 4.68 from the MC. The statistical analysis, as indicated by the P = 0.000004, suggests a significant similarity between the two. Moreover, the gamma analysis demonstrates excellent agreement, particularly for the less stringent criteria of 2%/2 mm (100%) compare to more stringent criteria 1%/1 mm. Moving to smaller field sizes, the differences become more pronounced, with increasing standard deviations and larger discrepancies of the mean PDD. Similar results were reported by Li et al. in their studies.[21] However, the result is statistically significant as P < 0.05, indicating a consistent similarity between IC and MC measurements. Interestingly, the gamma analysis reveals varying degrees of agreement, ranging from high (e.g. 95.39% for 25 cm × 25 cm) to lower values (e.g. 13.16% for 15 cm × 15 cm).

For the radiation beam profile, the largest field size of 30 cm × 30 cm, the gamma analysis suggests moderate agreement for 1%/1 mm criteria, ranging from 41.18% to 72.06%. However, as the criteria become less strict (2%/2 mm and 3%/3 mm), the agreement improves substantially, reaching high values of 82.16% to 100%. This indicates that while there may be some discrepancies at the smallest level of tolerance, the methods generally agree well when considering larger tolerances. At 10 cm × 10 cm field size, the agreement between IC and MC measurements improves, especially for less stringent criteria. The gamma values for 2%/2 mm range from 74.24% to 94.12%. Similarly, for the 5 cm × 5 cm field size, there is a noticeable improvement in agreement, with gamma values ranging from 79.41% to 100% for 2%/2 mm and 3%/3 mm criteria.

For CT-based 3D dose distribution in anthropomorphic pelvis phantom between TPS calculations and MC simulations, the study demonstrates that PRIMO MC simulations generally agree well with Eclipse TPS calculations for dose distribution across the PTV and anatomical organs. The high gamma index values suggest robust agreement, particularly notable for the bladder and femurs, whereas slightly lower agreement is observed for the rectum, especially at tighter gamma criteria [Table 3]. In Table 4, it compares dose volumes between the TPS and MC simulations for the bladder and rectum, along with statistical correlations. The comparisons were made at V₄₀, V₃₅, V₃₀, V₂₅, V₂₀, V₁₅, V₁₀, and V₅, showing varying degrees of agreement between TPS and MC doses for the bladder volumes, with high correlation coefficients and statistically significant P values (P = 0.0000).

The satisfactory agreement between the PRIMO simulation and experimental measured beam data and the 3D dose distribution of TPS, it is suggested that the PRIMO code should be validated and used as a tool to evaluate commissioning beam data and patient-specific quality assurance of treatment plans such as intensity-modulated radiation therapy and VMAT. The limitation of this PRIMO code is that it cannot be run on AMD processors, it works in Intel processors.[15]

CONCLUSIONS

Favorable agreement between the experimental measurements and PRIMO code was exhibited for both depth dose and dose profiles across the assessed field sizes. Considering the study’s outcomes, this code is capable of accurately simulating a medical LINAC and used as an independent verification software for radiotherapy beam scanning and plans computed by a TPS.

Conflicts of interest

There are no conflicts of interest.

Funding Statement

Nil.