Monte Carlo (MC) simulation is one of the most accurate methods for calculating dose distributions, particularly in heterogeneous tissues, where the effects of electron transport cannot be accurately modeled with conventional deterministic dose calculation algorithms [1,2]. Despite the accuracy of the MC simulation, large calculation times have limited its application in clinical routines [3]. Recently, with an increase in the computer processing speed, the performance of the MC algorithm has been improved, and the MC dose calculation became acceptable for clinical treatment planning with electron beams [4-6]. The electron Monte Carlo (eMC) algorithm is based on the macro MC method for the electron beam in the Eclipse treatment planning system (Varian Medical System, Palo Alto, CA, USA) [7-9]. The eMC algorithm increases the calculation speed while preserving the calculation accuracy in heterogeneous internal parts of patients, such as the lung and oral cavity [10,11].

However, some limitations hinder the use of the eMC algorithm. Several studies have demonstrated discrepancies between measurements and calculations, particularly for lower electron energies, smaller applicator sizes, and larger source-to-surface distances (SSDs) [10,12-14]. In the buildup region at 4 MeV, the eMC algorithm produces up to 5.4% lower absorbed dose than that of the full MC model. In the penumbra and out-of-field regions in water, the eMC calculation underestimates the absorbed doses by up to 3.3%, compared to the full MC model [15]. The eMC calculation overestimates the absorbed dose toward the shoulder region with a 25×25 cm² applicator at increased SSDs [15].

Varian Medical System has announced that the beam configuration with air profiles (APs) can improve the calculation accuracy with AP measurements at the source-to-detector distance (SDD) of 95 cm where the collimator jaws open appropriately for each machine, energy, and applicator [16]. The purpose of this study is to evaluate the performances of the eMC algorithm with the insertion of APs in terms of profile, percentage depth dose (PDD), and penumbra.

1. AP measurements and beam configuration

This study was conducted within electron energy ranges used at the author’s hospital. The electron energies of 6, 9, 12, and 16 MeV for VitalBeam (Varian Medical System) and 6, 9, 12, 16, and 20 MeV for the Clinac iX linear accelerator were used in this study. A Blue Phantom² scanning system (IBA Dosimetry GmbH, Schwarzenbruck, Germany) and two CC13 cylindrical ionization chambers (IBA Dosimetry GmbH) were used to acquire APs. The field chamber was placed at the SDD of 95 cm in air to measure APs. To remove pulsed beam fluctuations, the reference chamber was placed so that the active volume could be fully covered by the corresponding field sizes [17]. The measurement setup for APs is illustrated in Fig. 1a. The in-line and cross-line APs were measured, in which jaw positions were opened according to the applicator without an attached applicator [16]. The jaw sizes for each machine, energy, and applicator size are shown in Table 1. The measured APs were postprocessed by smoothing and rescaling; then, they were converted into the w2CAD format to register the measured beam data to Eclipse. The final APs with the w2CAD format were imported and configured according to the Eclipse reference guide document [16].

Table 1 . Jaw openings according to the applicator sizes and energies for VitalBeam and Clinac iX.

Applicator size (cm2)	Jaw openings (cm2)
	VitalBeam					Clinac iX
	6 MeV	9 MeV	12 MeV	16 MeV		6 MeV	9 MeV	12 MeV	16 MeV	20 MeV
6×6	20×20	20×20	11×11	11×11		20×20	20×20	11×11	11×11	11×11
10×10	22×22	20×20	15×15	15×15		20×20	20×20	14×14	14×14	14×14
15×15	22×22	20×20	19×19	18×18		20×20	20×20	17×17	17×17	17×17
20×20	27×27	25×25	25×25	23×23		25×25	25×25	25×25	23×23	22×22
25×25	32×32	30×30	30×30	28×28		30×30	30×30	30×30	28×28	27×27

Figure 1. Schematic diagrams of the measurement setup for (a) optional air profiles and (b) verifications.

2. Measurement of the reference dose distribution

To evaluate the accuracy of the eMC algorithm with APs, the dose profiles and PDD curves were measured using the Blue Phantom² scanning system. The measurement setup for reference dose distributions is shown in Fig. 1b. Blue Phantom² was positioned with the SSD of 100 cm. Similar to the measurement of APs, to remove pulsed beam fluctuations, the reference chamber was placed where the active volume could be fully covered by the corresponding field sizes [17]. For VitalBeam, the profiles were measured at the depth of 1.18, 1.58, 2.20 and 2.90 cm at 6, 9, 12, and 16 MeV, respectively. For Clinac iX, the measurement depths were 1.00, 1.40, 2.00, 2.70, and 3.30 cm at 6, 9, 12, 16, and 20 MeV, respectively. The depths were shifted upward by 0.15 cm, considering the effective measurement point, with an A25 applicator (25×25 cm²) and normalized to 100% at the center of the profiles. The PDD curves were measured with an A10 applicator (10×10 cm²) and normalized to 100% at the depth of the maximum dose.

3. eMC calculation

The dose distributions were calculated in a 40×40×40 cm³ virtual water phantom using beam models with and without APs. The eMC calculation options used in this study are listed in Table 2. For the number of particle histories option, the zero value means that the eMC calculation uses as many particles as required to reach the statistical uncertainty set in statistical uncertainty option. The random generator seed number is defined as the random number sequence used in the particle generator. If the seed value is set to 0, the EMC algorithm uses a randomly selected seed. The dose threshold for uncertainty was defined as the dose threshold to calculate statistical uncertainty [16]. The dose distributions with A25 applicators were exported in the coronal plane and normalized to 100% at the center of the profile using the RIT software (Radiological Imaging Technology, Inc., Colorado Springs, CO, USA). The absolute differences between calculated and measured dose distributions were averaged in the range of −10 to 10 cm to represent the discrepancies between the models with and without APs. The PDDs with A10 applicators were obtained and normalized to 100% at the depth of the dose maximum. Considering the effective measurement point, the comparison between the calculated and measured PDDs was started from the depth of 0.15 cm. Both calculated and measured penumbras were obtained by averaging the distances of the right and left sides between 20% and 90% of the central axis dose in the dose profiles [18].

Table 2 . Electron Monte Carlo (eMC) calculation parameters used in this study.

Calculation parameter	Value
Statistical uncertainty	1
Statistical uncertainty limit	3
Calculation grid size in cm	0.25
Random generator seed number	0
Number of particle histories	0
Dose threshold for uncertainty	50
Smoothing method	Three-dimensional Gaussian
Smoothing level	Medium

The discrepancies in the profiles between the measurements and calculations for VitalBeam are summarized in Table 3, while the sample distributions at 6 and 16 MeV are shown in Fig. 2. The accuracy of calculated profile was improved by 0.35%, 0.15%, 0.14%, and 0.38% on average at 6, 9, 12, and 16 MeV, respectively, when the beams were modeled with APs. For all energies, the calculations with APs improved the accuracy up to 0.5%. Although the calculations with APs still exhibited over- and under-estimation tendencies, the discrepancies were reduced at both low and high energies. The discrepancies in the profiles between the measurements and calculations for Clinac iX are summarized in Table 3, while the sample distributions at 6 and 20 MeV are shown in Fig. 3. The discrepancies were reduced by 0.16%, −0.31%, 0.94%, 0.42%, and 0.74% on average at 6, 9, 12, 16, and 20 MeV, respectively, with the insertion of APs. Except at 9 MeV, the calculations with APs improved the accuracy up to 0.95%. The calculations with APs at 9 MeV had lower accuracy than those without APs of 0.17% and 0.45% for the in-line and cross-line profiles, respectively.

Table 3 . Improvements between measurements and calculations for VitalBeam and Clinac iX.

Energy (MeV)	Direction	VitalBeam				Clinac iX
		Measurement depth (cm)	Calculation–measurement* (%)		Improvement (%)	Measurement depth (cm)	Calculation–measurement* (%)		Improvement (%)
			Without AP	With AP			Without AP	With AP
6	In-line	1.18	1.08	0.69	0.38	1.00	0.65	0.45	0.20
	Cross-line		1.07	0.75	0.32		0.48	0.37	0.11
9	In-line	1.58	0.91	0.67	0.24	1.40	0.23	0.40	−0.17
	Cross-line		0.76	0.71	0.05		0.15	0.60	−0.45
12	In-line	2.20	0.32	0.12	0.20	2.00	1.16	0.21	0.95
	Cross-line		0.19	0.11	0.08		1.20	0.28	0.92
16	In-line	2.90	0.96	0.46	0.50	2.70	0.69	0.22	0.47
	Cross-line		0.66	0.40	0.26		0.95	0.59	0.36
20	In-line	-	-	-	-	3.30	1.31	0.45	0.86
	Cross-line		-	-	-		1.07	0.46	0.61

Figure 2. Measured and calculated profiles with and without air profiles (APs) for VitalBeam: (a, c) in-line and (b, d) cross-line profiles at 6 and 16 MeV, respectively.

Figure 3. Measured and calculated profiles with and without air profiles (APs) for Clinac iX: (a, c) in-line and (b, d) cross-line profiles at 6 and 20 MeV, respectively.

The penumbras are shown in Table 4. For Clinac iX, the penumbra difference between the measurement and calculation without AP was up to 0.10 cm, while that with AP was up to 0.15 cm. For VitalBeam, the maximum difference between the measurement and calculation was 0.25 cm for both cases. Of note, no significant change in the difference between the measured and calculated penumbras was observed between the cases with and without AP. Table 5 shows the maximum and average difference between the PDD measurement and calculation with or without APs, while the sample distributions at low (6 MeV) and high (16 and 20 MeV) energies are shown in Fig. 4. For VitalBeam, although the measured PDDs exhibited differences up to 6.09%, 2.99%, 1.71%, and 1.45% without APs, those with APs were 5.68%, 3.02%, 1.95%, and 1.13% at 6, 9, 12, and 16 MeV, respectively. For Clinac iX, the measured PDDs exhibited differences up to 5.07%, 2.82%, 1.72%, 1.74%, and 0.82% without APs, while those with APs were 5.24%, 3.03%, 1.50%, 1.29%, and 1.00% at 6, 9, 12, 16, and 20 MeV, respectively. Large discrepancies were usually observed in the buildup region, particularly at low energies. This could not be improved even using eMC models with APs.

Table 4 . Comparison between the measurements and calculations for the penumbras for VitalBeam and Clinac iX.

Energy(MeV)	Direction	VitalBeam				Clinac iX
		Measurement depth (cm)	Calculation (cm)		Measurement (cm)	Measurement depth (cm)	Calculation (cm)		Measurement (cm)
			Without AP	With AP			Without AP	With AP
6	In-line	1.18	1.30	1.38	1.33	1.00	1.20	1.30	1.30
	Cross-line		1.30	1.35	1.30		1.20	1.30	1.28
9	In-line	1.58	1.10	1.10	0.98	1.40	1.15	1.18	1.15
	Cross-line		1.05	1.10	0.95		1.10	1.15	1.05
12	In-line	2.20	1.15	1.15	0.95	2.00	1.13	1.18	1.05
	Cross-line		1.15	1.15	0.95		1.15	1.10	1.08
16	In-line	2.90	1.25	1.28	1.03	2.70	1.18	1.23	1.13
	Cross-line		1.25	1.25	1.00		1.20	1.20	1.15
20	In-line	-	-	-	-	3.30	1.33	1.43	1.28
	Cross-line		-	-	-		1.30	1.40	1.30

Table 5 . Comparison of the mean and maximum differences in PDDs between the measurements and calculations for VitalBeam and Clinac iX.

Energy(MeV)	VitalBeam				Clinac iX
	With AP		Without AP		With AP		Without AP
	Mean (%)	Maximum (%)	Mean (%)	Maximum (%)	Mean (%)	Maximum (%)	Mean (%)	Maximum (%)
6	1.45	5.68	1.52	6.09	0.64	5.24	0.62	5.07
9	1.28	3.02	1.35	2.99	0.50	3.03	0.47	2.82
12	0.94	1.95	0.84	1.71	0.29	1.50	0.36	1.72
16	0.48	1.13	0.42	1.45	0.33	1.29	0.55	1.74
20	-	-	-	-	0.16	1.00	0.22	0.82

Figure 4. Comparison of the measured and calculated percentage depth dose (PDD) curves with and without air profiles (Aps) and corresponding dose differences at (a) 6 and (c) 16 MeV for VitalBeam and at (b) 6 and (d) 20 MeV for Clinac iX. Calculation with AP–measurement, difference between the calculation with AP and measurement value; Calculation without AP–measurement, difference between the calculation without AP and measurement value.

In this study, the accuracy of the eMC calculation was evaluated when the electron beams were modeled with optional APs in the treatment planning system. The accuracies of profiles were improved by modeling the electron beam with optional APs. The differences could be minimized when the electron beams were modeled by adding optional APs. Specifically, this reduction was considerable in the shoulder regions where the profiles were near the dose fall-off. According to the manufacturer’s document, optional APs could construct two-dimensional fluences in beam modeling. If optional AP was not measured, the radially symmetric fluences from the open field APs (40×40 cm²) are used for dose calculation. Because the actual fluences for each applicator size differ from those of open fields, the jaw size-specific measurements can improve the accuracies. The dose calculation accuracy for a given applicator can be improved by constructing a two-dimensional fluence that is appropriate for each applicator. Otherwise, the symmetric fluence in air with a 40×40 cm² open field can be applied for all applicators during the dose calculation [14,16]. To consider these properties, Varian Medical System recommends to include optional APs for the electron beam configuration [16].

Although no significant improvements in PDDs and penumbras were observed when eMCs were modeled with optional APs, the accuracies of profiles were improved overall. The PDD differences between measurement and eMC calculation have been reported in many studies [4,19,20], although electron beams have been modeled without optional APs. For 4 MeV, the eMC algorithm produced up to 5.4% lower doses than those of the full MC model in the buildup region and over-estimated the dose by up to 5.2% beyond the depth of the dose maximum, particularly at the end of the electron range [15]. This result could not be improved even with APs. The eMC algorithm largely underestimated the doses near the surface and overestimated them near the end point of the fall-off region compared to the measurement. Because this behavior was emphasized at low energies, the treatment plan should be carefully designed at low electron energy and prescription depth in the superficial region. It is necessary to improve the eMC algorithm to improve the calculation accuracy at low energy.

The accuracy of eMC calculation can be improved in dose profiles when the electron beams are modeled with optional APs.

This work was supported by the National Research Foundation of Korea (NRF), grant funded by the Korea government (MSIT) (2019R1F1A1041944), and the Radiation Technology R&D program through the National Research Foundation of Korea funded by the Ministry of Science and ICT (2019M2A2B4095126).

The authors have nothing to disclose.

All relevant data are within the paper and its Supporting Information files.

Conceptualization: Minsoo Chun, Jung-in Kim. Data curation and formal analysis: Jeongho Kim, Jiwon Sung. Funding acquisition: Minsoo Chun, Chang Heon Choi. Investigation: Jiwon Sung, Minsoo Chun. Methodology: Jiwon Sung, Hyeongmin Jin, Minsoo Chun. Supervision: Minsoo Chun, Jong Min Park, Jung-in Kim. Validation: Jiwon Sung, Jeongho Kim. Writing–original draft: Jiwon Sung. Writing–review & editing: Minsoo Chun.