Monte Carlo simulation of linac using PRIMO

Measurement equipment

All measurements were conducted on a Varian VitalBeam™ (Varian Medical Systems, Palo Alto, CA) linac equipped with a Millennium 120 leaf MLC. Photon beams of 6MV and 6MV FFF were used. A PTW BEAMSCAN water phantom (PTW Freiburg, Germany), an ion chamber (Semiflex 3D Type TW31021, PTW, Freiburg, Germany), and an electrometer (PTW UNIDOS E, T10009, PTW, Freiburg, Germany) were used in the measurements. The commercial software MEPHYSTO™ (PTW, Freiburg, Germany) was used to perform the evaluation of dose profiles. PRIMO software (version 0.3.64.1800_x64) was installed on a workstation (Windows 10 Enterprise, Intel Core i7-7820X CPU@3.6 GHz, RAM 32 GB).

Amorphous silicon-based electronic portal imaging device (EPID) was used to measure the transmission factor and DLG. The active area of EPID detector was 30 cm × 40 cm (1024 × 768 matrix) with pixel size of 0.39 mm. The images were acquired in “the integrated image” mode used 4DTC as the acquisition workstation at the source detector distance (SDD) of 105 cm. The frame rate of EPID is 9.6 frames/s. Portal dose image prediction (version 8.0, Varian Medical Systems, Inc., USA) was used to compare the predicted portal dose images with the measured ones. Dose image was calculated using the Portal Dose Image Prediction (PDIP) algorithm in the Eclipse™ version 13.6.23 (Varian Medical Systems Inc., Palo Alto, CA).

The dosimetric leaf gap (DLG) in Eclipse™ TPS was optimized to reduce the discrepancies between the measured dose distributions and the calculated ones of patient treatment plans. The Delta4 phantom system (Scandidos, Uppsala, Sweden) was used in the dose verification for the clinical treatment plans. Gamma-index evaluation method implemented in Delta4 was applied to quantify the discrepancies of dose distributions. Delta4 is a cylindrical polymethyl-methacrylate phantom with 22 cm in diameter and 40 cm in length. The mass density of the phantom was 1.19 g/cm3, and the relative electron density was 1.147. It consists of 1069 p-type Silicon diodes in a crossed array inside the phantom, with 5 mm resolution in central area and 10 mm resolution in the peripheral area. The software ScandiDos Delta4 allowed the users to compare the measured dose distribution with the dose distribution calculated using TPS.

Measurements of the critical parameters for TPS simulation

We measured the PDD and OAR of 6MV and 6MV FFF photon beam for Varian VitalBeam linac at Chinese Academy of Medical Sciences Cancer Hospital, Shenzhen center, respectively. The scan range of the detector in horizontal plane was 50 cm by 50 cm. The measurements were performed in continuous scanning mode at the speed of 10 mm/s. Different square fields (3 cm, 4 cm, 6 cm, 8 cm, 10 cm, 15 cm, 20 cm, 30 cm, and 40 cm) were used with a fixed source-to-phantom distance (SPD) of 100 cm.

Transmission factor and DLG are two crucial parameters to model the rounded MLC leaf in Eclipse™ TPS. The transmission factor is determined by the material and height of the MLC leaf, beam quality, and etc. EPID was used to measure the MLC transmission in two MLC-closed fields: one with MLC bank A closed and the other with MLC bank B closed as shown in Fig. 1. The transmission factor was calculated using the following equations:

$$tr\left( A \right) = R_ /R_$$

(1)

$$tr\left( B \right) = R_ /R_$$

(2)

$$R_ = \left[ } \right]$$

(3)

where tr(A) and tr(B) are transmission factors of MLC bank A and bank B, respectively. Ropen is the reading of the open field. RA and RB are the readings of closed MLC bank A and closed MLC bank B, respectively. RT is the average MLC leaf transmission for both MLC banks.

Fig. 1figure 1

The BEV projection of the completely blocked MLC field with MLC bank A closed (RA) and bank B closed (RB), respectively

DLG was measured using sweeping gap technique [42]. The sweeping gap test plans were designed in Eclipse™ TPS (Varian Medical Systems, Inc., USA), including dynamic sweeping gaps of 2 mm, 4 mm, 6 mm, 10 mm, 14 mm, 16 mm, and 20 mm (shown in Fig. 2), two closed-MLC fields, and one open-MLC field. The test plans were generated with gantry angle of 0 degree, collimator setting of 90 degree, SSD at 100 cm, MLC moving from − 6 to + 6 cm in dynamic mode at the speed of 2.5 cm/s. For each treatment plan, the jaws were set to 10 cm by 10 cm as the reference field. Each sweeping gap traveled across the reference field, and the delivered dose was 100 MU.

Fig. 2figure 2

DLG test plan with gap width of 20 mm

In order to evaluate the contribution of sweeping gap field, the MLC transmission reading RgT was subtracted from the initial ionization reading \(\cdot R_\). The corrected gap reading (\(_^}}\)) and RgT for each gap (g) were defined by Varian guideline as:

$$R_ = R_ \cdot \left[ } \right]$$

(4)

where g is the nominal gap width (unit: mm), the sweeping gap movement range is 120 mm. Rg is the initial sweeping gap field reading (CU values for EPID). The corrected gap readings were fitted using linear regression method. DLG was the value at the intersection between the extrapolated extension of the fitted line and y-axis (Fig. 6). R-squared was used to measure the goodness-of-fit for the linear regression model.

PRIMO simulation

The PRIMO simulation setup consists of three segments [31, 32, 43] as shown in Fig. 3. In segment 1 (s1), the upper part of the linac was simulated. The user could adjust the primary beam parameters including nominal energy, initial energy, energy FWHM, focal spot FWHM, and beam divergence. In s1, the four parameters were tuned to match the PDDs in different field size and OARs in different depths. In the segment 2 (s2), the field parameters were edited, including the treatment technique, beam weights, gantry start and end angles, collimator angle, couch angle, MLC type, aperture size, applicator, and isocenter location. In segment 3 (s3), the linac model was applied in patient and phantom geometry. The three segments can be grouped in a user-defined way [43].

Fig. 3figure 3

The three segments in PRIMO simulation

In PRIMO, Varian 2100 linac model was recommended to simulate TrueBeam for 6MV, while FakeBeam linac model is an experimentally based geometry of TrueBeam for 6MV FFF and 10MV FFF. In segment 1, we selected Varian 2100 and Fake Beam from PRIMO linac model list, as the initial models of 6MV and 6MV FFF Varian VitalBeam linac, respectively. The linac head geometry is shown in Fig. 4. The transport parameters of linac head components are shown in the Additional file 1: Table 1. To determine the beam characteristics, there were four crucial parameters in PRIMO, including initial electron energy, energy FWHM, FWHM of the focal spot size, and beam divergence. We fine-tuned the four crucial parameters to match the simulated PDD and OAR with our measurements. Among the four parameters, the initial electron energy was firstly determined based on the depth of the maximum dose on the depth dose curves based on field sizes of 10 cm × 10 cm. The other three parameters were adjusted until both simulated PDD and OAR had the highest GPRs compared with our measurements in all the considered field sizes (For field sizes smaller than 10 cm × 10 cm (included), the GPRs (1%/1 mm) were higher than 90%, other field sizes were higher than 85%).

Fig. 4figure 4

The illustration of head geometry for Varian VitalBeam™ operating in photon mode (From PRIMO user’s manual software version 0.3.(32–64).1880)

In our study, the search range of initial electron energy was 5.4–6.6 MeV, and the interval was 0.1 MeV. The energy FWHM varied from 0 to 0.1 MeV with an interval of 0.01 MeV. The FWHM of the focal spot size varied from 0 to 0.5 cm with an interval of 0.05 cm. The divergence of the parallel beams was considered to be zero degree.

In segment (s1), the PENELOPE computation engine was used to obtain the phase-space file. Splitting roulette was adopted as the variance reduction technique to improve simulating efficiency. In segment 2 (s2) and segment 3 (s3), the dose planning method (DPM) was employed to calculate dose distribution. The splitting factor in DPM was 300. Particle histories increased from 109 in s1 to 1010 in s2 and s3. The number of particle histories increased along with the increase of the field size to reduce the uncertainty.

Both PDD and OAR were simulated in the water phantom under the following condition: gantry angle, 0 degree; collimator angle, 0 degree; SSD, 100 cm; fixed bin size in the tallying volume, 0.2 × 0.2 × 0.2cm3. In our study, there were nine square field sizes considered, including 3 cm, 4 cm, 6 cm, 8 cm, 10 cm, 15 cm, 20 cm, 30 cm, and 40 cm. All the square fields were collimated by the jaws. The tallying volumes increased with the increase of the square field size. The corresponding tallying volumes in PRIMO were 9 × 9 × 35cm3, 12 × 12 × 35cm3, 18 × 18 × 35cm3, 24 × 24 × 35cm3, 30 × 30 × 35cm3, 40 × 40 × 35cm3, 50 × 50 × 35cm3, 60 × 60 × 35cm3, and 70 × 70 × 35cm3, respectively.

The model of Millennium 120 MLC was selected in PRIMO to evaluate the MLC model. The model consists of 40 central leaf pairs with a 5 mm projection width at the isocenter (SSD = 100 cm) and 20 outer leaf pairs with a width of 10 mm. The MLC transmission factor were obtained using Eqs. (1)–(3). The designed sweeping gap test plans were imported into PRIMO. The dose tallying volume in simulation was 15 × 15 × 10cm3. The point dose (Rg) was acquired at 5 cm below the dose tallying volume. The Rg readings of different sweeping gap test plans were fitted using linear regression method. DLG was acquired as the value at the intersection of the extrapolated fitting line and y-axis (Fig. 5).

Fig. 5figure 5

Comparison between simulations and measurements of PDD and OAR (The dose distribution was normalized to the maximum dose point). a PDD 6MV, 10 × 10 cm2, b PDD 6MV FFF, 10 × 10 cm2, c the gamma index for 6MV PDD, d the gamma index for 6MV FFF PDD, e OAR 6MV, 10 × 10 cm2 depth at 1.5 cm, f OAR 6MV FFF, 10 × 10 cm2 depth at 1.5 cm, g the gamma index for 6MV OAR, h the gamma index for 6MV FFF OAR

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