2.2.1 Output factors

After having optimized Emax and S, we calculated the output factors for all field sizes with no possibility of further optimization and then compared them to the ones measured at source-axis distance (SAD) of 800 mm. The output factors were considered acceptable if the difference was lower than 1%, as recommended by the SSRMP7 and AAPM8 in their recommendations for the quality control of medical linear accelerators.

2.2.2 Phantom measurements

We validated the MC model by comparing measured and MC calculated (with TPS) doses. The measurements were performed in four different phantoms (see Figure 1). Ionization chamber measurements (for phantoms shown in Figure 1a,c,d) were performed with an A1SL ionization chamber (Sun Nuclear, USA) metrologically traceable to the Federal Institute of metrology (METAS) and with a valid calibration for the MLC, and we used EBT3 GafChromic films (Ashland Inc., Wayne, NJ, USA) for the phantom shown in Figure 1b. For each measurement, the measured dose was corrected by the daily output variation of the CK. To calculate the dose distribution in these phantoms with the TPS, Accuray advised using the relative electron density (RED) of the phantom to set the mass density, because although the RED of the soft tissues in a human body are within 1% of their mass densities, plastic phantoms are not.9 The model validation consisted of six steps. From steps 1 to 5, the dose differences (ΔD) between the MC model calculation and the measurement were evaluated for different configurations in order to estimate the accuracy of the model. We fixed a maximum ΔD of ±2% to consider the model as clinically acceptable. However, a maximum ΔD of ±1% was expected to consider the MC model as really accurate. Step 6 consisted of calculating real treatment plans. The following sections describe each step.

Phantoms used for validating the Monte Carlo (MC) model (a) homogeneous phantom with ionization chamber insert, (b) homogeneous phantom with films insert, (c) heterogeneous phantom with lung slabs and ionization chamber insert, and (d) homogenous phantom with different possible depths of measurements with ionization chamber inserts

Step 1: Single beam in homogeneous phantom (ionization chamber measurements)

The goal of this step was to compare the MC calculated and measured doses in a homogeneous phantom (Figure 1a), at the center of the beam and at 5 cm depth. For that purpose, we calculated nine plans with different equivalent square field sizes (different field sizes and/or shapes) ranging from 20.0 to 53.2 mm with a single beam (beam entrance normal to the phantom surface) in the TPS. These plans were then exported to the CK and delivered to the phantom. The dose was measured with a A1SL ionization chamber and compared to the TPS dose to obtain the dose difference ΔD. The closer the ΔD was to 0, the more accurate the MC algorithm. Additionally, to determine if the MC algorithm should be used for all clinical situations, even for homogeneous regions where the FSPB algorithm is available, we also measured the ΔD for four plans (among the nine previous plans) calculated with the FSPB algorithm and compared the dose differences with the ones obtained with the MC algorithm.

Step 2: Single beam in homogeneous phantom (film measurements)

EBT3 GafChromic films were used to verify the accuracy of the model in high-dose gradient regions. The films were calibrated with an Elekta Synergy linear accelerator (Elekta AB, Stockholm, Sweden) against a farmer ionization chamber (Nuclear Enterprise, USA) with a 6 MV beam energy. The energy independence of the Gafchromic films10 made possible their use in the CyberKnife beam. The uncertainty related to film dosimetry is estimated to be ±2%.10 We used five plans already calculated in step 1 (with equivalent square field sizes of 14.2, 20.0, 10.1, 30.8, and 17.6 mm) to obtain fields with dimensions (in one direction) of, respectively, 10.9, 16.5, 21.2, 30.9, and 45.0 mm. The dose profiles were measured with EBT3 Gafchromic films in the homogeneous phantom (Figure 1(b)) at 5.1 cm depth. A GI between the films and the MC plans was performed for each film. The calculations were performed with a local 2% of maximum DD, 2 mm of maximum DTA, and a dose threshold of 10% of the maximum dose.

Step 3: Single beam in heterogeneous phantom

This step followed the same principle as step 1, but we performed the calculations and the measurements using a heterogeneous phantom with a lung insert (Figure 1c). Nine plans were created with different equivalent square field sizes ranging from 20.4 to 45.2 mm with a single beam. The dose was measured at the center of the beam at 10 cm depth with A1SL ionization chamber.

Step 4: Multiple beams in homogenous and heterogeneous phantoms

Four plans were calculated in the homogeneous phantom (Figure 1a) with 6, 10, 12, and 21 beams with several different entry angles. The dose measurements were performed at the center of the beam and at 5 cm in the homogeneous phantom. The same procedure was applied using a heterogeneous phantom with 6, 10, 14, and 20 beams with several different entry angles. The dose measurements were performed at the center of the beam at 10 cm depth.

Step 5: Different depths in homogeneous phantom

A plan with multiple beams of field sizes larger than 28.5 mm equivalent field size was calculated in the phantom showed in Figure 1d and the ΔD was evaluated at 3.0, 6.0, 9.0, 12.0, 15.5, and 19.5 cm depth. The phantom used for those measurements was not specific to the CK. Therefore, we inserted a fiducial on the phantom to help the positioning, but a higher uncertainty was however observed due to the impossibility to correct for rotations. To mitigate this, we performed each measurement four times, with phantom repositioning between each measurement, and compared the mean difference to the MC calculated dose.

Step 6: Patient-specific QAs

Step 6 consisted on the creation of five MLC plans using the MC algorithm and the irradiation of patient-specific QAs following our routine procedure to accept a treatment plan. The patient-specific QA of each MLC plan was performed with the Octavius detector 1000 SRS (PTW, Germany) and a global GI of 3% of DD and 1 mm of DTA was applied. We assumed these QAs too be clinically acceptable if at least 95% of the points fulfilled the GI criteria.