Optimizing the effective spot size and the dosimetric leaf gap of the AcurosXB algorithm for VMAT treatment planning

Abstract Purpose The aim of this study is to provide and test a new methodology to adjust the AcurosXB beam model for VMAT treatment plans. Method The effective target spot size of the AcurosXB v15 algorithm was adjusted in order to minimize the difference between calculated and measured penumbras. The dosimetric leaf gap (DLG) was adjusted using the asynchronous oscillating sweeping gap tests defined in the literature and the MLC transmission was measured. The impact of the four parameters on the small field output factors was assessed using a design of experiment methodology. Patient quality controls were performed for the three beam models investigated including two energies and two MLC models. Results Effective target spot sizes differed from the manufacturer recommendations and strongly depended on the MLC model considered. DLG values ranged from 0.7 to 2.3 mm and were found to be larger than the ones based on the sweeping gap tests. All parameters were found to significantly influence the calculated output factors, especially for the 0.5 cm × 0.5 cm field size. Interactions were also identified for fields smaller than 2 cm × 2 cm, suggesting that adjusting the parameters on the small field output factors should be done with caution. All patient quality controls passed the universal action limit of 90%. Conclusion The methodology provided is simple to implement in clinical practice. It was validated for three beam models covering a large variety of treatment types and localizations.

already shown in the literature, the effective target spot size can also affect the dosimetric accuracy of modulated plans. 2,3 All four parameters are associated with recommendations provided by the manufacturer 4 : measurement conditions for the transmission are provided, values for the effective target spot size are given depending on the algorithm and it is suggested to adjust the DLG based on the sweeping gap method. These recommendations have widely been discussed in the literature. 3,[5][6][7][8][9] For example, Gardner et al. 3 showed that for intracranial SRS VMAT planning on an Edge accelerator, the 0.5 mm effective target spot size yielded highest passing rates compared to the vendor recommended 1.0 mm effective target spot size. Because the sweeping gap tests do not account for the tongue and groove effect, 5 some authors suggested adjusting the DLG in order to improve the patient quality controls [7][8][9] which resulted in an increase of the DLG value compared to the sweeping gap tests. For example, the adjusted DLG value reported by Kim et al. 7  The aim of this study is to provide and test a methodology to adjust the AcurosXB beam model for VMAT treatment plans. The effective target spot size were adjusted in order to match the measured penumbras and the DLG was determined based on the aOSG tests defined by Hernandez et al. 5 The impact of the beam parameters on small field output factors was investigated using a design of experiment methodology. The methodology suggested was tested and validated for three beam models encompassing two energies and two MLCs. A comparison with the manufacturer recommendations was also performed.

| MATERIALS AND METHODS
Three beam models were considered in this study: one 6 MV beam on a TrueBeam Tx associated with a 120 Millennium MLC, one 6 MV beam on a TrueBeam STx associated with a 120 High Definition (120 HD) MLC, and one 6 MV FFF beam on a TrueBeam STx associated with a 120 HD MLC.
All calculations were performed with AcurosXB v15 algorithm with a 1 mm calculation grid. During commissioning, percentage depth dose, profiles in the crossline direction, diagonal profiles and field output factors were measured for field sizes ranging from 2 cm x 2 cm to 40 cm x 40 cm with a CC13 (IBA) ionization chamber.
Although, as stated by the manufacturer, "beam model should be accurate even though the measurement data does not contain very small field sizes (1 × 1 cm 2 and 2 × 2 cm 2 )", 4 data for the 2 cm x 2 cm field were measured as recommended by the guidelines from the AAPM. 11 No data was measured during commissioning for the 1 cm x 1 cm field since "depth dose curve and profile measurements for field sizes smaller than 2 × 2 cm 2 are ignored by the configuration program". 4 Correction factors of the IAEA/AAPM TRS 483 12 were applied to define the field output factors.

2.A | Adjustment of the source sizes on the penumbra
The effective target spot size in the X and Y directions (respectively σ X and σ Y ) models the broadening of the penumbra in X and Y direction. The modeling is done by applying a Gaussian smoothing to the energy fluence of primary photons. This parameter equals the width of the Gaussian distribution in the X/crossline or Y/inline direction at isocenter plane, expressed in millimeters. 4 σ X and σ Y were adjusted by comparing calculated and measured penumbras. Measurements were conducted with a Razor diode (IBA) with a sensitive area of 0.6 mm diameter at 10 cm depth with a Source-Surface Distance (SSD) of 90 cm and a measurement step of 0.1 mm in penumbra region (0.2 mm elsewhere). Similarly to the literature, 13 five field sizes defined by the MLC were studied: 0.5 cm x 0.5 cm and from 1 cm x 1 cm to 4 cm x 4 cm with a 1 cm stepping. Jaws were set to 10 cm x 10 cm. Penumbras were defined as the distance between the 20% and the 80% dose levels with the 100% set at the beam central axis for each profile, even for the FFF beam with regard to the small field sizes studied. σ X and σ Y were individually incremented from 0 to 2 with a 0.2 mm stepping. The mean deviation between calculated and measured right and left penumbras for all five field size was reported in the crossline (σ X ) and inline (σ Y ) directions.  Field output factors measurements were performed with a 60019 CVD diamond (PTW) and a Razor diode (IBA) at 10 cm depth with a SSD of 90 cm for field sizes from 0.5 to 2 cm with a 0.5 cm stepping and for field sizes of 3 and 4 cm. Fields were defined by the MLC and jaws were set to 10 cm x 10 cm. A reproducibility smaller than 1% was found between two sets of measurements. Correction factors from the IAEA-TRS483 12

and from
Casar et al. 16 were applied to the uncorrected ratio of readings of the 60019 CVD diamond and the Razor diode respectively. The difference between calculated and measured output factors was computed for both detectors and the mean value was considered for the analysis. The factors' effects were estimated for each level of each factor separately and their significance was interpreted by using an analysis of variance (anova) model with a significance level fixed at α = 1%.

2.D | Validation of the beam models
Once the parameters σ X , σ Y, DLG, and transmission were deter-

3.A | Measured versus calculated penumbras
The mean deviation between calculated and measured penumbras for the three beam models studied is shown in Fig. 1 in the crossline (X) and inline (Y) directions as a function of the effective target spot size (σ). Optimal values are given in 3.C | Impact of σ X , σ Y , DLG, and transmission on the small field output factors Parameters significantly influencing the field output factors are given in Table 3. A similar trend was observed for all beam models cm fields, the amplitude was very small (<0.2%) although significant.
For comparison, the amplitude of σ Y for the 0.5 cm x 0.5 cm field size could be up to 14%. Figure 3 represents the deviations between measured and calculated small field output factors. Two methodologies were followed to calculate the field output factors: one using the beam parameters optimizing the penumbra and the aOSG tests (given in Table 2) and one following the manufacturer recommendations. The median deviations were larger for the parameters found in this study but the differences were found not significant (paired t-test performed on each beam studied, α = 5%)

3.D | Patient quality controls
Results of the patient quality controls performed with EBT3 films are given in Table 4. The mean gamma pass rate exceeds the universal tolerance limit of 95% given by the AAPM Task Group No. 218 18 and all plans passed the universal action limit of 90%. Following the manufacturer's recommendations, similar gamma passing rates were found. Differences between the two beam models were not statistically significant for a 3% -2 mm gamma analysis as well as a 3% -1 mm gamma analysis (paired t-test, α = 5%).   Table 2 and differ largely from the values recommended by the manufacturer: σ X = 1.5 mm and σ Y = 0 mm.
However, using σ X = 1.5 mm would generate a mean deviation of up to 1 mm between the calculated and measured penumbras whereas using σ Y =0 mm would generate a smaller 0.2 mm mean deviation.
According to Glenn et al. 10  The DLG was adjusted by minimizing the mean dose deviation for aOSG tests. Corresponding DLG values for the three beams considered are given in Table 2   The originality of this study resides in highlighting that the choice of the optimal parameters (effective target spot size, DLG, and transmission) that maximizes the agreement between the calculated and measured small output factors must be done by considering the interaction between DLG and effective target spot sizes for field sizes smaller than 2 cm x 2 cm. When considering the values of the parameters described in  All patient quality controls realized with EBT3 films passed the universal action limit of 90% validating the custom parameters chosen for the beam models. Neither the gain in penumbra accuracy nor the loss in small field output factors agreement could be observed when comparing to the methodology provided by the manufacturer. A possible explanation could be the small magnitude of the differences expected (maximum 1 mm for the penumbra, maximum 1.5% for field output factors larger or equal to 1 cm) which cannot be detected with a 3% -2 mm or a 3% -1 mm gamma analysis. A bias in the comparison of the two methodologies was also introduced because plans were reoptimized in order to provide a clinically acceptable plan when using either the parameters found in this study or the manufacturer recommendations.

| CONCLUSION
This study presented and validated in three beam models a new methodology to determine the effective target spot size and DLG: tuning the effective target spot size in order to minimize the difference between calculated and measured penumbras and tuning the DLG by minimizing the mean dose deviation for aOSG tests in order to take into account the tongue-and-grove effect. It was shown with a design of experiments methodology that tuning the parameters in order to minimize the difference between calculated and measured small field output factors had to be done with caution since all parameters and many interactions can influence the calculated output factors. As a consequence, we recommend prioritizing adjusting the effective spot sizes based on field penumbras.

ACKNOWLEDGMENT
The authors thank Victor Hernandez for providing the DICOM files associated to the aOSG tests.

CONF LICT OF I NTEREST
The author have no relevant conflicts of interest to disclose.

SUPPORTING IN FORMATION
Additional Supporting Information may be found online in the Supporting Information section at the end of the article.