Assessment of beam‐matched linacs quality/accuracy for interchanging SBRT or SRT patient using VMAT without replanning

Abstract Purpose Dosimetric accuracy is critical when switching a patient treated with stereotactic body radiation therapy (SBRT) or stereotactic fractionated radiotherapy (SRT) among beam‐matched linacs. In this study, the dose delivery accuracy of volumetric modulated arc therapy (VMAT) plans for SBRT/SRT patients were evaluated on three beam‐matched linacs. Method Beam data measurements such as percentage depth dose (PDD 10), beam profiles, output factors, and multi‐leaf collimator (MLC) leaf transmission factor for 6 MV photon beam were performed on three beam‐matched linacs. The Edge™ diode detector was used for measurements of beams of field size less than 5 × 5 cm2. Ten lung and 15 brain plans were generated using VMAT with the same beam model. Modulation complexity score of the VMAT plan (MCSv) was used as a plan complexity indicator. Doses were measured using ArcCHECK™ and GafChromic™ EBT3 films. The measurements were compared with calculated doses through absolute dose gamma comparison using 3%/2 mm and 2%/2 mm criteria. Correlation between difference in passing rates among beam‐matched linacs and MCSv was evaluated using the Pearson coefficient. Point doses were measured with the A1SL micro ion chamber. Results Difference in beam outputs, beam profiles, and MLC leaf transmission factors of beam‐matched linacs were all within ±1%, except the difference in output factor for 1 × 1 cm2 field between linac 1 and 3 (1.3%). For all 25 cases, passing rates of measured doses on three linacs were all higher than 90% when using 2%/2 mm gamma criteria. The average difference in point dose measurements among three beam‐matched linacs was 0.1 ± 0.2% (P > 0.05, one‐way ANOVA). Conclusion Minimal differences in beam parameters, point doses, and passing rates among three linacs proved the viability of swapping SBRT/SRT using VMAT among beam‐matched linacs. The effect of plan complexity on passing rate difference among beam‐matched linacs is not statistically significant.


| INTRODUCTION
In any high-volume/high-throughput clinical center switching patients among available linacs can be very convenient and highly desirable.
It may be required due to sudden breakdown of any linac, unex- Small fields are often used in lung SBRT and brain SRT for delivering escalated dose to the target while limiting the toxicity of critical structures. 6 As suggested by Institute of Physics and Engineering in Medicine (IPEM) Report 103 and International Atomic Energy Agency (IAEA) Report 483, field sizes that result in loss of lateral charged particle equilibrium or partial occlusion of the primary photon source by the collimating devices on the beam axis, are under the category of small photon fields. [6][7][8] For fields smaller than 1.5 cm across, field size changes of 1 mm can lead to central axis dose differences greater than one percent 8 ; and for fields 1 cm across, sub-millimetre changes in field size can lead to dose uncertainties of several percent. 9,10 Volumetric modulated arc therapy (VMAT) has been increasingly used in lung and brain radiotherapy for its capability of normal tissue dose sparing without sacrificing target dose coverage. [11][12][13] The multi-leaf collimator (MLC) is an essential part in VMAT planning for beam modulation. As for VMAT of small fields, the positioning accuracy of MLC leaves plays an important role in shaping the steep dose gradient in order to deliver high dose to the target while maintaining low dose to normal tissues.

| METHODS
Three Elekta ™ (Elekta, Stockholm, Sweden) linear accelerators were installed in our institution including one Infinity ™ (i.e., linac 1) and one Synergy ™ (i.e., linac 2), both have 6 and 15 MV photon energies and are equipped with Agility ™ heads (80 MLC leaf pairs of 5 mm leaf width). The third linac is a Versa ™ (i.e., linac 3) that has 6 and 10 MV photon energies as well as 80 MLC leaf pairs of 5 mm width.
All these considered beams are with flattening filter. planning, the smallest beam model applied was 2 × 2 cm 2 . Therefore, the smallest target allowed for VMAT treatment should have at least a 2 × 2 cm 2 equivalent square field size per degree of gantry rotation from the beam's eye view. In addition, the minimum MU per degree was 0.3.  performed on all three beam-matched linacs. Beam profiles were measured for 2 × 2 cm 2 , 5 × 5 cm 2 , 10 × 10 cm 2 , and 30 × 30 cm 2 field sizes at 1.5 and 10 cm depths. PDD 10 were measured for beams of 2 × 2 cm 2 , 5 × 5 cm 2 , 10 × 10 cm 2 , and 30 × 30 cm 2 field sizes. Depth dose and beam profile measurements were conducted using the IBA Blue Phantom ™ scanning phantom system (IBA dosimetry, Germany). For photon beams used in SBRT, American Association of Physicists in Medicine (AAPM) Task Group 101 recommend that the detector should have a spatial resolution of higher than 1 mm for basic dosimetry data measurement. 18 The IBA CC13 ion chamber of 0.13 cm 3 cavity volume was used for measurements including beam profiles and output factors of field sizes larger than or equal to 5 × 5 cm 2 ; while the Edge ™ diode detector (Sun Nuclear Corporation, FL, USA) of 0.019 mm 3 volume was used for beams of field sizes less than 5 × 5 cm 2 (e.g., 2 × 2 cm 2 and 5 × 5 cm 2 ). The relative output factor was measured at 10 cm depth and 100 cm source to surface distance for field sizes ranging from 1 × 1 cm 2 to 30 × 30 cm 2 . To minimize the energy variation on output factor measurements, a 3 × 3 cm 2 was selected as an intermediate or reference field size to normalize the diode against the CC13 ion chamber measurements following the "Daisy-chain" approach in eq. (1).

2.A | Beam profile and output factor measurements
Measurements for output factor of specific field size were repeated three times with diode and ion chamber to evaluate the consistency of MU delivery and detector measurements.

2.B | Dose measurements for clinical SBRT and SRT plans
Ten lung cases were prescribed with 50 Gy in five fractions and 15 brain cases including primary and metastatic tumors were prescribed with 30 Gy or 25 Gy in five fractions. All the VMAT plans were generated in Pinnacle TPS using the same 6 MV beam model. Lung VMAT plans used two full arcs with jaw sizes ranging from 2.4 × 3.1 cm 2 to 4.3 × 3.9 cm 2 . Based on the location of brain tumor, VMAT plans used either multiple non-coplanar arcs (e.g., one full arc and one vertex with couch kick) or multiple coplanar partial arcs (e.g., two to four partial arcs for posteriorly located targets), with jaw sizes ranging from 1.6 × 3.0 cm 2 to 3.7 × 4.6 cm 2 . All the VMAT plans were measured using ArcCHECK ™ cylindrical diode array system (Sun Nuclear, FL, USA) and Gafchromic™ EBT3 films (Ashland Inc., NJ, USA). The films were placed in the acrylic film holder specifically designed for ArcCHECK [ Fig. 1(a)]. Films used for VMAT planar dose measurements and absolute dose calibration were from the same lot and scanned in the same portrait orientation with 300 dpi (dots per inch) resolution. ArcCHECK and film measurements were compared with the TPS calculated planar doses through absolute dose gamma comparison using 3%/2 mm and 2%/2 mm criteria. Point doses were measured and used as another independent verification of absolute dose. The Extradin A1SL (Standard Imaging, Inc., WI, USA) micro ion chamber of 0.053 cm 3 volume was placed in the middle of the acrylic insert inside the ArcCHECK [ Fig. 1(b)].
Differences in gamma passing rates of ArcCHECK measurements and point dose measurements among three linacs were analyzed using one-way ANOVA. ArcCHECK and ion chamber measurements were repeated on three different days at all three linacs to evaluate the measurement uncertainty. A P-value less than 0.05 was considered statistically significant.
The modulation complexity score of VMAT (MCSv) was applied to evaluate the plan complexity degree of a VMAT plan. 19,20 MCSv ranges from 0 to 1, and it approaches 0 for increasing degree of VMAT plan modulation. The correlation between difference in passing rates of each plan among matched linacs and its modulation complexity was evaluated using Pearson correlation coefficient.

| RESULTS
The variation in repeated output factor measurements using diode and ion chamber for three beam-matched linacs were all within ±0.4% of the average. Differences in beam output factors of 2 × 2 cm 2 to 30 × 30 cm 2 field sizes among three beam-matched linacs were all less than 1% ( Table 1). The maximum difference in output factor was 1.3% which was the difference in output factor of 1 × 1 cm 2 field size between linac 1 and 3. Differences in PDD 10 and MLC leaf transmission factors among three linacs were all less than 0.6% (Table 2). Beam profiles measurements, including flatness and symmetry, of different field sizes at 1.5 and 10 cm depths for beam-matched linacs were listed in  Fig. 3(a)]; while passing rates of film measurements were all higher than 90% using 3%/2 and 2%/2 mm gamma criteria [ Fig. 3(b)]. There was small difference in passing rates of Arc-CHECK measurements among three linacs while either using 3%/ 2 mm criteria (P > 0.05, one-way ANOVA) or 2%/2 mm criteria (P > 0.05, one-way ANOVA). Linac 1 and 3 demonstrated the maximum difference in passing rates of ArcCHECK measurements and ion chamber measurements among the group (Table 4). As demonstrated in Table 4, the average difference in absolute point doses between ion chamber measurements and TPS calculations was However, none of these differences was statistically significant.
MCSv of all VMAT plans ranged from 0.34 to 0.57. The correlation coefficients for the difference in passing rates of ArcCHECK, film and ion chamber measurements among three linacs and MCSv were 0.15-0.24, 0.14-0.26, and 0.11-0.22, respectively (Table 4).

| DISCUSSION
The average difference in measurements of beam profile, output factor (except for 1 × 1 cm 2 ), and MLC leaf transmission factor among three beam-matched linacs were less than ±1% indicating that these linacs are clinically identical. The difference in output factor for 1 × 1 cm 2 field size beam between linac 1 and 2 was 1.3%. However, model for beam of 1 × 1 cm 2 field size was not applied for VMAT planning in Pinnacle TPS and the smallest target allowed in our institution for VMAT treatment should have at least a 2 × 2 cm 2 equivalent square field size for each control point.
Beam of 1 × 1 cm 2 field size for 6 MV is considered as very small field size. 8 Even with stereotactic detectors, careful detectorphantom setup and detailed dose corrections, one might still find more than 10% discrepancies among the measurements of very small fields (<1 cm in diameter). 18 The major perturbations were caused by the volume averaging effect and the difference between the mass density of the detector and that of the medium. 9 Studies have reported that the effect of volume averaging for detectors up to 3 mm in size was only noticeable at field sizes of less than 8 mm. 9  In this study, all passing rates of film measurements were higher than 90% indicating accurate beam modeling and dose delivery.
Average passing rates of film measurements were lower than those of ArcCHECK measurements mainly due to uncertainty in software-

ACKNOWLEDGMENT
The authors would like to thank Gisele Pereira, PhD for the professional advice and contribution during beam measurements.

CONF LICT OF I NTEREST
No conflicts of interest. Point dose difference 2 is the difference in measured doses between two beam-matched linacs.