Dosimetric and mechanical equivalency of Varian TrueBeam linear accelerators

Abstract Purpose To investigate and improve the level of equivalency of Varian TrueBeam linear accelerators (linacs) in energy‐, dosimetric leaf gap‐ (DLG) and jaw calibration. Methods Eight linacs with four photon energies: 6 MV, 6 MV FFF, 10 MV FFF, and 15 MV, and three electron energies (on two linacs): 6, 9, and 12 MeV were commisioned and beam‐matched. Initially, symmetry of lateral profiles was calibrated for maximum field size. Energy‐matching was then performed for photons by adjusting diagonal profiles at maximum field size and depth of maximum dose to coincide with the reference linac, and for electrons by matching the range at percentage depth of ionization of 90%, 80%, and 50%. Calibration of DLG was performed for 6 MV and evaluated among the linacs. The relationship between DLG and the Gap value was investigated. A method using electronic portal imaging device (EPID) was developed and implemented for jaw calibration. Results Symmetry calibration for photons (electrons) was within 1% (0.7%), further improving the vendor's acceptance criteria. Photon and electron energy‐matching was within 0.5% and 0.1 mm, respectively. Calibration of DLG was within 0.032 mm among the linacs and utilizing the relationship between DLG and the Gap value resulted in an empirical calibration method which was implemented to simplify DLG adjustment. Using EPID‐based method of calibration, evaluation of the jaw‐positioning among the linacs for 30 cm × 30 cm field size was within 0.4 mm and in the junction area within 0.2 mm. Dose delivery error of VMAT‐plans were at least 99.2% gamma pass rate (1%, 1 mm). Conclusions High level of equivalency, beyond clinically accepted criteria, of TrueBeam linacs could be achieved which reduced dose delivery systematic errors and increased confidence in interchanging patients among linacs.


| INTRODUCTION
A high demand for radiotherapy treatments requires an effective workflow, especially in clinics with several linear accelerators (linacs).
A key component in achieving high efficiency is the ability to move patients to another linac without the need to adjust the treatment plan. This is accomplished by having dosimetrically and mechanically equivalent linacs, that is, linacs that are beam-matched. [1][2][3][4][5][6][7] When commissioning new linacs, they are often beam-matched by the vendor upon delivery. However, it has been shown that vendor specification might not be strict enough to ensure optimal matching. 1,3 According to vendor specifications, beam-matching refers to energymatching. However, as the level of complexity in treatments increases, the importance of other parameters increase. These include dosimetric leaf gap (DLG) which determines the positioning of the multileaf collimators (MLC) and is highly relevant for all dynamic treatments, and jaw positioning. [8][9][10] Ultimately, achieving nominally matched linacs enables moving patients among the linacs in case of malfunction, service etc. and hence enhancing the flexibility and the efficiency of the workflow in the clinic. Moreover once it is established that the linacs are nominally matched, only one set of beam-data is needed for modelling the beam in the treatment planning system (TPS). 11 Several studies have presented beam matching techniques and corresponding results for linacs of different vendors, models, and energies. 2,3,7,[12][13][14] Also, multi-institutional studies have been conducted to compare beam matching prestanda. 1,11,15 However, there is a lack of a complete set of data for energy matching, DLG-, and jaw position calibration for a significant number of linacs within one clinic which can serve as a reference for other clinics in the process of beam-matching TrueBeam linacs.
Eight linacs were installed at the radiotherapy department at Karolinska University Hospital (Stockholm, Sweden) with four photon energies: 6 MV, 15 MV, 6 MV FFF, and 10 MV FFF, and, on two linacs, three electron energies: 6, 9, and 12 MeV. The linacs were installed two at a time over a six months period. The linacs' components were all of the same series and they were factory-matched upon delivery. A group of five medical physicists (the authors of this article) were tasked with commisioning the linacs clinically within seven months of the installation of the first linac. The purpose of this work was to investigate the highest level of agreement among TrueBeam linacs, and to present the methodologies to achieve it.
Higher equivalency among beam-matched linacs reduces dose delivery systematic errors as well as increases the confidence in swapping patients among the linacs, having one set of beam-data in the TPS.
To the best of our knowledge, this is the first investigation of beammatching for more than three TrueBeam linacs at the same institution, as well as including DLG calibration and jaw calibration in the beam matching process. The high number of linacs in this work, coupled with measurements being conducted during a short time frame using the same equipment and methodologies, qualify the results as a reliable and credible reference for other clinics undergoing a similar task.

2.A | Symmetry calibration and energy-matching
Symmetry calibration for photons (electrons) was performed in water using the IBA Blue Phantom 2 and IBA Compact Chamber CC13 (Table 1), for all energies by measuring 40 cm × 40 cm (25 cm × 25 cm) lateral profiles in in-and crossline directions. The measurements setup for photons was performed at source-to-surface distance (SSD) = 90 cm and depth in water = 10 cm. For electrons, the setup was SSD = 100 cm and depth in water equals that of maximum depth dose d max . The aim was to adjust the beam steering in order to obtain the best symmetry value possible, regardless of whether profiles were already within the acceptance criteria from the factory.
A linac's energy quality is commonly characterized by the Tissue Phantom Ratio (TPR 20,10 ). 16 Consequently, TPR 20,10 measurements can be used for energy-matching among linacs. However, a more comprehensive method of photon energy-matching is measuring and matching diagonal dose profiles at d max , after symmetrizing the lateral dose profiles. This method offers more information about the beam profile of a specific energy compared to TPR 20,10 . 17 After obtaining optimized symmetry values the energy-matching of each photon energy was performed. The first installed linac was considered the reference to which all other linacs were matched. A pair of diagonal dose profiles were measured with SSD = 90 cm and depth in water = depth of maximum dose (i.e., 1.5 cm for 6 MV, 2.5 cm for 10 MV, 3.0 cm for 15 MV). The aim was to minimize the difference between the reference and the actual linac in the region above 80% and 60% of the central axis dose for flattened and unflattened beams, respectively (the latter roughly corresponding to 80 % of the full width half maximum (FWHM) value). The electron energies were matched by measuring the percentage depth of ionization (PDI) at SSD = 100 cm for 10 cm × 10 cm field size and adjusting the energy so that the electron range at the percentage depth of ionization 90%, 80%, and 50% (R90, R80 and R50) were tuned with the reference linac. Priority was given to match the

2.B | Reference dosimetry
Reference dosimetry was performed in accordance with TRS-398 Code of Practice (CoP) 16 for flattened photon beams and electron beams, and TRS-483 18 CoP for unflattened photon beams. TPR 20,10 was measured on all linacs and an average value was used to readout the appropriate k Q,Q0 . Note that for unflattened beams, determining TPR 20,10 required a correction to get an equivalent uniform field corresponding the reference field of 10 cm × 10 cm as described in TRS-483. 18 Similarly for electron beams, R50 was determined for both linacs and an average was used for the readout of the k Q,Q0 . The IBA FC65-G Farmer-type ionization chamber and IBA PPC40 plane parallel ionization chamber were used for photons and electrons, respectively (

2.D | Jaw position calibration
The position of the jaws is initially calibrated by the vendor's installer using the light field, after it has been verified that the radiation-

2.E | Beam-match verification
To verify the beam-matching, a set of water profile measurements with different geometries than those used during initial matching were performed on each linac and compared to those of the refer-  reference in a gamma evaluation, with 1%, 1 mm and 2%, 2 mm gamma criteria.

3.B | Reference dosimetry
The reference dosimetry audit of photon energies is summarized in Fig. 4 where the difference between measurements performed by the institution and the external audit is presented. Except for one measurement, all audit results showed lower dose output compared with the institutional results. These deviations are attributed to calibration coefficient difference since both parties used their own equipment with different traces of calibration. Furthermore, the differences were at most 0.6% resulting in acceptable outcome of the reference dose audit. The audit of the electron energy calibration is presented in Table 2 where it is observed that no difference above 0.6% was present.

3.C | Dosimetric Leaf Gap calibration and consistency
The DLG before and after calibration with corresponding Gap values for 6 MV are shown in Fig. 5. A clear pattern relating the Gap values and the DLG is visible before the calibration. However, this pattern diminishes after calibration, when the variations are less pronounced. Table 3 shows a comparison of DLG among the linacs after calibration where best match is for 6 MV because the calibration is performed using this energy. The other energies are measured for verification reasons.

3.E | Beam-match verification
An overview of the comparison among the linacs in TPR 20,10 is presented in Table 5 where the largest difference is 0.5%. Percentage depth dose difference among the seven linacs against the reference is presented in Fig. 7 where the largest difference is below 0.3 % excluding the build-up region.
The water profile verification measurements contain a large amount of data, which is why only the mean value of the global  TB1  TB2  TB3  TB5  TB6  TB7  TB8  L01  L02  L03  L05  L06 L07 L08 F I G . 3. Dose difference of diagonal dose profiles for 40 cm × 40 cm fields between seven linacs and the reference linac (L01-L08; L04 being the reference). The profiles were symmetrizied and normalized to the central axis dose for each linac before calculating the difference. The VMAT-plan dose delivery error among the linacs resulted in excellent agreement between the seven linacs and the reference linac. All evaluation acheived 100% pass rate with 2 %, 2 mm critera, and ≥99.2% pass rate with 1%, 1 mm criteria.

| DISCUSSIONS
The symmetry calibration resulted in values which are substantially lower than the vendor acceptance criteria (2%) (Fig. 2) Inline Crossline before before

Field size [cm]
F I G . 6. Field sizes of 10 cm × 10 cm 6 MV fields measured on eight linacs in water, before and after calibration. The boxes represent 25%-75% quartiles, the black lines in the boxes represent the median and the bars represent the range.   F I G . 7. Dose difference of PDD for 10 cm × 10 cm fields between seven linacs and the reference linac (L01-L08; L04 being the reference). Note that the depth is shown in the range of 1 to 30 cm. The vendor acceptance criteria for energy-matching is 0.5% difference from the reference value specified for the depth dose at 10 cm (D10). In this work, diagonal profiles of seven linacs are compared with the reference linac and setting the same tolerance of 0.5%. The results are all within the set tolerance except for 15 MV which exceeds this limit in the region outside 15 cm from the central axis (Fig. 3). This is attributed to the effect of the flattening filter for which small inconsistencies among the linacs affect the beam. Consequently, priority was given to match linacs at the central axis which offers higher clinical advantages due to treatments often are conducted in fields <30 cm × 30 cm, which resulted in higher discrepencies near the penumbra. The vendor acceptance criteria for electron energy-matching is specified as the difference between the reference and measured value of R90, R80 and R50. The criteria differs depending on the parameter: most strictly is 0.5 mm for R80 and 6 and 9 MeV. In this work, it is presented that 0.1 mm difference between the two linacs for all energies (  16 Therefore, having an optimized R50 between the two linacs reduces systematic errors when applying the same beam data in the treatment planning system and simplify routine QA procedures using the same k Q,Q0 and z ref . The disparity in DLG (Fig. 5) before the calibration is due to installer-to-installer differences in setting up the linac. Therefore, it is essential to measure and adjust the DLG in the commisionging process and consequently beam-matching. The DLG calibration reduced the maximum difference among the linacs from 39.9% being a more suitable method of jaw calibration than light field method.

| CONCLUSIONS
Energy matching and symmetry-, DLG-and jaw calibration for True-Beam linacs was performed with a high degree of precision, surpassing vendor acceptance criteria and international recommendations and was achievable within a reasonable time-frame. The resulting beam matching reduced systematic errors in dose delivery and increased the confidence in using the same beam data in the TPS and swapping patients among linacs.

Our task group thanks Dr Gloria Beyer at Medical Physics Services
Intl. Ltd., Cork, Ireland for giving us permission to use her data from the reference dosimetry audit at our department for publication.

CONF LICT OF I NTEREST
No conflict of interest.

APPEN DIX A CALIBRATION OF JAWS USING EPID
The linac is equipped with two pairs of jaws: X1 and X2 in the crossline direction and Y1 and Y2 in the inline direction. The workstation provides position sensor readout (PRO-value). Preparatory measurement for developing and implementing the EPID-method revealed an underestimation of field size as determined by EPID of 0.7 mm on average, compared to water measurements. This underestimation was accounted for and is denoted CORR EPID . The following step-bystep method follows the calibration of the X-jaws. The Y-jaw calibration follows identical procedure.
Step 1: vertical position of EPID Before each calibration, the EPID positioning in the vertical direction was visually verified using the SSD optical scale (98.8 cm to the surface equalling 100 cm to the detectors).
Step 2: evaluation of the jaws at two nominal positions The X1 zero cm position is evaluated as follows: • A profile is drawn over the junction area of the merged image to show any over-or underdosage which is recorded and denoted CAX_X1. This reveals the direction for which the jaw position should be corrected [ Fig. A1(a)].
• Using the tool to align an image, one of the images is moved so that the over-or underdosage is corrected. The magnitude of movement is recorded and denoted MOVE_X1. Note that it should be recorded as an absolute value since the CAX_X1 value determines in which direction the jaw should be corrected.
F I G . A1. View of the Portal Dosimetry where two merged 6 MV EPID-images are evaluated in the field junction resulting in (a) underdosage (before jaw calibration), (b) acceptable junction-dosage (after jaw calibration).
• If CAX_X1 is larger than 100 % → -MOVE_X1/2 which is the correction for the nominal value (zero cm).
If CAX_X1 is smaller than 100 % → MOVE_X1/2 which is the correction for the nominal value (zero cm).
The MOVE_X1 value is divided by 2 because the correction is based on two images. The correction is denoted X1_0 Corr .
The X2 15 cm position is evaluated as follows: • The field size in the X direction of the merged image is measured at the 50 % isodose level corresponding to the full width half maximum which is commonly used to defined the field size [ Fig.   A2(a)]. It is recorded and denoted FS_X2 measured .
CORR EPID is added to correct for the underestimation of field size by EPID and the FS_X2 measured value is divided by 2 because the correction is based on two images.
Similarly, X2 is placed at zero position and the X1 is placed at 15 cm. Two images are acquired with the EPID with 180°collimator rotation apart and evaluated using the same steps as described above. This will result in X2_0 Corr and X1_15 Corr .
Step 3. Calibration of the jaws Each jaw is calibrated separately. The calibration mode of the jaws at the workstation is set at nominal positions of 1 and 19 cm.
• A linear fit is modeled between zero cm and 15 cm, and X1_0 CORR and X1_15 CORR . This is performed to predict the corrected position of the jaws at 1 and 19 cm denoted X1 1cm and X1 19cm , respectively.
• The PRO-values are recorded at nominal position 1 and 19 cm, and denoted PRO_X1 1cm and PRO_X1 19cm , respectively.
• A linear fit is modelled between X1 1cm and X1 19cm , and PRO_X1 1cm and PRO_X1 19cm . This is performed to predict the corrected PRO-values for jaw positions at 1 and 19 cm denoted PRO_X1 1cmCORR and PRO_X1 19cm-CORR.
• PRO_X1 1cmCORR and PRO_X1 19cmCORR are inserted in the workstation and the jaws should be re-initialized.