Beam energy metrics for the acceptance and quality assurance of Halcyon linear accelerator

Abstract Purpose Establish and compare two metrics for monitoring beam energy changes in the Halcyon platform and evaluate the accuracy of these metrics across multiple Halcyon linacs. Method The first energy metric is derived from the diagonal normalized flatness (FDN), which is defined as the ratio of the average measurements at a fixed off‐axis equal distance along the open profiles in two diagonals to the measurement at the central axis with an ionization chamber array (ICA). The second energy metric comes from the area ratio (AR) of the quad wedge (QW) profiles measured with the QW on the top of the ICA. Beam energy is changed by adjusting the magnetron current in a non‐clinical Halcyon. With D10cm measured in water at each beam energy, the relationships between FDN or AR energy metrics to D10cm in water is established with linear regression across six energy settings. The coefficients from these regressions allow D10cm(FDN) calculation from FDN using open profiles and D10cm(QW) calculation from AR using QW profiles. Results Five Halcyon linacs from five institutions were used to evaluate the accuracy of the D10cm(FDN) and the D10cm(QW) energy metrics by comparing to the D10cm values computed from the treatment planning system (TPS) and D10cm measured in water. For the five linacs, the D10cm(FDN) reported by the ICA based on FDN from open profiles agreed with that calculated by TPS within –0.29 ± 0.23% and 0.61% maximum discrepancy; the D10cm(QW) reported by the QW profiles agreed with that calculated by TPS within –0.82 ± 1.27% and –2.43% maximum discrepancy. Conclusion The FDN‐based energy metric D10cm(FDN) can be used for acceptance testing of beam energy, and also for the verification of energy in periodic quality assurance (QA) processes.

A recent study demonstrated that the Halcyon platform can be validated with an ionization chamber array (ICA) and a 1D water scanner (1DS) without the need for a 3D water scanning system. 1 The commissioning verification was based on the AAPM Medical Physics Practice Guideline for Commissioning and QA of External Beam Planning Systems (MPPG5.a). 2 The diagonal normalized flatness (F DN ), which is calculated from open beam profiles measured with an ICA, was verified as a metric for monitoring beam energy and was more sensitive and reproducible than the traditional percent depth dose (PDD) energy metric. 3,4 Another method for determining photon beam energy uses a quad wedge (QW) which consists of two pairs of copper wedge-shaped attenuators along each of the diagonal detector axes of the ICA, with the wedge pairs being symmetrically opposed and the thin sections toward the array center. 5 The energy metric from the QW is the area ratio (AR), which is defined as the cumulative of measurements from a span of detectors in the presence of wedges and normalized to the cumulative of measurements from a similar detector set on the X and Y axes (open field profiles). 5 The purpose of this study was to establish a legitimate ICA method for D 10cm verification for the Halcyon linac for both commissioning and periodic quality assurance, without the cumbersome 1DS water tank.

| MATERIALS AND METHODS
Both F DN -based and AR-based energy metrics require calibration against a known energy metric that is chosen to be the percent depth dose (PDD) at a depth of 10 cm, D 10 (water), measured in water at 90 cm source to surface distance (SSD). This setup matches that the vendor provided reference data which were specified at 90 cm SSD due to the geometry limit of the machine bore.
To establish the relationships between F DN and AR with D 10 in water, beam energy is changed by adjusting the magnetron current in a non-clinical Halcyon corresponding to a change in beam energy from −10% to +5% off from its nominal value (Note that +10% produced an unstable beam). At each magnetron current setting, ICA measurements are acquired with an IC Profiler (Sun

2.A | Measurement setup and procedure
The Halcyon is an inline magnetron linear accelerator with no bending magnet, the beam energy can be changed by adjusting the magnetron current. Without a direct means of determining how changes in magnetron current (MI) would change energy, previously determined relationships were used between changes in diagonal normalized flatness F DN and changes in energy on a TrueBeam 6-MV FFF beam. 3 Each energy metric was measured at the nominal beam energy and at five intentionally created energy changes off -10.0%, -5.0%, -2.5%, +2.5%, and +5.0% from the nominal beam energy value (0%). After beam tuning to achieve stable dose rates and symmetric beam profiles for each MI setting, the beam parameters were saved to a file and later loaded for each tuned beam, which provided reproducible measurement setups.
Because the Halcyon does not have light field and radiation isocenter lasers, the ICA was set up in the following three steps 1 : (1) initial alignment with the outside bore lasers (virtual isocenter); (2) image guidance for final alignment with two orthogonal MV images; (3) acquisition of test profiles to verify the beam center and for fine-

2.C | ICA calibration and profile measurement
The detectors in the ICA were calibrated at the nominal beam energy on Halcyon linac at a detector depth of d max (1.4 cm = 0.9 cm inherent + 0.5 cm solid water), at an extended 110-cm SSD and 28 × 28 cm 2 field. The divergent field from the 100-cm SSD produced a 30.8 × 30.8 cm 2 field, which ensures that all detectors used in later measurements at 90 cm SSD were within the calibration field. The accuracy of the array calibration was evaluated according to previously proposed procedures, 6 and the calibration uncertainties were <0.5% for all detectors in the measurement field.
Beam profiles were measured for the maximum field size, with the ICA and at depth d max , with 90 cm SSD. Profiles were measured on four axes, in-plane, cross-plane, and diagonals at six MI settings corresponding to the nominal beam energy and five intentionally created energy changes from the nominal energy, using the single calibration measurement at the nominal beam energy.

2.D | Beam energy metrics
The percent depth dose at 10 cm depth, D 10 (water), from the PDD scanned in the water tank at 90 cm SSD with 10 × 10 cm 2 field size provided the standard energy metric. The off-axis points in the F DN are the points at the off-axis distances of approximately 90% and 60% of the maximum beam intensity, which are AE5.7 cm and AE15.6 cm, respectively, from the array center and located in a stable region of the profile. The relationship between D 10 (water) and F DN from ICA measurement is calibrated by acquiring profiles at the six beam energies. A linear fit is determined between F DN and D 10 (water) that can then be used to measure D 10 from F DN obtained from the ICA profile: where n and a are the slope and intercept values. Once this relationship is established, the D 10 (F DN ) reports the value of D 10 at 90 cm SSD with 10 × 10 cm 2 field size.

2.D.2 | Quad wedge profile energy metric
Another method for determining photon beam energy is from the beam profiles acquired using ICA with a quad wedge (QW) on top of the ICA surface. The two wedge pairs in the QW plate are symmetrically opposed to the thin sections toward the array center (see Fig. 1). In beam profiles acquired with ICA and QW combination, the AR under the wedges is related to the beam energy, and thus the AR can be used as an energy metric.
The AR from the QW profiles is the sum of measurement data under the wedges (along diagonal axes) normalized to the sum of measurement data from a similar detector set on the X and Y axes (open field profiles) 5 : where PD Area , ND Area , X Area , and Y Area represent the sum of corrected counts from the applicable detectors of the measured profiles for positive diagonal (PD), negative diagonal (ND), X, and Y axes, respectively.
The relationship between the measured AR and D 10 (water) is established by determining the AR from the QW profiles at six beam energies with known D 10 (water). A linear fit is determined between The IC array measurement setup positions with solid water buildup and QW plate.
| 123 AR and D 10 (water), which can then be used to determine D 10 (AR) from the measured profile with ICA/QW on a beam from the Halcyon linac: where m and b are the slope and intercept values and AR is the area ratio. Similar to D 10 (F DN ), D 10 (AR) also reports the value of D 10 at 90 cm SSD with 10 × 10 cm 2 field size.

2.D.3 | Evaluation of beam energy metrics
Once the D 10 (F DN ) and D 10 (QW) metrics were established in the non-clinical Halcyon, meaning that the linear coefficients [eqs. (1) and (3), respectively] were derived from the calibrations, the IC Pro-

3.A | Changes in percent depth dose
The PDD data were measured for 10 × 10 cm 2 field size with 90 cm SSD by the 1D water scanning system at the nominal clinical beam energy and at five energy changes from nominal (0%): -10.0%, -5.0%, -2.5%, +2.5%, and +5.0%. The PDD curves were normalized to d max depth for each energy, and an example of the effect of changes in beam energy on the changes in PDD curves is presented in Fig. 2. The D 10 values of these six beam energies can be obtained from the PDD curves.

3.B | Changes in the profile
Beam profiles were measured at d max , 90 cm SSD with a 28 × 28 cm 2 field size with and without QW, at the six beam energies (nominal clinical energy and five adjusted energy beams). The profiles were normalized to the corresponding central axis value for each beam energy, revealing the shape change in the profiles with the variation of the beam energy (Fig. 3).

3.D | Evaluation of beam energy metrics
The measured D 10 (F DN ) and D 10 (QW) values from five Halcyon linacs were compared with the measured D 10 (water) and calculated D 10 (TPS) values ( Table 2).
The differences of D 10 between F DN and treatment planning Comparison of the percent depth dose at a depth of 10 cm (D 10 ), scanned with a 1D water scanning system, and the D 10 values determined from the diagonal normalized flatness (F DN ) at two off-axis distances, 90% (H) and 60% (L) of maximum beam intensity, for five beam energies off the nominal energy (by -10.0%, -5.0%, -2.5%, 0%, +2.5% and +5.0%). Also shown are average values and differences (δ) for the difference in D 10 between F DN (average) and 1DS; the D 10 determined from quad-wedge profile (QW); and differences in D 10 between QW and 1DS. Data from one non-clinical Halcyon linac.
The linear relationship between the percent depth dose at 10 cm depth D 10 scanned using the 1D water scanner (1DS) and the area ratio from the QW profile measured with the ionization chamber array (ICA) and QW plate for beam energies off the nominal beam energy by -10.0%, -5.0%, -2.5%, +2.5% and +5.0%.
T A B L E 2 The percent depth dose at a depth of 10 cm (D 10 ) determined from the diagonal normalized flatness (F DN ) and from the quad-wedge (QW) profile of five Halcyon linacs from five institutions. Also shown are the difference in D 10 between F DN and TPS (QW and TPS) and the difference in D 10 between F DN and water scans (QW and water scans), along with their averages and standard deviations (σ).

D A T A A V A I L A B I L I T Y S T A T E M E N T
The data that support the findings of this study are available from the corresponding author upon reasonable request.