Monitoring linear accelerators electron beam energy constancy with a 2D ionization chamber array and double‐wedge phantom

Abstract Validate that a two‐dimensional (2D) ionization chamber array (ICA) combined with a double‐wedge plate (DWP) can track changes in electron beam energy well within 2.0 mms as recommended by TG‐142 for monthly quality assurance (QA). Electron beam profiles of 4–22 MeV were measured for a 25 × 25 cm2 cone using an ICA with a DWP placed on top of it along one diagonal axis. The relationship between the full width half maximum (FWHM) field size created by DWP energy degradation across the field and the depth of 50% dose in water (R50) is calibrated for a given ICA/DWP combination in beams of know energies (R50 values). Once this relationship is established, the ICA/DWP system will report the R50FWHM directly. We calibrated the ICA/DWP on a linear accelerator with energies of 6, 9, 12, 16, 20, and 22 MeV. The R50FWHM values of these beams and eight other beams with different R50 values were measured and compared with the R50 measured in water, that is, R50Water. Resolving changes of R50 up to 0.2 cm with ICA/DWP was tested by adding solid‐water to shift the energy and was verified with R50Water measurements. To check the long‐term reproducibility of ICA/DWP we measured R50FWHM on a monthly basis for a period of 3 yr. We proposed a universal calibration procedure considering the off‐axis corrections and compared calibrations and measurements on three types of linacs (Varian TrueBeam, Varian C‐series, and Elekta) with different nominal energies and R50 values. For all 38 beams on same type of linac with R50values over a range of 2–8.8 cm, the R50FWHM reported by the ICA/DWP system agreed with that measured in water within 0.01 ± 0.03 cm (mean ± 1σ) and maximum discrepancy of 0.07 cm. Long‐term reproducibility results show the ICA/DWP system to be within 0.04 cm of their baseline over 3 yr. With the universal calibration the maximum discrepancy between R50FWHM and R50Water for different types of linac reduced from 0.25 to 0.06 cm. Comparison of R50FWHM values and R50Water values and long‐term reproducibility of R50FWHM values indicates that the ICA/DWP can be used for monitoring of electron beam energy constancy well within TG‐142 recommended tolerance.

the full width half maximum (FWHM) field size created by DWP energy degradation across the field and the depth of 50% dose in water (R 50 ) is calibrated for a given ICA/DWP combination in beams of know energies (R 50 values). Once this relationship is established, the ICA/DWP system will report the R 50 FWHM directly. We calibrated the ICA/DWP on a linear accelerator with energies of 6, 9, 12, 16, 20, and 22 MeV. The R 50 FWHM values of these beams and eight other beams with different R 50 values were measured and compared with the R 50 measured in water, that is, R 50 Water. Resolving changes of R 50 up to 0.2 cm with ICA/DWP was tested by adding solid-water to shift the energy and was verified with R 50 Water measurements. To check the long-term reproducibility of ICA/DWP we measured R 50 FWHM on a monthly basis for a period of 3 yr. We proposed a universal calibration proce- Electron beam energy constancy is traditionally measured with solid water slabs during monthly QA. This procedure can be time consuming and becomes tedious on a linac with multiple electron energies as different thicknesses of solid water slabs are required to characterize each electron energy. In addition, a recent study has shown that the tolerances for electron beam energy checks using a two-depth method are highly nonlinear due to the differences in gradient of the percent depth dose (PDD) falloff region. 5 The concept of monitoring electron energy with a combination of a wedge and a linear detector has been extensively studied. The first published work 6 was by Moyer in 1981 who used an aluminum wedge placed on top of a radiographic film to measure electronbeam energy constancy for beam energies from 6 to 18 MeV and showed an overall uncertainty of ±0.4 MeV. Rosenow et al. used one-dimensional (1D) ionization chamber array combined with a simple wedge-shaped polystyrene phantom to measure beam energies.
They found that the full width at half maximum (FWHM) of the modified electron profiles correlated linearly with R 50 in the whole range of energies studied. 7 Using the same 1D ionization chamber array and similar wedge-shaped polystyrene phantom, Islam et al. 8 were able to reproduce depth ionization curves in polystyrene phantom and the results agree quite well within water measurements for beam energy ≤10 MeV. Wells et al. used a home-made doublewedge acrylic phantom placed on top of a 1D diode array, and they found that the sensitivity of the combination of the diode array and double-wedge technique is similar to water-based depth-dose measurements. 9 Other similar work has been done more recently using linear arrays combined with wedges for electron beam energy determination. 10,11 The extensive studies published over the years on monitoring electron energy with wedge shape attenuators did not result in changes in clinical practice.
In this work, we validated a commercial system for monitoring changes in electron beam energy based on the principle of a wedge-shaped attenuator. The goal of this work was to ensure that a change in practice to use this device we will still meet the dose points under each wedge, FWHM, is related to the R 50 values in beams of known energies. Once this relationship is established the ICA/DWP system will report a beam energy which we will be referred to as R 50 FWHM directly. We calibrated the R 50 baseline with the ICA/DWP on a linear accelerator with energies of 6, 9, 12, 16, 20, and 22 MeV.We measured R 50 FWHM with the ICA/DWP for the calibration beams and also for beam energies lowered by using plastic sheets to shift beam energies. In addition R 50 FWHM data collected on a monthly basis on our clinical beams for a period of 3 yr during routine QA were used to evaluate the long-term stability of both the device and out beam energies.
We noted that the manufacture's calibration procedure neglected the off-axis ratio creating a calibration that was linac and beam dependent. We hypothesized that by removing the off-axis ratio from the calibration, subsequent measurements could make the cali- monitoring of electron beam energy constancy with high accuracy (<1 mm error) and reproducibility (<1 mm variation).

| MATERIALS AND METHODS
The 2D ICA used in this work is IC Profiler which has 251 ion chambers at an effective depth of 0.

2.A | Calibration of electron beam energy metric R 50
In profiles acquired with a double-wedge, the off axis distance (OAD) is directly related to the amount of aluminum that the beam has penetrated to reach the detectors. Thus the OAD that results in the signal being reduced to 50% of the value on the open central axis (OAD 50 ) can then be directly related to beam energy. Rather than using the OAD 50 directly the ICA uses the full width at half maximum (FWHM) of the diagonal profile as its energy metric (Fig. 2). This minimizes the uncertainties associated with device setup. The relationship between R 50 in water and FWHM for each ICA/DWP combination is calibrated by the user in their electron beams by acquiring double wedge profiles and determining the FWHM in a number of beams with known R 50 . A linear fit is determined between FWHM and R 50 which can then be used to measure R 50 on beams from linear accelerators of the same design (make/model). We performed the calibration proce- The ICA software (IC PROFILER Software V3.4 and later) has the calculation of the R 50 to FWHM built in so once the relationship is established an R 50 value is reported directly to the user.    agreed within ±0.05 cm and 100% agreed within ±0.10 cm (Fig. 3).
The standard deviations were <0.014 cm. (Table 5). Clinac2) as well as on two Elekta machines, a Versa and an Infinity spanning a range of energies ( Table 1). The slopes, intercepts, and

3.D |
Pearson coefficient for the calibrations for each linac was calculated by the SNC software (Table 6). Difference in the linear fits between the different linac types were dominated by the high-energy beams  (Table 6). We found that "Self" calibration gave the best results with a maximum discrepancy of 0.07 cm, followed closely by "Same Type" calibrations with 0.08 cm with the worst results being "Cross Type" calibrations which had discrepancies of up to 0.25 cm.  The universal calibration that takes into account off-axis corrections was also determined for each of these machines. The universal calibration resulted in the linear fits that were machine independent [ Fig. 4(b)]. The discrepancies between R 50 FWHM and R 50 Water were slightly increased compared to the "Self" calibration, were equivalent to the "Same Type" calibration, and far superior to the "cross type" calibration [ Fig. 5(b)]. With the universal calibration, the maximum discrepancy between R 50 FWHM and R 50 Water for "Self" and "Same Type" was modestly reduced to 0.06 cm while the maximum discrepancy for the "cross type" was dramatically reduced to also be 0.06 cm (

3.E | Flatness and symmetry measurements with and without DWP
We measured flatness and symmetry of the principal axes (x and y axes) from the profiles acquired using ICA with and without the DWP. Five measurements were done for each case for each beam.
The difference in measured flatness and symmetry with and without the DWP showed that the effects of the DWP were <0.10% on flatness and <0.15% on symmetry (Table 8). This is expected as the DWP does not block the detectors along principal axes.

| DISCUSSION
The traditional method of detecting changes in electron beam energy is by comparing the relative dose (signal) at a known depth (or thickness of plastic phantom) against a reference dose determined at the time of commissioning. This procedure is time consuming and becomes tedious for a multiple electron energy linac since different depths are required to characterize each electron energy. The flatness and symmetry measured from beam profiles are traditionally performed with 2D array (diode or ionization chamber) or film, which is another setup and measurement.
Measuring changes in R 50 with an ionization chamber array combined with a double-wedge gives equivalent result as in water scans without requiring the user to change depths between energies as well as providing the flatness and symmetry measurement F I G . 5. Histogram distributions of the differences in R 50 full width half maximum with different calibrations and R 50 water. "Self" indicates using the calibration determined on that particular linac, "Same type" is on a linac of the same maker and model but not the same machine, "Cross type" is using a calibration determined on a different maker and model of linacs. (a) Individual calibrations from ICA software, (b) universal calibration by considering off-axis corrections.
T A B L E 7 Same as δF (%) −0.10 ± 0.00 −0.04 ± 0.05 0.04 ± 0.03 0.00 ± 0.00 0.05 ± 0.00 0.00 ± 0.00 0.05 ± 0.00 δS (%) −0.14 ± 0.05 0.08 ± 0.06 0.12 ± 0.04 0.07 ± 0.04 0.00 ± 0.00 0.11 ± 0.05 −0.01 ± 0.05 simultaneously. Compared to other approaches using 1D/2D planner array, 5-11 the method examined in this work has advantages: (a) the setup is easy and the baseline calibration is straightforward; (b) the Profiler software can directly report the value of R 50 ; (c) the flatness and symmetry in principal axes and the beam energy R 50 can be measured in one profile acquisition. We have also demonstrated that a modification of the calibration procedure to include the off-axis corrections in the calibration would allow this ICA/DWP to directly determine R 50 on different beams/machine types universally.
Furthermore, photon beam energy constancy metric, previous studies [15][16][17] have demonstrated that an ICA can be used to measure changes in the energy, characterized by off-axis ratio (e.g., in diagonal axes, diagonal normalize flatness, F DN ) with a higher sensitivity than can be achieved with percentage depth-dose measurements.
Thus, we are able to replace both the photon and electron beam energy and profiles constancy measurements with a more efficient set of measurements using 2D IC array.

| CONCLUSIONS
A convenient method for constancy checks of electron beam energies is described based on a commercially available ion-chamber array and double-wedge plate. In a single setup, this method is cap-