Quantification of beam steering with an ionization chamber array

Abstract Routine quality assurance for linear accelerators (linacs) usually involves verification of beam steering with a water scanning system. We established a beam steering procedure that uses a 2D ionization chamber array (ICA) and verified the equivalence of beam symmetry between the ICA and a water scanning system. The ICA calibration accuracy, reproducibility and stability were evaluated and the uncertainty in the measurement of beam symmetry due to the array calibration was examined. Forty‐five photon beams and 80 electron beams across 7 Varian C‐series and 4 TrueBeam linacs were steered in the radial and transverse directions using an ICA. After beam steering, profiles were re‐measured using the ICA and in‐water using a 3D Scanner (3DS). Beam symmetries measured with the ICA and 3DS were compared by (a) calculating the difference in point‐by‐point symmetry, (b) plotting the histogram distribution of the symmetry differences, and (c) comparing ICA and 3DS differences with their respective Varian symmetry protocol analysis. Array calibrations from five different occurrences (2012 to 2016) over six different beams reproduced within 0.5%. The uncertainty in beam symmetry was less than 0.5% due to the uncertainties in the array calibration. After all beams were steered using the ICA, the point‐by‐point symmetry differences between ICA and 3DS at the off‐axis positions of 20% and 80% of field size for all beam profiles indicated that 95% of point‐by‐point symmetry comparisons agreed within 0.7%, and 100% agreed within 1.0%; after steering with the ICA 97.8% of photon beam profiles (88 of 90) and 97.5% of electron beam profiles (156 of 160) had symmetry within 1% when measured with the 3DS. All photon and electron beam profiles had symmetry within 1.1% and 1.2%, respectively, for profiles measured with the 3DS. Our data demonstrate that a calibrated ICA can be used to steer photon and electron beams achieving beam symmetry within 1% when re‐measured with a 3D water scanning system.


| INTRODUCTION
Beam steering on a clinical linear accelerator (linac) is traditionally performed with a water scanning system during annual quality assurance (QA) checks to ensure the consistency of the beam profile. [1][2][3] The goal of the steering is to ensure that the beam is symmetric in both the in-plane and cross-plane directions. The use of a water scanning system to accomplish the beam steering process is considered the gold standard but is laborious, time consuming, and has uncertainties. 4 We propose that beam steering can be accomplished much more efficiently with no loss in accuracy using a two-dimensional (2D) array. A commercially available ionization chamber array (ICA) (IC PROFILER, Sun Nuclear Corp., Melbourne, FL) was used in this study. This ICA was previously demonstrated to be an effective tool for evaluating changes in photon beam energy, [5][6][7] which is another important part of linac annual QA.
The metric used most often for beam symmetry is the central axis (CAX) point difference symmetry which is defined as, where, D i and D -i are the measured profile intensities at a pair of points located on opposite sides and equal distance from the CAX along the same axis (mirror points), D CAX is the intensity at the central axis, and n is the number of mirror points sampled within 80% of the field size. Please note, some software (e.g. 3D scanner) only reports the absolute value.
The uncertainty in determining symmetry is directly related to the uncertainty in measuring the relative intensities at mirror points.
This uncertainty will have a systematic components due to the uncertainties in the corrected response of the detector(s) at each of these points and setup uncertainties in the alignment of the measurement system to the beam. There are also random components due to beam fluctuations as well as the random measurement uncertainties associated with any measurement system.
ICAs have large numbers of detectors, and the uncertainty in the calibration of the sensitivity between any pair of detectors at mirror points will result in systematic uncertainties in the symmetry mea-

2.A | Array calibration
The 2D ICA used here is IC Profiler which has 251 ion chambers at an effective depth of 0.9 cm. The detectors are arranged along the four axes, in-plane (y), cross-plane (x), and two diagonals.  and a periodic check (3 yr before). The percent error [P error n cf ð Þ] is defined 8 as: where: cf is the correction factor for a detector and cf is the mean correction factor of the detector across of the three calibrations done on the same day.

2.A.2 | Symmetry accuracy and array calibration
To measure the reproducibility of the beam profile measurements taking into account both the beam and detector stability, we measured the same profile five times each for five photon and five electron beams. All measurements were done for photons using a where D i (0°) is the intensity measured at a given detector with the array at its standard orientation and D Ài (180°invert) is intensity where Sym(i) is the difference between two measurements of profile intensity at mirror points with two detectors (a given detector and its mirror). Comparing Eqs. (4) and (3), the systematic errors of symmetry measurement due to ICA calibrations can be quantified by the calibration uncertainty C r . This was studied by applying the C r to an idealized perfectly symmetric profile modeled as a geometric function and to a measured profile.  1)]. This approach gives real-time feedback on the maximum difference between any pair of mirror points within the central 80% of the field. During the "learning curve" for this system, some beams were only steered within 1%, the symmetry criteria we set when beams were steered using a 3D water scanning system.
Subsequently, beams were steered to achieve symmetry within 0.5% which could be achieved with the real-time feedback available with the ICA.
Each beam was steered in both the radial and transverse axes using the "instantaneous rate" mode on the ICA and going back and forth between the 2 axes until the symmetry on both axes were acceptable. Our procedure for steering is to disable the beam steering servos, steer the beam, then re-zero the servos to the steered beam.
Once beam steering was done for each beam, a final profile was obtained with beam steering servos engaged and at the clinical dose rate, with the ICA in "total dose" mode and 200 MU being delivered.

2.C | Profile comparison with ICA and 3DS
To evaluate the accuracy of beam steering done with the ICA, we    were less than 0.5% for all detectors in the field across the five different calibrations (Fig. 1). For electron beams, the detectors located in the field edge had larger variations but were still within 0.8%, this was not observed for photon beams. No significant differences were found among the various array calibrations even though they spanned 4 yr suggesting that the device has good short-term reproducibility and long-term stability with respect to the array calibrations. (r) as our metric. We found the max(r) to be less than 0.07% (Table 1) for all beams with electron beams having lower random uncertainty than photon beams.

3.A.2 |
To determine the systematic component of symmetry uncertainty due to the array calibration, we calculated the maximum calibration uncertainty max(C r ) [Eq. (3)] on the x-and y-axes in each beam (Fig. 2). The max(C r ) of detectors within the central 80% of the field size for all beams was less than 0.4% ( Table 2). The maximum calibration uncertainty max(C r ) with electrons, in general, shows a lower uncertainty than photons. The max(C r ) is the systematic uncertainty in the array calibration and will set an upper bound for the accuracy of GAO ET AL.
| 171 symmetry measurements. The total uncertainty in symmetry measurements will be max(C r ) + ffiffiffi 2 p Ámax(r), which is the maximum systematic uncertainty combined with the random uncertainty max( r ). For all beams max(C r ) is an order of magnitude greater than max(r) thus the random portion of the uncertainty can be neglected.
To demonstrate that the maximum calibration uncertainty max(C r ) sets a bound for the accuracy of symmetry, we performed a simulation study by calculating the symmetry from a numerically modeled perfect beam profile and a 3DS measured beam profile that had a maximum point symmetry of 0.2% by applying the measured 6 MV ICA calibration uncertainties C r . We obtained the maximum point symmetry of 0.3% for the model profile and 0.4% for the scanned profile ( Fig. 3), whereas the max(C r ) of the 6 MV beam was 0.37%.

3.B | Beam steering with the ICA
We steered 45 photon beams and 80 electron beams using the ICA and the procedures we developed although some of this data were acquired before we finalized our procedures. After the steering process was completed, we captured final profiles with the ICA. The profiles were also captured in water with the 3DS either later that same day or on the next day.
To demonstrate how ICA based steering would work in clinical practice, we examined the probability that a beam steered using an ICA would result in a beam with a symmetry of 1.0% or less when measured using the 3DS system, for our current clinical standard.
We calculated the cumulative histogram of symmetry measured showed that 97.8% of photon beam profiles (88 of 90) and 97.5% of electron beam profiles (156 of 160) had symmetry within 1%. All photon and electron beam profiles had symmetry within 1.1% and 1.2%, respectively. The beams with symmetry greater than 1% were all steered during our "learning curve" before we had set the goal for steering with the ICA to be less than 0.5% symmetry.

3.C | Comparison of beam profiles between ICA and 3DS
Comparisons were done between the ICA and 3DS profiles in several ways: We plotted the ICA and 3DS data on the same graph for F I G . 4. The cumulative distributions of photon beam symmetry and electron beam symmetry measured in water with the 3DS after the beams were steered with the ICA. These data represent 90 photon and 160 electron beam profiles acquired on both C-series and TrueBeam machines. graph and quantitatively compared by calculating the difference in point-by-point symmetry at each ICA detector location (Fig. 5). We found that the shape of the profiles was consistent when the two systems were used at the same SSD and the same effective depth.
The differences in density between the ICA and water resulted in a 1 mm difference in source-to-detector distance, which was not considered significant for this analysis.
We then calculated the point-by-point symmetry differences [Eq. (5)] between the ICA and the 3DS measured profiles at the offaxis positions of 20% and 80% of field size. Histogram analysis of the point-by-point symmetry comparisons indicated that 95% agreed within 0.7% and 100% agreed within 1.0% (Fig. 6) between the two systems.
We then compared the symmetry measurement from the ICA software using the predefined "Varian protocol" with the value from the 3DS also using the "Varian protocol" for photon (Fig. 7a) and electron (Fig. 7b) beams. Notably, the 3DS reports only the absolute value and not the direction of symmetry, whereas the ICA reports both. To have a more complete comparison we re-calculated the symmetry in Excel again using the "Varian protocol" to have an identical metric from ICA and 3DS systems for both photons (Fig. 8a) and electrons (Fig. 8b). We found that the two systems to be consistent at the level of 0.08% AE 0.32% for photons and 0.01% AE 0.37% for electrons using the re-calculated symmetry data only.

| DISCUSSION
The gold standard for beam steering has traditionally been a 3D water scanning system. However, a 2D detector array is far easier to setup and the real-time feedback greatly speeds up the steering process. Our findings show that with proper calibration and procedures, beams steered with a 2D detector array can achieve the same quality in symmetry as beams steered with a 3D water scanner.
The 2D ICA used in this work had a process by which the user could recalibrate the array as well as a built-in check procedure for the accuracy of the calibration. This array was also found to have good short-and long-term stability. Physicists using other types of detector arrays will need to ensure that those detector arrays are suitable for this type of work.
We found that to effectively match the ICA measured symmetry results with those of using the 3D water scanner, we needed to: (1) Validate the array calibration to ensure that it does not introduce systematic errors; (2) Use the correct symmetry metric and understand how different software packages may report the same metric slightly different;

and
(3) Have the correct symmetry goal for steering such that with random and systematic errors there is a high probability that the "true" symmetry will be <1%. We recommend 0.5% or better as the goal for steering with an ICA.
The annual quality assurance on a linear accelerator is typically done with a 3D water tank, which is used for beam steering, energy checks, and profile consistency checks. Previous studies 5-7 have demonstrated that an ICA can be used to measure changes in the energy of photon beams with a higher sensitivity than can be achieved with percentage depth dose measurements. This work can be combined with the previous studies to further reduce the need for the 3D water scanner in the annual QA process.

| CONCLUSION S
We have demonstrated that with the correct equipment and procedures, a 2D detector array can be used to steer linear accelerator photon and electron beams and achieve a resultant beam symmetry that matches that of a 3D water scanning system. However, this is true only if the array used has good calibration, the correct symmetry metric, and the correct symmetry goal during beam steering. Use of the ICA greatly speeds up the steering process because of its real-time feedback and reduces effort by eliminating the need to setup a 3D water scanning tank.
F I G . 7. A comparison of symmetry measured and reported with the ICA vs. that measured and reported with the 3DS. The symmetry reported by the software for each system demonstrated that the ICA and 3DS use slightly different symmetry metrics even when both are set to the Varian symmetry protocol. We separated the results from Varian C-series (black) and TrueBeam (red), and found that results did not depend on the type of machine.
F I G . 8. A comparison of symmetry measured with the ICA vs. that measured with the 3DS. The symmetry was recalculated in Excel to provide an identical symmetry metric between the ICA and 3DS systems. We separated the results from Varian C-series (black) and TrueBeam (red), and found that results do not depend on the type of machine.