Use of a commercial ion chamber detector array for the measurement of high spatial‐resolution photon beam profiles

Abstract Linear accelerator (linac) commissioning and quality assurance measurements are time‐consuming tasks that often require a water tank scanning system to acquire profile scans for full characterization of dosimetric beam properties. To increase efficiency, a method is demonstrated to acquire variable resolution, photon beam profile data using a commercially available ion chamber array (0.5 cm detector spacing). Field sizes of 2 × 2, 5 × 5, 10 × 10, and 15 × 15 cm2 were acquired at depths in solid water of d max, 5 cm, and 10 cm; additionally, beam profiles for field sizes of 25 × 25 and 40 × 40 cm2 were acquired at 5 cm depth in solid water at x‐ray energies of 6 and 23 MV. 1D composite profiles were generated by combining discrete point measurements made at multiple couch positions. The 1D composite profile dataset was evaluated against a commissioning dataset acquired with a 3D water tank scan system utilizing (a) 0.125 cc ion chamber for 5 × 5, 10 × 10, 15 × 15, 25 × 25, and 40 × 40 field sizes and (b) a solid state detector for 2 × 2 cm2 field size. The two datasets were compared to the gamma criteria at 1%/1 mm and 2%/2 mm tolerance. Almost all pass rates exceeded 95% at 2%/2 mm except for the 6 MV 2 × 2 cm2 field size at d max. Pass rates at 1%/1 mm ranged from 51% to 99%, with an average pass rate of 82%. A fourfold reduction in MU was achieved for scans larger than 15 × 15 cm2 using this method compared to the water tank scans. Further, dynamic wedge measurements acquired with the ion chamber array showed reasonable agreement with the treatment planning system. This method opens up new possibilities for rapid acquisition of variable resolution 2D–3D dosimetric data mitigating the need for acquiring all scan data with in‐water measurements.

radiation therapy (IMRT), volumetric modulated arc therapy (VMAT), and stereotactic radiotherapy (SRT) are among modern treatment modalities that need accurate commissioning of beam data. 1-3 Wide use of these technologies suggests that inaccurate beam models in the treatment planning system used to optimize and plan the linac delivery has the potential to do widespread harm. High quality data must be acquired at the time of commissioning and verified annually to ensure that the dose delivered by the linac matches the model in the planning software.
Two categories of data collected during commissioning are scan data and non-scan data. Scan data require translation of a radiation sensor through the beam to measure percent depth dose (PDD), inline, and crossline profiles at different depths for open and wedge fields that are common for photon and electron beams. Non-scan data include static point measurements, often normalized relative to a reference condition, as needed to measure inter-and intra-leaf leakages for the multileaf collimator (MLC), scatter factors, tray and wedge factors, cone factors, and virtual source positions for electron beam. 4 Historically, scan data are collected in liquid water since it provides a fluid medium for continuous movement of a radiation detector, and the fact it closely mimics radiation transport in the human body. In contrast, non-scan data such as output factors may be measured in solid water even though solid water does not completely represent the properties of liquid water. 5, 6 As a matter of convenience, solid water is commonly used for monthly quality assurance measurements due to ease of setup, whereas use of a water tank scan system is generally reserved for annual QA or commissioning when continuous scan data (or large sets of point measurements) are needed.
One issue with use of a water tank is that scans of large field sizes require long beam delivery times. Since the radiation detector effectively reports a point measurement, it must be stepped through the entire distance of the beam profile at a scan speed that maintains sufficient signal integration time to achieve low noise at each point. Detector arrays offer simultaneous point measurements at regularly spaced intervals, offering the potential to acquire scan data without the need to translate the system through the entire beam.
Others have utilized detector arrays for leaf positioning accuracy and for the acquisition of commissioning measurements, but reported that the low data density limited its use for commissioning. 7 Utilizing couch shifts with fractional distances of the detector spacing is one method to improve data density with a detector array.
In this paper we demonstrate this method and use it to acquire variable resolution photon beam profiles and compare the data to commissioning scans acquired in a water tank.

| MATERIALS AND METHODS
Scan profile data were acquired using an IC-Profiler™ (Sun Nuclear, Melbourne, FL) and a TrueBeam™ linac (Varian, Palo Alto, CA).
Translations of the detector array relative to the beam central axis (CAX) were used to acquire multiple measurements of a single radiation field size. To increase the data density a Python™ script interleaved data and a single aggregate scan profile was produced and renormalized. Data points were interleaved by accounting for the displacement from the CAX, and the final scan resolution exceeded the array detector spacing.

2.A | Geometry and scan equipment
The IC-Profiler™ is a multi-axis ion chamber array with detector spacing along the X and Y axis of 5 mm, excluding the two detectors nearest to the center on X axis, and 7.07 mm on diagonal arrays.
The measurement range along the X and Y axis is 32 and 45 cm on diagonals. The IC-Profiler™ was placed on the couch atop 10.0 cm of solid water for backscatter and under varying thicknesses of solid water to achieve different depths (Fig. 1). The detector array was aligned with central axis (CAX) using the light field crosshairs, inroom guidance lasers, and 50 monitor unit (MU) was delivered in the IC-Profiler™ integration time. Field sizes and SSD values used for data acquisition are shown in Table 1. The Y detector array was used for the small field measurements because of the lack of the two detectors nearest to the center on X axis.

2.C | Scan reconstruction
All composite scan data was reconstructed using a custom Python™ software tool. To construct in-line and crossline beam profiles from the detector array data, the IEC61217 coordinate system was used to transform from the IC-Profiler™ coordinate system to the radiation isocenter coordinate system. 8 In the X and Y directions, the 33rd detector was the central detector. The IC-Profiler™ omits two detectors around the central detector in X direction. Equations (1) and 2 assign the position coordinates in units of cm. Since the array is 2D, there is only one detector in Z the direction.
(2) Table 2 shows sample calculation of the coordinates based on the measurements. X S and Y S are the couch lateral and longitudinal position coordinates, respectively. ΔX S and ΔY S are the differences between the successive values after applying a couch shift. If we consider that the radiation isocenter is located at (X F = 0 cm, Y F = 0 cm, Z F = 0 cm), and the IC-Profiler™ central detector is at (X p , Y P , Z P ), after shifting the support (couch) to X S = 0.1 cm, F I G . 1. Experiment setup for 5 cm depth crossline acquired with couch shifts of (a) 0 cm, (b) 0.1 cm, and (c) 0.2 cm.
T A B L E 1 Field sizes and SSD values used for data acquisition.
Square field sizes (cm 2 ) Depths (cm) SSD (cm) MU Energy (MV) | 325 the IC-Profiler™ will be located at (−0.1, 0, 0 cm) with respect to the isocenter. Equation (3) and (4) transform the IC-Profiler™ data to the radiation isocenter coordinate system. This transformation is valid even if the couch is rotated 90°. Figure 2 illustrates the three independent coordinate systems when the couch is oriented normally (at 0°) and when it is rotated 90°.
In the above equations: position, X P = IC-Profiler™ "x" position, Y P = IC-Profiler™ "y" position, ΔX S = Support (couch) "x" position, ΔY S = Support (couch) "y" position, and θ is the support (couch) rotation, as defined in 2.D | Gamma analysis comparison to water tank data Gamma analysis was used to quantify the agreement between the IC-Profiler™, and water tank profiles at the equivalent depth and field sizes using two gamma tolerance levels (1%/1 mm, and 2%/ 2 mm criteria). 9 In order to calculate the equivalent depth, we assumed 5 cm solid water was same as 5 cm water in tank; also, we corrected for the IC-Profiler™ shift to the effective point of measurement and the 0.9 cm inherent buildup in the IC-Profiler™ array.
The 3D Scanner water tank data were acquired during linac commissioning using the SNC125c (Sun Nuclear, Melbourne, FL) ion chamber for 5 × 5, 10 × 10, 15 × 15, 25 × 25, and 40 × 40 cm 2 field sizes. The width of the ion chamber was oriented in the scan direction (smallest direction), and the measurement step size was 0.05 cm. The EDGE Detector™ (Sun Nuclear, Melbourne, FL) was used for 2 × 2 cm 2 field size for both 6 and 23 MV photon beams.
The SNC125c 0.125 cc volume ion chamber was used to measure fields equal and larger to 4 × 4 cm 2 . For the 2 × 2 cm 2 field sizes the EDGE Detector™ was used to mitigate blurring in the penumbra regions. 4 Gamma analysis was performed using the npgamma Python™ code. 10 For fair comparison of the IC-Profiler™ data and the EDGE Detector™ data, the EDGE detector data was convolved with a rectangular function whose width was that of the individual IC-Profiler™ chamber.
T A B L E 2 Sample calculation of the coordinates based on the measurements when the couch is oriented normally.

3.A | Scan reconstruction
The custom Python™ script returned composite resolution scan pro-   ison to the IC-Profiler™ data at the 2 × 2 cm 2 field size. Good agreement to within about 95% pass rate was seen at the 2%/2 mm level.

3.B | Gamma analysis comparison to water tank data
Note, without convolution, the pass rate was drastically reduced to only 60%. This reduced pass rate suggests that the IC-Profiler™ can measure small field sizes at 2 × 2 cm 2 , but the resultant profiles are blurred by the detector size due to the volumetric effects. Figure 4 plots dose difference between the convolution and non-convolution method for 6 MV, 2 × 2 cm 2 field size, and 10 cm depth. The difference between these two is minor in all regions with the exception of the field edges. Lack of agreement is expected at the edges due to the high gradient regions and the resultant volumetric averaging effect of the larger detector volume in the IC-Profiler™.
Therefore, while technically possible to capture the field at a reduced SSD, the data shows large discrepancy in the gamma pass rate. Data acquisition at reduced SSD is thus not recommended by the authors, which limits the maximum field size that can be measured to 32 cm in X or Y. Table 5 shows gamma pass rate to increase as the resolution increases, i.e., more couch shifts yield better agreement to the commissioning water tank data. At the highest resolution of 0.05 cm the gamma pass rate was 100% using 2% 2 mm criteria, and 65.75%

Data in
using 1% 1 mm criteria.

| DISCUSSION
Within the range of field sizes from 5 × 5 to 15 × 15 cm 2 , the IC-Profiler™ array was able to acquire profile scans of 6 and 23 MV beams within 2%/2 mm agreement to a water tank scanning system.
Note that a correction factor was not applied for the comparison of solid water and liquid water measurements. 1%/1 mm agreement was substantially lower, suggesting that this technique can not accurately reconstruct measured profiles to better than 2%/2 mm. While the demanding gamma criterion in patient QA is 2%/2 mm, a DTA of 2 mm (may imply a deviation of 10% of the field size for a (2 × 2 cm 2 ) field. The reason for not measuring 23 MV for the small fields (2 × 2 cm 2 ) is that we don't do small field treatments with high energy (23 MV). Also, clinically we don't use 40 × 40 field sizes for high energy (23 MV).
Dose profiles agreed best to the water tank data in regions where the dose >20% of D max . However, the gamma pass rates

ACKNOWLEDG MENTS
Thank you to the physics faculty at Rhode Island Hospital who provided encouragement for this project.

CONFLI CT OF INTEREST
The authors declare no conflict of interest. F I G . 5. Comparison between 60°EDW for 6 MV, 100 cm SSD, 5 cm depth, 10 × 10 cm 2 field size using IC-Profiler™ composite (composite point spacing = 0.1 cm) and TPS Exported Data with Y2 jaw, and voxel size 0.12 cm. Normalization was only performed on the composite profile.

R E F E R E N C E S
T A B L E 5 Dosimetric agreement of 2 × 2 cm 2 , 3D Scanner tank data (Edge detector) convolved to match IC-Profiler™ data at various composite point spacing. E = 6 MV, inline scans, 5 cm depth.