An analysis of the ArcCHECK‐MR diode array's performance for ViewRay quality assurance

Abstract The ArcCHECK‐MR diode array utilizes a correction system with a virtual inclinometer to correct the angular response dependencies of the diodes. However, this correction system cannot be applied to measurements on the ViewRay MR‐IGRT system due to the virtual inclinometer's incompatibility with the ViewRay's multiple simultaneous beams. Additionally, the ArcCHECK's current correction factors were determined without magnetic field effects taken into account. In the course of performing ViewRay IMRT quality assurance with the ArcCHECK, measurements were observed to be consistently higher than the ViewRay TPS predictions. The goals of this study were to quantify the observed discrepancies and test whether applying the current factors improves the ArcCHECK's accuracy for measurements on the ViewRay. Gamma and frequency analysis were performed on 19 ViewRay patient plans. Ion chamber measurements were performed at a subset of diode locations using a PMMA phantom with the same dimensions as the ArcCHECK. A new method for applying directionally dependent factors utilizing beam information from the ViewRay TPS was developed in order to analyze the current ArcCHECK correction factors. To test the current factors, nine ViewRay plans were altered to be delivered with only a single simultaneous beam and were measured with the ArcCHECK. The current correction factors were applied using both the new and current methods. The new method was also used to apply corrections to the original 19 ViewRay plans. It was found the ArcCHECK systematically reports doses higher than those actually delivered by the ViewRay. Application of the current correction factors by either method did not consistently improve measurement accuracy. As dose deposition and diode response have both been shown to change under the influence of a magnetic field, it can be concluded the current ArcCHECK correction factors are invalid and/or inadequate to correct measurements on the ViewRay system.

out magnetic field effects taken into account. In the course of performing ViewRay IMRT quality assurance with the ArcCHECK, measurements were observed to be consistently higher than the ViewRay TPS predictions. The goals of this study were to quantify the observed discrepancies and test whether applying the current factors improves the ArcCHECK's accuracy for measurements on the ViewRay. Gamma and frequency analysis were performed on 19 ViewRay patient plans. Ion chamber measurements were performed at a subset of diode locations using a PMMA phantom with the same dimensions as the ArcCHECK. A new method for applying directionally dependent factors utilizing beam information from the ViewRay TPS was developed in order to analyze the current ArcCHECK correction factors. To test the current factors, nine ViewRay plans were altered to be delivered with only a single simultaneous beam and were measured with the ArcCHECK. The current correction factors were applied using both the new and current methods. The new method was also used to apply corrections to the original 19 ViewRay plans. It was found the ArcCHECK systematically reports doses higher than those actually delivered by the ViewRay. Application of the current correction factors by either method did not consistently improve measurement accuracy. As dose deposition and diode response have both been shown to change under the influence of a magnetic field, it can be concluded the current ArcCHECK correction factors are invalid and/or inadequate to correct measurements on the ViewRay system.

| INTRODUCTION
Magnetic resonance imaging-guided radiation therapy has tremendous potential for real-time image guidance during treatment delivery. The ViewRay system (ViewRay, Inc., Oakwood Village, OH, USA) is the world's first MRI-guided delivery system, and uses a ring gantry with three cobalt-60 ( 60 Co) treatment heads mounted 120°apart, each with an independent double-focused multileaf collimator (MLC). 1 The system is capable of delivering a variety of treatment options, including adaptive and intensity-modulated radiation therapy, all with simultaneous image guidance using its integrated 0.35 T MRI system. Given the novelty and complexity of this new system, robust delivery verification procedures must be developed and tested to ensure accurate treatment delivery. The ViewRay system presents a unique challenge to IMRT QA devices due to its ability to deliver up to three simultaneous beams in the presence of a significant magnetic field. to have an accuracy and precision acceptable for clinical IMRT and VMAT quality assurance. 2,3 However, it must be noted that these studies did not use the MRI-compatible ArcCHECK and all measurements were performed without the presence of a significant magnetic field.
Despite the success of the ArcCHECK's correction system coupled with its virtual inclinometer algorithm, the correction system is unable to be utilized for measurements on the ViewRay system, as the algorithm assumes there is only a single incident beam in any 50 ms time interval. Consequently, correction factors are not currently applied to ArcCHECK measurements performed for patientspecific quality assurance on the ViewRay at our institution. Additionally, the current correction factors were determined without magnetic field effects taken into account. Dose deposition at interfaces of materials with different stopping powers, such as those found near diodes in the ArcCHECK, and diode response have been shown to change under the influence of magnetic fields. [4][5][6][7] As the correction factors are determined by the diodes' responses, it is possible the current factors are not valid for measurements within the ViewRay's 0.35 T magnetic field.
All manufacturer-recommended procedures for maximizing agreement between the ArcCHECK and the ViewRay TPS were followed during commissioning of the ArcCHECK at our institution. This includes adjusting the electron density of the ArcCHECK image dataset in the ViewRay TPS until 3%/3 mm gamma passing rates are near 100% for reference treatment plans. Maximum agreement between the ViewRay TPS and the ArcCHECK at our institution was achieved with an electron density value of 1.125 g cm À3 .
In the course of performing patient-specific quality assurance measurements with the ArcCHECK for the first patients treated on the ViewRay at our institution, it was observed the ArcCHECK measurements were consistently higher than the ViewRay TPS predictions. Accordingly, the goals of this study were to quantify the observed discrepancies and test whether applying the current correction factors improves the ArcCHECK's accuracy for measurements on the ViewRay system.

2.A | Quantify discrepancies
To quantify the discrepancies between the ViewRay TPS and Arc-CHECK measurements, 19 ViewRay patient plans were analyzed.
Gamma analysis was performed using the SNC Patient software using a 10% global threshold. 8 Analysis was performed with parameters set at 3%/3 mm, 2%/2 mm, and 1%/1 mm. The "Apply Measurement Uncertainty" option in the SNC Patient software was used for the ArcCHECK measurements. Frequency analysis on the differences between the ViewRay TPS and ArcCHECK measurements was also performed. Ten diode measurements in high dose, low gradient regions within their respective plans were then chosen to compare with Accredited Dosimetry Calibration Laboratory (ADCL)-calibrated Exradin A1SL ionization chamber (Standard Imaging, Middleton, WI, USA) measurements in the same locations. Each of the chosen diode measurements failed gamma analysis at 3%/3 mm. Ion chamber measurements were performed in a phantom with the same size and shape as the ArcCHECK, provided by the Sun Nuclear Corporation (see Fig. 1). The manufacturer claimed that the phantom is composed of PMMA. In place of diodes, the phantom has holes drilled in it to fit Exradin A1SL ion chambers, with PMMA plugs to fill the holes not being used. The holes are drilled such that ion chamber measurements can be taken at locations corresponding to diodes in the ArcCHECK. Measurements with the ion chamber phantom were performed with the ArcCHECK's central PMMA plug inserted into the phantom's central cavity.
The ViewRay treatment planning system and the ArcCHECK report dose-to-water. To acquire the dose-to-water for ion chamber measurements in the PMMA phantom, a modified form of the dose formalism presented by Seuntjens et al. was used in this work. 9 The Seuntjens et al. formalism relates measurements made in solid nonwater phantoms to the absorbed dose-to-water that would be obtained using a water phantom and the AAPM's Task Group 51 (TG-51) protocol. The dose-to-water at a defined depth z ref from an ion chamber measurement in a PMMA phantom is given by (1) where M raw is the raw charge measurement, P ion , P pol , P elec , and P TP are the standard corrections used for reference dosimetry of highenergy photon beams, k Q is the "beam quality factor" which converts the calibration coefficient to the beam of interest, and N CoÀ60 D;w is the ADCL calibration coefficient for dose to water from a 60 Co beam. 11 For this work, ion recombination and polarity corrections were not applied but expected ranges for the factors from published data were incorporated into the uncertainty budget for the measurements (see Table 1).
For measurements within the ViewRay's 0.35 T magnetic field, it is necessary to include an additional factor which accounts for magnetic field effects to the chamber's response, notated P MF in eq. 1. It has been shown that while the dose distribution from a high-energy photon beam in a homogeneous medium is only slightly affected by the presence of a magnetic field, there is a large impact on the dose distribution at tissue-air interfaces due to the altered point spread kernel of secondary electrons. 6,7,12 As an ion chamber is a gas-filled cavity, its response in an otherwise homogeneous medium is dependent on the strength and orientation of the magnetic field in a way that the medium's dose distribution is not. The change in a chamber's response is dependent on many factors, including the magnetic field strength, presence and size of air gaps around the chamber, chamber design, and orientation of the chamber with respect to the magnetic field. 5,12-14 A characterization of the A1SL's response within the ViewRay environment has not yet been published. However, literature suggests the potential response dependency of chambers similar to the A1SL is 1% or less. [13][14][15] For this work, a correction factor was not applied, but the potential response dependency was incorporated into the uncertainty budget for the measurements.
It is important to note k Q and N CoÀ60 D;w are defined for the specific TG-51 measurement setup of a 10 cm 9 10 cm field and depth of 10 cm in a rectangular water phantom. 11 As the experimental setup differs significantly from these conditions, there is additional | 163 uncertainty in the use of each of the factors due to possible changes in the scatter conditions around the chamber. k Q was assumed to be 1.000 for this work, as defined by TG-51 for 60 Co beams, and estimates of the uncertainty for each factor were derived from literature and incorporated into the experiment's uncertainty budget in Table 1.
As the ion chamber phantom material is PMMA and not water, it is necessary to apply additional corrections to the ion chamber measurements in order to obtain the absorbed dose-to-water. 9 These corrections are contained in the bracketed expression in eq. 1. for the A12 chamber between PMMA and water reported by Seuntjens et al. is 1.000 and the A1SL chamber has the same wall material as the A12, this factor was assumed to be unity for this work. The ratio of P ion values between PMMA and water reported by Seuntjens et al. is close to unity. As we did not apply a P ion correction to our measurements, but incorporated the factor's expected range into our uncertainty budget, the difference in P ion between measurements in water and PMMA is within our stated uncertainty. With all of these considerations taken into account, eq. 1 simplifies to (2) with all of the known dependencies taken into account in the uncertainty budget for the measurements.
To validate the experimental method, additional patient plan measurements were taken, consisting of isocenter ion chamber measurements at the center of both the ArcCHECK and the ion chamber phantom and at a point where the ArcCHECK and ViewRay TPS agree within 1%. These measurements were performed to verify the dose calibration of the ArcCHECK.

2.B | Test current correction factors
In order to analyze the current ArcCHECK correction factors, it was necessary to develop a method of applying the factors to ArcCHECK measurements of ViewRay plans. As the ArcCHECK's virtual inclinometer is not compatible with multiple simultaneous beams, the new method was required to derive beam information an alternate way. As the beam delivery angles for each plan are known by the ( where F i,k is the fraction of dose to diode i from beam k and the C factors are the four correction factors currently used for ArcCHECK measurements, correcting for dependencies on angular incidence, variation between individual diodes, field size, and phantom heterogeneity. The derivation of eq. 3 is given in Appendix A. eq. 3 was

| RESULTS AND DISCUSSION
The gamma analysis results for the ArcCHECK measurements of 19 ViewRay patient plans are displayed in  Figure 2 shows frequency and cumulative frequency plots of the differences in cGy between the ViewRay TPS and ArcCHECK measurements for the same 19 patient plans, both with and without a 10% global threshold applied. Figure 3 shows the frequency and cumulative frequency plots of the percent difference between the ViewRay TPS and ArcCHECK for measurements meeting a 10% global threshold. For a random measurement uncertainty or error process, Figs. 2(a) and/or 3(a) would be expected to show Gaussian distributions centered about zero. 18,19 However, it can be seen there is a clear positive offset, meaning the ArcCHECK is consistently reporting doses higher than the ViewRay TPS.
In Figs. 2(c) and 2(d), it can be seen the 50% cumulative frequency point is located at differences of approximately 6 cGy for all of the measurements, and at 5 cGy for the measurements meeting a 10% global threshold. This means that half of all of the Arc-CHECK measurements on the ViewRay system disagree with the TPS predictions by at least 6 cGy and applying the 10% threshold only slightly reduces this value. In Fig. 3, it can be seen the 50% cumulative frequency point is at a difference of approximately 5%.
Using a global definition for the 2% gamma analysis parameter, a 5% local difference will pass gamma analysis only for diodes measuring doses that are at least 40% of the maximum measured dose.
Combined with the fact that 5 cGy is 2.5% of a 2 Gy per fraction plan, it is not surprising many of the plans fail gamma analysis at 2%/2 mm. Figure 4 and Table 3 display the results of the ion chamber measurements. It can be seen that the ViewRay TPS's average difference from the delivered dose, as measured by the ion chamber, is within the measurement uncertainty. The ViewRay TPS agrees with the ion chamber within uncertainty for nine out of the ten measurement locations. However, for all 10 measurement locations, the ArcCHECK measurements are significantly higher than the ion chamber, and the differences cannot be attributed to measurement uncertainty.
Using a one-sided t-test, the calculated P-value for the differences between ArcCHECK comparisons to the ion chamber and ViewRay TPS comparisons to the ion chamber is less than 0.00001.
Defining statistical significance at P < 0.05, the ArcCHECK's average difference from the ion chamber is therefore significantly different than the ViewRay TPS's average difference. The results of the Single Beam Experiment are given in Table 4 and Figs. 5 and 6, and the results from applying corrections on the original ArcCHECK measurements are given in Tables 5 and 6 and   Table 4, a statistically significant P-value of 0.004 is calculated for the differences between the New Algorithm Corrected and Uncorrected 1%/1 mm datasets. However, at 3%/3 mm, the calculated P-value is 0.28 and is therefore not significant. It is also interesting to note that the spread in passing rates is significantly lower with the new algorithm compared to both the SNC corrected and uncorrected datasets.
In Fig. 5, it can be seen that while applying the current correction factors with the new method seems to shift the discrepancy curve slightly closer to zero, the effect is very minor and there is still a significant positive offset. It can be seen in Table 4  In addition to the above results, the ArcCHECK corrections mode measurement showed similar frequency analysis results to the MATLAB implementation of the SNC algorithm, as shown in Fig. 6.
All of the diode readings between the two datasets agreed within a

Measurement Number
ViewRay TPS ArcCHECK F I G . 4. Bar graph depicting differences between ion chamber measurement and ViewRay TPS calculation (black) and ArcCHECK measurement (red). Error bars are representative of total k = 1 measurement uncertainty, derived using the uncertainty budget in Table 1.  This indicates leakage is not contributing significantly to the observed discrepancies between the ArcCHECK and ViewRay TPS. These results were verified by repeating the original measurements for nine of the plans, with the repeated measurements matching these results. As the plans measured were the same as those used in the Single Beam Experiment, the same correction factors were applied. Using a two-sided t-test for dependent samples, the P-value for differences between the uncorrected and new algorithm corrected datasets at 3%/3 mm is 0.33, and is not significant. However, at 1%/1 mm, the P-value is 0.017. Applying the corrections therefore significantly lowers the average 1%/1 mm gamma passing rate.   Additionally, there may be changes in angular response when multiple beams, each with an independent dose rate, are simultaneously incident on diodes. These possible dependencies will need to be investigated in the future.
The frequency plots and ion chamber comparisons show negligible difference between the corrected and uncorrected ArcCHECK measurements, as seen in Figs. 8 and 10. Only half of the corrected measurements were closer to the ionization chamber measurements than the uncorrected ArcCHECK measurements, and the improvements were very minor. Using a two-sided t-distribution, the calculated P-value for the differences between the two sets is 0.73, and is therefore not significant.

| CONCLUSION
Using the ArcCHECK in the ViewRay environment consistently results in significant discrepancies between measured and planned doses. Applying the current correction factors does not consistently improve the ArcCHECK's accuracy for measurements on the View-Ray system. The current correction factors are therefore invalid and/ or inadequate to correct the observed discrepancies between the ArcCHECK and ViewRay systems.

ACKNOWLEDG MENTS
This work was funded by the Bhudatt Paliwal Professorship and the UWMRRC. The authors would like to thank the Sun Nuclear Corporation for the use of their phantom, and specifically thank Jakub Kozelka for the many discussions on this subject and for providing data and MATLAB code.

CONFLI CT OF INTEREST
The authors have no conflict of interest to report. APPENDIX A.

DERIVATION OF EQ. 3.
According to Kozelka et al. and the Sun Nuclear Corporation's reference guide for the version of the ArcCHECK used at our institution, the dose to a single diode i for measurement update j is where N ref is the reading to dose calibration factor in Gy/reading and M corr,i,j is the fully corrected diode reading. 2, 17 The corrected diode reading is given by M corr;i;j ¼ M i;j C AD;i;j C ID;i;j C FS;i;j C HF;i;j ; where M i,j is the raw diode reading with background subtracted, C AD is a factor correcting for the average angular dependence of the diodes for the given incidence angle, C ID is the correction for individual deviations between the diodes for the given incidence angle, C FS is the field size correction, and C HF is termed the heterogeneity correction, which is used to match the diode response to an ion chamber measurement in a homogeneous PMMA phantom. 17 The total dose to diode i for an entire measurement session is then where, for simplicity, all of the correction factors have been grouped into a single variable C i,j , and J is total number of measurement updates, given by the total measurement time divided by 50 ms/update. If we define a new variable F i,k to represent the fraction of dose delivered to diode i by a specific fixed-beam k, the total dose to diode i is also given by Also, the total raw measurement with background subtracted for diode i is where K is the total number of fixed-beams in the treatment plan.
Combining eqs. 4 through 6 and rearranging, the total corrected dose to diode i is Fi;k Ci;k : (A6) Applying eq. 7 to the ViewRay ArcCHECK measurements, for which the calibration factor is already applied, the corrected ArcCHECK diode dose is D TOT;corr;i ¼ D TOT;uncorr;i P K k¼1 Fi;k CAD;i;kCID;i;kCFS;i;kCHF;i;k : (A7) ELLEFSON ET AL.