Radiotherapy for patients with multiple brain metastases has shifted from whole-brain irradiation to stereotactic radiotherapy (SRT), with single isocenter multitarget (SIMT) SRT irradiation becoming more popular recently [1] . This has been shown to provide excellent local control while minimizing neurocognitive decline [2] [3] . Furthermore, treating multiple targets of SIMT simultaneously can significantly reduce treatment time when compared to irradiating each target separately [4] . Reducing treatment time can improve patient comfort, compliance, efficiency, and clinic workflow [5] - [7] .

SIMT for intracranial targets typically results in a steep dose gradient around multiple and small targets, with no target at the isocenter (IC). Therefore, even minor misalignments can significantly alter the dose entering the target, resulting in unacceptable errors and undesirable clinical outcomes [5] [8] . Hence, it is strongly advised to conduct patient-specific quality assurance (PSQA) before treatment [9] - [11] . However, accurate dosimetry is difficult due to lateral electronic disequilibrium, under-sampling, and volume-averaging effects caused by detectors with volumes close to the irradiation field due to the target’s small size, and difficulty in detector [10] [12] [13] . Furthermore, multiple off-axis lesions must be measured because the target is not at the IC [5] [14] . Therefore, there are more challenges than with PSQA when using common irradiation methods like intensity-modulated radiation therapy (IMRT) and volumetric-modulated arc therapy (VMAT).

There are currently several devices available for PSQA of SIMT SRT, including low and high detector-density ionization chamber/diode arrays [15] - [20] , small-volume ionization chamber/diamond detectors [21] , films [21] , radiochromic gel dosimeters [22] , electronic portal imaging devices [23] , machine delivery log files [24] [25] , and polymer gels [26] . Each of the tools mentioned above has both advantages and disadvantages. Recently, there is also a Monte Carlo independent calculation system specialized for SIMT [27] [28] .

Leon et al. used five commonly available PSQA tools: Sun Nuclear ArcCHECK (AC) [17] and SRS MapCHECK [15] [16] , GafChromic EBT Radiochromic Film [21] , machine log files [24] [25] , and Varian Portal Dosimetry [11] . The sensitivity to various multi-leaf collimator (MLC) and dose-related errors, as well as the criteria for gamma analysis for correctly detecting them, were investigated in conjunction with clinical objectives. They propose evaluating SIMT PSQA results separately based on the size of the PTV and its distance from the IC. To the best of our knowledge, only a few papers have thoroughly evaluated the characteristics of AC in terms of parameters such as PTV size and distance from the IC in SIMT. Therefore, we investigated the relationship between the PSQA’s gamma pass rate (GPR) and parameters related to treatment planning to better understand the characteristics of AC in SIMT.

Figure 2 displays the GPRs for the four criteria. In the 3%/2 mm criterion, increasing GS from 1 mm (default) to 1.5 mm and 2 mm reduced mean GPR by 2.9% and 5.3%, respectively. Similarly, in the other criteria, changing the GS resulted in a decrease in GPR, with the decrease being greater in the more severe criteria. There were no significant differences between the different GSs in any of the criteria. (GS1.5 mm: 3%/2 mm, 2%/2 mm, 2%/1 mm, and 1%/1 mm were p = 0.31, 0.38, 0.39, and 0.36, respectively) (GS2.0 mm: 3%/2 mm, 2%/2 mm, 2%/1 mm, and 1%/1 mm were p = 0.08, 0.10, 0.08, and 0.07, respectively). For the calculation times shown in Table 2(a) , GS1.5 mm and GS2.0 mm were 245 s (67%) and 290 s (79%) faster than GS1.0 mm.

For the number of evaluated detectors shown in Table 2(b) , increasing the TH from 10% to 20% resulted in an average of 154 fewer detectors being evaluated,

Abbreviations: GS, grid size; AD, absolute dose; RD, relative dose; TH, threshold.

but there were no significant differences in pass rates across all criteria (3%/2 mm, 2%/2 mm, 2%/1 mm, and 1%/1 mm were p = 0.43, 0.69, 0.80, and 0.74 for, respectively).

When comparing absolute and relative dose dosimetry, the mean GPR was higher for relative dose in all criteria, and the variation in GPR was smaller. Only the relative dose differed significantly from the absolute dose in all criteria (3%/2 mm, 2%/2 mm, 2%/1 mm, and 1%/1 mm were p = 0.0056, 0.0013, 0.0023, and 0.0017 for, respectively). In all cases, relative dosimetry had a greater number of active detectors, approximately 54 more on average ( Table 2(b) ).

The effect of DD or DTA on the GPR was investigated by examining the default mean GPR based on various criterion. When comparing Figure 2(a) 3%/2 mm and (b) 2%/2 mm, the GPR decreased from 91.8% to 86.4% for the same DTA criteria (p = 0.091). Similarly, when comparing Figure 2(c) 2%/1 mm and (d) 1%/1 mm, GPR fell from 67.8% to 60.2% (p = 0.158). In contrast, comparing Figure 2(b) 2%/2 mm and Figure 2(c) 2%/1 mm with different DTA, the GPR decreased relatively significantly (18.6%) from 86.4% to 67.8% (p < 0.001).

Figure 3 depicts the relationship between the four parameters and the GPR. The relationship between equivalent MLC field size and GPR is depicted in Figure 3(a-1) and Figure 3(a-2) . The median of minimum and average equivalent MLC field sizes were 9.5 mm and 12.7 mm, respectively. Figure 3(a-1) demonstrates that the GPR decreases when the minimum equivalent MLC field size of multiple targets is small, particularly when it is less than 10 mm (R² = 0.498). Figure 3(a-2) depicts the relationship between the average equivalent MLC field size and GPR for each plan. The average equivalent MLC field size showed a stronger correlation than the minimum equivalent MLC field size (R² = 0.596).

Figure 3(b) depicts the relationship between the max dose difference in the chamber and GPR. The higher the max dose difference in the chamber, the lower the GPR (R² = 0.282).

Figure 3(c) depicts the relationship between the max target-IC distance and GPR, which shows a low correlation (R² = 0.146).

Figure 3(d) shows that the GPR decreased slightly as the modulation factor increased (R² = 0.238).

Figure 4(a) depicts the relationship between the minimum equivalent MLC field size and the max dose difference of isocenter dose. In all treatment plans, the chamber’s max dose difference was the target with the smallest equivalent MLC field size among all targets. As with GPR, the max dose difference of isocenter dose increased when the equivalent MLC field size was less than 10 mm (R² = 0.380).

The relationship between “equivalent MLC field size (minimum and average)” and “modulation factor” is illustrated in Figure 4(b-1) and Figure 4(b-2) . The modulation factor correlated more strongly with the minimum equivalent MLC field size than with the average equivalent MLC field size. (R² = 0.332 and R² = 0.084 for the minimum and average, respectively).

Figure 5 depicts the dose distribution as measured with an actual multidimensional detector. Figure 5(b)-(d) focus on the b, c, and e cross sections of the distribution in (a), respectively, with the detector measurements on the vertical axis and the detector location on the horizontal axis. Figure 5(b) and Figure 5(d) show a good agreement between the TPS and measured doses in the target’s central region. On the other hand, the left side of Figure 5(c) depicts a slightly off-center part of the target with measured values that are generally lower than those of the TPS and a point of failure.

When multiple regression analysis was performed with GPR as the dependent variable, the coefficient of determination (R²) was 0.851, and the adjusted coefficient of determination (Adj. R²) was 0.786. The F-value was 13.05, and the p-value was 1.51e−05, so the model as a whole was statistically significant. The significant positive influence was the number of evaluated detectors, with a regression coefficient of 0.1179 and a p-value of 0.001. The p-value for minimum target volume was 0.093, which was not statistically significant, but the regression coefficient

was 0.8566. There was no significant difference for the other variables.

This study investigated the relationship between GPR and treatment plan-dependent parameters such as PTV size and distance from the isocenter in patient QA using ArcCHECK in SIMT.

It reported that in previous studies, a smaller GS (1.0 mm) results in a higher GPR, which is consistent with our findings [30] . AAPM TG 101 recommends a GS of 2 mm or less for SBRT [31] while Medical Physics Practice guideline 9.a. states that a 1 mm GS in the TPS calculation may be required for very small targets [10] . The multiple brain metastases in this study were small targets, with a median target volume of 0.8 cm³ and a median diameter of 1.16 cm when assumed to be a sphere. Therefore, a smaller GS enabled more accurate dose calculation, demonstrating the utility of a smaller GS. The smaller the GS, the longer the calculation time, but even at the maximum, it was within 10 minutes, so if it is within an acceptable range, a GS of 1.0 mm or less is recommended.

Different TH (10% and 20%) and dose evaluation (relative and absolute dose) varied the number of active detectors. Increasing the TH from 10% to 20% was considered so that the evaluation could focus on the higher dose range. The difference in TH reduced the number of active detectors by an average of 154; however, there was no significant difference in GPR results. If the TH had been higher, the outcomes might have been different. In comparison to the absolute dose mode, the relative dose mode had more active detectors ( Table 2(b) ), and a higher GPR. This is because the relative dose adjusts the dose so that the GPR is maximized, and in many cases, the measured dose is lower than planned due to the wide detector spacing, so the analysis shifts to increase the dose. However, in the event of a dose error, the relative dose mode may underestimate the error, so the absolute dose, as recommended by the guideline, is preferred [32] .

We investigated the effect of the criteria DD or DTA on the GPR. When DTA was 1 mm tighter, the GPR decreased significantly. Specifically, in Table 3 , GPR decreased from 86.4% at 2% 2 mm to 67.9% at 2% 1 mm, an average decrease of 18.6%. On the other hand, stricter DD criteria resulted in a lower GPR, but not a noticeable decrease. In Table 3 , GPR decreased by an average of only 5.4%, from 91.8% at 3% 2 mm to 86.4% at 2% 2 mm. Therefore, when compared to DD, DTA was found to be significantly related to the GPR, possibly due to the small size of the SIMT SRT target, steep dose gradient, and misalignment of the ACs, all of which directly resulted in a lower GPR. Lee et al. also found that changing the GPR from 3%/2 mm to 2%/2 mm reduced the average GPR by 2.20% while changing from 2%/2 mm to 2%/1 mm decreased the average pass rate by 11.21% [30] . They also noted that meeting the DTA standard of 1 mm appears to be difficult even for homogeneous plans like DCAT, and their findings were consistent with those in this study. It can be said that this study has provided a guide to the GPR for each criterion when using ArcCHECK as a multi-dimensional detector.

Table 3 presents a comparison of previous studies. Although different studies used different criteria, all performed gamma analysis in global mode with a TH of 10%. Because they were limited to SRT cases, studies with a single target were included. The average GPR for a single target exceeded 90%, even with the stringent criterion (2mm/1%) ( Table 3 (b) [32] , (c) [30] , and (d) [30] ). However, using the 2%/1 mm criterion, the mean GPR of our results was significantly lower than that of all three previous studies ( Table 3 (a) [32] , (e) [33] , and (f) [11] ). Table 3(e) shows that only 11 of the 40 plan samples were intracranial, and many of them had relatively large targets (target volume sizes ranged from 0.43 cm³ to 161.13 cm³, with a mean volume of 35.81 cm³). For Table 3(f) , absolute dose calibration was performed on the measurement day, and the setup was done by MV imaging devices. In our study, we obtained the absolute dose calibration annually, and we trust our laser in setting up AC. Therefore, we assume that these differences in settings influenced the GPR. For Table 3(a) , the difference in arc number may have influenced the results. Although VMAT had more modulation than DCAT, the median number of arcs was less than half (4.3 vs. 10). It is difficult to make a simple comparison because the low-dose range expands when fewer MUs are irradiated with more arcs. Namely, as illustrated in Figure 5(c) , there were numerous areas where the measured doses were lower than calculated doses at low doses. This could explain why irradiation in DCAT resulted in lower GPR than in VMAT.

Gamma analysis was conducted in Global mode and a threshold of 10% was employed for all studies.

Figure 5 shows that TPS and measured values tended to agree at the detector rows that received a direct beam. However, the measured values were lower than the TPS at the beam’s edge (low-dose area), which is slightly further away from the target, and this area contributed to the decrease in GPR in many cases. Figure 3(a-1) shows that the GPR decreases when the minimum equivalent MLC field size is less than 10 mm. This is also probably due to detector spacing. The multidimensional detector used in this study had a detector spacing of 10 mm, which may have resulted in an underestimated dose. Figure 3(b) shows that the max dose difference of isocenter dose also tends to increase when the equivalent MLC field size is less than 10 mm, like the GPR. This could be because the correction for small irradiation fields, known as k-factor, factors that add up to an irradiation field of less than 10 mm, is not recommended. Therefore, both the ionization chamber and the multidimensional detector may underestimate the dose when the equivalent MLC field size is below 10 mm. As depicted in Figure 3(a-1) and Figure 3(a-2) , it was more related to average size than minimum size. This could be because many of the targets were small to begin with, making average, a measure of the sum of multiple targets, more relevant. The GPR tends to decrease as the modulation factor increases. In particular, while not as large as the average equivalent MLC field size, the modulation coefficient is related to the minimum equivalent MLC field size, so we believe there was a correlation. Prabhakar et al found a strong correlation of R² = 0.97 between the equivalent square field size (the standard 4 * Area/Perimeter) of the IMRT plan and the GPR of 3%/2 mm, indicating that GPR depends on the field size [34] . DCAT produced similar results, despite using a different field size calculation method.

However, there was little correlation between max target-IC distance and GPR ( Figure 3(d) ). Although we could not find any reports on the relationship between GPR and target-IC distance, we hypothesized based on the two reports that GPR may decrease as target-IC distance increases (ExacTrac-based alignment has an error of up to 2.2 mm at distances greater than 10 cm between target-IC concerning spatial accuracy [14] . Target-IC distance influences target coverage, with smaller targets having a larger effect [35] .) However, in this study, we could not accurately investigate the relationship between target-IC distance and GPR, including the effect of rotation, because all measurements were taken with the couch set to 0˚. Therefore, it is possible that the target-IC distance has less of an effect on GPR and that the effect has been reduced because the couches have not been rotated.

Multiple regression analysis showed that the GPR at 2% 2 mm was greater when there were more detectors (number of evaluated detectors) that detected a dose of 10% or more of the prescribed dose. The number of evaluated detectors is thought to increase when the targets are far apart or the targets are large (The correlation coefficient between the number of evaluated detectors and the maximum distance between the target ICs was 0.60, and the correlation coefficient with the number of targets was 0.54, indicating a moderate correlation.). Previous research has also stated that larger targets result in higher GPR. On the other hand, it is generally thought that the further apart the targets are, the greater the likelihood of a larger error, but with the number of evaluated detectors increasing, the GPR tends to be larger in the AC than when the targets are close to each other. This is likely to be a phenomenon unique to the AC. In other words, when the targets are small and close to each other, the number of detectors that evaluate them decreases, and the impact of the detectors that fail increases, so even if there are no problems with the treatment plan, the GPR may decrease.

There are some limitations to this study. The first is that the evaluation does not consider error detection sensitivity. Several previous studies have reported that AC does not have high sensitivity to gantry and collimator rotation errors, as well as MLC positioning errors. For example, Liang et al. reported that the minimum reliably detectable gantry rotation and MLC leaf positioning errors were 2˚ and 4 mm, respectively [36] . Leon et al. found that MLC positioning errors were consistently undetectable [11] . Tutty et al. found that the AC could detect introduced errors in the delivery of treatment plans with large target volumes of about 3 cm using the 3%/1 mm gamma criterion, but was insensitive to introduced errors in treatment plans with smaller target volumes of about 1.5 cm [37] . In contrast, it is more sensitive to setup errors in couch translation and rotation. The 2%/2 mm gamma criterion results in a 6.7% ± 3.5% and 14.5% ± 6.6% reduction in GPR for 2 mm translation and 2° rotation errors, respectively [38] . AC error detection limits should be considered when performing PSQA. Second, measuring was impossible with the couch rotated. AAPM TG 218 recommends the true composite (TC) method. This is because the TC method is preferred for PSQA of SRS and SBRT treatments, in which the measurement device is placed on the couch with actual treatment parameters such as gantry, collimator, couch angle, jaws, MLC leaf position, MU, and the radiation beam is delivered to simulate treatment delivery to the patient [39] . The findings and conclusions in this study may be inaccurate when compared to the results of PSQA obtained using the TC method. More specifically, the results are likely to be worse if the couch’s residual rotational error is considered.

AC has been linked to several negative outcomes. Low spatial resolution causes a sharp drop in GPR when the criteria are tightened. The response is low due to the low dose at detectors located outside the direct beam area. In other words, the detector array’s configuration and resolution significantly affect the experimental calculation of gamma due to under sampling of the dose distribution, blurring effects, noise, or a combination of both. However, it is unaffected by volume averaging, unlike ionization chambers. The measurement is nearly independent of target size and positional relationship, and it can be completed in a single step. This saves a significant amount of physics QA time. In high-volume radiotherapy facilities, it can improve physics throughput while reducing human error. After the text edit has been completed, the paper is ready for the template. Duplicate the template file by using the Save As command, and use the naming convention prescribed by your journal for the name of your paper. In this newly created file, highlight all of the contents and import your prepared text file. You are now ready to style your paper.

This study used AC to investigate the relationship between target- and treatment plan-dependent parameters and the GPR to determine the utility and caution in using PSQA with AC in SIMT. Because the average equivalent MLC field size is moderately correlated with the GPR, it was clear that the GPR drops significantly when the target is small, particularly below 10 mm.

The authors have nothing to report.