Modulation indices and plan delivery accuracy of volumetric modulated arc therapy

Abstract Purpose We evaluated the performance of various modulation indices (MI) for volumetric modulated arc therapy (VMAT) to predict plan delivery accuracy. Methods The specific indices evaluated were MI quantifying the mechanical uncertainty (MI t), MI quantifying the mechanical and dose calculation uncertainties (MI c), MI for station parameter optimized radiation therapy (MISPORT), modulation complexity score for VMAT (MCS v), leaf travel modulation complexity score (LTMCS), plan averaged beam area (PA), plan averaged beam irregularity (PI), plan averaged beam modulation (PM), and plan normalized monitor unit (PMU) to predict VMAT delivery accuracy. By utilizing 240 VMAT plans generated with the Trilogy and TrueBeam STx, Spearman's rank correlation coefficients (r) were calculated between the MIs and measures of conventional methods. Results For the Trilogy system, MI c showed the highest r values with gamma passing rates (GPRs) (r = −0.624 with P < 0.001 for MapCHECK2 and r = −0.655 with P < 0.001 for ArcCHECK). For TrueBeam STx, MI c also showed the highest r values with GPRs (r = −0.625 with P < 0.001 for the MapCHECK2 and r = −0.561 with P < 0.001 for the ArcCHECK). The MI t and MI c showed the highest r values to the MLC position errors for the Trilogy and TrueBeam STx systems (r = 0.770 with P < 0.001 and r = 0.712 with P < 0.001, respectively). The PA showed the highest percent of r values (P < 0.05) to differences in the dose‐volume parameters between original VMAT plans and actual deliveries for the Trilogy systems (30.9%). Both the MI t and MI c showed the highest percent of r values (P < 0.05) to differences in the dose‐volume parameters between original VMAT plans and actual deliveries for the TrueBeam STx systems (31.8%). Conclusion To comprehensively review the results, the MI c showed the best performance to predict the VMAT delivery accuracy.


| INTRODUCTION
Advanced radiotherapy techniques, such as intensity-modulated radiation therapy (IMRT) and volumetric modulated arc therapy (VMAT), facilitate conformal deliveries of prescription doses to target volumes, while minimizing doses to normal tissue proximal to the target volumes with intensity modulation. 1,2 Moreover, the intensity modulation of IMRT and VMAT enables the generation of steep dose gradients between the target volumes and particular organs at risk (OARs) close to the target volumes. 3 This could reduce radiotherapyinduced complications, as well as escalate the prescription doses to increase the therapeutic effect of radiotherapy. 3 Especially, VMAT can rapidly deliver equal or superior dose distributions, compared to those of IMRT by simultaneous modulations of multi-leaf collimator (MLC) movements, gantry speeds, and dose-rates. 1,3 However, the intensity modulation increases the uncertainty of the planned dose delivery to a patient during actual treatment, which is an adverse effect of IMRT or VMAT. 4 Since high intensity modulation is involved in the complicated mechanical movements of the linac, such as MLC movements, and the frequent use of small or irregular fields with relatively low dose calculation accuracy, there might be a clinically significant discrepancy between the intended treatment plan and its actual delivery in highly modulated IMRT or VMAT plans. [5][6][7][8] In this respect, patient-specific pre-treatment quality assurance (QA) according to international guidelines is highly recommended to verify plan delivery accuracy before patient treatment for both IMRT and VMAT. 4,[9][10][11] As a patient-specific pre-treatment QA, 2D gamma analysis between the measured planar dose distributions with 2D dosimeters and the calculated dose distributions in the treatment planning system (TPS) is widely adopted in clinical settings. 12,13 Although gamma analysis is a practical and convenient method to evaluate the similarity of two distributions, recent studies pointed out the clinical irrelevance of the gamma passing rates. 14,15 As an alternative method for patient-specific pre-treatment QA according to gamma analysis, several studies recommended that the recorded log files in the linac control system during beam delivery be analyzed. 11,14,[16][17][18] However, this method has an intrinsic disadvantage in that it is dependent on the linac control system. In addition, it is hard to determine the clinically relevant tolerance levels for each VMAT mechanical parameter for the linac log file analysis method. On the other hand, several studies suggested a modulation index as a patient-specific pre-treatment QA method by quantification of the modulation degree of VMAT plans. 5,6,8,19,20 The modulation index is advantageous in terms of efficiency since it can be calculated at the planning level, which reduces resources in the clinic. Li and Xing suggested a modulation index (MI SPORT ) by quantifying movements of MLCs weighted by segmental monitor unit (MU) for VMAT. 5 They did not demonstrate the performance of MI SPORT as a pre-treatment QA method for VMAT but only used MI SPORT as a tool to suggest station parameter optimized radiation therapy (SPORT). Masi et al. suggested the modulation complexity score for VMAT (MCS v ) and leaf travel modulation complexity score (LTMCS). 6 These indicators were modifications of the modulation complexity score (MCS), which was originally suggested by McNiven et al. to evaluate the modulation degree of IMRT plans. 6 Du et al. suggested several modulation indices for VMAT, which were plan averaged beam area (PA, average area of beam apertures), plan averaged beam irregularity (PI, deviations of the aperture shapes from a circle), plan averaged beam modulation (PM, extent of a large open field being broken into multiple small segments), and plan normalized monitor units (PMU, MU normalized by the fractional prescription dose). 19 The modulation indices by Du et al. focused on the calculation of dose uncertainties due to frequent use of irregular or small beam segments rather than using mechanical uncertainties during plan delivery. We also suggested a modulation index, which evaluates the modulation of VMAT mechanical parameters (MI t ) by analyzing the speed and acceleration of MLC movements, gantry rotation variations, and dose-rate variations. 8 Furthermore, we suggested a modulation index that considers both the mechanical parameter modulations and irregularity of the beam aperture shapes defined by the MLCs with the thinning algorithm (MI c ). 20    Before VMAT dose distribution measurements, the output of the linacs were calibrated according to the American Association of Physicists in Medicine (AAPM) Task Group (TG) 51 protocol. 21 Both the MapCHECK2 and the ArcCHECK arrays were calibrated according to the manufacturer guidelines before performing VMAT dose distribution measurements. For the local gamma evaluation, gamma criteria of 3%/3 mm, 2%/2 mm, 2%/1 mm, 1%/2 mm, and 1%/1 mm were used. Doses equal to or <10% of the prescription dose was ignored when calculating gamma passing rates. 4,10 SNC software (Sun Nuclear Corporation, Melbourne, FL, USA) was used to calculate local gamma passing rates for both the MapCHECK2 and Arc-CHECK measurements. 2.E | Dose-volumetric parameter differences between the original VMAT plans and the VMAT plans reconstructed with log files

2.D | Log file analysis
The DICOM-RT formatted log files were imported into the Eclipse system, and dose distributions were calculated in the patient CT images used for generating the original VMAT plan. When calculating dose distributions from the log files, the dose calculation grid size was kept identical to that of original VMAT plan calculation (1 mm).
Clinically relevant dose-volumetric parameters under previous studies and guidelines were calculated with the original VMAT plan, as well as VMAT plans reconstructed from the log files. 22,23 The differences in the dose-volumetric parameters between the dose distributions reconstructed with the log files and those of the original VMAT plans were acquired. Since there were two sets of log files (Map-CHECK and ArcCHECK2 measurements) for each VMAT plan, two sets of differences in the dose-volumetric parameters were acquired.
We averaged those differences for each VMAT plan. For H&N VMAT plans, a total of 48 dose-volumetric parameters were examined (Table S1). For prostate VMAT plans, a total of 29 dose-volumetric parameters were examined for both primary and boost plans (Table S1). For brain, liver, and spine VMAT plans (not SABR), 27, 22, and 24 dose-volumetric parameters were investigated, respectively (Table S1). For lung, spine, and liver SABR VMAT plans, 32, 17, and 33 dose-volumetric parameters were examined, respectively (Table S1). A total of 309 dose-volumetric parameters were examined in this study.

2.F | Calculation of modulation indices
In this study, a total of nine modulation indices were calculated,

2.G | Correlation analysis
To evaluate the performance of the previously suggested modulation indices, Spearman's rank correlation coefficients (r) were calculated between the modulation index values and the conventional patientspecific pre-treatment QA values, such as gamma passing rates, the differences in the mechanical parameters between calculation and delivery, and dose-volumetric parameter differences between the original VMAT plans and the VMAT plans reconstructed from the log files. To examine the statistical significance of the values of r, we also calculated P values for each value of r. Correlations of each modulation index were analyzed against the local gamma passing rates with various gamma criteria, the differences in the mechanical parameters (MLC positions, gantry angles, and delivered MUs) between calculation and plan delivery, and the differences in the dose-volumetric parameters between the original VMAT plans and the VMAT plans reconstructed from the log files. For the dose-volumetric parameter differences, because a large number of dose-volumetric parameters were examined in this study (a total of 309 dosevolumetric parameters), we just calculated the percent of r values with corresponding P < 0.05, which was regarded as statistically significant in this study.

3.A | Values of the calculated modulation indices
The calculated modulation indices are shown in Table 1.
As VMAT modulation increases, it is known that the values of MI t , MI c , MI SPORT , PI, PM, and PMU increase while the values of MCS v , LTMCS, and PA decrease. 5,6,8,20 For the VMAT plans with the C-series linac, H&N VMAT plans showed the highest modulation according to every modulation index

3.B | Local gamma passing rates
The local gamma passing rates with various gamma criteria of VMAT plans for various treatment sites as measured with the MapCHECK2 and ArcCHECK are shown in Table 2.
For the VMAT plans with C-series linac, the MapCHECK2 measurements indicated that the H&N plans showed the lowest gamma passing rates with 3%/3 mm and 2%/2 mm, while the prostate primary plans showed the lowest gamma passing rates with the rest of the gamma criteria. However, the ArcCHECK measurements indicated that the H&N VMAT plans consistently showed the lowest gamma passing rates, regardless of the gamma criteria. Both the MapCHECK2 and the ArcCHECK measurements indicated that the local gamma passing rates of the liver plans were the highest in general. The gamma passing rates with the MapCHECK2 array were generally coincident with those from the ArcCHECK array.  3.C | Differences in the mechanical parameters between the original VMAT plans and the log files The mechanical parameter differences between the original VMAT plans and the log files recorded during the VMAT deliveries are shown in Table 3.
For the plan delivery with the C-series linac, the MLC positioning errors were largest when delivering the H&N VMAT plans, while those differences were the lowest when delivering prostate boost plans. The MU delivery errors were largest for spine VMAT plans, while they were smallest for prostate plans.  delivery errors in the SABR VMAT plans with the TrueBeam STx system were generally larger than those in the C-series linac system.

3.D | Correlation between the local gamma passing rates and the modulation indices
Spearman's rank correlation coefficients between the modulation index values and the local gamma passing rates acquired with the Cseries linac are shown in Table 4 with their corresponding P values.
Only r values with P < 0.05 are shown. Spearman's rank correlation coefficients between the modulation index values and the local gamma passing rates acquired with the TrueBeam STx system are shown in Table 5, along with their corresponding P values. Only r values with P < 0.05 are shown.
T A B L E 3 Differences in mechanical parameters between the original VMAT plans and log files during plan delivery    decreased in this study. 5,6,8,19,20 However, for the PA, the opposite tendency was observed in this study to that of a previous study by Du et al., showing that an PA values increased with modulation degree. 19 This was caused by the discordance between the average sizes of the beam apertures of the VMAT plans and the modulation degree of VMAT plans because VMAT plans with various target volumes were analyzed in this study. For example, the H&N plans showed higher modulation than the others, while the average beam apertures were larger than the others in order to accommodate their large target volumes. In the case of lung SABR, the modulation degree was low owing to generally round-shaped target volumes of the lung SABR and relatively large distance between OARs and the target volumes, while the target volume sizes were small. Therefore, the average beam aperture sizes of the highly modulated VMAT VMAT plans showed the lowest modulation. 5,6,8,19 The gamma passing rates with the MapCHECK2 array showed similar results to those with the ArcCHECK array, and both showed the lowest gamma passing rates in the H&N VMAT plans in general.

3.E | Correlation between the mechanical parameter differences and the modulation indices
To review the correlations of the modulation indices with the local gamma passing rates, MI c showed the strongest correlations with the gamma passing rates for both the MapCHECK2 and ArcCHECK arrays, as well as in the C-series linac and TrueBeam STx systems.
The MI c seems potentially to be an alternative to gamma evaluation.
The gamma passing rates with the C-series linac showed more statistically significant r values with the modulation indices than did the gamma passing rates with the TrueBeam STx system. Since the TrueBeam STx delivers VMAT plans more accurately using the integrated control system (i.e. supervisor), than did the C-series linac, the delivery errors of the TrueBeam STx might be smaller than those of the C-series linac. 24 This can also be seen in the mechanical errors from the log files. The smaller delivery errors from the TrueBeam STx system resulted in higher gamma passing rates, as shown in Table 3. Therefore, although the modulation degree of VMAT plans with TrueBeam STx changed significantly, the delivery errors were smaller with the TrueBeam STx than those with the C-series linac.
Therefore, it became hard to find correlations between the modulation index and gamma passing rates and then modulation index should be used carefully with the TrueBeam STx system.  the MLC positioning errors of TrueBeam STx (r = 0.712 with P < 0.001), which was consistent with previous studies. 20 The MI t and MI c indices seem to be used to predict mechanical errors during VMAT delivery at the planning level.
To review the correlations of modulation indices with the differences in the dose-volumetric parameters between the original VMAT plans and the VMAT plans reconstructed from the log files, the opposite tendency was observed between the result of C-series linac and that of the TrueBeam STx system. The percent values of statistically significant correlation coefficients for correlations between MI t and MI c with the dose-volumetric parameter differences were lower than those for other modulation indices in the C-series linac. However, the opposite tendency was observed for the TrueBeam STx system. Further study may reveal the cause of this opposite tendency, and these studies will be performed in the future.
Unfortunately, we cannot analyze the clinically unacceptable VMAT plans in this study. Every VMAT plan showed gamma passing rates higher than 90% for global gamma passing rates with a gamma criterion of 2%/2 mm (data are not shown), which was the recommended tolerance level for VMAT by Heilemann et al. 10 Therefore, we cannot determine the tolerance levels for each modulation index evaluated in this study. By utilizing clinically unacceptable VMAT plans, we could recommend tolerance levels for various modulation indices in the future. Furthermore, a multi-institutional study will be performed in the near future to comprehensively assess the performance of modulation indices in relation to the measures of VMAT delivery accuracy with a gamma criterion of 3%/2 mm recommended by the AAPM TG 218 report. 26 To comprehensively review the correlations between the previ- Therefore, MI c seems to be the most appropriate indicator for representing the accuracy of VMAT delivery.

| CONCLUSION
In this study, we comprehensively evaluated various types of modulation indices reported in the previous studies by correlation analysis.
To review the correlations between modulation indices and the measures of VMAT delivery accuracy comprehensively, MI c showed best capability to predict the accuracy of VMAT plan delivery. The MI c index demonstrated potential to support or to be an alternative to pre-treatment patient-specific QA for VMAT in this study. Since the modulation indices, including the MI c , can be calculated at the planning level, adopting the modulation indices in the clinic to verify VMAT plans is expected to reduce resources in busy clinical settings.

CONFLI CT OF INTEREST
The authors have no conflict of interest to declare.