The Inuence of SSO on the Optimization Result of Nasopharynx Carcinoma Plan

To study the inuence of Monaco 5.4 treatment planning system (TPS) on the dosimetry of radiotherapy for nasopharynx carcinoma (NPC) under the condition of different segment shape optimization (SSO) times. Fifteen patients with T 3-4 N 0-2 M 0 stage nasopharyngeal carcinoma were enrolled, and each case was designed with SSO of 3, 5, 7 and 10 times respectively. The dose results of the target area and the major organs at risk (OAR) were statistically analyzed by DVH statistics; moreover, the isodose lines of 70Gy, 60Gy and 54Gy were intercepted at the same plane in the transverse, coronal and sagittal views and the segment shapes were compared at the angle of 30°, 120°, 240° and 330° in beam eye view (BEV); In addition, optimization time (OT), delivery time (DT), segments# and MU# were obtained and analyzed by optimization console; the plans were veried and analyzed by using ArcCheck phantom.

obtain the most suitable shape of the sub-elds for the plan through several times of segments shape optimization (SSO), and each SSO contains several inter loops and outer loops. In retrospect of 100 cases of nasopharyngeal carcinoma from 2019 to 2020, we interpreted the optimization process by the optimization console function, and we found that Monaco TPS 5.1 version was xed for 5 times of SSO. However, planning for nasopharyngeal carcinoma is one of the most complex types of radiotherapy plan design [5,6,7,8] . The nasopharynx is adjacent to important normal tissues such as brainstem, spinal cord, lens and parotid glands, in the meanwhile, the target area is usually large and irregular [9,10,11] .
Therefore, how to design higher quality plan more e ciently has become an important research topic. In Monaco TPS 5.4 version, the optimization of SSO was upgraded from xed times to autonomous de nition, which led to whether different SSO settings would have an impact on the optimization results. In this paper, the differences of different SSO plans were compared, so as providing a reference for clinical design of NPC plans.

Data
Case selection and plan design: 15 patients with T 3 − 4 N 0 − 2 M 0 NPC were enrolled in the study. Axial cinematic scanning was performed in free breathing condition, the CT rotation time was 0.8 seconds, the axial thickness was 2.5 mm, the voltage was 120 KV and the current was 350 mAs. All images were uploaded to Monaco 5.4 TPS, and the target area was contoured by radiotherapy physicians with more than 5 years working experience in accordance with NCCN2020 NPC treatment guidelines, and the target area was reviewed by chief physicians with more than 10 years working experience. The plan was designed by a senior clinical physicist with more than 10 years of Monaco TPS experience.

Plan Design
Dual full volumetric modulated arc therapy (VMAT) can generate precise conformal dose distribution and was used in all the plans [12] . Under condition of the functions and TPS parameter settings remain unchanged, XVMC optimization was performed for 3, 5, 7 and 10 times of SSO; a fraction dose of 2Gy, a fraction of 30, and the dose constraint of OARs was carried out according to QUANTEC (Quantitative Analysis of Normal Tissue Effects in the Clinic) report. The dose results, conformity index (CI) and homogeneity index (HI) of target area and major OARs of different SSO plans were statistically analyzed by DVH statistics [13] . The multi-leaf collimator (MLC) shapes were intercepted and compared at 30°, 120°, 240° and 330° in the BEV interface.
The dose structures of PGTV 70 and PTV 60 target areas were established, and the prescription dose coverage rates were calculated by Formula (1). Since 54Gy covers the structure of PTV60 and PTV54 target areas at the same time, the dose structure of 54Gy was cut into two dose structures, PTV 60 − 54Gy and PTV 54 − 54Gy , at the interface layer of the two target areas, for calculation and evaluation respectively; transverse, coronal and sagittal dose nephograms of 70Gy, 60Gy and 54Gy were intercepted and compared in the same image layer; OT, DT, segments# and MU# were obtained and analyzed by optimization console. The plan test environment is a standard HP Z8 desktop server equipped by Elekta.

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Where R(%) is the prescription dose coverage rate, V Gy (cm 3 ) is the volume of the assessed dose coverage, and V Target (cm 3 ) is the volume of the assessed target area.
Plan Veri cation 60 cases in 15 groups were imported into ArcCheck for plan veri cation, and the results of plan veri cation were statistically analyzed.

Statistical analysis methods
Data was collected by SPSS 22.0, and paired t-test was performed on the dose results, P < 0.05 was considered statistically signi cant. In Monaco 5.1 TPS, SSO5 was the default value, so the results of other groups were matched with those of SSO5 group by paired t-test.

Comparison of dose results between groups
The target dose results (Table 1) and the major OARs dose results data ( Table 2) of 60 cases in 15 groups with the same parameters except SSO were read by Monaco TPS DVH statistics function. Under the calculation method of target area priority, PGTV 70 and PTV 60 reached similar results in the percentage of prescription dose coverage, while PTV 54 had signi cant difference; in the dose statistics of D 2 and D mean in each target area, the SSO3 result was signi cantly higher than that of other groups; in comparison of HI and CI results, CI results showed signi cant difference, and HI results showed different performance in different target areas. In the statistical analysis of the major OARs dose results, In the statistical analysis of the major OARs dose results, the maximum dose and volume dose optimization results gradually decreased with the increase in the number of SSOs, while the results of the SSO7 group and the SSO10 group were similar.  Figure 1. In the 70Gy dose nephogram distribution, there was dose spillover outside the PGTV 70 target area in SSO3 and SSO5 groups, and SSO3 group was more signi cant than SSO5 group; in the dose nephogram distribution of 60Gy and 54Gy, dose curve gradually tightened at the three views with the increase of SSO.
Statistics and comparative analysis were performed on the prescription dose coverage rates of PGTV 70 and PTV 60 and the dose coverage rates of target areas PTV 60-54 and PTV 54-54 in the plan, as shown in Figure 2.
There were signi cant differences in dose coverage rates among SSO3, SSO5 and SSO7 groups, in the meanwhile, although SSO10 group had more advantages than SSO7 group, the differences between groups had been signi cantly reduced.
Comparison of sub-eld shape between groups In the BEV interface, sub-eld shapes of different SSO groups at 30°, 120°, 240° and 330° were captured, as shown in Figure 3. In the four different angles, the shape of the sub-eld was similar, but the combined volume of the sub-eld decreased with the increase of SSO, especially in the neck part.

Comparison of characteristic parameters of Monaco TPS between groups
The number of segment#, accelerator monitor units (MU#), optimization time (OT), and delivery time (DT) was obtained from the console window of Monaco 5.4 TPS, as shown in Figure 4. With the increase of SSO, segment# and DT increased, while MU# decreased, but the amplitude was very small; in contrast, OT changed signi cantly, the difference between adjacent groups was more than 100s, besides, the difference between SSO3 and SSO10 groups was more than 500s.

Comparison of validation results between groups
Each SSO group plans were veri ed by using ArcCheck, and results were analyzed by using SNC Patient validation analysis software under 3%-3 mm Gamma [14] , as shown in Figure 5. Results of all the plans in each group met the clinical requirements, and there was a little differenced between different SSO plans in the same group.

Discussion
XVMC algorithm is the core of Monaco TPS. The optimization processes of plan can be obtained and analyzed by the optimization console function. It is found that the whole optimization process is through several times of SSO optimization to get the nal dose distribution results. Each SSO is an optimization cluster and it is similar to a large volume iterative optimization, which contains several sub-optimizations of inter loops and outer loops. The quasi -annealing algorithm is followed within each optimization cluster and the quasi -genetic algorithm is followed between clusters [15,16,17] .
In version 5.1, the SSO optimization process consists of once sub-eld generation optimization (the rst SSO optimization), thrice sub-eld alignment optimizations (the second to the fourth SSO optimization) and once sub-eld selection and merger optimization(the fth SSO optimization). In version 5.4, the sub-eld alignment optimization has been upgraded from a xed number of 3 times to a user-de ned time. It has promoted the change of planning design e ciency and plan quality.
Since each SSO optimization is equivalent to an iterative optimization of a large volume, the formula of dose in uenced by the number of iterations proposed by Llacer J et al. in 2001 can be referred to derive the formula (2) of dose in uenced by the number of SSO [18,19] . When the accumulated dose of the current beam being evaluated is closer to the accumulated dose of adjacent units, the value of the in uence rate will approach 0, and the closer it approaches 0, the more uniform dose distribution will be. Therefore, smaller value of the in uence rate is the recommended and accepted value scheme of SSO [20] .
Note: Where ∆σ is the in uence rate of SSO on dose; α is the dose ltration factor; j and θ is the current beam and the adjacent unit; β is the dose receiving weight of the adjacent unit; N SSO is the optimization times of SSO; D j is the dose of target to be evaluated; D θ is the dose of the adjacent unit.
The statistical analysis results of dose results in this study indicated that both the assessment values of the target area and the major OARs were improved to varying degrees with the increase number of SSO, that is, the difference between the dose of the evaluated grid and the dose of the adjacent grid gradually decreased with the increase in the number of SSO, and the in uence rate value obtained according to formula (2) will gradually decrease; it follows that the increase in the number of SSO will promote the development of plan results towards better plan quality. In the analysis of dose nephograms at same layers, the same conclusion can be drawn. Where SSO3 has obvious 70Gy dose spillover outside the structure of PGTV 70 target area, and SSO5 has a small amount of spillover, while SSO7 and SSO10 had no 70Gy dose spillover and were tightly wrapped around PGTV 70 . In addition, the same trend was also found in the difference comparison of dose coverage in the target area.
In the two studies conducted by Llacer J et al. in 2003 and, the number of iterations and initial intensity in intensity modulation optimization have guiding signi cance for the quality of the plan, however, when the number of iterations is large enough to a certain value, the plan has reached the optimum, and the plan results cannot be further optimized by continuing calculation [21,22] . On the contrary, small and high frequency changes with low eigenvalues appear, which is not conducive to the implementation of treatment plans. SSO3 ~ SSO10 plans in this study, the results of both the target area and the major OARs, or dose nephograms at same layers, have re ected the increase of the number of SSO optimization times on improving the quality of plan, but there had no bottleneck or small and high frequency changes with low eigenvalues to SSO optimization, thus it can be seen that 10 times of SSO optimization did not reach the limit of XVMC optimization. More times of SSO optimization will help improve the quality of the plan further. However, the indicators of the target area and major OARs of SSO7 and SSO10 are pretty close, and the dose nephograms distribution is similar. Therefore, more times of SSO optimization will have less improvement on the quality of NPC plan, and there may be optimization bottleneck of small and high frequency changes with low eigenvalues. In addition, as the number of SSO optimization increased from 3 to 10 times, in the comparison of sub-eld shapes at 4 same angles, the sub-eld alignment area gradually decreased with the increase of the number of SSO optimization, and a few isolated island sub-elds appeared in the 10 times of SSO optimization. Therefore, in order to meet the requirements of complex NPC plans, the positioning accuracy of MLCs and the stability of gun current needed to be higher, and the emergence of isolated island sub-eld would be a big challenge to the pass rate of clinical plans. However, in this study, all the ArcCheck veri cation results of the 3-10 times of SSO optimization met the acceptance criteria of clinical plan, and the results were similar. Therefore, the 3-10 times of SSO optimization were all suitable for the application of NPC clinical plan.
In the comparison of NPC plans with different SSO optimization times, although segment# and DT showed an increasing trend, there was no signi cant difference, it could be attributed to the same restriction on the number of sub-elds for all plans in Monaco TPS parameter setting. While MU# showed a decreasing trend, there were two main reasons. Comparison of sub-eld shape at same angle, with the number of SSO optimization increased, the sub-eld alignment area decreased, and the irradiation area decreased, thus resulting in the decrease of the demand for MU#; In addition, as the number of SSO optimization increased, the calculation accuracy of the particle mass stop ratio increased, that is, the energy of per unit particle was more fully utilized, thus reducing the demand for MU# [23] . Furthermore, it would help to decrease secondary cancer risk (SCR) in VMAT due to low doses to healthy tissues induced by scatter and leakage radiation from gantry head [24,25,26,27] . The statistical results of OT showed the most obvious difference, and the difference between adjacent groups was greater than 100s. The average OT of SSO10 group was more than 1000s, but the improvement effects of SSO10 group on the plan quality was not signi cantly improved compared with that of SSO7 group, and it did not get a good plan quality-speed-bene t ratio. Besides, the high number of SSO optimization required better hardware support for Monaco services, especially memory for oating-point storage and release.

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In brief, for the clinical plan design of NPC, more SSO optimization times will help to improve the plan quality.
However, under the premise of balancing e ciency of the plan design and quality of the plan, 7 times of SSO optimization are recommended. The datasets used and analysed during the current study are available from the corresponding author on reasonable request.   Different SSO plan sub-eld shape alignment Note: A~D are SSO3~SSO10 plan groups, each group is 30°, 120°, 240° and 330° from the left.

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