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 final 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-field generation optimization (the first SSO optimization), thrice sub-field alignment optimizations (the second to the fourth SSO optimization) and once sub-field selection and merger optimization(the fifth SSO optimization). In version 5.4, the sub-field alignment optimization has been upgraded from a fixed number of 3 times to a user-defined time. It has promoted the change of planning design efficiency and plan quality.
Since each SSO optimization is equivalent to an iterative optimization of a large volume, the formula of dose influenced by the number of iterations proposed by Llacer J et al. in 2001 can be referred to derive the formula (2) of dose influenced 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 influence rate will approach 0, and the closer it approaches 0, the more uniform dose distribution will be. Therefore, smaller value of the influence rate is the recommended and accepted value scheme of SSO.
Note: Where ∆σ is the influence rate of SSO on dose; α is the dose filtration factor; j and θ is the current beam and the adjacent unit; β is the dose receiving weight of the adjacent unit; NSSO is the optimization times of SSO; Dj is the dose of target to be evaluated; Dθ 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 influence 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 PGTV70 target area, and SSO5 has a small amount of spillover, while SSO7 and SSO10 had no 70Gy dose spillover and were tightly wrapped around PGTV70. 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 in 2004, the number of iterations and initial intensity in intensity modulation optimization have guiding significance 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 reflected 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-field shapes at 4 same angles, the sub-field alignment area gradually decreased with the increase of the number of SSO optimization, and a few isolated island sub-fields 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-field would be a big challenge to the pass rate of clinical plans. However, in this study, all the ArcCheck verification 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 significant difference, it could be attributed to the same restriction on the number of sub-fields for all plans in Monaco TPS parameter setting. While MU# showed a decreasing trend, there were two main reasons. Comparison of sub-field shape at same angle, with the number of SSO optimization increased, the sub-field 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#. 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 significantly improved compared with that of SSO7 group, and it did not get a good plan quality-speed-benefit ratio. Besides, the high number of SSO optimization required better hardware support for Monaco services, especially memory for floating-point storage and release.