## 4 Discussion  
We would like to emphasize that the applicator displacements during brachytherapy treatment for cervical cancer led to radical changes in dose distribution [54]. With the advent of MRI-guided brachytherapy, the opportunity to improve outcomes by increasing the target dose while minimizing the dose to the OAR is essential for the management of locally advanced cervical cancer. Hence, the dose-delivery uncertainty by applicator displacements is of significant relevance within the dose distribution. Many studies have demonstrated that applicator displacement is a problem of critical importance. [PERSON] et al. [22] quantified the dosimetric impact of applicator displacements and applicator reconstruction uncertainties through simulated planning studies of virtual applicator shifts. In addition, [PERSON] et al. [21] reported 2 mm errors in applicator reconstruction. However, the reconstruction approach was rather limited due to the finite slice thickness, resulting in several sources of uncertainty. [PERSON] et al. [29] developed a real-time applicator position monitoring system with a 1 mm accuracy during long wait times between imaging and treatment. Nevertheless, the real-time monitoring system still depends on the accuracy of distance computability between the camera and marker. Furthermore, the applicator shift and intra- and inter-fractional organ movement are inevitable, and this leads to errors in fractional dose delivery. [PERSON] et al. [16] found geometrical shifts as large as \(6\pm 7\) mm in the posterior direction during PDR delivery. Several studies have previously reported such movements relative to target and organs [16; 17; 18; 28]. While these efforts may reduce required dose-delivery errors, there will always remain residual uncertainties. As mentioned in the above sections, the variations of the DVH parameter due to the applicator displacements could have occurred (Figure 3). The incorporation of applicator displacement worst-case scenarios into the robust optimization with the use of a MAD function may enable the robust optimization approach to minimize the dose delivery uncertainty in a single plan approach for HDR brachytherapy treatment planning. [PERSON] et al. [55] found the importance of adaptive planning method for cervical cancer HDR brachytherapy; however, a simulation device is not routinely available in some institution. Hence, a robust optimization method with a multi-objective genetic algorithm in a single plan approach for minimizing dose delivery uncertainty by potential applicator displacements was proposed. In our study, the robustness of the treatment plan was quantified using the MAD function and could have found the optimal solution of the area of DVH bands defined by worst-case scenarios. We demonstrated the feasibility of using our robust optimization strategy to minimize the dose-delivery uncertainty by potential applicator positional displacements. The dwell positions and times were determined in a way that optimally improved the plan quality according to GEC-ESTRO Gyn Working Group recommendations. Compared to manual plan approaches, our robust optimization method resulted in a reduced standard deviation on DVH parameters while maintaining the target-dose coverage and sparing the OAR, as well as reducing EQD2 in most of the cases. Similarly, the EQD2 and the standard deviation of DVH parameters of robust optimized plan in the Table 1 showed their values to be lower compared to those of the inverse plan without considering applicator displacement assumption. The resulting robustness plans from our strategy might be worth considering according to EMBRACE protocol guidance. Evaluation of the effects of irregularly shaped targets on robust optimization outcomes shows that it was difficult to find an optimized plan for the target with a higher asymmetric ratio because the dose distribution of brachytherapy sources was symmetrically isotropic.