Forty PCAs, who received 16-fraction and 12-fraction CIRT at our center from October 2018 to January 2020, were selected from our clinical database. Syngo (V13B, Siemens, Germany) with a LEM was used for their clinical treatment planning. Thirty-eight patients received 16-fraction CIRT with 4.00 Gy(RBE) to 4.10 Gy(RBE) dose per fraction and two patients received 12-fraction CIRT with a dose per fraction of 4.50 Gy(RBE). Rectum dose-volume histograms (DVH) from Syngo were collected for validation purposes.
Framework of the study
Figure 1 describes the framework of the study. Two strategies were employed, the MKM LQ strategy and the LEM LQ strategy,
For the MKM LQ strategy, in Step 1.1 (LQ), the MKM rectum constraints for 16-fraction CIRT were converted to the MKM rectum constraints for 12-fraction, 8-fraction, and 4-fraction CIRTs based on a LQ model. This conversion was conducted in line with previous work by Uhl M et al. An a/b ratio of 3.9 Gy for the rectum  was used. In Step 1.2 (RBE conversion), three MKM rectum constraints were converted to the LEM rectum constraints for 12-fraction, 8-fraction, and 4-fraction CIRTs using a RBE-conversion model.
For the LEM LQ strategy, in Step 2.1 (RBE conversion), the MKM rectum constraints for 16-fraction CIRT were converted to the LEM rectum constraints for 16-fraction CIRT using the RBE-conversion model. In Step 2.2 (LQ), the LEM rectum constraints for 16-fraction CIRT were converted to the LEM rectum constraints for 12-fraction, 8-fraction, and 4-fraction CIRTs, based on the LQ model.
RBE-conversion model and LQ model
Our previous study  established a RBE-conversion model for 16-fraction CIRT, this study additionally developed three RBE-conversion models respectively for 12-fraction CIRT with MKM prescriptions 5.3 Gy(RBE)/fx, for 8-fraction CIRT with MKM prescription 7.0 Gy(RBE)/fx, and for 4-fraction CIRT with MKM prescription 10.0 Gy(RBE)/fx. These works were done with our research treatment planning system Raystation (8A, Raysearch, Sweden). Similarly, 10 patients were randomly selected from 40 enrolled patients. Their planning CTs and contouring from Syngo were exported to the Raystation (V8A, Raysearch, Sweden). The clinical target volumes included the prostates and the periphery seminal vesicles at high risk. The planning target volumes were generated based on the clinical target volumes by adding 10.0 mm in the left-right directions, 5.0 mm in the head-feet directions, and 3.0 mm in the superior-inferior directions. The process of model establishment in brief were that the MKM plans were generated and optimized to fulfill the MKM prescriptions, and then LEM plans were generated by recalculating the physical doses from MKM plans. Based on the isodose volumes from the MKM and LEM plans, a conversion curve for converting the MKM doses to LEM doses was established.
For the LQ model, the following equation was used:
where α/β is 3.9 Gy, d is the dose per fraction, and N is the total fractionation.
Rectum constraints for 16-fraction CIRT
NIRS published their rectum dose constraints for 16-fraction CIRT [10, 14] with MKM, which were percentage volume constraints. Choi  et al. from Centro Nazionale di Adroterapia Oncologica (CNAO), Italy, first converted NIRS constraints to LEM. Based on that, they additionally injected their experience and published their own constraints, which were absolute volume constraints. In this study, CNAO constraints were compared to the constraints from our previous study and then converted to the LEM rectum constraints for 12-fraction, 8-fraction, and 4-fraction CIRT based on our two strategies. To perform MKM LQ strategy on the CNAO constraints, their LEM constraints were converted backward to the corresponding MKM constraints based on our RBE-conversion model.
The LQ model is an analytical approach. However, the RBE-conversion model were based on only 10 patients. To evaluate its conversion uncertainty, the other 30 patients were used to generate a new RBE-conversion model for 16-fraction CIRT and compared to the counterpart which based on 10 patients.
Clinical follow-up data were collected and compared to the LEM rectum constraints for 16-fraction CIRT and 12-fraction CIRT. Patients were followed up by a radiation oncologist at one month, then every three months after CIRT completion in the first two years, every six months in the next three years, and yearly afterward. Late toxicity was evaluated according to the toxicity criteria of the Radiation Therapy Oncology Group and the European Organization for Research and Treatment of Cancer .