Twenty patients with early-stage NSCLC who underwent lung SBRT were enrolled in this study. Patient characteristics are summarized in Table 1. This study was approved by the Institutional Review Board (IRB No. B230237) at the Kobe University Hospital. The internal target volume (ITV) sizes ranged from 1.5 to 30.6 cm3, while the PTV sizes ranged from 7.6 to 68.7 cm3. All patients were immobilized using the Vaclok immobilization system (Engineering System Co., Ltd., Nagano, Japan) and underwent four-dimensional computed tomography (4DCT) using a real-time positioning management system (RPM, Varian Medical Systems, Palo Alto, CA, USA). Additionally, free-breathing planning 3DCT images were acquired using a CT scanner (Aquilion large bore; Canon Medical Systems, Otawara, Japan) with a resolution of 512 × 512 pixels for slice thickness of 1 mm. The ITV was defined based on the 4DCT on 3DCT. PTV was defined as ITV plus isotropic 5 mm 3D margin. The lungs, spinal cord, ribs, heart, and trachea were contoured as organs at risk (OAR). The planning organ at risk volume (PRV) was generated by adding a 3 mm isotropic margin to the spinal cord.

Varying PIL treatment plans were generated using a treatment planning system (Eclipse ver.15.6, Varian Medical Systems, Palo Alto, CA, USA) for TrueBeam STx with HD120 MLC, using a 6X-FFF beam. The prescribed dose of 48 Gy was delivered in four fractions to cover 95% of the PTV. Four plans with PILs set at 60%, 70%, 80%, and 90% were generated using two treatment planning techniques for each patient: d-VMAT [17] as a simplified plan and c-VMAT as a high-complexity plan. Therefore, eight plans were generated for each patient.

The c-VMAT treatment plan (181°–30° or 330°–179° partial coplanar two arc, collimator angles of 30° and 330°) with aperture shape controller (ASC) off for varying PIL was optimized. The dose-volume histogram (DVH) parameters for the GTV were adjusted to achieve varying PIL during the VMAT optimization. The dose constraints for the OAR, ring structure, and normal tissue objectives (NTO) remained fixed during all inverse optimizations for each patient to facilitate the comparison of treatment planning methods. The final dose distribution was calculated with an Anisotropic Analytical Algorithm (AAA) using a 1.25 mm calculation resolution and heterogeneity correction.

The d-VMAT treatment plan for varying PIL was reoptimized. The treatment planning workflow for d-VMAT is shown in Fig. 1. First, the DCA plan (181°–30° or 330°–179° partial coplanar two arc, collimator angles of 30° and 330°) was generated using the arc geometry tool. MLCs were fitted to the PTV with − 2, 0, 2, and 5 mm MLC margins for the 60%, 70%, 80%, and 90% PIL plans, respectively. Subsequently, a very high priority in the ASC was selected using the Photon Optimizer (PO) and the 3D volume dose distribution was calculated using the AAA ver.15.6.06 with heterogeneity correction. After creating the dose distribution for DCA, normalization was set to off, and the VMAT optimization was restarted. The option “use the current plan as an intermediate dose for optimization” was selected, and the process returned to MR Level 1 to continue the VMAT optimization calculation. The final dose distribution was calculated using grid sizes of the same dose calculation, employing the same algorithms as in c-VMAT.

Illustration of d-VMAT treatment planning workflow. The calculated DCA dose was used as the intermediate dose for VMAT optimization

The d-VMAT and c-VMAT plans for varying PIL were compared using several dose indices, including the dose to 98% of the PTV (D98%), dose to 2% of the PTV (D2%), minimum dose to the ITV (D100%), maximum dose to the PRV of the spinal cord, percentage of bilateral lungs receiving a dose equal to or exceeding 20 Gy (Lung V20Gy), and percentage of bilateral lungs receiving a dose equal to or exceeding 5 Gy (Lung V5Gy). Dose constraints for the ribs were excluded due to the overlap between the PTV and the ribs in some cases. Additionally, in this study, all registered cases had peripheral lung cancer. As the doses to the heart, esophagus, and great vessels were sufficiently low, they were excluded from the evaluation. Target conformity was assessed using the Paddick conformity index (CI) [22]. The CI is defined by the following equation:

$$\text= \frac}_}^} \times \text},$$

where TVPIV denotes the target volume covered by the prescribed isodose, TV is the PTV volume, and PIV is the volume covered by the prescribed isodose. The dose gradient was evaluated using a gradient index (GI) [23] defined as follows:

where V50% corresponds to the volume covered by a dose that is equal to or greater than 50% of the prescribed dose. The dose gradient for the d-VMAT plan was assessed and compared with that for c-VMAT. Moreover, we assessed the relationship between the PTV size and GI for each plan and PIL. Plan complexity was assessed using the number of total monitor unit (MU) and the modulation complexity score for VMAT (MCSv) [24]. We calculated MCSv using the Eclipse Scripting API (ESAPI). Additionally, we measured the beam-on time for d-VMAT plan and c-VMAT plan for 70% PIL. The Wilcoxon signed-rank test (p < 0.05, considered statistically significant) was employed to assess the statistical significance of the target and OAR dose indices, CI, GI, and plan complexity parameters (MU and MCSv).