A 2π solid angle-based heuristic framework for non-coplanar VMAT in multiple brain metastases

This study proposes a 2π solid angle-based heuristic framework for non-coplanar volumetric modulated arc therapy (VMAT) in patients with multiple brain metastases (MBM) to automate treatment angle selection. Approach: Fifty-two patients with MBM (2-8 targets) were retrospectively included. A hybrid heuristic framework was constructed: first, a volume-weighted cumulative tumor-skin distance (VW-CTSD) metric was introduced to quantify geometric requirements in the 2π solid angle space and to automatically identify non-coplanar trajectories minimizing normal brain exposure. Subsequently, a blocking factor (BF)-based sub-arc segmentation and collimator-angle selection strategy determined the sub-arc splitting and collimator angles. Using 30 Gy/5 fractions, three plans were generated for each patient: manual expert planning (Pref), VW-CTSD-guided trajectory selection alone (Ptsd), and the proposed combined heuristic strategy (Pcom). Dosimetric metrics and plan parameters were compared. Main results: All plans met clinical goals. Ptsd achieved automated trajectory selection with plan quality comparable to Pref. Values are presented as median (P25-P75). Compared with Pref, Pcom improved CI [0.86 (0.85-0.89) to 0.89 (0.85-0.91)] and reduced GI [3.37 (3.17-3.79) to 3.09 (2.74-3.48)]. Pcom also reduced normal brain tissue (NBT) V12Gy, MU, and complexity metric (CM) from 92.45 (62.54-141.46) to 83.57 (50.30-125.10) cc, from 2391 (2144-2527) to 1938 (1845-2085), and from 0.22 (0.21-0.24) to 0.20 (0.19-0.21), respectively. Control-point aperture analysis showed X-axis narrowing [129.75 (110.60-146.35) to 101.91 (83.34-120.20) mm] and Y-axis expansion [98.70 (80.13-105.86) to 119.17 (103.38-133.48) mm] in Pcom. All Pcom-versus-Pref comparisons for these metrics were statistically significant (P < 0.001). Significance: The proposed combined heuristic framework reduced NBT dose, GI, MU, and CM, suggesting its potential as a practical automated approach for non-coplanar VMAT angle selection in patients with MBM.