A 2πsolid angle-based heuristic framework for non-coplanar VMAT in multiple brain metastases.

Objective.This study proposes a 2πsolid 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 2πsolid angle space and to automatically identify non-coplanar trajectories minimizing normal brain exposure. Subsequently, a blocking factor-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.Ptsdachieved automated trajectory selection with plan quality comparable toPref. Values are presented as median (P25-P75). Compared withPref,Pcomimproved 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)].Pcomalso reduced normal brain tissue (NBT)V12Gy, MU, and 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 showedX-axis narrowing [129.75 (110.60-146.35) to 101.91 (83.34-120.20) mm] andY-axis expansion [98.70 (80.13-105.86) to 119.17 (103.38-133.48) mm] inPcom. AllPcom-versus-Prefcomparisons 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.