Distance-adaptive geometric margins for residual rotational uncertainty in single-isocenter multitarget stereotactic radiosurgery

Abstract Background and purpose Single isocenter multitarget stereotactic radiosurgery improves efficiency for multiple brain metastases, but residual rotational uncertainty increases with target-to-isocenter distance, raising the risk of geometric miss and coverage loss. We derived an analytic model for rotational error propagation and a distance-adaptive geometric margin strategy for risk stratification and quality assurance. Materials and methods Target displacement from residual rotations was derived using rigid body kinematics and validated with a Monte Carlo cohort of one million randomly generated targets uniformly distributed within a 200 mm radius sphere. Rotations were modeled as independent zero-mean Gaussian errors with standard deviations of 0.2°, 0.5°, and 1.0°. Analytic target registration error was compared with the exact rigid body matrix method. Dose-coverage performance was evaluated using V100 % with a 95 % pass criterion. Pass rate under a fixed 1 mm margin was assessed, and the minimum required margin was solved inversely. Results The analytic model closely matched the matrix method, with a maximum residual below 0.2 mm. Risk increased sharply with distance. At 0.5° uncertainty, a failure transition occurred near 100 mm, where mean V100 % remained 95.0 % but pass rate dropped to 52.1 %. The required margin reached 2.14 mm at 100 mm and exceeded 3 mm at 150 mm. Conclusions Distance-dependent amplification of residual rotations causes distal target instability that mean coverage can obscure. Distance-adaptive geometric margins combined with improved rotational accuracy, can reduce distal failure risk while limiting normal tissue cost.