Deterministic Margin Selection Tool for Single Iso Multi-Target Radiosurgery
Abstract
Purpose
We introduce a deterministic, analytic framework for single‑isocenter, multi‑target radiosurgery to derive the minimal geometric margin that corresponds with a user‑specified level of target coverage. The model correlates target size, allowable rigid rotation about the isocenter, and distance from isocenter with an explicit coverage‑loss metric (for example GTV V100 = 95%), to produce a closed‑form margin estimation for each met.
Methods
Assuming rigid‑body rotation about a fixed isocenter, we derive expressions for the maximal displacement of a spherical target as a function of its diameter and off‑axis distance. The overlap of this displaced target with a spherical dose distribution at its expected location can be mathematically computed. By varying the margin, the size of the dose distribution sphere can be adjusted such that there is maximum overlap for a given acceptable rotation. The formulation accepts a maximum rotation angle, representing immobilization and setup uncertainty, and yields margins as an explicit function of target diameter and distance from isocenter. We validate analytic predictions for target diameters spanning 2–30 mm, distance from isocenter 0–75 mm, and rotation tolerances up to 2°
Results
Margins scale nonlinearly with increasing radial distance and decreasing target size. Smaller peripheral targets require substantially larger margins than larger centrally located lesions. With a 1° rotational tolerance and a mandated GTV V100 of 95%, a 5‑mm tumor requires margins of 0.5mm and 1.5mm at 30 mm and 75mm from isocenter, respectively, while a 20‑mm tumor under the same conditions requires corresponding margins of 0.1mm and 0.8mm. The model identifies parameters where single‑isocenter strategies remain clinically acceptable and where multiple isocenters are preferable.
Conclusion
The instantaneous margin calculation of this model allows for lesion‑specific margins within a single isocenter technique, providing a deterministic and easily implemented clinically actionable method for objective margin selection in multi‑target radiosurgery.