Selection of single-isocenter for multiple-target stereotactic brain radiosurgery to minimize total margin volume

Treating multiple brain metastases with a single isocenter improves efficiency but requires margins to account for rotation induced shifts that increase with target-to-isocenter distance. A method to select the single isocenter position that minimizes the total volume of normal tissue treated during multi-target stereotactic radiosurgery (SRS) is presented. A statistical framework was developed to quantify the impact of uncertainties on planning target volumes (PTV). Translational and rotational shifts were modeled with independent, zero mean, Gaussian distributions in three dimensions added in quadrature. The standard deviations of errors were varied from 0.5-2.0 mm and 0.5 degrees-2.0 degrees. The volume of normal tissue treated due to margin expansions required to maintain a 95% probability of target coverage was computed. Tumors were modeled as 4-40 mm diameter spheres. Target separation distance was varied from 40-100 mm for two- and three-lesion scenarios. The percent increase in PTV was determined relative to an isocenter at the geometric centroid of the targets for the optimal isocenter that minimized the total normal tissue treated, and isocenters at the center-of-mass (COM) and center-of-surface-area (CSA). For two targets, isocenter placement at the optimal location, COM, and CSA, reduced the total margin versus an isocenter at midline up to 17.8%, 17.7%, and 17.8%, respectively, for 0.5 mm and 0.5 degrees errors. For three targets, optimal isocenter placement reduced the margin volume up to 21%, 19%, and 14%, for uncertainties of (0.5 mm, 0.5 degrees), (1.0 mm, 1.0 degrees), and (2.0 mm, 2.0 degrees), respectively. COM and CSA provide useful approximations to select the optimal isocenter for multi-target single-isocenter SRS for two or three targets with maximum dimensions 40 mm and separation distances 100 mm when uncertainties are 1.0 mm and 1.0 degrees. CSA provides a more accurate approximation than COM. Optimal treatment isocenter selection for multiple targets of large size differences can significantly reduce total margin volume.