Optimization of treatment isocenter location in single-isocenter LINAC-based stereotactic radiosurgery for management of multiple brain metastases

Purpose: Single-isocenter linear accelerator (LINAC)-based stereotactic radiosurgery (SRS) has become a promising treatment technique for the management of multiple brain metastases. Because of the high prescription dose and steep dose gradient, SRS plans are sensitive to geometric errors, resulting in loss of target coverage and suboptimal local tumor control. Current planning techniques rely on adding a uniform and isotropic setup margin to all gross tumor volumes (GTVs) to account for rotational uncertainties. However, this setup margin may be insufficient, since the magnitude of rotational uncertainties varies and is dependent upon the distance between a GTV and the isocenter. In this study, we designed a framework to determine the optimal isocenter of a single-isocenter SRS plan for multiple brain metastases using stochastic optimization to mitigate potential errors resulting from rotational uncertainties.

Methods: Planning target volumes (PTVs), defined as GTVs plus a 1-mm margin following common SRS planning convention, were assumed to be originally treated with a prescription dose and therefore covered by the prescription isodose cloud. The dose distribution, including the prescription isodose, was considered invariant assuming small rotations throughout the study. A stochastic optimization scheme was developed to determine the location of the optimal isocenter, so that the prescription dose coverage of rotated GTVs, equivalent to the intersecting volumes between the rotated GTVs and original PTVs, was maximized for any random small rotations about the isocenter. To evaluate the coverage of GTVs, the expected $V_{100\%}$ undergoing random rotations was approximated as the sample average $V_{100\%}$ undergoing a predetermined number of rotations. The expected $V_{100\%}$ of each individual GTV and total GTVs was then compared between the plans using the optimal isocenter and the center-of-mass (CoM), respectively.

Results: Twenty-two patients previously treated for multiple brain metastases in a single institute were included in this retrospective study. Each patient was initially treated for more than three brain metastases (mean: 7.6; range: 3-15) with the average GTV volume of 0.89 cc (range: 0.03-11.78 cc). The optimal isocenter found for each patient was significantly different from the CoM, with the average Euclidean distance between the optimal isocenter and the CoM being 4.36 ± 2.59 cm. The dose coverage to GTVs was also significantly improved (paired t-test; p < 0.001) when the optimal isocenter was used, with the average $V_{100\%}$ of total GTVs increasing from 87.1% (standard deviation as std: 11.7%; range: 39.9-98.2%) to 94.2% (std: 5.4%; range: 77.7-99.4%). The volume of a GTV was positively correlated with the expected $V_{100\%}$ regardless of the isocenter used (Spearman coefficient: $\rho =0.66$ ; p < 0.001). The distance between a GTV and the isocenter was negatively correlated with the expected $V_{100\%}$ when the CoM was used ( $\rho =-0.21$ ; p = 0.004), however no significant correlation was found when the optimal isocenter was used ( $\rho =-0.11$ ; p = 0.137).

Conclusion: The proposed framework provides an effective approach to determine the optimal isocenter of single-isocenter LINAC-based SRS plans for multiple brain metastases. The implementation of the optimal isocenter results in SRS plans with consistently higher target coverage despite potential rotational uncertainties, and therefore significantly improves SRS plan robustness against random rotational uncertainties.