A general algorithm for distributed treatments of multiple brain metastases.

Purpose Stereotactic radiosurgery (SRS) has become a primary treatment for multiple brain metastases (BM) but may require distribution of BMs over several sessions to make delivery time and radiation toxicity manageable. Contrasting to equal fraction dose in conventional fractionation, distributed SRS delivers full dose to a subset of BMs in each session while avoids adjacent BMs in the same session to reduce toxicity from overlapping radiation. However, current clinical treatment planning for distributed SRS relies on manual BM assignment, which can be tedious and error prone. This work describes a novel approach to automate the distribution of BM in the Gamma Knife (GK) clinical workflow. Methods We represent each BM as an electrostatic field of the same polarity that exerts repulsive forces on other BMs in the same session. This representation naturally leads to separation of close BMs into different sessions to lower the potential energy. Indeed, the BM distribution problem can be formulated as minimization of the total potential energy from all treatment sessions subject to delivery time constraints in mixed-integer quadratic programming (MIQP). We retrospectively studied eight clinical GK cases of multiple BM and compared the automated MIQP solution with clinically used BM distribution to demonstrate the efficacy of the proposed approach. Results With the problem size equal to the number of BMs times the number of sessions, this MIQP can be solved in a minute on a personal workstation. The MIQP solution effectively separated BMs for a given number of treatment sessions and evened out the delivery time distribution among sessions. Compared to the clinically used manual BM distributions in paired t-test for a similar range of delivery time variation, the automated BM distributions had lower energy objectives (range of decrease: [11% 89%]; median: 25%; P= .0173), more uniformly distributed treatment volumes (range of decrease for the normalized standard deviation of volume distribution: [0.02 0.95]; median: 0.16; P= .013), more scattered BMs in each treatment session (range of increase for the mean minimum BM distance: [0 14] mm; median: 6 mm; P= .008), and lower overall V12 (range of decrease: [0.0 1.6] cc; median: 0.2 cc; P= .052). Moreover, without distribution, i.e. with all BMs treated in the same session, V12 was substantially larger compared to both manual and automated BM distributions; the increase ranged from 0.1 cc to 16.6 cc with median of 1.3 cc. Conclusions The proposed approach models the clinical practice and provides an efficient solution for optimal selection of BM subsets for distributed SRS. Further evaluations are underway to establish this approach as a tool for improving clinical workflow and to facilitate systematic study on the benefits of distributed SRS treatments.