Optimization of target grouping in distributive stereotactic radiosurgery using the excel evolutionary solver

Distributive stereotactic radiosurgery (dSRS) is a form of fractionation where groups of metastases are treated with a full single-fraction dose on different days. The challenge with dSRS is determining optimal target groupings to maximize the distance between targets treated in the same fraction. This study aimed to develop and validate an accessible optimization technique for distributing brain metastases into optimal treatment fractions using a genetic algorithm.

The Evolutionary Solver in Excel was used to optimize the grouping of target volumes for distributive SRS fractionation. The algorithm's performance was tested using three geometric test cases with known optimal solutions, 400 simulations with randomly distributed target volumes, and clinical data from five GammaKnife patients. The objective function was defined as the sum of average distances between target volumes within each fraction, with constraints ensuring 2-5 targets per fraction, each target being assigned to only one fraction, and a constraint on the minimum distance between any two targets in the same fraction.

The Evolutionary Solver successfully identified optimal target groupings in all geometric test cases. Compared to random groupings, the mean distance between target volumes increased by 9%, from 68.1 ± 0.8  to 74.2 ± 1.1 mm post-optimization, while the minimum distance between targets increased by 57%, from 24.9 ± 5.9  to 39.1 ± 7.5 mm. In clinical test cases, the mean distances improved from 81.6 ± 11.9 mm for manual target grouping to 85.6 ± 14.5 mm for optimized target grouping. The minimum separation improved from 35.2 ± 14.5 mm with manual grouping to 51.6 ± 14.7 mm with optimized grouping, corresponding to a mean improvement of 16.4 ± 6.1 mm.

The Evolutionary Solver in Excel provides a systematic and reproducible method for optimizing distributive target groupings in SRS and enhances spatial separation.