Gamma Knife treatment planning with new degrees of freedom

Abstract: The Leksell Gamma Knife® is an instrument designed for high precision treatment of tumours and lesions located in the brain and upper spine. Today, the radioactive cobalt-60 sources can only move linearly along the radiation unit, but the machine could be modified to include rotational motion as well. We extend an existing linear programming approach to inverse planning for the Gamma Knife by examining the benefits from rotational degrees of freedom. The improvements offered from rotations are limited, but easy to make use of. We investigate the model in four patient cases, and find that an upper bound on the improvement of the optimization cost function is between 4.5% and 7.0% depending on case. With a total of four angles distributed uniformly over a 45 degree interval, one can in each case achieve a solution that performs up to within 1% of this bound. The average maximal improvements in terms of clinical metrics are 0.5% selectivity and 1.9% gradient index, at the cost of 5.9% worse beam-on time. No statistically significant change in coverage is found. A dynamic model based on column generation is proposed, which allows treatment during constant velocity angular motion and can achieve practically the same plan quality as the model with uniformly distributed angles at a significantly lower problem size. A similar algorithm can be designed to locate the most effective angles in a non-uniform manner that achieves better plans with fewer added rotational degrees of freedom. Trade-offs between memory and solution times are used to successively reduce the RAM occupation by around 90% and make significantly larger models computationally feasible to solve. A voxel clustering approach with emphasis on surface voxels, adapted to the radiosurgical framework, can significantly reduce the problem size while still producing competitive plans.