# A linear programming approach to inverse planning in Gamma Knife radiosurgery

arXiv: https://arxiv.org/abs/1806.03016 · HTML: https://mlsanity.com/paper/1806.03016/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jun 2018.

## Built on by (most cited first, 1 of 1)

- [Efficient Radiation Treatment Planning based on Voxel Importance](https://mlsanity.com/paper/2405.03880/) (2024)

## Abstract (arXiv)

Leksell Gamma Knife is a stereotactic radiosurgery system that allows fine-grained control of the delivered dose distribution. We describe a new inverse planning approach that both resolves shortcomings of earlier approaches and unlocks new capabilities. We fix the isocenter positions and perform sector-duration optimization using linear programming, and study the effect of beam-on time penalization on the trade-off between beam-on time and plan quality. We also describe two techniques that reduce the problem size and thus further reduce the solution time: dualization and representative subsampling. The beam-on time penalization reduces the beam-on time by a factor 2-3 compared with the naive alternative. Dualization and representative subsampling each leads to optimization time-savings by a factor 5-20. Overall, we find in a comparison with 75 clinical plans that we can always find plans with similar coverage and better selectivity and beam-on time. In 44 of these, we can even find a plan that also has better gradient index. On a standard GammaPlan workstation, the optimization times ranged from 2.3 to 26 s with a median time of 5.7 s. In conclusion, we present a combination of techniques that enables sector-duration optimization in a clinically feasible time frame.