Stochastic Local Search for the Direct Aperture Optimisation Problem

Intensity modulated radiation therapy (IMRT) is a widely applied cancer treatment technique that aims at effectively deliver radiation to cancerous cells while sparing surrounding healthy tissues. To this end, the radiation coming from a linear accelerator is modulated using a physical device called multi-leaf collimator. Traditionally, a sequential approach is applied to generate treatment plans in IMRT. In this approach, the optimal intensities for each beam angle are computed (Fluence Map Optimisation, FMO), and then a sequencing problem is solved to obtain the collimator setup (aperture shapes) required to achieve the intensities computed for the FMO problem. The sequencing step is critical as the treatment plans computed to solve the FMO problem are not clinically acceptable. Unfortunately, treatment plans obtained by the sequencing step are severely impaired w.r.t. those obtained in the FMO step. One approach that aims to deal with the problem described above is the Direct Aperture Optimisation (DAO) approach. The DAO problem aims at simultaneously determining deliverable aperture shapes and a set of radiation intensities. This approach considers both physical and delivery time constraints, allowing to generate clinically acceptable treatment plans. In this paper, we propose a stochastic local search algorithm to solve the DAO problem. Our approach alternates the search between two neighbourhood definitions; the first focused on the fluence map (intensities) and the second on the aperture shapes. We analyse the algorithmic components, parameters, and overall results obtained by our algorithm on a set of clinical prostate cancer cases. We compare the obtained treatment plans to the ones obtained by the traditional two-step approach. Results show that our algorithm is able to find deliverable treatment plans without major impairments in treatment plans quality.