Optimal marker placement in hadrontherapy: Intelligent optimization strategies with augmented Lagrangian pattern search

Purpose: In high precision photon radiotherapy and in hadrontherapy, it is crucial to minimize the occurrence of geometrical deviations with respect to the treatment plan in each treatment session. To this end, point-based infrared (IR) optical tracking for patient set-up quality assessment is performed. Such tracking depends on external fiducial points placement. The main purpose of our work is to propose a new algorithm based on simulated annealing and augmented Lagrangian pattern search (SAPS), which is able to take into account prior knowledge, such as spatial constraints, during the optimization process. Material and methods: The SAPS algorithm was tested on data related to head and neck and pelvic cancer patients, and that were fitted with external surface markers for IR optical tracking applied for patient set-up preliminary correction. The integrated algorithm was tested considering optimality measures obtained with Computed Tomography (CT) images (i.e. the ratio between the so-called target registration error and fiducial registration error, TRE/FRE) and assessing the marker spatial distribution. Comparison has been performed with randomly selected marker configuration and with the GETS algorithm (Genetic Evolutionary Taboo Search), also taking into account the presence of organs at risk. Results: The results obtained with SAPS highlight improvements with respect to the other approaches: (i) TRE/FRE ratio decreases; (ii) marker distribution satisfies both marker visibility and spatial constraints. We have also investigated how the TRE/FRE ratio is influenced by the number of markers, obtaining significant TRE/FRE reduction with respect to the random configurations, when a high number of markers is used. Conclusions: The SAPS algorithm is a valuable strategy for fiducial configuration optimization in IR optical tracking applied for patient set-up error detection and correction in radiation therapy, showing that taking into account prior knowledge is valuable in this optimization process. Further work will be focused on the computational optimization of the SAPS algorithm toward fast point-of-care applications.