Beam orientation selection, whether manual or protocol-based, is the current clinical standard in radiation therapy treatment planning, but it is tedious and can yield suboptimal results. Many algorithms have been designed to optimize beam orientation selection because of its impact on treatment plan quality, but these algorithms suffer from slow calculation of the dose influence matrices of all candidate beams. We propose a fast beam orientation selection method, based on deep learning neural networks (DNN), capable of developing a plan comparable to those developed by the state-of-the-art column generation method. Our model’s novelty lies in its supervised learning structure (using column generation to teach the network), DNN architecture, and ability to learn from anatomical features to predict dosimetrically suitable beam orientations without using dosimetric information from the candidate beams. This may save hours of computation.
A supervised DNN is trained to mimic the column generation algorithm, which iteratively chooses beam orientations one-by-one by calculating beam fitness values based on Karush-Kush-Tucker optimality conditions at each iteration. The DNN learns to predict these values. The dataset contains 70 prostate cancer patients-50 training, 7 validation, and 13 test patients-to develop and test the model. Each patient’s data contains 6 contours: PTV, body, bladder, rectum, and left and right femoral heads. Column generation was implemented with a GPU-based Chambolle-Pock algorithm, a first-order primal-dual proximal-class algorithm, to create 6270 plans. The DNN trained over 400 epochs, each with 2500 steps and a batch size of 1, using the Adam optimizer at a learning rate of 1×10-5 and a 6-fold cross-validation technique.
The average and standard deviation of training, validation, and testing loss functions among the 6-folds were 0.62±0.09%, 1.04±0.06%, and 1.44±0.11%, respectively. Using column generation and supervised DNN, we generated two sets of plans for each scenario in the test set. The proposed method took at most 1.5 seconds to select a set of five beam orientations and 300 second to calculate the dose influence matrices for 5 beams and finally 20 seconds to solve the fluence map optimization. However, column generation needed around 15 hours to calculate the dose influence matrices of all beams and at least 400 seconds to solve both the beam orientation selection and fluence map optimization problems. The differences in the dose coverage of PTV between plans generated by column generation and by DNN were 0.2%. The average dose differences received by organs at risk were between 1 and 6 percent: Bladder had the smallest average difference in dose received (0.956±1.184%), then Rectum (2.44±2.11%), Left Femoral Head (6.03±5.86%), and Right Femoral Head (5.885±5.515%). The dose received by Body had an average difference of 0.10± 0.1% between the generated treatment plans.
We developed a fast beam orientation selection method based on a DNN that selects beam orientations in seconds and is therefore suitable for clinical routines. In the training phase of the proposed method, the model learns the suitable beam orientations based on patients’ anatomical features and omits time intensive calculations of dose influence matrices for all possible candidate beams. Solving the fluence map optimization to get the final treatment plan requires calculating dose influence matrices only for the selected beams.