Modeling ray angles in deep learning based dose calculation algorithms

A fundamental tool in radiotherapy treatment planning is the dose calculation algorithm, which models the dose that will be distributed for given beam parameters and patient geometry. Various available algorithms include Monte Carlo simulations (MC) and pencil beam algorithms (PBA), with the former being computationally expensive but offering high precision and the latter sacrificing precision for speed. A recent study presents the deep-learning based Dose Transformer Algorithm (DoTA) which provides MC accuracy at speeds 33 times faster than PBA. However, as currently implemented, DoTA dose computations assume that each ray enters the patient geometry perpendicularly, while clinical treatment plans consist of many diverging rays with angles of entry up to 5°. In this project, we extend the current model to include angular dependency. The resulting models DoTA-A and DoTA-S improve on DoTA by including angle of entry as an additional input on top of the beam energy and patient geometry. DoTA-A includes the actual angle values as input, while for DoTA-S an expected beam shape is precalculated with a trajectory based on the angle of entry. A training dataset of more than 30.000 samples with MC baseline dose is generated from a public patient dataset, using a 2 mm resolution. The architecture of the models is similar to that of DoTA, with convolutional layers extracting important spatial features from the input geometry and a transformer layer using a self-attention mechanism to weigh token inter-dependence.The models DoTA-A and DoTA-S are evaluated and compared on different test sets with MC baseline doses. Both models are shown to be more accurate than PBA, with DoTA-S having the best performance by most metrics. We demonstrate the relevance of ray angles in dose calculations by comparing DoTA-A and DoTA-S to perpendicular MC predictions, which were considered ground-truth for DoTA. The models DoTA-A and DoTA-S compute dose distributions at an average speed of 10 ms to 15 ms per dose, with the predictions achieving an average relative error of 1% across various test sets. The average relative error of the perpendicular MC predictions lies around 3%, demonstrating the importance of angle of entry as an input variable in dose calculation algorithms. The gamma pass rates (for δ=1%, Δ=3mm) of a full treatment plan with dose distributions predicted by our models are 97.60% for DoTA-A and 95.74% for DoTA-S, indicating that there is no strictly better model between the two.Applied Mathematic