Millisecond speed deep learning based proton dose calculation with Monte Carlo accuracy

Objective. Next generation online and real-time adaptive radiotherapy workflows require precise particle transport simulations in sub-second times, which is unfeasible with current analytical pencil beam algorithms (PBA) or Monte Carlo (MC) methods. We present a deep learning based millisecond speed dose calculation algorithm (DoTA) accurately predicting the dose deposited by mono-energetic proton pencil beams for arbitrary energies and patient geometries. Approach. Given the forward-scattering nature of protons, we frame 3D particle transport as modeling a sequence of 2D geometries in the beam's eye view. DoTA combines convolutional neural networks extracting spatial features (e.g. tissue and density contrasts) with a transformer self-attention backbone that routes information between the sequence of geometry slices and a vector representing the beam's energy, and is trained to predict low noise MC simulations of proton beamlets using 80 000 different head and neck, lung, and prostate geometries. Main results. Predicting beamlet doses in 5 +/- 4.9 ms with a very high gamma pass rate of 99.37 +/- 1.17% (1%, 3 mm) compared to the ground truth MC calculations, DoTA significantly improves upon analytical pencil beam algorithms both in precision and speed. Offering MC accuracy 100 times faster than PBAs for pencil beams, our model calculates full treatment plan doses in 10-15 s depending on the number of beamlets (800-2200 in our plans), achieving a 99.70 +/- 0.14% (2%, 2 mm) gamma pass rate across 9 test patients. Significance. Outperforming all previous analytical pencil beam and deep learning based approaches, DoTA represents a new state of the art in data-driven dose calculation and can directly compete with the speed of even commercial GPU MC approaches. Providing the sub-second speed required for adaptive treatments, straightforward implementations could offer similar benefits to other steps of the radiotherapy workflow or other modalities such as helium or carbon treatments.