Mitigating inherent noise in Monte Carlo dose distributions using dilated U-Net

Purpose: Monte Carlo (MC) algorithms offer accurate modeling of dose calculation by simulating the transport and interactions of many particles through the patient geometry. However, given their random nature, the resulting dose distributions have statistical uncertainty (noise), which prevents making reliable clinical decisions. This issue is partly addressable using a huge number of simulated particles but is computationally expensive as it results in significantly greater computation times. Therefore, there is a trade-off between the computation time and the noise level in MC dose maps. In this work, we address the mitigation of noise inherent to MC dose distributions using dilated U-Net - an encoder-decoder-styled fully convolutional neural network, which allows fast and fully automated denoising of whole-volume dose maps.

Methods: We use mean squared error (MSE) as loss function to train the model, where training is done in 2D and 2.5D settings by considering a number of adjacent slices. Our model is trained on proton therapy MC dose distributions of different tumor sites (brain, head and neck, liver, lungs, and prostate) acquired from 35 patients. We provide the network with input MC dose distributions simulated using $1\times {10}^6$ particles while keeping $1\times {10}^9$ particles as reference.

Results: After training, our model successfully denoises new MC dose maps. On average (averaged over five patients with different tumor sites), our model recovers $D_{95}$ of 55.99 Gy from the noisy MC input of 49.51 Gy, whereas the low noise MC (reference) offers 56.03 Gy. We observed a significant reduction in average RMSE (thresholded >10% max ref) for reference vs denoised (1.25 Gy) than reference vs input (16.96 Gy) leading to an improvement in signal-to-noise ratio (ISNR) by 18.06 dB. Moreover, the inference time of our model for a dose distribution is less than 10 s vs 100 min (MC simulation using $1\times {10}^9$ particles).

Conclusions: We propose an end-to-end fully convolutional network that can denoise Monte Carlo dose distributions. The networks provide comparable qualitative and quantitative results as the MC dose distribution simulated with $1\times {10}^9$ particles, offering a significant reduction in computation time.