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 × 106 particles while keeping 1 × 109 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 D95 of 55.99 Gy from the noisy MC input of 49.51 Gy, whereas the low noise MC (reference) offers 56.03 Gy. We observe 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 10s vs. 100 min (MC simulation using 1 × 109 particles). CONCLUSIONS We propose an end-to-end fully convolutional network that can denoise Monte Carlo dose distributions. The networks provides comparable qualitative and quantitative results as the MC dose distribution simulated with 1 × 109 particles, offering significant reduction in computation time.

[1]  T Pawlicki,et al.  Removing the effect of statistical uncertainty on dose-volume histograms from Monte Carlo dose calculations. , 2000, Physics in medicine and biology.

[2]  H Paganetti,et al.  Experimental assessment of proton dose calculation accuracy in inhomogeneous media. , 2017, Physica medica : PM : an international journal devoted to the applications of physics to medicine and biology : official journal of the Italian Association of Biomedical Physics.

[3]  Yanjie Wang,et al.  Multi-scale dilated convolution of convolutional neural network for image denoising , 2019, Multimedia Tools and Applications.

[4]  David S Followill,et al.  Pencil Beam Algorithms Are Unsuitable for Proton Dose Calculations in Lung. , 2017, International journal of radiation oncology, biology, physics.

[5]  I El Naqa,et al.  A comparison of Monte Carlo dose calculation denoising techniques , 2005, Physics in medicine and biology.

[6]  Bram van Ginneken,et al.  A survey on deep learning in medical image analysis , 2017, Medical Image Anal..

[7]  Jaakko Lehtinen,et al.  Noise2Noise: Learning Image Restoration without Clean Data , 2018, ICML.

[8]  Zhenkuan Pan,et al.  Multi-scale dilated convolution of convolutional neural network for crowd counting , 2019, Multimedia Tools and Applications.

[9]  Hongming Shan,et al.  3-D Convolutional Encoder-Decoder Network for Low-Dose CT via Transfer Learning From a 2-D Trained Network , 2018, IEEE Transactions on Medical Imaging.

[10]  A. Nahum,et al.  Monte Carlo dose calculations and radiobiological modelling: analysis of the effect of the statistical noise of the dose distribution on the probability of tumour control , 2000, Physics in medicine and biology.

[11]  Kevin Souris,et al.  Fast multipurpose Monte Carlo simulation for proton therapy using multi- and many-core CPU architectures. , 2016, Medical physics.

[12]  John Aldo Lee,et al.  Multi-organ Segmentation of Chest CT Images in Radiation Oncology: Comparison of Standard and Dilated UNet , 2018, ACIVS.

[13]  P. Dutilleux An Implementation of the “algorithme à trous” to Compute the Wavelet Transform , 1989 .

[14]  Alexei A. Efros,et al.  Image-to-Image Translation with Conditional Adversarial Networks , 2016, 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[15]  Thomas Brox,et al.  U-Net: Convolutional Networks for Biomedical Image Segmentation , 2015, MICCAI.

[16]  T Pawlicki,et al.  Effect of statistical uncertainties on Monte Carlo treatment planning , 2005, Physics in medicine and biology.

[17]  C. Ma,et al.  Dosimetric verification of IMRT treatment planning using Monte Carlo simulations for prostate cancer , 2005, Physics in medicine and biology.

[18]  T Knöös,et al.  Limitations of a pencil beam approach to photon dose calculations in lung tissue. , 1995, Physics in medicine and biology.

[19]  H. Paganetti Range uncertainties in proton therapy and the role of Monte Carlo simulations , 2012, Physics in medicine and biology.

[20]  Mingxuan Sun,et al.  Dilated Deep Residual Network for Image Denoising , 2017, 2017 IEEE 29th International Conference on Tools with Artificial Intelligence (ICTAI).

[21]  Mark Meyer,et al.  Kernel-predicting convolutional networks for denoising Monte Carlo renderings , 2017, ACM Trans. Graph..

[22]  Helen H Liu,et al.  Report of the AAPM Task Group No. 105: Issues associated with clinical implementation of Monte Carlo-based photon and electron external beam treatment planning. , 2007, Medical physics.