Aleatoric and epistemic uncertainty extraction of patient-specific deep learning-based dose predictions in LDR prostate brachytherapy

Abstract

Objective: In brachytherapy, deep learning (DL) algorithms have shown the capability of predicting 3D dose volumes. The reliability and accuracy of such methodologies remain under scrutiny for prospective clinical applications. This study aims to establish fast DL-based predictive dose algorithms for LDR (low-dose rate) prostate brachytherapy and to evaluate their uncertainty and stability.

Approach: Data from 200 prostate patients, treated with 125I sources, was collected. The Monte Carlo (MC) ground truth dose volumes were calculated with TOPAS considering the interseed effects and an organ-based material assignment. Two 3D convolutional neural networks, UNet and ResUNet TSE, were trained using the patient geometry and the seed positions as the input. The dataset was randomly split into training (150), validation (25) and test (25) sets. The aleatoric (associated with the input data) and epistemic (associated with the model) uncertainties of the DL models were assessed.

Main results: For the full test set, with respect to the MC reference, the predicted prostate D90 metric had mean differences of -0.64% and 0.08% for the UNet and ResUNet TSE models, respectively. In voxel-by-voxel comparisons, the average global dose difference ratio in the [-1%,1%] range included 91.0% and 93.0% of voxels for the UNet and the ResUNet TSE, respectively. One forward pass or prediction took 4 ms for a 3D dose volume of 2.56M voxels (128×160×128). The ResUNet TSE model closely encoded the well-known physics of the problem as seen in a set of uncertainty maps. The ResUNet TSE rectum D2cc had the largest uncertainty metric of 0.0042.

Significance: The proposed DL models serve as rapid dose predictors that consider the patient anatomy and interseed attenuation effects. The derived uncertainty is interpretable, highlighting areas where DL models struggle to provide accurate estimations. The uncertainty analysis offers a comprehensive evaluation tool for model assessment.