Incorporating human and learned domain knowledge into training deep neural networks: A differentiable dose-volume histogram and adversarial inspired framework for generating Pareto optimal dose distributions in radiation therapy

Purpose: We propose a novel domain-specific loss, which is a differentiable loss function based on the dose-volume histogram (DVH), and combine it with an adversarial loss for the training of deep neural networks. In this study, we trained a neural network for generating Pareto optimal dose distributions, and evaluate the effects of the domain-specific loss on the model performance. Methods: In this study, three loss functions — mean squared error (MSE) loss, DVH loss, and adversarial (ADV) loss — were used to train and compare four instances of the neural network model: (a) MSE, (b) MSE + ADV, (c) MSE + DVH, and (d) MSE + DVH+ADV. The data for 70 prostate patients, including the planning target volume (PTV), and the organs at risk (OAR) were acquired as 96 × 96 × 24 dimension arrays at 5 mm³ voxel size. The dose influence arrays were calculated for 70 prostate patients, using a 7 equidistant coplanar beam setup. Using a scalarized multicriteria optimization for intensity-modulated radiation therapy, 1200 Pareto surface plans per patient were generated by pseudo-randomizing the PTV and OAR tradeoff weights. With 70 patients, the total number of plans generated was 84 000 plans. We divided the data into 54 training, 6 validation, and 10 testing patients. Each model was trained for a total of 100,000 iterations, with a batch size of 2. All models used the Adam optimizer, with a learning rate of 1 × 10⁻³. Results: Training for 100 000 iterations took 1.5 days (MSE), 3.5 days (MSE+ADV), 2.3 days (MSE+DVH), and 3.8 days (MSE+DVH+ADV). After training, the prediction time of each model is 0.052 s. Quantitatively, the MSE+DVH+ADV model had the lowest prediction error of 0.038 (conformation), 0.026 (homogeneity), 0.298 (R50), 1.65% (D95), 2.14% (D98), and 2.43% (D99). The MSE model had the worst prediction error of 0.134 (conformation), 0.041 (homogeneity), 0.520 (R50), 3.91% (D95), 4.33% (D98), and 4.60% (D99). For both the mean dose PTV error and the max dose PTV, Body, Bladder and rectum error, the MSE+DVH+ADV outperformed all other models. Regardless of model, all predictions have an average mean and max dose error <2.8% and 4.2%, respectively. Conclusion: The MSE+DVH+ADV model performed the best in these categories, illustrating the importance of both human and learned domain knowledge. Expert human domain-specific knowledge can be the largest driver in the performance improvement, and adversarial learning can be used to further capture nuanced attributes in the data. The real-time prediction capabilities allow for a physician to quickly navigate the tradeoff space for a patient, and produce a dose distribution as a tangible endpoint for the dosimetrist to use for planning. This is expected to considerably reduce the treatment planning time, allowing for clinicians to focus their efforts on the difficult and demanding cases.