Differentiable Gamma Index-Based Loss Functions: Accelerating Monte-Carlo Radiotherapy Dose Simulation

The Gamma index Passing Rate (GPR) is considered the preferred metric to evaluate dose distributions in order to deliver safe radiotherapy treatments. For this reason, in the context of accelerating Monte-Carlo dose simulations using deep neural networks, the GPR remains the default clinical metric used to validate the predictions of the models. However, the optimization criterion that is used for training these neural networks is based on loss functions that are different than GPR. To address this important issue, in this work we introduce a new class of GPR-based loss functions for deep learning. These functions allow us to successfully train neural networks that can directly yield the best dose predictions from a clinical standpoint. Our approach overcomes the mathematical non-differentiability of the GPR, thus allowing a successful application of gradient descent. Moreover, it brings the GPR computation time down to milliseconds, therefore enabling fast trainings. We demonstrate that models trained with our GPR-based loss functions outperform models trained with other commonly used loss functions with respect to several metrics and display a 15% improvement of the GPR over the test data. Code is available at https://rb.gy/vf5jwv.