Dual-energy CT based mass density and relative stopping power estimation for proton therapy using physics-informed deep learning

Proton therapy requires accurate dose calculation for treatment planning to ensure the conformal doses are precisely delivered to the targets. The conversion of CT numbers to material properties is a significant source of uncertainty for dose calculation. The aim of this study is to develop a physics-informed deep learning (PIDL) framework to derive accurate mass density and relative stopping power maps from dual-energy computed tomography (DECT) images. The PIDL framework allows deep learning (DL) models to be trained with a physics loss function, which includes a physics model to constrain DL models. Five DL models were implemented including a fully connected neural network (FCNN), dual-FCNN (DFCNN), and three variants of residual networks (ResNet): ResNet-v1 (RN-v1), ResNet-v2 (RN-v2), and dual-ResNet-v2 (DRN-v2). An artificial neural network (ANN) and the five DL models trained with and without physics loss were explored to evaluate the PIDL framework. Two empirical DECT models were implemented to compare with the PIDL method. DL training data were from CIRS electron density phantom 062M (Computerized Imaging Reference Systems, Inc., Norfolk, VA). The performance of DL models was tested by CIRS adult male, adult female, and 5-year-old child anthropomorphic phantoms. For density map inference, the physics-informed RN-v2 was 3.3%, 2.9% and 1.9% more accurate than ANN for the adult male, adult female, and child phantoms. The physics-informed DRN-v2 was 0.7%, 0.6%, and 0.8% more accurate than DRN-v2 without physics training for the three phantoms, respectfully. The results indicated that physics-informed training could reduce uncertainty when ANN/DL models without physics training were insufficient to capture data structures or derived significant errors. DL models could also achieve better image noise control compared to the empirical DECT parametric mapping methods. The proposed PIDL framework can potentially improve proton range uncertainty by offering accurate material properties conversion from DECT.