Deep learning estimation of effective atomic number for HU to RED calibration in dual energy photon counting CT

This study introduces a deep learning (DL) approach to improve relative electron density (RED) estimation in dual-energy CT (DECT) through precise effective atomic number (EAN) prediction. A benchtop photon-counting detector CT acquired spectral images of a tissue-equivalent phantom, and a modified U-Net was trained on synthetic data to directly estimate EAN. Predicted EANs were converted to RED using a physics-based model. Performance was assessed on eight materials using mean absolute error (MAE), relative error, and residuals, with results compared to conventional Rutherford and stoichiometric methods. The DL model achieved an MAE of 0.08% for EAN, outperforming Rutherford (1.59%) and stoichiometric (1.54%) approaches. For RED estimation, DL reached a MAE of 0.62%, with residuals ranging from − 0.01 to 0.02 of theoretical values. Calibration analysis showed high linearity for conventional ΔHU-RED curves (R² ≈ 0.9995), but the DL-based method showed slightly higher linearity (R² = 0.9998). Overall, in this phantom study, the DL framework improved RED accuracy and HU–RED linearity compared with analytical methods. By providing a highly linear ΔHU–RED calibration curve in the phantom experiments conducted in this study, it enhances material differentiation and has the potential to support more precise dose calculations in future clinical applications.