Estimation of Proton Stopping Power Ratio and Mean Excitation Energy Using Electron Density and Its Applications via Machine Learning Approach

Abstract

Purpose: The purpose of this study was to develop a simple flexible method for accurate estimation of stopping power ratio (SPR) and mean excitation energy (I) using relative electron density (ρe). Materials and Methods: The model was formulated using empirical relationships between SPR, mean excitation energy I, and relative electron density. Some examples were implemented, and a comparison was carried out using other existing methods. The needed coefficients in the model were estimated using optimization tools. Basis vector method (BVM) and Hunemohr and Saito (H-S) method were applied to estimate the ρe used in the application section. 80 kVp and 150 kVpSn were used as low and high energy, respectively, for the implementation of dual-energy methods. Results: All the examples of the proposed method considered have modeling error that is ≤0.32% and testing root mean square error (RMSE) ≤0.92% for SPR with a mean error close to 0.00%. The method was able to achieve modeling RMSE of 2.12% for mean excitation energy with room for improvement. Similar or better results were achieved in application to BVM. Conclusion: The method showed robustness in application by achieving lower testing error than other presented methods in most cases. It achieved accurate estimation which can be improved using the machine learning algorithm since it is flexible to implement in terms of the function (model) degree and tissue classification.

Keywords

• computed tomography image
• machine learning
• mathematical model
• optimization
• proton stopping power ratio
• proton therapy
• tumor treatment