Theoretical and Semi-Empirical Investigation of Electron Mass Stopping Power in Human Blood and Water

In this work a theoretical and semi-empirical analysis of the mass stopping power of human blood in the electron kinetic energy interval of 110–270 MeV and of liquid water in the same interval has been carried out. The theoretical calculations were done by the relativistic Bethe–Bloch equations and a three-parameter semi-empirical equation, which is a function of the electron kinetic energy (T), was obtained by fitting a non-linear curve in MATLAB. The results have been compared with reference values obtained from the ESTAR database of the National Institute of Standards and Technology (NIST) to check the accuracy and reliability of the proposed models. The following statistical parameters were used for the assessment: Pearson’s correlation coefficient, the root mean square error (RMSE), the mean absolute error (MAE) and the standard deviation of paired differences. The results indicated that the semi-empirical prediction results were in excellent agreement with the ESTAR reference data: for liquid water, 99.99% accuracy was reported and for human blood, 98.80% accuracy was reported. The values of RMSE were 0.0576 and 8.1790 MeV·cm²/g, respectively. The theoretical and semi-empirical results also showed very close linear correlation between them, with the Pearson’s correlation coefficient being 0.999719 for water and 0.999769 for blood, but it was found that there are significant differences between their numerical values. These results show that a very high correlation does not necessarily mean numerical agreement and the need to correctly describe the stopping power contributions that depend on energy at high electron energy. The proposed semi-empirical equation was in good agreement with the ESTAR reference data and may be useful for modelling the electron mass stopping power in biological materials and may be also helpful in further radiation dosimetry studies.

Keywords: Electron kinetic energy; Electron mass stopping power; Human blood; Liquid water; Semi-empirical equation; Bethe–Bloch equation; ESTAR database.