Research Article

Formulation and Validation of a Generalized Semi-Empirical Equation for Calculating Electron CSDA Range in Human Tissues (Brain and Eye Lens) for Radiation Therapy Dosimetry

Abstract

The accurate determination of the range of high-energy electrons in human biological tissues is of great significance in radiation therapy planning and clinical radiation protection. In this work, we developed a single semi-empirical formula for the Continuous Slowing Down Approximation (CSDA) range of electrons in human tissues with special attention to brain and eye lens tissues and used the International Commission on Radiological Protection (ICRP) reference standards for the energy range 100-550 MeV. The semi-empirical nonlinear power-law expression f(T) = (a × Tb) + c is parameterized using constants a = 34.12, b = 0.2348 and c = -67.5. The semi-empirically predicted ranges (f) were systematically compared to the standard reference values (SRV) obtained from the National Institute of Standards and Technology (NIST) ESTAR database (Estar). An exceptional correlation coefficient of R = 0.99998 (R2 = 0.99996) was found for both brain and eye lens tissues in the statistical analysis. The mean absolute percentage error (MAPE) was very low at 0.177% for the eye lens and 1.652% for brain tissue, whereas, the root mean square error (RMSE) was very low at 0.108 g/cm2 for eye lens and 1.034 g/cm2 for brain tissue. Importantly, the results demonstrate that this single semi-empirical formulation is applicable and can be used in radiotherapy to accurately predict the range of electrons in all soft tissues in the human body, offering an efficient, accurate and real-time analytical tool to replace the time-consuming Monte Carlo simulation.

Authors affiliation:

Dahlia K. Gatea: Department of Physics, College of Science, University of Basrah, Basrah, Iraq.

How To Cite: D.K. Gatea. Formulation and Validation of a Generalized Semi-Empirical Equation for Calculating Electron CSDA Range in Human Tissues (Brain and Eye Lens) for Radiation Therapy Dosimetry. Journal of Biomedicine and Biosensors, 6(4):11–15, 2026. https://doi.org/10.58613/jbb643