Generalized multi-energy model for computing radiation treatment parameters on image domain and automated model-selection framework
- 1Department of Mathematics, University of Nigeria, Nsukka 410001, Nigeria.
Abstract
This study developed a general n-energy mathematical model that predicts relative electron density (ρe), effective atomic number (Zef), mean excitation energy (I) and stopping power ratio (SPR) using computed tomography image, and developed an algorithm for best model selection. Mathematical proof is provided. Some numerical examples were carried out and the results were compared. The proposed method includes most of the existing methods as a special case. All the examples of the proposed method considered have modeling error that’s less than or equal to 0.85% and 0.89% for SPR and ρe, respectively, with mean error close to 0.00% and low median absolute error. The method was able to achieve modeling root mean square error of 0.85% and 1.61% for I and Zef, respectively, with some flexibility for improvement. The mathematical model showed to be more general by including most of the other existing models and presents a direction to formulating new ones. It shows little or no bias on prediction since it has mean error that is close to zero in almost all predictions and low median absolute error. The algorithm gives the leverage to select the best model, improve the model and automation.
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BibTeX
@article{chika2026generalized,
title = {{Generalized multi-energy model for computing radiation treatment parameters on image domain and automated model-selection framework}},
author = {Charles E Chika},
journal = {World journal of radiology},
year = {2026},
month = oct,
doi = {10.4329/wjr.126287},
url = {https://europepmc.org/article/PMC/PMC13720571},
note = {CC BY-NC},
}
RIS
TY - JOUR
TI - Generalized multi-energy model for computing radiation treatment parameters on image domain and automated model-selection framework
AU - Charles E Chika
PY - 2026
DA - 2026/10/28
JO - World journal of radiology
DO - 10.4329/wjr.126287
UR - https://europepmc.org/article/PMC/PMC13720571
AB - This study developed a general n-energy mathematical model that predicts relative electron density (ρe), effective atomic number (Zef), mean excitation energy (I) and stopping power ratio (SPR) using computed tomography image, and developed an algorithm for best model selection. Mathematical proof is provided. Some numerical examples were carried out and the results were compared. The proposed method includes most of the existing methods as a special case. All the examples of the proposed method considered have modeling error that’s less than or equal to 0.85% and 0.89% for SPR and ρe, respectively, with mean error close to 0.00% and low median absolute error. The method was able to achieve modeling root mean square error of 0.85% and 1.61% for I and Zef, respectively, with some flexibility for improvement. The mathematical model showed to be more general by including most of the other existing models and presents a direction to formulating new ones. It shows little or no bias on prediction since it has mean error that is close to zero in almost all predictions and low median absolute error. The algorithm gives the leverage to select the best model, improve the model and automation.
SN - 1949-8470
ER -