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Improved Asymptotic Expansions in High- and Low-Dose Ranges for Generalized Multi-Hit Model of Radiation-Induced Cell
Lei Zhao1, Jiahuan Tian2, Giovanni Borasi3
1Institute of Environmental Systems Biology, College of Environmental Science and Engineering, Dalian Maritime University, Dalian, 116026, Liaoning, China.
Radiation Research
|June 18, 2021
Summary
This study improves asymptotic expansions for the generalized multi-hit (GMH) model, enhancing fits for radiation-induced cell survival curves at low and high doses. The new expansions accurately reflect GMH model behavior and offer practical dose ranges for application.
Area of Science:
- Radiobiology
- Mathematical Modeling
- Cellular Radiation Response
Background:
- The generalized multi-hit (GMH) model offers improved fitting for radiation-induced cell survival curves.
- Previous asymptotic expansions were found to approximate the generalized single-hit single-target (GSHST) model, not the GMH model.
- Accurate asymptotic behavior of the GMH model is crucial for understanding radiation effects across different doses.
Purpose of the Study:
- To improve asymptotic expansions for the GMH model in low- and high-radiation dose ranges.
- To validate the improved expansions against non-linear fitting of the GMH model using experimental cell line data.
- To determine the accuracy, effectiveness, and applicable dose ranges of the refined asymptotic expansions.
Main Methods:
- Utilized the limit formula of the incomplete gamma function to derive improved asymptotic expansions for the GMH model.
- Reduced the improved GMH expansions to known GSHST expansions by setting the upper limit of repairable damages to one.
- Conducted numerical simulations comparing improved expansions with non-linear fitting for six cell lines and analyzed relative errors.
Main Results:
- The improved asymptotic expansions accurately approximate the GMH model's behavior in both low and high radiation dose ranges.
- The GMH model, with these improved expansions, exhibits generalized linear-quadratic-linear (LQL) characteristics.
- Numerical simulations confirmed good agreement between the improved expansions and GMH model fitting, with error analysis defining applicable dose ranges.
Conclusions:
- The refined asymptotic expansions provide a more accurate representation of the GMH model's behavior, particularly at dose extremes.
- These expansions enhance the understanding of radiation-induced cell survival curves and the underlying biological mechanisms.
- The study establishes practical guidelines for applying these improved expansions within specific radiation dose ranges.
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