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Modeling the Cell Inactivation Process for High LET Particles by Using the Law of Mass Action

L Perles

L A Perles*, U Titt, D Mirkovic, R Mohan, UT MD Anderson Cancer Center, Houston, TX

SU-E-T-297 Sunday 3:00PM - 6:00PM Room: Exhibit Hall

Purpose: To develop a method to model the cell inactivation caused by photons or light ions irradiation that accurately describes the survival curves for various linear energy transfer (LET) as well as high dose survival curves.

Methods: We adapted the law of mass action widely used in physical chemistry to model the cell inactivation process through a differential equation. Its solution depends on two parameters, D₀ and p. D₀ is positive and represents the dose that causes a survival of 37%; p is a dimensionless parameter equal or greater to 1. We evaluated our model using data available in the literature for four human cancer cell lines (DU-145, CP3, U1690 and H460) exposed to ¹³⁷Cs and doses up to 20 Gy; and to V79 cells exposed to 240 kVp x-rays and to light ions (protons, deuterons and ³He) of various LET ranging from 10 to 105 keV um⁻¹.

Results: Our model was capable to fit survival curves for the human cancer cell lines up to 20 Gy as good as the linear quadratic model. Dâ‚€ was determined with uncertainty better than 4% and ranged from 2.7 to 3.8 Gy; p was determined with uncertainty better than 6% and ranged from 1.3 to 1.7. For the V79 data, the parameters Dâ‚€ and p exhibited a well-defined exponential dependence on the LET. Also, the p was found to approach 1 asymptotically, as predicted by the theory. The RBE as a function of LET was also accurately determined.

Conclusion: The adapted law of mass action for the radiobiology provides an accurate model to study the cell survival curves under various conditions. Furthermore, it sets useful limits to the parameters that could be verified experimentally.

Funding Support, Disclosures, and Conflict of Interest: NCI grant P01CA021239

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