Relationships between linear-quadratic parameters for cells irradiated in the presence and absence of cisplatin

Relevance. According to experimental data, administration of the drug cisplatin into the tumor during radiation therapy can increase its effectiveness. To date, there is no model that can predict the effectiveness of such therapy. The development of such a model is an important task for planning therapy. The goal of this work is to find analytical relationships for the survival of cells exposed to the combined effect of radiation and cisplatin in vitro. Materials and methods. Based on digitized experimental data on cell survival from a number of publicly published works, the corresponding linear-quadratic (LQ) approximation coefficients for survival were found for irradiation without the drug \( \alpha_R , \beta_R \), and for combined exposure to radiation and cisplatin \( \alpha_{RC} , \beta_{RC} \). Next, a regression analysis of the resulting set of coefficients and cell survival when exposed to cisplatin alone \( S_C \)  was performed. Results and Discussion.\( \alpha_{RC} \)  was found to be statistically dependent on \( \alpha_R, \beta_R \) and \( S_C \). This dependence could be described by several models, the best of which in terms of a number of indicators was \( \alpha_{RC} = \alpha_R + \alpha_R \ln S_C \), where \( \alpha = -4.27 \pm 0.57 \) is a parameter that is the same for all cell types and experimental conditions. It was found that \( \beta_{RC} \) is statistically dependent on \( \beta_R \). No signs of dependence of \( \beta_{RC} \) on \( \alpha_R \) and \( S_C \) were found. The best model for \( \beta_{RC} \) was \( \beta_{RC} = \beta_R \). These models are simple, but they allow predicting the value of cell survival under the combined effect of radiation and cisplatin \( S_{RC} \) from the values \( \alpha_R , \beta_R \) and \( S_C \) only approximately. The obtained models are collated with kinetic equations and a mechanistic interpretation is given, which is based on the hypothesis of a decrease in the rate of recovery of cells from potentially lethal lesions r , with an increase in the radiation dose and cisplatin concentration. Conclusion. The type of statistical dependence of LQ coefficients \( \alpha_{RC} \) and \( \beta_{RC} \) on \( \alpha_R , \beta_R \) and \( S_C \) has been found. In the case of high toxicity of cisplatin (low values of \( S_C \)), the combination of the above-mentioned models for \( \alpha_{RC} \) and \( \beta_{RC} \) allows to make a useful for practical application prediction of cell survival \( S_{RC} \). The results of this work will help for the future construction of more complex models of the combined effects of radiation and cisplatin, and may also have practical application in the case mentioned above.