A Modified Lethal and Potentially Lethal Model for Ultra-High Dose Rate FLASH RT

Abstract

Recently, ultra-high dose rate (> 40Gy/s) radiotherapy (FLASH RT) has gained widespread interest among researchers and clinicians owing to its remarkable normal tissue sparing as well as efficient tumor control compared to conventional radiotherapy (CONV RT) with dose rates around 0.03 Gy/s. As radiobiology modeling has been the foundation of the contemporary clinical practice in radiation oncology, the urgent need for robust mathematical modeling of this paradigm-shifting treatment, FLASH RT, is difficult to overstate. This work proposes a phenomenological model as a potential candidate to explain the observed phenomena. In this study, we combined the oxygen depletion hypothesis and Curtis’ Lethal and Potentially Lethal (LPL) model. Following the oxygen depletion hypothesis on FLASH-induced normal tissue sparing, we introduced a flipped sigmoid shape function to explicitly model the time-dependent component of the radiation-induced lethal and potentially lethal lesion production rates when cells experience oxygen depletion. We conducted both numerical and analytic analyses after we selected a Logistic-type function for demonstration. Parameters from Curtis' LPL model fitting of the C3H 10T 1/2 mouse cell survival data, a generic oxygen enhancement ratio, and two newly introduced parameters describing the time scale and transition width for radiation-induced oxygen depletion were employed in our model. Both numerical and analytical tools were used to obtain the cell survival probability prediction for our modified LPL model. We demonstrated that our modified LPL model would generate asymptotical cell survival probability that decreases exponentially as the radiation dose increases in FLASH RT. Also, the numerical study indicated that our modified LPL model could produce significantly reduced normal tissue cell killings in FLASH RT. For tumor cells, since their cell environment is typically hypoxic, the mechanism mentioned above will have limited impact, and hence tumor cell death will remain at the level similar to that from CONV RT with the same total dose. We also provided an approximated analytical solution of our model’s cell radiation survival prediction for future FLASH RT study. Our modified LPL model predicts that, for normal tissue cells, the difference in the logarithm of surviving fraction between FLASH RT and CONV RT is asymptotically proportional to the radiation dose, and the cell’s oxygen enhancement ratio minus one. This modified LPL model has the potential to explain the prominent normal tissue sparing effect of FLASH RT, with interpretable parameters. Future studies are necessary to quantitatively validate the model predictions in systematically conducted FLASH RT experiments.