Purpose: Ultra-high dose-rate (FLASH) irradiation has produced remarkable normal tissue sparing while keeping the tumor cell control rate similar to Conventional (CONV) irradiation in recent in-vitro/in-vivo experiments. This study mathematically explores the cell survival fraction (SF) and radiation dose relationship based on the radiation-induced oxygen depletion hypothesis. A straightforward single ultra-short radiation pulse FLASH experimental setup is utilized for this proof-of-concept investigation.
Methods: When an ultra-short radiation pulse hits a cell, it causes a sudden drop in intracellular oxygen tension. Oxygen diffusion will subsequently restore the concentration over a time called characteristic time τ. Radiation can cause direct and indirect damages to a cell. The probability that the damages are 'fixed' by oxygen molecules to form DNA lesions in the cell is assumed to decrease exponentially in time with a decaying constant λ. Using quasi-static approximation, we estimate the cell's Oxygen Enhancement Ratio reduction during its intracellular oxygen tension recovery. Combining SF at the high dose rate limit from Curtis' Lethal and Potentially Lethal (LPL) Model, we then derive the radiation cell SF following a single FLASH radiation pulse.
Results: We have derived the cell radiation SF following a single FLASH pulse. The result indicates that single-pulse FLASH irradiation's sparing effect depends on τ, λ, the cell's LPL model parameters and OER parameters, and its initial intracellular oxygen tension ρ₀. A large amount of radiation dose is usually needed to make the FLASH sparing effect observable. The effect is prominent for a cell in aerobic condition and diminishes when a cell is in a hypoxic state. Numerical analysis is performed for the C3H10T1/2 cell to demonstrate our results.
Conclusion: The radiation-induced oxygen depletion hypothesis is a leading theory to explain the FLASH RT effect. Our results lend potential quantitative validations. More studies are needed to understand the FLASH effect clearly.
Funding Support, Disclosures, and Conflict of Interest: This work is supported by a Great Plains IDeA-CTR Pilot Grant.