Analytical Approach to Calculate Normal Tissue Complication Probability and Tumor Control Probability for Ultra-High Dose Rate Radiation (FLASH) Based on Linear-Quadratic Model 📝

Author: Santosh K. Agarwalla, Nrusingh C. Biswal, Shree C, Harikrishnan Suresh Kumar, Jajati K. Nayak, Prema P., Sarath K S, Tamil Selvan S, Hem D. Shukla 👨‍🔬

Affiliation: Variable Energy Cyclotron Centre, Department of Physics, Fakir Mohan University, Department of Radiation Oncology, University of Maryland School of Medicine, Department of Sciences, Amrita Vishwa Vidyapeetham 🌍

Abstract:

Purpose: The rapid oxygen depletion in tissues during irradiation is the most accepted mechanism of the FLASH effect. However, the Normal Tissue Complication Probability (NTCP) and Tumor Control Probability (TCP) of tissues after FLASH irradiation are not analytically calculated. This study aimed to find an analytical expression for calculating NTCP and TCP of tissues with FLASH radiation.

Methods: We introduced the Oxygen Enhancement Ratio (OER) obtained from the oxygen kinetic model into the modified Poisson cell kill model by redefining LQ parameters, deriving the analytical expression of NTCP for FLASH-RT. Similarly, we considered LQ parameters and OER to re-derive the analytical expression of TCP for FLASH-RT, based on the sigmoidal function of relative effectiveness (RE).

Results: In the case of FLASH-RT, the NTCP and TCP for bladder, rectum, femoral head, and neck tissues were calculated using the analytical expressions derived in this work. We observed that for bladder tissue, with a total dose of 40 Gy, a FLASH-RT dose rate of 100 Gy/s, exhibits NTCP around 0%; whereas at lower dose rates (<4 Gy/s), NTCP is around ~100%. In contrast, TCP due to the FLASH dose rate does not show a remarkable change from the conventional dose rate. For a total dose beyond 30 Gy, the calculation of TCPs for any dose rate, completely merges and gives a nearly constant value. A similar trend is observed for the rectum, femoral head, and neck tissues, and in agreement with the published experimental values.

Conclusion: The NTCP and TCP of different tissues are calculated for FLASH radiation theoretically confirming that the NTCP due to FLASH is remarkably less than conventional radiations. These results show that these models can be applied to get NTCP and TCP estimates for pre-clinical and clinical research and treatment purposes for FLASH-RT.

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