Pulse-resolved tumor control probability modeling for FLASH radiotherapy using a variable-time treatment-course framework

OBJECTIVE: FLASH radiotherapy introduces beam temporal structure at the pulse and sub-pulse scale, whereas most tumor control probability (TCP) models are formulated at the fraction or treatment-course scale. This study developed TCP_LRF, a pulse-resolved extension of the published Lee-Rosen time-dependent TCP formulation, here denoted TCP_LR, to connect FLASH beam microstructure, oxygen/radical kinetics, biological repair, and treatment-course repopulation.
Approach: TCPLR was used as the parent treatment-course TCP model because it accommodates variable interfraction timing and kick-off-time-dependent accelerated repopulation. Its conventional cumulative survival term was replaced by a FLASH-aware survival term derived from a reduced-order oxygen/radical ordinary differential equation kernel. Each FLASH fraction was represented as a pulse train. The same oxygen/radical kinetics, lesion-yield calculation, and post-fraction repair layer were also implemented for standard-dose-rate continuous delivery to provide an internal comparator. The implementation was verified against uniform-dose benchmarks reported in the original Lee-Rosen publication describing TCP_LR and then evaluated using exploratory FLASH, repair, pulse-structure, and standard-dose-rate scenarios.
Main results: Conventional verification reproduced published benchmark trends, with maximum absolute differences of 1.44, 1.21, and 3.48 percentage points for head-and-neck, breast, and prostate cases, respectively. In a 3 × 8 Gy starter case, calibrated null-FLASH TCP was 0.790. Moderate chemistry and strong radical recombination yielded TCP values of 0.713 and 0.703, respectively, whereas mild oxygen limitation reduced TCP to 0.276. Standard-dose-rate continuous delivery produced negligible oxygen depletion under null and moderate chemistry assumptions, while deliberately oxygen-limited standard-dose-rate cases showed reduced TCP.
Significance: This exploratory framework provides a mechanistic treatment-course TCP platform for hypothesis testing in FLASH radiotherapy. It demonstrates how pulse microstructure and continuous standard-dose-rate delivery can be evaluated within the same published variable-time TCP_LR formulation, while showing that FLASH TCP behavior depends on oxygen/radical kinetic assumptions, pulse structure, repair, and oxygen availability rather than being universally preserved or reduced.