WEIGHTING TRACK SUPERIMPOSITIONS IN ULTRAHIGH DOSE RATE EXPERIMENTS REPORTING A FLASH EFFECT: A COMBINED CHEMICAL TRACK STRUCTURE-STOCHASTIC ANALYSIS

Background and Aims: Among the most investigated hypotheses for a radiobiological explanation of the FLASH effect in radiotherapy, intertrack recombination between chemical species produced by particle tracks arriving within a close spatiotemporal regime, associated with elevated dose rates, has been proposed as a potential driver of damage quenching. The extent of such proximity is intrinsically determined by the temporal modulation of the beam, besides the radical diffusion. In this work, we introduce an analytical framework that expresses track spatiotemporal closeness directly from the beam structure, accounting for stochasticity to identify the proximity scales relevant for modeling and characterizing FLASH-relevant irradiation conditions. Methods: Track arrivals are modeled as a spatiotemporal Poisson random measure, assuming statistical independence in time and spatial uniformity over the irradiated field, to account for the effect of stochastic fluctuations. The time-dependent intensity is constructed directly from irradiation parameters (dose, dose rate, LET, target density, and size) and extended to include explicitly pulsed delivery through periodic macro/micro-pulse structures. Closed-form expressions are derived for the expected number of tracks within a prescribed spacetime proximity window, using autocorrelation functions of the pulse structure. Results: The proposed model provides explicit criteria linking beam temporal structure to track proximity statistics. Micro-pulse structure influences track coincidence only at times shorter than the micro-pulse period, while at longer times the behavior converges to that of the macro-pulse envelope. Similarly, macro-pulse effects vanish when observation times exceed the pulse repetition period, recovering the continuous-beam limit (Figure 1). The analytical predictions for population heterogeneous chemistry were coupled with multi-track simulations performed with an extended version of TRAX-CHEM to assess the impact of track coincidence on heterogeneous chemical stages (Figure 2). TRAX-CHEM simulations confirm that, under realistic UHDR conditions, intertrack interactions at the heterogeneous chemistry scale are generally negligible, becoming appreciable only for low-LET radiation combined with exceptionally high instantaneous dose rates. Conclusions: This work establishes a quantitative framework connecting beam delivery parameters to multiscale track interaction probabilities. By identifying the temporal and spatial regimes where intertrack effects are relevant, the model provides practical guidance for simplifying or refining radiation damage simulations and clarifies the role of beam structure in UHDR scenarios.