Purpose: Laser-accelerated ultra-high dose rate proton therapy offers dose rates on the order of 10⁹ Gy/sec. Such dose rates reduce delivery to nanosecond timescales, equivalent to the lifetime of chemical species within a biological medium. This means reactive chemical species from individual tracks could interact and recombine, and tracks can no longer be considered independently. This work investigated the temporal evolution of chemical species for a range of proton LETs to quantify inter-track interactions.
Methods: The TOPAS-nBio Monte Carlo toolkit was used to find the radial dimensions of proton tracks from 1 MeV to 100 MeV between 1 ps to 1 μs timepoints, defined as the radius which contained 80% of the physical and chemical interactions. From this, the likelihood of interaction was calculated using the geometric probability of incident track areas overlapping as a function of dose, time and LET.
Results: Track radius ranged from 50 to 254 nm, increasing with diffusion time after irradiation, and falling with LETs above 2 keV/μm. Physical inter-track effects were rare at clinical doses, with a probability of 32% for 2 Gy of 100 MeV protons, falling to 0.4% for 1 MeV protons due to reduced fluence and track area. Radiochemical overlap probabilities at 1 μs were larger due to diffusion, with over 90% overlap probability predicted for 80 and 100 MeV protons. However, when considering the reduced lifetime of chemical species in cells due to biological scavenging, the likelihood of inter-track effects remains small, with a maximum probability of 29% for a shorter 1 ns diffusion time.
Conclusion: The likelihood of track overlaps has been evaluated in a pure water and scavenging setup, considering both the physical and chemical stages of irradiation. These observations suggest that inter-track interactions play a negligible role at clinically relevant doses, even at ultra-high dose rates.