The effect of non-ionizing excitations on the diffusion of ion species and inter-track correlations in FLASH ultra-high dose rate radiotherapy

Purpose. We present a microscopic mechanism that accounts for the outward burst of 'cold' ion species (IS) in a high-energy particle track due to coupling with 'hot' non-ion species (NIS). IS refers to radiolysis products of ionized molecules, whereas NIS refers to non-ionized excitations of molecules in a medium. The interaction is mediated by a quantized field of acoustic phonons, a channel that allows conversion of thermal energy of NIS to kinetic energy of IS, a flow of heat from the outer to the inner core of the track structure. Methods. We perform step-by-step Monte Carlo (MC) simulations of ionizing radiation track structures in water to score the spatial coordinates and energy depositions that form IS and NIS at atto-second time scales. We subsequently calculate the resulting temperature profiles of the tracks with MC track structure simulations and verify the results analytically using the Rutherford scattering formulation. These temperature profiles are then used as boundary conditions in a series of multi-scale atomistic molecular dynamic (MD) simulations that describe the sudden expansion and enhanced diffusive broadening of tracks initiated by the non-equilibrium spectrum of high-energy IS. We derive a stochastic coarse-grained Langevin equation of motion for IS from first-principle MD to describe the irreversible femto-second flow of thermal energy pumping from NIS to IS, mediated by quantized fields of acoustic phonons. A pair-wise Lennard-Jones potential implemented in a classical MD is then employed to validate the results calculated from the Langevin equation. Results. We demonstrate the coexistence of 'hot' NIS with 'cold' IS in the radiation track structures right after their generation. NIS, concentrated within nano-scale volumes wrapping around IS, are the main source of intensive heat-waves and the outward burst of IS due to femto-second time scale IS-NIS coupling. By comparing the transport of IS coupled to NIS with identical configurations of non-interacting IS in thermal equilibrium at room temperature, we demonstrate that the energy gain of IS due to the surrounding hot nanoscopic volumes of NIS significantly increases their effective diffusion constants. Comparing the average track separation and the time scale calculated for a deposited dose of 10 Gy and a dose rate of 40 Gy s(-1), typical values used in FLASH ultra high dose rate (UHDR) experiments, we find that the sudden expansion of tracks and ballistic transport proposed in this work strengthens the hypothesis of inter-track correlations recently introduced to interpret mitigation of the biological responses at the FLASH-UHDR (Abolfath et al 2020 Med. Phys. 47, 6551-6561). Conclusions. The much higher diffusion constants predicted in the present model suggest higher inter-track chemical reaction rates at FLASH-UHDR, as well as lower intra-track reaction rates. This study explains why research groups relying on the current Monte Carlo frameworks have reported negligible inter-track overlaps, simply because of underestimation of the diffusion constants. We recommend incorporation of the IS-NIS coupling and heat exchange in all MC codes to enable these tool-kits to appropriately model reaction-diffusion rates at FLASH-UHDR. Novelty. To introduce a hypothetical pathway of outward burst of radiolysis products driven by highly localized thermal spikes wrapping around them and to investigate the interplay of the non-equilibrium spatio-temporal distribution of the chemical activities of diffusive high-energy particle tracks on inter-track correlations at FLASH-UHDR.