A semiclassical model of the immediate temperature distribution surrounding the track of heavy ions with therapeutic energies.

Abstract

Objective.Spikes of high temperature and pressure are created in the vicinity of heavy ions, especially at the Bragg peak. The expected subsequent thermoacoustic effects are however not well understood. In particular, the distribution of the densely packed primary interactions has not been considered in molecular dynamics (MDs) simulations or shock wave solutions. In this work, we derive a dedicated model to describe the primary interactions and their radial distribution, applicable to the modeling of acoustic and thermodynamic effects at the nanoscale.Approach.Starting from first principles, we assemble a semiclassical model of the energy loss of the primary heavy ions, consistent with the expected linear energy transfer and parametrized with the distance from the track. Based on the interaction energies, we then disentangle the primary energy depositions, i.e. the primary excitations and binding energies of the secondary electrons. Thereby we obtain the radial distribution of the primary interactions, independent of empirical parameters. Our theoretical description is kept general, however, numerical results are presented for protons stopped in water. Validity and uncertainties of our model are analyzed in detail.Main results.Following from the sought radial energy distribution, we find that the primary interactions are the dominant energy depositions below a radius of 1 nm. This can give rise to thermal spikes as high as 10³ K even for low-Zprojectiles, such as protons stopped in water. The presented model is valid down to primary proton energies of approximately 0.5 MeV.Significance.Our results can be used to revise the thermodynamic modeling at the nanoscale and investigate their potential involvement in the intriguing biological response to novel modalities such as FLASH or spatially fractionated radiotherapies. Also, our findings can be integrated into microscale track structure Monte Carlo codes, orab initioMD simulations, for more accurate modeling in the nanometer domain.