Analytical approximation of the nanoscale dose distribution in an irradiated medium with an embedded nanoparticle

In this work we propose an analytical approach describing the dose distribution around a NP embedded in a medium. The approach describes the following sequence of events: The homogenous and isotropic creation of secondary electrons under incident photon fluence; travel of the created electrons toward the NP surface and their escaping from the NP with different energies and angles; deposition of energy in surrounding medium. The radial dose distribution around the NP was found as the average energy deposited by the escaped electrons in a spherical shell at a distance r from the NP center normalized to its mass. The continuous slowing down approximation and the assumption that created electrons travel in a straight-line path were used. As result, a set of analytical expressions describing the dose distribution was derived. The expressions were applied to the calculation of the dose distribution around spherical gold NPs of different size embedded in water. It was shown that the dose distribution is close to the 1/r² dependence and practically independent of the NP radius.