Impact of metal nanoparticles on cell survival predicted by the local effect model for cells in suspension and tissue. Part 1: theoretical framework

This work investigates the change in cell survival predicted by the local effect model (LEM) for an irradiated cell containing metal nanoparticles (MNPs) depending on the distribution of neighboring cells and the uptake of MNPs into the cells. In this first part of the paper, the theoretical framework is described, which is based on analytical weighting functions for the energy deposition around a single MNP and radially symmetric distributions of MNPs. The weighting functions allow calculation of the radial profile of the absorbed dose in the cell nucleus as well as the mean dose and the mean square of the dose in the nucleus. The latter two quantities determine cell survival according to the LEM. The weighting functions are applied to isolated cells in a localized MNP distribution, cells in solution, and densely packed cells in tissue. It is shown that only for the idealistic case of complete uptake of MNPs it is sufficient to consider an isolated cell, as this otherwise leads to significant underestimation in more realistic situations. In the case of cells in tissue, the MNP concentration within the range of secondary particles around the cell must be taken into account. Different packing densities of the cells may lead to values differing by up to 30% for the mean dose in the cell nucleus, depending on the conceived scenario for the uptake of MNPs. The weighting function offers a versatile method for assessing cell survival under irradiation in the presence of MNPs by the LEM, which is more general than previously reported approaches which relied on a power-law dependence of the radial dose distribution.