Figure 5. Predicted relative biological effectiveness (RBE) of irradiations of MDA-231 cells (survival parameters α = 0.019 ± 0.025, β = 0.052 ± 0.007¹⁰) in the presence of 500 µg/mL of gold nanoparticles for a variety of nanoparticle sizes exposed to 40 keV X-rays (a) and 20 nm nanoparticles exposed to a variety of energies (b).

These values were calculated either through as the modification in average dose through the addition of the GNPs (circles), or using the Local Effect Model (squares). The change in macroscopic dose is small, on the order of a few %, in good agreement with the ratio of energy absorption coefficients between gold and water (dotted line). By contrast, the LEM predicts significantly higher effectiveness in all conditions, with strong dependencies on both nanoparticle diameter and incident photon energy. Increasing nanoparticle diameter significantly reduces the RBE, which can be understood as the result of increasing numbers of low-energy electrons being trapped inside the nanoparticle and not contributing to dose in the water volume. The dashed line is an empirical fit, as described in the text. The variation with energy was found to be well described by assuming that each ionising event in a gold nanoparticle contributes a fixed additional probability of a lethal event in a cell, which was characterised by a single empirical fitting parameter, taken to be constant at all energies. Good agreement with modelled values was seen at all points, except immediately above gold's K-edge in plot b, where a significant increase in RBE is observed. This is the result of the majority of the photoelectrons which result from K-shell events being produced at relatively low energies (<5 keV), causing them to contribute much more significantly to short-range dose inhomogeneities than at other energies which are distant from absorption edges.