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Veronica added section_Results_subsection_Radial_dose__.tex
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\section{Results}
\subsection{Radial dose simulations}
The simulated dose distribution profiles following a single ionizing event by a 2 nm diameter GNP in water during irradiation with different monoenergetic photons with energies ranging from 20 keV to 15 MeV are shown in figure \ref{radial_dose}, panel C.
The actual shape of the radial dose profile to be found in a realistic treatment was obtained through a weighted superposition of monoenergetic profiles, using specific photon spectra. For this work, spectra resulting from 160 kVp, 6 and 15 MV irradiation in water were analysed to evaluate the GNP ionization rate. The spectra are reported in the same figure (panel A and B). Some representative radial dose distributions evaluated from the complete photon spectra are also reported in the plot in panel C. Radial dose profiles were simulated also for 160 kVp (not reported here), in order to provide the physical input parameters for the survival simulation to be compared with the in-vitro data at low energy.
Form the simulated dose profiles in water, ionization rates per gray are also extrapolated. Considering the spectra at the surface of the hypothetical patient, the values $\bar{N}^0_\text{ion} = 4 \times 10^{-7}, 2.35 \times 10^{-7}$, and $2.25 \times 10^{-7}$ per GNP per Gy, were obtained for 160 kVp, 6 MV and 15 MV respectively. The latter values are in line with what would be expected at megavoltage energies by the gold mass attenuation coefficient and are consistent with those reported in \cite{McMahon_2011, McMahon_2011a}. These rates show that, at megavoltage energies, most of the nanoparticles do not contribute in the dose-deposition processes.
