deletions | additions       diff --git a/Mat&Met - dose radial profile.tex b/Mat&Met - dose radial profile.tex  index b2d505f..3097cfe 100644  --- a/Mat&Met - dose radial profile.tex  +++ b/Mat&Met - dose radial profile.tex 
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A radial symmetry distribution of the energy deposition from secondary electrons emitted from the nanoparticle was assumed [McM11a] and reconstructed through the simulations. The phase-space of the secondary electrons was sampled on the GNP surface and the following energy deposits in the water volume surrounding the nanoparticles were histogrammed radially, putting the GNP at the origin, with a bin width of 1 nm up up to a distance of 5000 nm. The simulated dose distribution profiles following a single ionizing event by a 2 nm GNP in water during irradiation with different monoenegergetic photons with energies between 20 keV and 15 MeV are shown in figure [radial dose, panel A]. The actual shape of the radial dose profile to be found in a realistic treatment irradiation was obtained through a weighted superposition of the 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. It was observed that the different energy spectra shapes were not fundamental to the investigation, as the only relevant parameter resulted to be the probability of ionization per nanoparticle per Gy. An example of the radial energy deposition profile evaluated for the simulated photon and secondary electron spectrum of a 6 MV Linac, sampled at a depth of 5 cm in a water phantom, is reported in figure [radial dose, panel B and C]. The obtained dose distribution profiles were used as input to a radial function which was exploited to calculate the number of lethal events upon a determinate distance from the nanoparticles center. GNPs ionization rates were extrapolated from the simulations and found to be $4 \pm 10^{−7}$, $2.35 \times 10^{−7}$ and $2.25 \times 10^{−7}$ per GNP per Gy for 160 kVp, 6 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 calculated in \cite{MacMahon_2011}. \cite{McMahon_2011}.