deletions | additions       diff --git a/Mat&Met - dose radial profile.tex b/Mat&Met - dose radial profile.tex  index f655035..b2d505f 100644  --- a/Mat&Met - dose radial profile.tex  +++ b/Mat&Met - dose radial profile.tex 
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\subsection{Materials and Methods}  \subsubsection{GNP dose enhancement radial profile simulations}  Knowledge of range and type of secondary particles, such as Auger electrons, photoelectrons or characteristic X-rays, and their variation with the primary photon energy is fundamental to develop a model delineating the GNP-photon interactions. Monte Carlo simulations were carried out using the Geant4 simulation toolkit in which 2 nm GNPs placed at the center of a $10^3$ $\mu$m$^3$ cube of water were uniformly irradiated with different photon energies ranging from 50 keV to 15 MeV. Processes like Auger, photoelectric emission, and interaction of secondaries in nearby atoms were simulated to evaluate the ionization density following irradiation. Energetic cutoff of 10 eV were used for the production of secondary particles. In figure [tracce] are illustrated different track structures A radial symmetry distribution  ofionizing events occurring at  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 inside the following energy deposits in the water volume surrounding the nanoparticles were histogrammed radially, putting the GNP at the origin, with  a 10 bin width of 1  nm GNP up up to a distance of 5000 nm. The simulated dose distribution profiles  following a 40 single ionizing event by a 2 nm GNP in water during irradiation with different monoenegergetic photons with energies between 20  keV irradiation. 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}.