deletions | additions       diff --git a/M&M - stochastic.tex b/M&M - stochastic.tex  index ea017f7..1826a02 100644  --- a/M&M - stochastic.tex  +++ b/M&M - stochastic.tex 
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Since quantities needed to evaluate Eq. AM are stochastic variables, a Monte Carlo approach was applied to the LEM-AM to evaluate the cell survival as a function of dose and GNP concentration.  A set of $N_c = 1000$ cells was simulated with a total number of GNPs, $N_\text{GNP}$, inside each cell nucleus generated from a Poisson distribution. The average number of GNPs per cell was considered as a free parameter of the model to be fitted to the experimental data. A Poissonian process was also simulated to identify the number of ionization events for each GNP inside the nucleus. Thephoton spectra dependent  average number of ionizations per GNP per Gy, from which the number of ionization events was evaluated, is photon spectra dependent and it  was extrapolated from the Monte Carlo simulations, simulations. Considering the spectra at the surface of the hypothetical patient, the values  $\bar{N}^0_\text{ion} = 4.0 \times 10^{-7}$, $2.35 \times 10^{-}7$ and $2.25 \times 10^{-7}$ per GNP per Gy, 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}. The possibility of having more than one ionization event per GNP was considered in the simulations even if the probability decreases rapidly as the number increases, in order to observe the effects that more than one ionization from the same nanoparticle could give.