deletions | additions       diff --git a/M&M - stochastic.tex b/M&M - stochastic.tex  index d44c899..078fba5 100644  --- a/M&M - stochastic.tex  +++ b/M&M - stochastic.tex 
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Since quantities defined in Eq. \ref{eq_lemam}, $S_\text{GNP}^{(j)}$ and $N_\text{GNP}$, have to be intended as stochastic variables, a Monte Carlo approach was applied to the LEM-AM to evaluate the cell survival as a function of dose and GNPs concentration. A set of $N_c = 1000$ cells was simulated generating different random uniform distributions of GNPs inside their nuclei. The total number of GNPs, $N_\text{GNP}$, inside each nucleus followed a Poisson distribution. The average number of GNPs was considered as a free parameter of the model to be adjusted to experimental data.  A Poissonian process was also simulated to identify the number of ionization events for each GNP inside the nucleus, where the average number of ionization per GNP per Gy, $N_\text{ion}$, was estimated from Monte Carlo simulations. This number depends on the total dose D delivered to the cell. The possibility of having more than one ionization event per GNP was included 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. GNPs ionization rates were extrapolated from the simulations and found to be $4 \times 10^{−7}$, $2.35 \times 10^{−7}$ 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 reported in \cite{McMahon_2011,McMahon_2011a}.