this is for holding javascript data
Andrea Attili added M&M - stochastic.tex
over 9 years ago
Commit id: a00e999f7d8b26c9192e22d1bbda92eab1da06bb
deletions | additions
diff --git a/M&M - stochastic.tex b/M&M - stochastic.tex
new file mode 100644
index 0000000..d44c899
--- /dev/null
+++ b/M&M - stochastic.tex
...
\subsubsection{Stochastic evaluation}
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.
