deletions | additions       diff --git a/subsection_Clinical_response_evaluation_subsubsection__.tex b/subsection_Clinical_response_evaluation_subsubsection__.tex  index badfeb1..250db97 100644  --- a/subsection_Clinical_response_evaluation_subsubsection__.tex  +++ b/subsection_Clinical_response_evaluation_subsubsection__.tex 
...
\subsection{Clinical response evaluation}  \subsubsection{GNPs distribution}  In an ideal scenario labeled nanoparticles that combine the intrinsic EPR effect with an active targeting  should be preferentially taken up by cancerous cells. A model with a Dirac delta-like distribution of GNPs was supposed for this work \textit{i.e.}, the GNPs concentration was assumed to be at its highest inside the tumor volume, and at its lowest in the normal tissues surrounding it. Given the right premises, this means that the dose enhancement due to the presence of gold should be observed exclusively in the cancerous cells.  It was assumed a A  (relatively) fast washout effect that cleans the treatment region from GNPs in the interfraction period (24 h). h) was assumed.  This assumption is supported by in-vivo \textit{in vivo}  estimations of the time constant of the GNPs uptake decay \cite{Miladi2014}. In this scenario a complete somministration administration  procedure should be repeated for each fraction. From these premises it follows that a similar GNPs distribution can be found for each fraction. Amodel with a Dirac delta-like distribution of GNPs was supposed \textit{i.e.}, the GNPs concentration was assumed to be at its highest inside the tumor volume, and at its lowest in the normal tissues surrounding it. Given the right premises, this means that the dose enhancement due to the presence of gold should be observed exclusively in the cancerous cells.  A  saturation ofthe  GNPs uptake in the tumor cells was also assumed. Each tumor cell was set to contain a maximum number of nanoparticles $N_\text{max} = \bar N_\text{GNP}$, while the concentration of GNPs to be found in the normal tissues varied with a parameter $\sigma$, essentially expressing the accuracy of the uptake selection. The distribution of GNPs was thus calculated by the following: \begin{equation}  f_\text{GNP} U_\text{GNP}  = e^{- \frac{d^2(x_i,PTV)}{2 \frac{d^2(x_i,\text{PTV})}{2  \sigma^2}} \end{equation}  \noindent  where $d^2(x_i,PTV)$ $d^2(x_i,\text{PTV})$  represents the minimal distance from each voxel \textit{i} of the normal tissues to the tumor region. Different values of sigma were considered to evaluate the distribution: in particular, $\sigma = 0 \ mm$ (relative to a precise concentration of GNPs inside the tumor volume alone), and $\sigma = 5, 10, 20, 30, 50 \ mm$ (relative to increasingly defective distributions with increasing number of GNPs in the normal tissues surrounding the tumor). Also, different values of the maximum number of nanoparticles to be found inside the tumor volume, each relative to a nominal concentration of GNPs, were considered.