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\subsubsection{Additive model approximation}  In order to have a full local dose distribution throughout a cell, the heterogeneities introduced by gold nanoparticles have to be added to the uniform background dose level delivered by photons which do not interact with the nanoparticles. A relatively simple approximation of the LEM, here called additive model (LEM-AM), was formulated by considering the contribution of different nanoparticles in a cell as non-synergistic. In this approximation it is assumed that an a  uniform nanoparticle distribution inside the cell nucleus can be described as a system containing a certain number of GNPs which are independent to one another \textit{i.e.}, whose associated induced dose distributions do not overlap significantly with one another. This approximation is justified by the very low ionization rates estimates estimated  per GNP. Sincethe  nanoparticles do not interact, they can be thought to be independent systems systems,  each giving their own contributions. The net contribution to the survival of the cell can be thus evaluated by multiplying each survival given by one single nanoparticle, and then combining it with a background survival in which there are no nanoparticles \begin{equation}\label{eq_lemam} \begin{equation}  \label{eqn:eq_lemam}  S  = {S_\gamma} \times_{MF} S_\text{GNP}  = {S_\gamma} \times_{MF} \prod_{j=1}^{N_\text{GNP}} S^{(j)}_\text{GNP}