deletions | additions       diff --git a/M&M - LEM.tex b/M&M - LEM.tex  index 086ccff..ce3700d 100644  --- a/M&M - LEM.tex  +++ b/M&M - LEM.tex 
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= -\int_{V_N} (\alpha_\gamma D_r + \beta_\gamma D_r^2)\ \frac{\text{d}r}{V_N}  \end{equation}  where $n_\text{leth}$ is the density of lesions induced by a local dose $D_r$ delivered in an (supposedly infinitesimal) sub-volume located at a point $r$, and $V_N$ is the volume of the cell nucleus. Thus, in case of a uniform dose, the equation gives back the standard LQ parametrization describing the response to photon irradiation of the cell as a whole, but, when inhomogeneous doses such as those given by GNPs are introduced, the quadratic term causes greater level of damage, explaining why locally heterogeneous doses induce greater biological effects. Following these premises and assuming an uniform radiosensitivity in the nucleus volume, the parameters $\alpha_\gamma$ and $\beta_\gamma$ in Equation \ref{eq_lem} can be identified with the experimentally observed LQ parameters for the irradiation of cells without the GNPs. In this study, the experimental cell control survival LQ parameters from MDA-MB-231 breast cancer cells for 160 kVp, 6 MV and 15 MV irradiations were used \cite{Jain_2011} (see Table \ref{tab_LQ}). The effective radius of each nucleus was set to $R_N=3.5\text{ }\mu\text{m]$ \cite{Fu_2012}.