Reply to comment on ‘Reproducibility study of Monte Carlo simulations for nanoparticle dose enhancement and biological modeling of cell survival curves’ [Biomed Phys Eng Express 2023;9:045004]

Rabus has highlighted several important aspects on the use of the local effect model for which we are very grateful, specifically the reduction from 3D to 2D. We discuss how our approach can be modified to fall in line with the submitted comments and also discuss concerns regarding "macroscopic dose estimates".

Reply to concerns regarding 'LEM approach in 2D' Rabus (2023) has highlighted several important aspects on the use of the local effect model in his detailed and well laid out comment to our recent article (Velten and Tomé 2023) for which we are very grateful; specifically his comments regarding the overestimation of the number of lethal lesions by using a cut through the equatorial plane of the gold nanoparticle (GNP) to obtain the radial dose in 2D.The average number of lethal lesions is obtained from the volume integral which assuming cylindrical geometry can be rewritten as is the 3D dose kernel averaged over the cylinder's axis of symmetry.In our recent article we omitted this averaging when reducing the dose kernel from 3D to 2D (Velten and Tomé 2023).The resulting difference in the kernel assuming a 2 μm thick cell are shown in figure 1.At distances less than 100 nm the dose around the GNP is reduced by one order of magnitude or more, which will significantly reduce the predicted number of lethal lesions with GNPs inside the nucleus.The differences between the two kernels become smaller at increasing distances and qualitatively negligible past 2 μm.It is clear that this approximation has its limitations.Namely, it assumes that the GNP are located in the center (with respect to z) of the cylinder and that contributions from GNP outside the cell of interest are negligible.The latter appears reasonable, at least to first order, given the sharp dose fall off around the GNP decreasing to well below 1 mGy at 10 μm distance (Velten and Tomé 2023).
Using this new dose kernel, the modeled survival curves change significantly as pointed out by Rabus, shown in figure 2 for 80 keV photons irradiating a cell with uniform distribution of GNP.
Reply to concerns regarding 'macroscopic dose estimates' Rabus (2023) correctly assumes that we report the dose without GNPs as 'macroscopic dose', perhaps imprecisely, but did so in the spirit of previous work where dose has been reported assuming reference conditions without dose modifying agents (McMahon et al 2011a, 2011b, Lin et al 2015, Velten and Tomé 2023).This we believe is in line with translational aspects of the use of dose modifying agents in which prescription doses for external and internal radiotherapy are usually given without the dose modifying effects of cell survival being accounted for.
While increased absorption in GNPs leads to an increase in macroscopically averaged dose, this might not necessarily translate into an increase of the same magnitude in dose to the tissue in which the GNP are located.Moreover, it has been suggested in previous work that predicted increases in macroscopically averaged dose are not enough to entirely explain the observed reductions in cell survival (McMahon et al 2011a, Jain et al 2011).Lastly, average dose with GNPs is not an independent quantity, since local changes in dose deposition around GNPs contribute to the overall macroscopically averaged dose.

Figure 1 .
Figure 1.Comparison of 2D dose kernels of 80 keV photons incident on 50 nm diameter GNP, obtained by using a cut through the equatorial plane of the GNP (  3 D 2D,blue) and using a 2D kernel obtained by averaging the 3D kernel over the z-dimension (⟨ ⟩ 3D , z orange).

Figure 2 .
Figure 2. Survival fractions modeled for uniform cellular distribution of 50 nm GNP and irradiation with 80 keV photons using the cut through the center of the 3D dose kernel (  3 D 2D,blue) and using a 2D kernel obtained by averaging the 3D kernel over the z-dimension (⟨ ⟩ 3D , z orange) compared to without GNP (black).