The aim of this study is to build a simulation framework to evaluate the number of DNA double strand breaks (DSBs) induced during in vitro targeted radionuclide therapy (TRT). We validated this tool by characterizing early DSB induction by [177Lu]Lu-DOTA-[Tyr3]octreotate (177Lu-DOTATATE), a commonly used TRT for neuroendocrine tumors. Methods: A multiscale approach is implemented to simulate the number of DSBs produced by the cumulated decays over 4 hours of the beta and IC-electrons components of 177Lu-DOTATATE. The approach involves 2 sequential simulations performed with Geant4/Geant4-DNA. The radioactive source is sampled according to uptake experiments on the distribution of activities within the medium and cells (polygonal mesh models), assuming instant and permanent internalization. A phase space (PHSP) is scored around the nucleus of the central cell. Then, the PHSP is used to generate particles entering the nucleus containing a multi-scale description of the DNA in order to score the number of DSBs per particle source. The final DSB computations are compared to experimental data, measured by immunofluorescent detection of 53BP1 foci. Results: A significant difference was found in the DSB yields induced by activity fractions in cell and medium, which is explained by the specific energy distributions. The average number of simulated DSBs is 14 DSBs/cell (range: 7 - 24 DSBs/cell) compared to 13 DSBs/cell (2-30) experimentally determined. We found a linear correlation between the mean absorbed dose to the nucleus and the number of DSBs/cell: 0.014 DSBs/cell mGy-1 for internalization in the Golgi apparatus and 0.017 DSBs/cell mGy-1 for internalization in the cytoplasm. Conclusion: Our results demonstrate that integrating realistic cellular and organelle geometries and their uptake with a simulation chain characterizing biological damage is crucial to model DNA damage and hence, to find more reliable dose-effect correlations for DSBs with TRT.