Framework to calculate ²²⁵ Ac, ¹⁷⁷ Lu, and ¹⁶¹ Tb radiation dose and biological effect in metastatic castration‐resistant prostate cancer treatment

Abstract Background In the treatment of metastatic castration‐resistant prostate cancer (mCRPC), the standard radionuclide 177 Lu (β⁻ emitter) is being challenged by alternatives, particularly the α‐emitter 225 Ac and Auger electron emitter 161 Tb, due to their superior radiobiological properties. These include higher linear energy transfer (LET) and shorter ranges, which enhance localized cell killing while minimizing off‐target effects. While these radionuclides induce DNA damage both in source‐cells and neighboring cells (crossfire effect), their distinct radiation profiles provide critical metrics to compare their therapeutic efficacy. By quantifying these differences, especially in micrometastatic settings, the optimal radionuclide for specific clinical scenarios could be selected. Purpose This Study aims to develop a comprehensive pipeline based on Monte Carlo (MC) simulations to compare the therapeutic efficacy of 225 Ac, 177 Lu, and 161 Tb in the treatment of mCRPC based on clinically administered activity (7.4 GBq for 177 Lu, 161 Tb, and 7 MBq for 225 Ac) in a multi‐cell model. Besides evaluating the absorbed dose at the cellular level, the Biological Effect Cell Kernel (BECK) method is proposed to compare the radiobiological effect of radionuclides, accounting for the crossfire effect using 3D convolution. Methods A 2 µm resolution cell model was constructed with a 20 µm cell, an 8 µm nucleus diameter, and a 26 µm center‐to‐center distance. This configuration resulted in a cellular fraction of 0.24 mL/g, in agreement with that estimated from six prostate cancer patients using CT Perfusion. The prostate time‐integrated activity (TIA) in the model was estimated from a patient based on a dynamic 300 MBq 18 F‐DCFPyL PET scan after scaling to account for the higher administered activity in therapy. The TOPAS‐nBio MC tool was used to calculate the absorbed dose and the DNA breaks in the cell model. To account for the crossfire effect, we created the BECK, an isotropic 3D kernel, demonstrating the DNA breaks in the source‐containing cell, and those induced in its neighboring cells. The BECK was convolved with the 3D TIA maps of the cell model to obtain the DNA break maps. Results The cellular absorbed dose was higher than the macro‐scale dose based on SPECT‐derived TIA, by 31.3%, 15.7%, and 39.8% for 225 Ac, 177 Lu, and 161 Tb, respectively. At the single‐cell level, 225 Ac induced markedly higher DNA breaks per source – 48 double‐strand breaks (DSBs), and 32 complex DSBs, compared to 177 Lu – 0.022 and 0.017, and 161 Tb – 0.083 and 0.073, respectively. Crossfire effects were dominant for 255 Ac and 177 Lu at ∼75% and less pronounced for 161 Tb at ∼41%. The maximum ranges at which 99.99% of the total DNA breaks were observed were approximately 85 µm for 225 Ac, 150 µm for 177 Lu, and 110 µm for 161 Tb. Conclusions DPKs and BECKs of 2 2 ⁵Ac, ¹⁷⁷Lu, and ¹⁶¹Tb were developed to quantify cellular‐level dose distributions and biological efficacy, revealing micrometer‐scale heterogeneity accentuated by short‐range emissions (α, CEs, AEs). Results demonstrate ¹⁶¹Tb's optimal performance for micrometastases—surpassing ¹⁷⁷Lu's efficacy with lower toxicity than 2 2 ⁵Ac—while relative biological effectiveness predicts activity requirements: 2 2 ⁵Ac << ¹⁶¹Tb < ¹⁷⁷Lu.

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