The good efficacy of radioligand therapy (RLT) targeting prostate specific-membrane antigen (PSMA) for the treatment of metastatic castration-resistant prostate cancer (mCRPC) has been recently demonstrated in several clinical studies. However, the treatment effect of 177Lu-PSMA-ligands is still suboptimal for a significant fraction of patients. In contrast to external beam radiotherapy, the radiation dose distribution itself is strongly influenced by the heterogeneous tumour microenvironment. Although microdosimetry is critical for RLT treatment outcome, it is difficult to clinically or experimentally establish the quantitative relation. We propose an in silico approach to quantitatively investigate the microdosimetry and its influence on treatment outcome for PSMA-directed RLT of two different radioisotopes 177Lu and 225 Ac. The ultimate goal is optimize the combined 177 Lu and 225 Ac-PSMA therapy and maximize the anti-tumour effect, while minimizing irradiation of off-target tissues.Clinical relevance- With the proposed hybrid model we show that 177Lu-PSMA-ligands treatment assures a more homogeneously distributed dose and a lower dependency of the treatment outcome on the domain vascularisation. On the other hand, the 225Ac-PSMA-ligands treatment shows a much stronger efficacy in killing tumor cells with an equivalent mean dose distribution even in an hypoxic environment.