Introduction

Metastatic castration-resistant prostate cancer (mCRPC) carries a poor prognosis despite multiple approved therapies with antiproliferative, immunologic, and endocrine effects (1). Targeted radionuclide therapy for mCRPC has gained much interest secondary to the development of small molecules and antibodies that target the prostate-specific membrane antigen (PSMA) (2). PSMA is a surface protein that is overexpressed in over 90% of prostate cancer cases, including mCRPC, and is a promising molecular target for radionuclide delivery based on the clinical success of PSMA-targeted imaging (3). PSMA-targeted radionuclide therapy was shown to successfully treat mCRPC with efficacy on both visceral and osseous metastases (4).

The most commonly used radionuclide in PSMA-targeted therapy is the beta emitter ¹⁷⁷Lu-PSMA-617 (4). With a half-life of 6.6 days, ¹⁷⁷Lu emits low-linear energy transfer (LET) beta particles with a maximum energy of 0.5 MeV and a soft tissue range of 1.7 mm (5). An alternative strategy in PSMA-targeted radionuclide therapy is the use of an alpha emitter such as ²²⁵Ac-PSMA-617 (6). Alpha particles deposit MeV-scale energy within <100 µm range as a form of high-LET radiation, efficiently causing double-strand DNA breaks that lead to cytotoxicity (7). Specifically, ²²⁵Ac decays with a half-life of 9.9 days to produce four alpha particles with 47-85 µm range (6). While there is relative paucity of pre-clinical and clinical literature on ²²⁵Ac-PSMA-617 compared to ¹⁷⁷Lu-PSMA-617, the limited available literature on ²²⁵Ac-PSMA-617 shows a higher biochemical response rate with survival benefit even among patients who previously failed ¹⁷⁷Lu-PSMA-617 therapy (8,9).

Clinical studies that involve ¹⁷⁷Lu-PSMA-617 generally have used 4-9 GBq of radioactivity compared to 4-8 MBq for ²²⁵Ac-PSMA-617 therapy (6,10). The common use of a 1,000-fold lower dose for ²²⁵Ac-PSMA-617 is based on empirical results and extrapolation of organ-level ¹⁷⁷Lu-PSMA-617 dosimetry (11,12). From a physics perspective, the required radioactivity of ²²⁵Ac-PSMA-617 vs. ¹⁷⁷Lu-PSMA-617 to produce a comparable cytotoxic effect on the cellular level remains to be investigated.

The present study used subcellular dosimetry in a 3-dimensional prostate cancer model to calculate the relative efficacy of ²²⁵Ac-PSMA-617 vs. ¹⁷⁷Lu-PSMA-617 for the delivery of absorbed and equivalent radiation doses to the cell nuclei of a single cell, micrometastasis, and macroscopic tumor. An estimation of the equivalent administered doses for the two radiopharmaceuticals was then performed.

Materials and Methods

Biophysical Modeling

Based on the existing literature, several assumptions were made for modeling the radiolabeled PSMA-617 therapy. Once bound to the PSMA protein on the cell surface, the radiolabeled PSMA-617 molecules were considered internalized (Figure 1A) (13). The activity was then considered uniformly distributed within the cytoplasm, based on the endosomal localization of the intracellular PSMA-radiotherapeutic complex (14).

Each prostate cancer cell was modeled as a sphere that contains a concentric, spherical nucleus (Figure 1B) (15). The cellular and nuclear diameters of 14 and 10 µm were used, respectively, based on the previously published cultured human prostate cancer cell measurements (16). For multicellular dosimetry, prostate cancer cells were considered densely packed in a 3-dimensional face-centered cubic structure with maximal packing efficiency, where each cell was in contact with 12 adjacent cells as previously illustrated (17). The distance between a given cell and each shell of neighboring cells was calculated up to the desired tumor size using a sub-lattice approach (18).

Subcellular Dosimetry

The physical decay data of the ²²⁵Ac and ¹⁷⁷Lu were obtained from the MIRD Radionuclide Data and Decay Schemes (19). MIRDcell v2.1 (Newark, NJ) was used to obtain the self and cross-dose S values for the decay of ²²⁵Ac and ¹⁷⁷Lu, including the daughter isotopes of ²²⁵Ac (15). The contribution from every cell in the tumor model was considered for cross-dose calculation. The radiation dose to the cell nucleus at the center of the tumor was used to estimate the cytotoxic efficacy for one decay event in each tumor cell. The conversion from absorbed dose to equivalent dose was made using the value of 5 for the relative biological effectiveness (RBE) of alpha particles (11,20).

The equivalent dose per decay was first scaled by the physical half-lives of the radionuclides to account for the difference in residence time to compare the equivalent dose per administered activity. The difference in the tumor cell uptake per administered activity was estimated by the relative tumor uptake level between ²²⁵Ac-PSMA-617 and ¹⁷⁷Lu-PSMA-617. The tumor uptake levels were based on the recently published ex vivo biodistribution work in the RM-1 mouse model of prostate cancer with 100% PSMA expression (21).

Subcellular dosimetry was first performed in a single cell to compare the relative efficacy of ²²⁵Ac-PSMA-617 and ¹⁷⁷Lu-PSMA-617 in circulating tumor cells. Then, micrometastatic disease was modeled up to 100 µm diameter. Finally, in a macroscopic tumor (>2 mm radius), the results of subcellular dosimetry were compared against conventional macroscopic dosimetry based on uniform distribution of activity within a spherical volume (Figure 1B).

The study did not involve any statistical analysis.

Results

Single-cell Dosimetry

For each decay event, ²²⁵Ac-PSMA-617 deposited 0.129 Gy in the nucleus resulting in a 464-fold higher absorbed dose compared to ¹⁷⁷Lu-PSMA-617, which deposited 2.78×10^-4 Gy. The equivalent dose per decay was 2,320-fold higher in favor of ²²⁵Ac-PSMA-617 taking into account the RBE of 5.

Micrometastasis

As the size of the micrometastasis increased, the absorbed dose from ²²⁵Ac-PSMA-617 initially linearly increased up to approximately 50 µm in radius (R²: 0.99), and then reached an asymptote at approximately 85 µm to reach 2.06 Gy per decay in each tumor cell (Figure 2A). In comparison, the absorbed dose from ¹⁷⁷Lu-PSMA-617 continued to increase linearly (R²: 0.99) with the tumor size and reached 3.55×10^-3 Gy per decay at 100 µm radius (Figure 2B). In relative scale, the equivalent dose per decay was over 4,000-fold higher for ²²⁵Ac-PSMA-617 compared to ¹⁷⁷Lu-PSMA-617 up to 60 µm radius (Figure 2C). As the tumor size increased, the relative dose difference between the two radiopharmaceuticals gradually decreased, reaching a 2,900-fold difference at 100 µm tumor radius.

Macroscopic Tumor

The absorbed dose per decay in each tumor cell was 165-fold higher for ²²⁵Ac-PSMA-617 (2.06 Gy) compared to ¹⁷⁷Lu-PSMA-617 (1.25×10^-2 Gy), which translated to an 823-fold difference in equivalent dose with RBE of 5, based on subcellular dosimetry. Using the conventional dosimetry, ²²⁵Ac-PSMA-617 and ¹⁷⁷Lu-PSMA-617 deposited 2.25 Gy and 1.26×10^-2 Gy per decay, resulting in a 178-fold and 892-fold difference in the absorbed and equivalent doses, respectively.

Relative Equivalent Dose Per Administered Activity

The longer physical half-life of ²²⁵Ac conferred 50% longer residence time to ²²⁵Ac-PSMA-617 compared to ¹⁷⁷Lu-PSMA-617. After scaling using this factor, the relative differences in equivalent dose per administered activity (²²⁵Ac-PSMA-617 vs. ¹⁷⁷Lu-PSMA-617) were 3,480-fold, 4,350-fold, and 1,230-fold for a single cell, 100 µm-radius micrometastasis, and macroscopic tumor, respectively. Then, using 3.4 times higher uptake per administered activity for ²²⁵Ac-PSMA-617 (4.66% injected dose/g of tumor) compared to ¹⁷⁷Lu-PSMA-617 (1.36% injected dose/g of tumor) (21), the relative differences in equivalent dose per administered activity (²²⁵Ac-PSMA-617 vs. ¹⁷⁷Lu-PSMA-617) were 11,800-fold, 14,900-fold, and 4,200-fold for a single cell, 100 µm-radius micrometastasis, and macroscopic tumor, respectively.

Discussion

Dosimetry using imaging-based measurements of ²²⁵Ac-PSMA-617 uptake is challenging due to the low administered activity and unfavorable physical decay characteristics of ²²⁵Ac with low gamma emission probability and the competing Bremsstrahlung radiation (11). Therefore, previous dosimetry on ²²⁵Ac-PSMA-617 and ²²⁵Ac-PSMA-I&T extrapolated the uptake of respective ¹⁷⁷Lu-labeled analogs on imaging (11,12,22). Alternatively, extrapolation of ⁶⁸Ga-PSMA-617 uptake on positron emission tomography was previously used for dosimetry of ²¹³Bi-PSMA-617 (20). However, recent studies have shown that the degree of radiolabeled PSMA-617 uptake differs based on the radionuclide (23,24), which suggests that independent characterization of ²²⁵Ac-PSMA-617 uptake will improve its dosimetry. At present, the only study that examined the tumor uptake of ²²⁵Ac-PSMA-617 and ¹⁷⁷Lu-PSMA-617 is the pre-clinical study by Current et al. (21), where ex vivo activity measurements were used for accurate uptake estimation. The study was based on a mouse model without human validations, thus we considered the 3.4-fold higher ²²⁵Ac-PSMA-617 uptake only as a possibility and interpreted the unscaled results as the lower bound of the relative efficacy of ²²⁵Ac-PSMA-617.

Conventional organ-level dosimetry fails to take into consideration the subcellular distribution of the radiopharmaceutical even if accurate tumor uptake measurements could be obtained. It leads to radiation dose overestimation for an alpha emitter with cytoplasmic localization, such as ²²⁵Ac-PSMA-617, and underestimation for an alpha emitter with nuclear localization. In addition, organ-level dosimetry cannot be applied to microscopic tumor deposits that are smaller than the range of alpha or beta particles. In contrast, the dosimetry model used in the present study incorporates the subcellular location of a radiopharmaceutical for accurate estimation of alpha and beta radiation dose at all tumor sizes of interest.

Two observations of interest were made in a macroscopic tumor. First, ²²⁵Ac-PSMA-617 delivered at least 1,230-fold higher and possibly 4,200-fold higher equivalent dose per administered activity compared to ¹⁷⁷Lu-PSMA-617, which may explain the better efficacy of ²²⁵Ac-PSMA-617 when 1,000-fold lower activity was administered in the clinical setting and even with subsequent de-escalation to 4 MBq doses (8,25). Second, conventional macroscopic dosimetry calculation resulted in no difference for ¹⁷⁷Lu-PSMA-617 and overestimation by 9% for ²²⁵Ac-PSMA-617 compared to the subcellular dosimetry estimates of the radiation dose to the cell nuclei. The cross-fire effect of beta particles resulted in normalization of radiation dose within the tumor regardless of the subcellular source location for ¹⁷⁷Lu-PSMA-617, whereas the subcellular dose estimation for ²²⁵Ac-PSMA-617 was slightly lower due to the absence of alpha emission from the cell nucleus. For both ²²⁵Ac-PSMA-617 and ¹⁷⁷Lu-PSMA-617 therapy, conventional organ-level dosimetry yields acceptable dose estimates in measurable tumors.

In micrometastatic disease and circulating tumor cells, the alpha particles from ²²⁵Ac-PSMA-617 were far more potent than beta particles from ¹⁷⁷Lu-PSMA-617, resulting in at least 3,000-4,000 times and possibly 10⁴ times higher efficacy per administered activity. The findings are in keeping with the recognized advantage of alpha radiation in killing single cells and micrometastatic clusters (7). Therefore, at currently used doses, ²²⁵Ac-PSMA-617 likely exerts a stronger cytotoxic effect on radiologically occult metastases, which will otherwise survive ¹⁷⁷Lu-PSMA-617 treatment due to insufficient cross-fire effect. While the therapeutic effect on micrometastatic disease may not produce a large decline in PSA, it potentially contributes to the overall survival and progression-free survival benefits that are seen in ²²⁵Ac-PSMA-617 therapy (8,9).

The calculated relative efficacy values can be applied to estimate the dose contribution from each radionuclide in the setting of tandem therapy with ²²⁵Ac-PSMA-617/¹⁷⁷Lu-PSMA-617. For example, in a previously used treatment regimen that involves the median activities of 5.3 MBq ²²⁵Ac-PSMA-617 and 6.9 GBq ¹⁷⁷Lu-PSMA-617, the dose contribution of ²²⁵Ac-PSMA-617 relative to ¹⁷⁷Lu-PSMA-617 would be at least 94% for a macroscopic tumor. The contribution would increase to at least 270% and 330% for a single cell and micrometastatic cluster, respectively. The present study focused on radiolabeled PSMA-617 due to the larger body of available literature, but the results can be applied to dosimetry of PSMA-targeted radionuclide therapy using other molecules such as ²²⁵Ac/¹⁷⁷Lu-PSMA-I&T.

The present study used physical dose estimates for comparison of theoretical efficacy, but its translation to clinical efficacy would be affected by differences in the radiobiological effects of alpha and beta particles. For example, untargeted effects, such as bystander or abscopal effect, may modify the dose-efficacy relationship by different degrees for alpha and beta particles (26). Direct DNA damage due to high-LET alpha particles does not require the presence of oxygen, whereas hypoxia has a high impact on low-LET radiation, which relies on reactive oxygen species formation for cytotoxicity (27,28). In addition, cytotoxicity due to high-LET radiation was previously shown to be independent of dose rate, likely due to the difficulty in repairing complex double-strand DNA breaks (29). Proliferating cells are more susceptible to ionizing radiation in general, but the cell cycle status of target cells affects the efficacy of low- and high-LET radiation to different extents (30). Beyond radiobiological considerations, increased tumor cell death may not necessarily produce a meaningfully better disease response or survival benefit on a patient level. Therefore, much remains to be known about the downstream consequences beyond radiation dose deposition in radionuclide therapy of prostate cancer.

Study Limitations

In addition to the difficulty in tumor ²²⁵Ac-PSMA-617 uptake estimation, our study has several limitations. Mainly, the assumptions made in the simplified dosimetry model may be challenged. Intra-tumor heterogeneity in PSMA expression has been reported (31), and variable non-spherical shapes of prostate cancer cells were previously described (16). When ²²⁵Ac decays before the internalization into endosomes, the daughter isotopes are no longer linked to PSMA-617 due to the recoil energy of alpha decay, which results in reduced dose deposition to the target cell (32). Radiation dose deposition outside the cell nucleus can also result in cytotoxicity by indirect effects (33). The RBE of 5 for alpha radiation is commonly employed (11,20) and is an oversimplification as discussed above, lacking validation in the setting of ²²⁵Ac-based therapy in prostate cancer. Finally, the study does not address the toxicity that is associated with PSMA-targeted radionuclide therapy, which is not necessarily PSMA-mediated (34).

Conclusion

The equivalent radiation dose deposited by alpha-emitting ²²⁵Ac-PSMA-617 is higher in measurable disease and especially higher in microscopic disease compared to beta-emitting ¹⁷⁷Lu-PSMA-617 at commonly administered doses based on subcellular dosimetry. Possible differences in tumor uptake based on the labeled radionuclide can lead to further amplification of the relative efficacy of ²²⁵Ac-PSMA-617. Additional research is needed for tumor ²²⁵Ac-PSMA-617 uptake characterization on both macroscopic and microscopic levels, as well as for an improved understanding of the biological effectiveness of alpha radiation in prostate cancer.

Ethics

Ethics Committee Approval: Not applicable.

Informed Consent: Not applicable.

Peer-review: Externally and internally peer-reviewed.

Financial Disclosure: The author declared that this study has received no financial support.