This study was a retrospective analysis of the first cycle of five patients diagnosed with mCRPC and treated with 7.7 ± 0.2 MBq [225Ac]Ac-PSMA-I&T (Table 1). All patients gave written consent to undergo radioligand therapy (RLT). All data has been irreversibly anonymized before evaluation. The local ethics committee approved the study (project no. 22–0544). Patients were hospitalized for 48 h after injection, as obliged by the German law for radiation protection. Further details on labelling and therapy can be found in the publication by Zacherl et al. [4].

During their stay in the ward, the patients were scheduled for two post-therapeutic abdominal SPECT/CT scans 24 and 48 h post-injection (p.i.). SPECT/CT acquisition was performed on a dual-headed Symbia T2 SPECT/CT (Siemens Medical Solutions, Erlangen, Germany) equipped with a high-energy collimator and a 3/8″ crystal. Sixteen projections per head were obtained with a matrix size of 128 × 128 pixels (4.7952 × 4.7952 mm2) and an acquisition time of 210 s per projection. SPECT/CT imaging used the 440 keV (213Bi) and 218 keV (221Fr) photopeaks of the 225Ac decay chain (width of 20% for both peaks) [10, 13, 18]. In addition, a lower peak at 78 keV (width, 50%) was measured [19,20,21,22]. A low-dose CT scan (110 keV, CareDose, slice thickness 3 mm) was performed along with each SPECT scan. To improve patient comfort, patients were positioned with arms down, whereupon the arms were fixed close to the torso via a cloth belt. To obtain additional knowledge about the excretion of 213Bi compared to 225Ac, two urine samples were collected from all patients right before or right after each SPECT/CT scan.

SPECT images for all photopeaks were reconstructed using an in-house maximum-a-posterioriexpectation-maximization (MAP-EM) algorithm. Attenuation correction was performed based on the low-dose CT, while scatter correction employed a transmission-dependent scatter correction (TDSC) method [23]. Resolution modelling was based on a pre-simulated 2D point-spread-function model [10]. For the 440 keV peak, the 80th iteration was used for the analysis. For the 78 and 218 keV peaks, the 100th iteration was used for the analysis.

To convert measured counts per second and per voxel (cps/voxel) to becquerel per milliliter (Bq/ml), calibration factors were determined for each energy window. This was performed using a cylindrical calibration phantom (diameter of 25.5 cm; total volume of 8.7 l), homogeneously filled with an activity concentration of 524 Bq/ml (total activity of 4.56 MBq). A large volume-of-interest (VOI) was placed in the reconstructed cylinder volume to extract the average counts per pixel. Imaging and reconstruction of the calibration phantom were carried out using the same protocol as used for patient imaging.

Reconstructed SPECT/CT images were analyzed using PMOD (Version 3.609, PMOD Technologies, Zurich, Switzerland). For each of the patients, the kidneys and all of the lesions that were visible in the abdominal region were evaluated (Table 1; no lesions were available in the field of view for patient 1). Before segmentation, all SPECT images were filtered for noise suppression using a Gaussian filter with a full-width-half-maximum of 30 mm. This filter parameter was chosen as it provides the best compromise between signal-to-noise ratio and recovery coefficients in kidneys and lesions, similar to a previous study [10]. Both kidneys were segmented using the CT accompanying each SPECT scan. Lesions were segmented using an isocontour of 80% of maximum tissue intensity on the SPECT acquired at 24 h post-therapy. These VOIs were transferred to the SPECT at 48 h afterwards. In case of misalignment with the SPECT/CT 24 h p.i., VOIs were manually shifted. Lesion segmentation was performed separately for each of the peaks.

Mean standardized uptake values (SUV) in the VOIs were calculated for kidneys and lesions at 24 and 48 h p.i. for the three peaks. The 213Bi and 221Fr SUV were tested for correlation (via Python 3.9 Pearson correlation coefficients). These SUVs were then also compared to the SUV for 78 keV.

The total VOI activities at 24 and 48 h p.i. were then loaded into Spyder (Python 3.9) software, and a conventional mono-exponential model (Eq. 1) was fitted to the data points to generate the time-activity curve (TAC). The mono-exponential model is given by the following:

$$A\left(t\right)=A\left(t_0\right)\cdot e^\left(2\right)}}\cdot t\right)},$$

(1)

where \(_\) is the effective half-life (\(_=\frac}\left(2\right)}_}}+_}}}\), where \(_}}\) and \(_}}\) are biological and physical decay constants, respectively); \(A(t)\) is the total VOI activity at a given time point \(t\) post-injection. The effective half-life (\(_\)) and initial activity (\(A\left(_\right)\)) were used as the free parameters during the fitting process.

From the fitted model (Eq. 1), the lesion and kidney effective half-lives for 213Bi and 221Fr were determined from the 440 and 218 keV SPECT images, respectively. These effective half-lives were tested for correlation afterwards (via Python 3.9 Pearson correlation coefficients). The lesion and kidney effective half-lives were also derived based on imaging of the 78 keV, and respective values were compared with those obtained for 213Bi and 221Fr. The RBE-weighted absorbed doses of the kidneys and lesions were estimated based on the MIRD formalism [24] with the usage of a RBE of 5 [11]. Kidney and lesion dosimetry accounted for self-irradiation only. The RBE-weighted absorbed doses were calculated using three different methods. For the first two methods, the 440 (213Bi) and 218 (221Fr) keV peaks were used separately. Here, it was assumed that the localization of 225Ac and all subsequent daughters is described by SPECT imaging of either 440 (213Bi) (referred to as method 1 in this paper) or 218 (221Fr) keV peak (referred to as method 2 in this paper), respectively. For the third method (referred to as method 3 in this paper), the RBE-weighted absorbed doses for 225Ac were derived by combining the 213Bi and 221Fr components. The first component is based on the assumption that the localization of 225Ac, 221Fr, and 217At is described by SPECT imaging of the 221Fr photopeak at 218 keV due to the short half-lives of 221Fr and 217At (4.8 min and 32 ms, respectively [13]). More precisely, dosimetry was performed based on the effective half-life as extracted from 221Fr SPECT imaging at 24 and 48 h p.i. and by summing up the energy deposition due to self-irradiation by 225Ac,221Fr, and 217At. For the second component, it was similarly assumed that 213Bi SPECT imaging is representative for 213Bi and all subsequent daughters. S-values were taken from the open-access online resource OpenDose [25]. The SPECT images of the 78 keV peak were not included in the dosimetry analysis.

Additionally, the statistical analysis via Python 3.9 Wilcoxon signed-rank testing was performed to compare the kidney and lesion absorbed doses. For every patient, each kidney was compared with each lesion (a total of 13 kidney-lesion pairs). This method was chosen to provide sufficient data for comparison and to increase statistical power.

For each of the urine samples, 1 ml was pipetted into a test tube immediately after sample collection and analyzed for at least 6 h in a HIDEX gamma counter (HIDEX, Turku, Finland), until secular equilibrium was reached. Counts were measured in the same photopeaks as for the SPECT acquisitions. For 213Bi, the obtained data points were then fitted by using a model (Eq. 2), which describes the total activity of 213Bi via two components: 213Bi, which is generated by 225Ac decaying in the samples (first term of the equation), and 213Bi activity being already present in the samples at the time of sample collection (second term of the equation):

$$_}}\left(t\right)=_}}\left(0\right)\left(\frac_}}}_}}-_}}}\right)\left(^_}}\cdot t}-^_}}\cdot t}\right)+_}}\left(0\right)^_}}\cdot t}.$$

(2)

\(t\) is the time passed after sample collection; \(_}}\left(t\right)\) is the total 213Bi activity over time; \(_}}\left(0\right)\) and \(_}}\left(0\right)\) refer to the 225Ac and 213Bi activity at the time of sample collection (t = 0), and \(_}}\) and \(_}}\) are the 213Bi and 225Ac physical decay constants, respectively [26]. In this equation, the short-lived daughter nuclides 221Fr and 217At are ignored, assuming that 225Ac decays directly into 213Bi. By fitting the aforementioned model to the data points acquired by the gamma counter measurement, \(_}}\left(0\right)\) and \(_}}\left(0\right)\) can be derived.