A Consensus Time for Performing Quality Control of 225 Ac-Labeled Radiopharmaceuticals

Background: As 225 Ac-labeled radiopharmaceuticals continue to show promise as targeted alpha therapeutics, there is a growing need to standardize quality control (QC) testing procedures. The determination of radiochemical purity (RCP) is an essential QC test. A significant obstacle to RCP testing is the disruption of the secular equilibrium between actinium-225 and its daughter radionuclides during labeling and analysis. In order to accelerate translation of actinium-225 targeted alpha therapy, we aimed to determine the earliest time point at which the RCP of an 225 Ac-labeled radiopharmaceutical can be accurately calculated. Results: Six ligands were conjugated to macrocyclic metal chelators and labeled with actinium-225 under conditions designed to generate diverse incorporation yields. RCP was determined by radio thin layer chromatography (radioTLC) followed by exposure of the TLC plate on a phosphor screen either 0.5, 2, 3.5, 5, 6.5, or 26 h after the plate was developed. The dataset was used to create models for predicting the true RCP using pre-equilibrium measurements at early time points. The 585 TLC measurements span RCP values of 1.8% to 99.5%. The statistical model created from these data predicted an independent data set with high accuracy. Predictions made at 0.5 h are more uncertain than predictions made at later time points. This is primarily due to the decay of bismuth-213. At 2 h the mean average error is < 3%. A measurement of RCP > 90% at this time point predicts a true RCP > 97%. These findings were independently validated using NaI(Tl) scintillation counting and high resolution gamma spectroscopy on a smaller set of samples with 10% ≤ RCP ≤ 100%. Conclusions: RCP of 225 Ac-labeled radiopharmaceuticals can be quantified with acceptable accuracy at least 2 h after radioTLC using various methods of quantifying particle emissions. This time point best balances the need to accurately quantify RCP with the need to safely release the batch as quickly as possible. determine the earliest at which analysis of the TLC plate be performed with high predictive accuracy for Herein we present a statistical analysis of over 500 radioTLC results performed at various time points with vectors that gave a range of radiometal complexation. Using this analysis, we predict the RCP at secular equilibrium for radiopharmaceuticals bearing either bifunctional DOTA or bifunctional N,N′ -bis[(6-carboxy-2-pyridyl)methyl]-4,13-diaza-18-crown-6 (macropa) chelating moieties from multiple measurements taken before equilibrium is reached. Our model proposes a suitable time at which the RCP of 225 Ac-labeled radiopharmaceuticals can be predicted with sufficient accuracy to permit batch release.


Introduction
Targeted alpha-particle therapy (TAT) shows great promise in the treatment of cancer most recently exemplified by the successful introduction of 223 RaCl2 (Xofigo®) for the treatment of skeletal metastases (1)(2)(3). Recently, TAT using astatine-211 (4,5), lead-212 (6), bismuth-213 (7)(8)(9), and actinium-225 (10,11) has been investigated for the treatment of multiple cancers. Actinium-225 decays through six daughter radionuclides to stable bismuth-209 by emission of four alpha particles and two beta particles with a halflife of 9.92 days. The high yield of alpha particles per decay (12,13) and the growing supply (14) contribute to an increasing number of investigators exploring the use of actinium-225 for TAT. Clinical evaluations of [ 225 Ac]Ac-DOTATOC (15), [ 225 Ac]Ac-PSMA-617 (16-18), and [ 225 Ac]Ac-DOTA-Substance P (19) report significantly improved responses in patients with neuroendocrine tumors, prostate cancer, and glioma, respectively. Dramatic responses are even observed in patients refractory to beta-particle therapy (11). In addition to these small molecule radioligands, [ 225 Ac]Ac-J591 is currently in Phase I clinical trials for radioimmunotherapy of prostate cancer (20). Given these early and promising findings clinical investigations using actinium-225 TAT will likely continue to grow.
Each batch production of a radiopharmaceutical for clinical use must undergo quality control (QC) testing to meet release criteria before being dispensed to the patient. A critical release parameter is radiochemical purity (RCP); the proportion of the total radioactivity in a sample present as the desired radiolabeled species, the 225 Ac-labeled vector. Currently, the RCP of 225 Ac-labeled radiopharmaceuticals is primarily assessed using radio thin-layer chromatography (radioTLC) and a mobile phase that effectively separates non-complexed radiometals and radiolabeled impurities from the desired radiopharmaceutical. However, the complex decay chain of actinium-225 renders quantification of RCP challenging because daughter radionuclides may not be complexed to the vector and may distribute across the chromatographic plate in a manner that overlaps with the radiolabeled vector. Highly accurate quantification of RCP for 225 Ac-labeled radiopharmaceuticals requires secular equilibrium to be reached between actinium-225 and its daughter radionuclides. Secular equilibrium is reached after 20 h (27,28), but such a long delay in assessment is impractical in a clinical production setting. Consequently, sites producing 225 Ac-labeled radiopharmaceuticals wait between 1 h and 12 h after running the TLC plate before quantifying RCP (11,23,29,30). Such a range of practices introduces variability to the radiopharmaceutical production and QC process. Ultimately, this may lead to confounding results when clinical evaluations are compared across multiple sites and potentially delay approval of the radiopharmaceutical by governing regulatory agencies.
To work toward a consensus quality control protocol for 225 Ac-labeled radiopharmaceuticals, we aimed to determine the earliest time at which analysis of the TLC plate can be performed with high predictive accuracy for RCP. Herein we present a statistical analysis of over 500 radioTLC results performed at various time points with vectors that gave a range of radiometal complexation. Using this analysis, we predict the RCP at secular equilibrium for radiopharmaceuticals bearing either bifunctional DOTA or bifunctional N,N′bis[(6-carboxy-2-pyridyl)methyl]-4,13-diaza-18-crown-6 (macropa) chelating moieties from multiple measurements taken before equilibrium is reached. Our model proposes a suitable time at which the RCP of 225 Ac-labeled radiopharmaceuticals can be predicted with sufficient accuracy to permit batch release.

Radiolabeling Experiments
In order to generate a diverse range of radiochemical yields, reactions were performed using various chelators conjugated to a targeting vector, varying the concentration of the chelator-vector conjugate, and varying reaction time and temperature. All reactions were performed in triplicate. Six small molecule ligands targeting prostate-specific membrane antigen (PSMA), RPS-072 (31), RPS-074 (32), EuK-106 (33), EuK-107 (33), RPS-088, and RPS-092 ( Figure S1), were prepared as stock solutions of 0.01-1 mg/mL in DMSO. Actinium-225 (9.25 MBq) was obtained from a thorium generator (34) at Canadian Nuclear Laboratories and supplied as the dried [ 225 Ac]AcCl3 salt. The [ 225 Ac]AcCl3 was dissolved in 1 mL 1 M NH4OAc, pH 7.0, transferred by pipette to a 50 mL centrifuge tube (Corning), and diluted to 45 mL in 1 M NH4OAc. One mL of the stock solution, containing approximately 205 kBq [ 225 Ac]Ac(OAc)3, was transferred by pipette to a plastic Eppendorf tube placed on a digital ThermoMixer (Eppendorf) heating block. Then 20 µL of the ligand stock solution (0.01-1 mg/mL in DMSO) was added and the reaction was shaken at 300 rpm at either 25 °C or 95 °C for 15 min (Table 1). A 3 µL aliquot of the reaction mixture was withdrawn and deposited on the origin of a silica gel 60-coated aluminum plate (Sigma Aldrich) after incubating the reaction for 1 min, 5 min, and 15 min.

Compound
Chelator Reaction conditions for radiolabeling. Conditions were selected to increase diversity rather than to maximize radiochemical yield. The chelator associated with each molecule is indicated. Full structures are provided in Figure S1.

Analysis of Reaction Yield
After the final aliquot was deposited, the plate was immediately run in freshly prepared mobile phase comprised of 10% v/v MeOH/10 mM EDTA (in H2O). A separate plate containing a 3 µL aliquot of a solution of [ 225 Ac]Ac-EDTA was run as a control. The plates were developed until the solvent front traveled at least 60% of the total plate length (35-45 min). Upon removal from the mobile phase, the plates were dried and then assayed by direct exposure on a phosphor screen for a 2 min at 0.5 h, 2 h, 3.5 h, 5 h, 6.5 h, and 26 h after drying using a Cyclone Plus Storage Phosphor System (Perkin Elmer). The phosphor screen was erased with homogenous white light (5 min exposure) between assay exposures. The retention factors, Rf, of the radiolabeled vectors were 0.0-0.3, while [ 225 Ac]Ac-EDTA (and daughter radionuclides present at time of spotting) migrated mainly toward the solvent front (Rf > 0.7). Labeling yields were determined using OptiQuant™ software (Perkin Elmer) by fitting a boxed grid to the plate and quantifying the counts in all regions. Radiochemical yield was defined as the ratio of the counts in the box corresponding to the labeled product to the sum of the counts in all boxes ( Figure 1). Experimentally-determined radiolabeling yield was plotted as a function of analysis time using GraphPad Prism 8 (GraphPad Software).

Statistical predictive modeling:
All statistical modeling was performed in the R environment (version 3.5.0, R Foundation for Statistical Computing, Vienna, Austria). Ninety-nine observation sets (11 initial reaction conditions x 3 reaction times x 3 replicates) were randomly assigned to training and validation sets (66 sets to the training set and 33 sets to the validation set). As the labeling percentage for the samples were bounded between 0 (0%) and 1 (100%), a generalized linear model with binomial link was fit to the data in the training set to model the relationship between the empirically-measured yield at 26 h (defined as the true RCP) and the time of each observation, the yield of the observation at that time point, and the interaction between the two. Samples with a value of 0.9 or more at 26 h were weighted 10 times more than the other samples in the model in order to optimize our model for predictions of values in this area. Predictions from the model were made in the validation set and mean absolute error (MAE) was calculated in the validation set for strata of each time (predictions using data at 0.5 h, 2 h, 3.5 h, 5 h, and 6.5 h). We also report a predicted outcomes table, where the generalized linear model was retrained using the entire dataset, continuing to weight the samples in the manner described above. The predicted RCP at 26 h from the model for each of the measured values is reported as well as 95% prediction intervals.
We fit a random forest classification model (35,36) on the training set to predict labeling percentage above a given threshold. The predictors in this model include the time that a given observation is made and the yield of that observation. Models were fit using a discrimination threshold of 0.9 (90%) or 0.95 (95%). For a threshold of 0.9, there were 140 observations ≥ 0.9 in the data set, and 190 observations < 0.9. For a threshold of 0.95, there were 125 observations ≥ 0.95 in the data set, and 205 observations < 0.95. A receiver operating characteristic (ROC) curve is plotted for each classification model in the validation set, and area under the curve (AUC) and 95% confidence interval (CI) are reported.
The model was validated using an independent data set consisting of observations made at 0.5, 1.5, 2.0, 2.5, and 26 h. The MAE of the predictions are reported at each time point.

Mathematical modeling
The decay of actinium-225 and its daughter nuclei was modeled based on ten general assumptions: 1. All low probability emissions in the actinium-225 decay chain ( Figure 1A) were disregarded ( Figure  1B). 2. The detection efficiency of β-and α-emissions by the phosphor screen was considered to be equal.  3+ . This assumption is based upon the size selectivity of macropa towards metals with larger atomic radii (39). 5. There are at least 320 times more actinium-225 atoms than bismuth-213 atoms in solution at any given time point, therefore 99% of the bismuth-213 is bound by DOTA in the time that 1% of the actinium-225 is chelated. 6. At time 0 after spotting and before running the TLC, all the activity is at the origin. 7. The TLC plate can be divided into three sections, representing the radiolabeled complex (1, Figure  1C), [ 225 Ac]Ac(OAc)3 (or [ 225 Ac]Ac-EDTA) that was not bound at the time of spotting (3, Figure 1C), and a mixture of [ 225 Ac]Ac-EDTA that did not run homogenously and daughter nuclei emitted while the plate was running (2, Figure 1C). The content of these sections was determined experimentally by radioTLC analysis of the [ 225 Ac]Ac(OAc)3 control. 8. All metal ions that were uncomplexed at the time of spotting migrated with the solvent front (Rf > 0.7). 9. The two main radioactive equilibria governing the activity distribution on the TLC plate are those established by actinium-225 and bismuth-213 when purified from their precursors. 10. Lead-209 (t1/2 = 3.25 h) has a sufficiently long half-life that its contribution to radiochemical equilibrium must be taken into account. Consequently, each actinium-225 and bismuth-213 disintegration, which produces 6 and 3 particles, respectively, must be discounted due to the slower decay of lead-209 to bismuth-209. Equations describing the expected activity in each grid of the TLC plate were derived and plotted using Origin (OriginLab). Expected activity distribution was determined by solving the equations at 0.5 h, 2 h, 3.5 h, 5 h, 6.5 h, and 26 h. A 3-dimensional (3D) surface plot of analysis time versus experimentallydetermined radiolabeling yield was derived for each group of compounds sharing the same chelator moiety. Similar three-dimensional (3D) plots were prepared for analysis time versus mathematically modeled radiolabeling yield. Differences between experimentally-derived radiolabeling yield and modelpredicted yield were compared statistically by a paired t-test. A threshold of p < 0.05 was used to define statistical significance.

Radiolabeling
Mean radiolabeling yield after 1 min, as assessed 26 h after running the TLC, ranged from 2.7 ± 0.55% to 98.8 ± 0.09%. The highest radiochemical yields were obtained with the macropa-conjugates RPS-074 and RPS-088, which exceeded 97% at a ligand concentration of 9-10 μM. The range after 5 min was 3.8 ± 1.95% to 99.0 ± 0.04%, and the range after 15 min was 11.2 ± 5.25% to 99.2 ± 0.32%. RPS-074 and RPS-088 were rapidly labeled at 25 °C, and there was no significant change in labeling yield when ligand concentration decreased from approximately 10 μM to approximately 1 μM. At a ligand concentration of approximately 0.1 μM, radiolabeling yield was highly variable, ranging from 5.9% to 92.1%. EuK-107, bearing an amine analogue of the 3p-C-DEPA chelator, was rapidly labeled at 95 °C, while DOTA-containing RPS-072 reached 93.2 ± 1.21% after 15 min at 95 °C and a ligand concentration of 9 μM. In agreement with previously published results (33), EuK-106 was labeled poorly (24.8 ± 2.36%) even after 15 min at 95 °C.  Table 1. Activity distribution on the TLC plates was visualized at the specified times using a Cyclone Plus Storage Phosphor System. Quantification of labeling was performed using OptiQuant™ software. Each data point represents a unique measurement, with measurements taken from the same reaction at different time points joined by a curve. A. DOTAcontaining ligands (RPS-072, EuK-106, EuK-107). B. Macropa-containing ligands (RPS-074, RPS-088, RPS-092). C. All Compounds Three clusters of radiolabeled compounds were observed ( Figure 2). For those compounds that were efficiently labeled (> 85% as determined at 26 h), early analysis time underestimated radiolabeling yield (RCY). The radiolabeling of compounds labeled with moderate efficiency, 50% ≤ RCY ≤ 75% at 26 h, was estimated with reasonable accuracy at early analysis times. Finally, the labeling of compounds with low RCY (< 40% at 26 h), is overestimated at early analysis times.

Statistical predictive modeling
We developed a statistical model to predict the true RCP of an unpurified reaction based on pre-secularequilibrium measurements. The predicted RCP and true RCP are well matched for reactions with high yield (RCY ≥ 85%) and low yield (RCY ≤ 25%). In the intermediate range 25% ≤ RCY ≤ 85%, predictions generally overestimate the true RCP ( Figure 3). The accuracy of the predictions is lowest at 0.5 h, at which time MAE is 0.053 (5.3%). For TLC reads performed from 2 h onwards, the accuracy of the model is high. MAE is 3.2% at 2 h, decreases to 2.6% at 3.5 h and 5 h, and 2.9% at 6 h. This indicates that labeling yield may be overor underestimated by no more than 3% after 2 h. The analysis was also performed separately for the macropa-containing ligands RPS-074, RPS-088, and RPS-092, and for the DOTA-containing ligands RPS-072, EuK-106, and EuK-107. Neither sub-analysis differed significantly from the analysis using the entire data set ( Figure S2-S4, Tables S1, S2). The model was validated using an independent data set collected for radiolabeling of a macropaconjugated antibody ( Figure S5). The predictions of the model were highly accurate, with an MAE of 1.3% at 0.5 h that decreases to 0.9%, 0.8%, and 0.8% at 1 h, 1.5 h, and 2 h, respectively (Table S3). We therefore used our statistical model to predict the true RCP on the basis of TLC measurements at earlier time points. Our model predicts that labeling yield in excess of 90%, as measured at any time point, is highly likely to translate to a true labeling yield greater than 95% ( We derived two classification models to further evaluate the accuracy of our predictions. With a discrimination threshold of 0.9, which corresponds to 90% labeling yield, the predictive accuracy of the model is 99% (160/162) ( Figure 4A). Both of the incorrect predictions are made at the 0.5 h analysis time point. An increase of the discrimination threshold to 0.95 results in a slight decrease in predictive accuracy to 91% (147/162) ( Figure 4B). Much of the discrepancy between prediction and true outcome is due to "false positives" (14/162), in which the prediction overestimates the true yield. The AUC of both curves exceeds 0.95, confirming the high accuracy of the tests.

Decay modeling
Independently, we developed a physical decay model to explain the shapes of the curves in Figure 2 and support our interpretation of the activity distribution on the radioTLC plate. This implies that all labeled compounds, irrespective of structure, are located in grid section 1 ( Figure 1C) immediately after running the TLC, 40% of the metals not bound by the ligands (parent and daughter radionuclides that did not run homogeneously on the TLC plate) are in section 2, and the remaining 60% of these metals are in section 3. 3. For ligands bearing macropa, 60% of the bismuth-213 not bound by the ligands (30% of the initial amount due to decay) is in section 3, and 40% (20% following decay) is in section 2 immediately after running the TLC. 4. For ligands bearing DOTA or DOTA derivatives, the majority of bismuth-213 will be complexed by the ligands and retained in section 1. Small activities of daughter radionuclides will be observed in sections 2 and 3.
On this basis, activity in each TLC grid was expressed as a sum of the activities corresponding to actinium-225 and bismuth-213. For the ligands RPS-072, EuK-107, and EuK-106, which contain DOTA or a DOTA derivative, the sums are described by the equations in Figure 5A. Activity in section 1 of the TLC is due to the contribution of the decay of bound actinium-225, the contribution of bismuth-213 generated from actinium-225 decay, and the contribution of bound bismuth-213 that was present as part of the initial equilibrium. The activity in section 2 is due to actinium-225 that was not bound by the ligands and did not run homogeneously on the TLC plate, and bismuth-213 generated by the decay of this actinium-225 ( Figure S6). Finally, the activity in section 3 is due to the bulk of the actinium-225 (which migrated with the solvent front upon transformation to the 225 Ac-EDTA complex) and the bismuth-213 produced by the decay of this actinium-225 ( Figure 6). The equations describing macropa-containing ligands RPS-074, RPS-088, and RPS-092 are presented in Figure 5B. Activity in section 1 of the TLC is due to actinium-225 bound by the ligands and daughter radionuclides generated by decay of the parent actinium-225 ( Figure S7). The contributions to section 2 are actinium-225 and bismuth-213 that were not bound by the ligands at the time of spotting and did not run homogeneously on the TLC plate, and the decay of the actinium-225 to its daughters. Activity in section 3 is due to the contribution of the bulk actinium-225 and the bulk bismuth-213, transformed into EDTA complexes upon exposure to the mobile phase, and the daughter radionuclides generated by decay of actinium-225 ( Figure 6). The physical decay model supports our interpretation of the activity distribution on the TLC plate and rationalizes the shapes of the curves plotted in Figure 2. Early measurement of the DOTA-containing ligands overestimates the labeling yield when the true yield is ≤ 40% (Figure 7). When the yield is ≥ 80%, however, early measurement underestimates the true value. This is largely due to discrepancies in TLC section 1 ( Figure S8). Activity in TLC sections 2 and 3 is underestimated at early time points, but the difference between predicted yield and true yield is less than 3% over the 26 h. These deviations from the true yield also arise in the modeled data, indicating that they are a consequence of the disruption of secular equilibrium rather than a systematic experimental error.
By contrast, early measurement underestimates the labeling yield for macropa-containing ligands, particularly when true reaction yield is high (≥ 80%) (Figure 7). In this case, the discrepancy is the result of overestimation of actinium-225 in sections 2 and 3 of the TLC grid ( Figure S6). As secular equilibrium is approached, the differences between the experimentally-determined yield or the decay-modelled yield and the true yield reduce significantly, independent of the chelating moiety ( Figure S9). The differences are statistically significant at the 30 min and 2 h analysis times (p < 0.01), but not at later analyses (p > 0.1) (Table S4).

Discussion
Despite the 9.92 d half-life of actinium-225, it is advantageous to be able to administer a 225 Ac-labeled radiopharmaceutical as soon as possible after radiosynthesis is completed. One advantage is the simplification of logistics: the radiopharmaceutical can be prepared and administered locally during normal business hours. Ideally, the radiolabeling is performed with high efficiency, allowing the reaction mixture to be buffered and directly administered to the patient without a purification step. It is therefore advantageous to determine as quickly as possible whether an additional purification step is required to remove uncomplexed actinium-225 prior to administration of the radiopharmaceutical. Secondly, a shorter shelf-life may guarantee the radiochemical purity of the radiopharmaceutical by virtue of minimizing the number of decays that occur while the compound is in its final formulation, thereby avoiding product decomposition owing to radiolysis. Each decay of actinium-225 results in the emission of one α-particle, with simultaneous recoil of the francium-221 daughter nucleus. This alpha recoil energy is sufficient to liberate the daughter nucleus from the chelator into solution, potentially leading to the administration of non-targeted ionizing radiation to the patient (40). Furthermore, the α-particle itself may induce radiolytic damage to the radiopharmaceutical. If this damage occurs to the targeting moiety of the ligand, it may reduce in vivo targeting and lead to further accumulation of radioactivity in nontarget tissue.
The desire to quickly release the production batch must not supersede the importance of accurately assessing the purity of the compound before administration. In the case of 225 Ac-labeled radiopharmaceuticals, this can be done by using a form of solid state detection, such as phosphor imaging.
In this scenario, all particles are detected, and the sensitivity of the approach is enhanced. However, γ particles are detected by the phosphor screen with a different efficiency than α and β particles. In addition, the disruption of the secular equilibrium further complicates the analysis of radiochemical purity. To further complicate the analysis, an initial activity of 37 MBq actinium-225 reaches secular equilibrium with francium-221 after 55 min and with bismuth-213 after approximately 6.5 h (41). On this basis, we analyzed the TLC plates 6.5 h and 26 h after they were run, a time point at which actinium-225 is in secular equilibrium with all of its daughter radionuclides. We selected four earlier time points, separated by 90 min intervals in order to investigate meaningfully different QC scenarios -waiting 30 min or 60 min after running the TLC may not have a major impact on release testing, but waiting 2 h rather than 30 min may be more significant. These intervals also accommodated the logistical constraints imposed by the experiments. In total, we made 585 observations spanning labeling yields from 1.8% to 99.5%. The measurements were more heavily distributed toward the extremes, with 42% of observations lying in the range 90-100%, and 21% lying in the range 0-20% ( Figure S9). It is likely that the unequal distribution of measurements influenced our models. However, with protocols for radiolabeling DOTA and macropa with actinium-225 now well established, a dataset weighed heavily by yields > 90% is consistent with the typical radiopharmacy experience.
An alternative strategy to the use of phosphor imaging is to use γ-spectrometry (11,23,42). Our mathematical model excluded francium-221 due to its short half-life, but its decay results in a 218 keV γemission that is detected by both phosphor imaging and γ-spectrometry. This 218 keV γ-emission can be used to indirectly detect and quantify actinium-225 (11,23,42). Quantification by this method is only possible after waiting at least 60 min for the equilibrium between actinium-225 and francium-221 to be reached (11). Our data confirm that measurements taken before 60 min do not accurately represent the true purity, but closely correspond to measurements taken at the same time point using phosphor imaging. The purities assessed at later time points are virtually identical by both radioanalytical methods ( Figure S11). Consequently, our statistical modeling also applies to γ-spectrometry. These experiments are described in full in the Supporting Information.
Our decay model broadly rationalizes the distribution of activities that we observed on the TLC plates. Deviations between both modeled yields and empirically-measured yields and the true yield were substantial during the first 2 h of analysis before the values converged as secular equilibrium was approached (Figure 7). In general, the modeled values and measured values closely agree: the values differ by < 3% after 2 h. These differences are likely the result of a combination of the underlying simplifications of the model. In particular, the model does not consider the contribution of daughter nuclei emitted during decays of actinium-225 (or bismuth-213) that occur while the TLC plate is running in the mobile phase. These daughter nuclei will migrate up the TLC plate but will not reach the solvent front because they were generated later than the uncomplexed metal ( Figure 6). The model therefore overestimates the rate of decay of radioactivity from the TLC grid sections. Although experimental measurements were used to calibrate the decay model, ultimately the model only requires adequate separation of radiolabeled compounds from uncomplexed metals. This suggests that our results are generalizable to any suitable radioTLC method, such as scintillation counting.
Our initial iteration of the statistical modeling assigned equal weights to each measurement. The fit is generally good ( Figure S2). As the aim of these studies is to arrive at a model that can be used primarily to assess the radiochemical purity of mixtures in the 90-100% range, we explored a model in which measurements in this region were given extra weight. This is because reactions with true purity < 90% will likely require purification prior to administration, meaning that highly accurate quantification of the yield is only necessary for purities > 90%. We therefore assigned a weight of 10 times more to each observation > 90%. The result is a model that fit slightly better in upper extreme, and less well in other regions. The weighted model predicts slightly higher true yields for measurements > 90% (Table S2), but both models demonstrate similar MAE (Tables S3). As these predictions may prevent unnecessary purification procedures to be performed and reduce analysis time, we validated our weighted model against an independent data set. Predictive accuracy was extremely high (± 1%) ( Figure S5). By contrast, accuracy of the non-weighted model was slightly lower (± 3%). This suggests that our choice of predictive statistical model is justified.
The mean average error of our model decreases substantially from 30 min to 2 h. This implies that radiochemical purity can be more accurately predicted by analyzing the TLC plate at least 2 h after it is removed from the mobile phase. Quantification of yield at earlier time points may over-or underestimate the true yield depending on the chelating moiety. This is because of the different affinities that the chelators have for the daughter radionuclides of actinium-225. For reactions performed at 95 °C using DOTA, bismuth-213 present in the reaction mixture will be complexed and contribute to the counts detected in grid section 1 of the TLC plate. At early analysis time points, therefore, the activity of the 225 Aclabeled compound may be overestimated. It is likely that chelation of bismuth-213 may increase relative to actinium-225 at lower temperatures due to more rapid labeling kinetics (43), increasing the degree to which early measurements may be misleading. By contrast, bismuth-213 present in the reaction mixture will be incompletely complexed by macropa at any reaction temperature. Consequently, it will migrate along with any actinium-225 that is not bound to the ligands, leading to an underestimation of radiochemical yield.

Conclusions
As TAT with actinium-225 continues to demonstrate clinical promise, there is a growing need to standardize QC procedures for 225 Ac-labeled radiopharmaceuticals for safety and regulatory requirements. A major challenge is the ability to accurately quantify radiochemical purity given the time required for actinium-225 to reach secular equilibrium. We compiled a large dataset of empiricallymeasured radiolabeling yields using multiple radioligands conjugated to DOTA, derivatives of DOTA, or macropa by collecting measurements at various times after running a TLC. Our generalized model confirms that predictive accuracy improves after 30 min and is comparable at all time points from 2 h to 6 h. On this basis we argue that the 2 h analysis time point best balances the need to accurately assess the purity of the radiopharmaceutical with the need to release it for administration as quickly as possible.

41.
Tichacek  Figure S1. Precursors for 225 Ac labeling. Figure S2. Prediction of labeling yield using a training set in which all observations are assigned an equal weight.  Table S2. Mean absolute error (MAE) of predictions made using a model that assigned equal weight to each observation. MAE was calculated by taking the average absolute value of the difference between each prediction and unity. Predictions were made for a model constructed using data from all ligands, the ligands containing the macropa chelator, and the compounds containing DOTA or a DOTA-derivative. Figure S3. Prediction of labeling yield using a training set derived from macropa-conjugated ligands only. Figure S4. Prediction of labeling yield using a training set derived from DOTA-conjugated ligands only. All DOTA measurements randomly assigned to the training set, meaning that the validation set contains DOTA-106 and DOTA-107 predictions only. Figure S5. Predicted yield versus true yield for an independent data set collected by labeling a macropaderived antibody with 225 Ac. Predictions were made using the weighted model.

RadioTLCs Visualized by Phosphor Imaging
A 0.5 mL aliquot containing approximately 100 kBq [ 225 Ac]AcCl3 in 1 M NH4OAC was diluted to 1 mL in 10 mM EDTA and incubated at 95 °C for 15 min. A 3 µL aliquot was spotted at the origin of a silica TLC plate and run in a 10% v/v MeOH/10 mM EDTA mobile phase. The reaction was performed in triplicate. The plate was visualized by exposure to a phosphor screen beginning at 30 min after removing the plate from the mobile phase. Figure S6. [ 225 Ac]Ac-EDTA. The TLC plate was exposed on a phosphor plate for 2 min and visualized 30 min after removal of the TLC plate from the mobile phase.  Figure S8. 3D surface plot comparing the difference between experimentally-measured (preequilibrium) activity and the true activity in each TLC section (as defined in Figure 1C) as a function of analysis time. X-axis: Analysis time (post-TLC). Y-axis: True radiolabeling yield. Z-axis: Difference between measured yield and expected yield. Figure S9. Plot of significance as a function of analysis time. P values are derived for the difference between experimentally-measured radiolabeling yield and decay modeled yield at various times of analysis. P < 0.05 was used to define statistical significance.  Table S4. P values for the difference between experimentally-measured labeling yields and decay modeled yields. Figure S10. Distribution of measurements. Measurements are grouped in ranges of 10, i.e. 0-10%, 10-20%, etc.

Analysis of Reaction Yield: NaI(Tl) Scintillation Detector
Three model systems were prepared by incubation of 1 mL solutions of 205 kBq in 1 M NH4OAc with either 18.2 µM EuK-106 for 1 min at 95 °C, 9.0 µM RPS-072 for 5 min at 95 °C, or 10.4 µM RPS-088 for 15 min at 95 °C. Each reaction was analyzed in triplicate by depositing 3 µL aliquots of the reaction mixture on the origin of a silica gel 60-coated aluminum plate (Sigma Aldrich). The plates were run in 10% v/v MeOH/10 mM EDTA (in H2O) as described above. The plates were then cut into three sections and the sections were counted separately using a NaI(Tl) scintillation detector with multi-channel analyzer (Canberra). Regionsof-interest were defined from 190-250 keV and 400-480 keV to quantify the contributions of 221 Fr (γ = 218 keV) and 213 Bi (γ = 440 keV). RCP was calculated by determining the ratio of counts in the 190-250 keV region in the section containing the product to the sum of the counts in the 190-250 keV regions on all three sections.
We compared the RCP as assessed by phosphor imaging to the purity as determined using NaI(Tl) scintillation detection. We selected as representative examples for comparison one reaction resulting in a low (< 25%) final product yield, one reaction with intermediate yield (25% < RCY < 75%), and one reaction with a high (> 90%) yield. The purities as assessed by the two methods closely agree ( Figure S11). Figure S11. RCP of three reactions determined by either phosphor imaging (solid gray line) or scintillation detection with multichannel analyzer (dashed black line). The TLC plates were analyzed from 0.5 h to 48 h after running in a 10% MeOH/10 mM EDTA mobile phase.
On the basis of these results, we suggest that the mathematical modeling developed using the phosphor imaging data is also applicable to assessment of RCP by NaI(Tl) scintillation detection with a multichannel analyzer. Consequently, the recommended time of analysis is also 2 h after removing the TLC plate from the mobile phase. High resolution gamma spectroscopy was also used to assess RCP. TLC plates were prepared and run as described above and immediately cut into three sections. Beginning 15 min after the TLC plates were removed from the mobile phase, each section was counted separately for 10 min in a Ge(Li) detector. The total time required to count each TLC strip was 33 min. RCP was defined as the ratio of the counts due to the 218 keV peak in the bottom section to the total number of counts due to the 218 keV peaks. The purity of the [ 225 Ac]Ac-RPS-088 was determined to be > 99% ( Figure S13) at 1 h after removing the TLC plate from the mobile phase, the time at which all three TLC sections had been counted. The purity of the [ 225 Ac]Ac-RPS-088 was determined to be 10.6 ± 1.5% ( Figure S13). By comparison, the true purities, as assessed by phosphor imaging at 24 h, of these two reactions were 96.6 ± 1.4% and 13.2 ± 0.6%, respectively. We therefore propose that high resolution gamma spectroscopy