Gamma counting protocols for the accurate quantification of ²²⁵Ac and ²¹³Bi without the need for a secular equilibrium between parent and gamma-emitting daughter

Abstract

Background

Quantification of actinium-225 through gamma counter measurements, when there is no secular equilibrium between actinium-225 and its gamma emitting daughters bismuth-213 and/or francium-221, can provide valuable information regarding the possible relocation of recoiled daughters such that related radiotoxicity effects can be evaluated. This study proposes a multiple time-point protocol using the bismuth-213 photopeak with measurements before secular equilibrium between actinium-225 and bismuth-213, and a single time-point protocol using both the francium-221 and bismuth-213 photopeak while assuming secular equilibrium between actinium-225 and francium-221 but not between bismuth-213 and actinium-225.

Results

Good agreement (i.e. 3% accuracy) was obtained when relying on a multiple time-points measurement of bismuth-213 to quantify both actinium-225 and excess of bismuth-213. Following scatter correction, actinium-225 can be accurately quantified using the francium-221 in a single time-point measurement within 3% of accuracy. The analysis performed on the stability data of [²²⁵Ac]Ac-DEPA and [²²⁵Ac]Ac-DOTA complexes, before secular equilibrium between bismuth-213 and actinium-225 was formed, revealed considerable amounts of unbound bismuth-213 (i.e. more than 90%) after 24 h of the radiolabeling most likely due to the recoiled daughter effect.

Conclusion

Both protocols were able to accurately estimate ²²⁵Ac-activities provided the francium-221 energy window was corrected for the down scatter of the higher-energy gamma-emissions by bismuth-213. This could prove beneficial to study the recoiled daughter effect and redistribution of free bismuth-213 by monitoring the accumulation or clearance of bismuth-213 in different tissues during biodistribution studies or in patient samples during clinical studies. On the other hand, the single gamma counter measurement protocol, although required a 30 min waiting time, is more time and cost efficient and therefore more appropriate for standardized quality control procedures of ²²⁵Ac-labeled radiopharmaceuticals.

Supplementary Information

The online version contains supplementary material available at 10.1186/s41181-022-00174-z.

Introduction

Targeted alpha-therapy (TAT) has shown promising results when overcoming resistance to β-emitters in clinical applications (Kratochwil et al. 2014; Ballal et al. 2020). The efficiency of α-particles relies on their short penetration range within tissue (40–100 μm, Allen et al. 2014) and their high linear energy transfer (LET). ²²⁵Ac (actinium-225) is considered a promising candidate for TAT and a highly cytotoxic radionuclide due to its relatively long half-life (9.9 days) and the yield of a total of four α particles ²²¹Fr (francium-221): 4.9 min half-life, 6 MeV α-particle; ²¹⁷At (astatine-217): 32.3 ms half-life, 7 MeV α-particle; ²¹³Bi (bismuth-213): 45.6 min half-life, 6 MeV α-particle; ²¹³Po (polonium-213): 4.2 µs half-life, 8 MeV α-particle) in its decay chain. In addition, two gamma rays are emitted in the decay chain, 218 keV [11.4%] by ²²¹Fr and 440 keV [25.9%] by ²¹³Bi, which can be used for activity measurements. Indeed, most preclinical studies report ²²⁵Ac activities which are based on activity measurements of ²¹³Bi or ²²¹Fr while assuming secular equilibrium (SEq) between ²²⁵Ac and the measured daughter (Kruijff et al. 2019; Miederer et al. 2004a; Borchardt et al. 2003; Beyer et al. 1990), which means activity measurements based on the gamma emissions by either ²²¹Fr or ²¹³Bi are approximately equal to the activity of ²²⁵Ac. However, emission of a high-energy α particle can cause nuclear recoil effect (Kozempel et al. 2018). This recoil energy experienced by the daughter nuclei is sufficient to break the chemical bond between the daughter and the targeting vector (Kruijff et al. 2015), resulting in the so-called recoiled daughter effect (RDE) and causing at least partial release of radioactive daughter nuclei from the original targeting molecule or delivery vehicle (Kruijff et al. 2015). Loss of affinity to the molecular carrier can lead to a redistribution of recoiling radioactive daughters and induce radiation related side effects, such that RDE is often assumed to be the main cause of radiotoxicity for the organs at risk (OAR) and one of the main reasons for limiting the amount of activity of ²²⁵Ac-labeled radionuclides administered to patients (Ballal et al. 2020; Kratochwil et al. 2017, 2015; Khreish et al. 2020; Cordier et al. 2010). Redistribution of recoiled daughter radionuclides can also offset the SEq between ²²⁵Ac and daughter radionuclides, such that indirect measurement of the activity concentration of ²²⁵Ac by measuring the activity concentration of its gamma-ray emitting daughters ²²¹Fr or ²¹³Bi can be biased. Only a few studies (Kruijff et al. 2019; Miederer et al. 2004a, 2008; Poty et al. 2019; Nedrow et al. 2017; Schwartz et al. 2011; Song et al. 2009) have considered measurements before and during SEq between ²²⁵Ac and ²¹³Bi, to evaluate the relocation of ²¹³Bi, and in very limited cases also between ²²⁵Ac and ²²¹Fr, to evaluate the relocation of ²²¹Fr. Recoiling ²¹³Bi was reported to have affinity to kidney tissue (Kruijff et al. 2019; Song et al. 2009; Drecoll et al. 2009), while ²²¹Fr was associated with uptake in the gastrointestinal tract (Miederer et al. 2004b) and kidneys (Song et al. 2009). However, it should be noted that relocation of ²²¹Fr is generally not considered as relevant because of the very short physical half-life of ²²¹Fr (4.9 min), such that ²²¹Fr is considered as the closest proxy to quantify ²²⁵Ac activity concentrations.

In the context of TAT, gamma counting (GC) is a frequently used technique for ex vivo quantification of ²²⁵Ac-labeled radiopharmaceuticals (Castillo Seoane et al. 2020), especially since in vivo nuclear imaging techniques, such as single-photon emission computed tomography (SPECT), have limited potential to allow accurate quantitative imaging of ²²⁵Ac concentrations in tissues because of the low branching ratio of gamma-emissions in the decay chain and the low administered activities. Therefore, other measurement techniques, such as GC, represent an asset for dosimetry and radiotoxicity estimates, both preclinically and clinically. In a preclinical setting, GC allows biodistribution studies of ²²⁵Ac-labeled radiopharmaceuticals to estimate the absorbed doses by tumoral and healthy tissue. In addition, GC provides valuable information regarding the possible relocation of recoiled daughters, which is of interest to evaluate related radiotoxicity effects. In a clinical setting, GC measurements of blood and urine samples can be considered to determine plasma and renal clearance of radiopharmaceuticals, which in turn can be used for compartmental modeling of pharmacokinetics to estimate the radiation burden to OAR (Siegel et al. 1999).

In addition, GC measurements play an important role in the quality control (QC) of ²²⁵Ac-labeled radiopharmaceuticals to confirm sufficiently high radiochemical yield (RCY) before administration to patients. For this purpose, the activity distribution on an instant thin-layer liquid chromatography (iTLC) strip is analyzed using GC measurements to estimate the fraction of bound and unbound ²²⁵Ac and its daughter ²¹³Bi. These GC measurements are usually based on the gamma emissions by ²²¹Fr, which is at SEq with ²²⁵Ac within approximately six half-lives of ²²¹Fr (~ 30 min) (Hooijman et al. 2021).

However, limited research has been done on GC measurements to quantify ²²⁵Ac activity when there is no SEq between ²²⁵Ac and its gamma emitting daughters ²¹³Bi and/or ²²¹Fr. Generally, GC measurements are delayed ensuring sufficient time for ²¹³Bi to reach SEq with ²²⁵Ac, and to provide an unbiased estimation of the ²²⁵Ac-activity. The limitation of this approach is that, once in SEq, any additional ²¹³Bi activity which was originally present in the measured sample before the start of the GC measurements cannot be traced back. Nonetheless, there is a growing interest to quantify ²¹³Bi activity which is not related to the parent–daughter decay of ²²⁵Ac, but that is generated by the potential RDE and relocation of ²¹³Bi. Therefore, the aim of this study is to develop and validate GC protocols to accurately quantify both ²²⁵Ac activity and a potential accumulation or clearance of ²¹³Bi activity compared to SEq between ²²⁵Ac and ²¹³Bi. We proposed (1) a multiple time-point protocol using the ²¹³Bi photopeak with measurements before SEq between ²²⁵Ac and ²¹³Bi, and (2) a single time-point protocol using both the ²²¹Fr and ²¹³Bi photopeaks, while assuming SEq between ²²⁵Ac and ²²¹Fr but not between ²¹³Bi and ²²⁵Ac. Using these two protocols, we evaluated the amount of unbound ²¹³Bi for two different chelators [²²⁵Ac]Ac-DEPA(7-[2-(bis-carboxymethyl-amino)-ethyl]-4,10-bis-carboxymethyl-1,4,7,10- tetraazacyclododec-1-yl-acetic acid) and [²²⁵Ac]Ac-DOTA (1,4,7, 10-Tetraazacyclododecane-1, 4,7,10-tetracetic acid) using iTLC strips after incubation in human serum to evaluate stability and RDE as part of QC tests after radiolabeling.

Materials and methods

Radioisotopes and preparation of [²²⁵Ac]-labeled constructs

²²⁵Ac samples were obtained from recurrent (trimestral, 6 MBq) milkings of an in-house ²²⁹Th stock obtained from a processed ²²⁹Th capsule as described by Boden et al. (2017). Milkings were performed with the aid of a tandem system of extraction chromatography columns using TEVA and DGA columns obtained from TrisKem, France. A first batch of ²²⁵Ac was used to evaluate the GC linearity and the effect of the sample volume variation on the GC detection efficiency (for details on the sample volume variations see Additional file 1).

Additionally, ± 1.3 MBq of ²²⁵Ac was used to elute 1.19 MBq of ²¹³Bi (using 0.1 M HCl/ 0.1 M NaI) from an ²²⁵Ac/²¹³Bi generator loaded with an AG MP-50 cation exchange resin (Ahenkorah et al. 2021). The eluate ²¹³BiI₄⁻/²¹³BiI₅²⁻ was used to prepare two samples, one containing ²²⁵Ac in SEq with ²¹³Bi and ²²¹Fr for the GC calibration, and one containing pure ²¹³Bi to determine the photon scatter contribution of ²¹³Bi gamma-emissions in the photopeak window of ²²¹Fr.

Two other solutions of ²²⁵Ac doped with additional ²¹³Bi were prepared to create a mixture of ²²⁵Ac in SEq with ²¹³Bi and additional, pure ²¹³Bi, to simulate non-equilibrium conditions between ²²⁵Ac and ²¹³Bi. As such, the total activity of ²¹³Bi was given by:

$$A_{\text{total}}=A_{21{\text{3}}_{\text{Bi}}}+A_{{225}_{\text{Ac}}}$$ 1

where $A_{{225}_{\text{Ac}}}$ is the activity of ²¹³Bi in SEq with ²²⁵Ac. This was done by starting from a solution (~ 0.5 mL) of ²²⁵Ac in SEq with its decay progeny and adding 0.2 mL (and 0.3 mL) of the stock solution of pure ²¹³Bi to 0.3 mL (and 0.2 mL) of the solution of ²²⁵Ac to obtain two samples with additional ²¹³Bi activity (total sample volume ~ 0.5 mL).

²²⁵Ac-constructs were synthesized by adding [²²⁵Ac]Ac(NO₃)₃ (1–2 MBq, 100 μL, 0.05 M) to a Tris–HCl buffer (0.37 M, pH 8.5, chelex treated) solution containing DEPA or DOTA (50 µM) and reacting in a glass vial for 60 min at 95 °C. ²²⁵Ac-constructs were purified using a C₁₈ Plus Sep-Pak cartridge (Waters Co., Milford, MA, USA) by loading the reaction mixture, rinsing with water (5 mL) to remove unreacted [²²⁵Ac]Ac(NO3)₃, and eluting the purified complex with absolute ethanol (0.5 mL) as described by Cassells et al. (2021). After purification, radiolabeled aliquots were applied immediately to the test media.

The radioactive composition of all reference samples (i.e. stock solutions) were determined via high-resolution gamma spectrometry analysis using a high-purity germanium (HPGe) detector (Mirion-Canberra, Meriden, USA) calibrated for photon energy and detection efficiency. ²²⁵Ac quantities were determined indirectly via measurements of ²²¹Fr and ²¹³Bi photopeaks once SEq was established. ²¹³Bi quantities were determined via measurement of a pure ²¹³Bi sample as fast as possible after elution. The content mass of the sample was verified gravimetrically and the exact volumes of the radioactive samples in each test tube were determined by weighing each tube before and after filling with an analytical balance (model ABP-200-4M; KERN & SOHN GmbH, Germany). The reference activity in each test tube was determined from the volume of each sample and the activity concentration of the reference stock solution. The relative statistical uncertainty of the reference activity concentration of each of the calibration stock solutions was always within 3.2% at 95% CI (coverage factor k = 2).

Gamma counter measurements

Gamma counter activity measurements were done in a 2480 Wizard² gamma counter (Perkin Elmer, Waltham, MA, USA) using a measurement protocol optimized to limit the overall measurement uncertainty (cfr. details in the Additional file 1). This gamma counter consists of a single 75-mm-diameter and 80-mm-high NaI(Tl) well-type detector. Each radioactive sample was measured for 60 s in a standard tube (5 mL plastic vials of 75 mm height and 12 mm diameter), using a fixed energy window of 175–282 keV (${\text{EW}}_{{221}_{\text{Fr}}}$) and 378–520 keV (${\text{EW}}_{{213}_{\text{Bi}}}$) corresponding to the main photopeaks of ²²¹Fr (218 keV) and ²¹³Bi (440 keV), respectively. The measurement in each EW setting was automatically corrected for dead time, background, and measurement time and expressed as counts per minute (CPM).

First, the linear range of GC measurements for the two energy windows was determined, together with the GC calibration factor (CF). For the impact of different sample volumes on the detection efficiency, we refer to the Additional file 1.

Assuming SEq between ²²⁵Ac and ²¹³Bi (and thus ²²¹Fr), the calibration factors for ${\text{EW}}_{{213}_{\text{Bi}}}$ ($C{F}_{{213}_{\text{Bi}}}$) and ${\text{EW}}_{{221}_{\text{Fr}}}$ ($C{F}_{{221}_{\text{Fr}}}$) were determined from GC measurements as:

$$C{F}_{{213}_{\text{Bi}}}=\frac{CP{M}_{{\text{EW}}_{{213}_{\text{Bi}}}}}{A_{{225}_{\text{Ac}}}}$$ 2

$$C{F}_{{221}_{\text{Fr}}}=\frac{CP{M}_{{\text{EW}}_{{221}_{\text{Fr}}}}}{A_{{225}_{\text{Ac}}}}$$ 3

If there is SEq between ²²⁵Ac and ²²¹Fr but not between ²²⁵Ac and ²¹³Bi, we want to have the CPM measured with ${\text{EW}}_{{221}_{\text{Fr}}}$ to be independent of the ²¹³Bi activity. Therefore, we needed to correct for the down scatter of the higher high-energy gamma rays of ²¹³Bi into the ${\text{EW}}_{{221}_{\text{Fr}}}$ (Fig. 1). Hence, the scatter contribution of ²¹³Bi to ${\text{EW}}_{{221}_{\text{Fr}}}$ ($CP{M}_{{213}_{\text{Bi}}\to {\text{EW}}_{{221}_{\text{Fr}}}}$) was determined as function of $CP{M}_{{\text{EW}}_{{213}_{\text{Bi}}}}$ by performing GC measurements using both ${\text{EW}}_{{221}_{\text{Fr}}}$ and ${\text{EW}}_{{213}_{\text{Bi}}}$ for a pure ²¹³Bi sample which was measured for more than 5 h to cover different $CP{M}_{{\text{EW}}_{{213}_{\text{Bi}}}}$ values. As such GC measurements using the ${\text{EW}}_{{221}_{\text{Fr}}}$ can be corrected for the ²¹³Bi down scatter by subtracting the activity-dependent scatter contribution of ²¹³Bi to the ${\text{EW}}_{{221}_{\text{Fr}}}$ using the following expression:

$$CP{M}_{{\text{SC,EW}}_{{221}_{\text{Fr}}}}=CP{M}_{{\text{EW}}_{{221}_{\text{Fr}}}}-CP{M}_{{213}_{\text{Bi}}\to {\text{EW}}_{{221}_{\text{Fr}}}}$$ 4

Fig. 1.

GC photon energy spectrum measured for ²²⁵Ac, in SEq with both ²²¹Fr and ²¹³Bi, and for pure ²¹³Bi

This resulted in a calibration factor for the scatter-corrected ${\text{EW}}_{{221}_{\text{Fr}}}$ to accurately estimate ²²⁵Ac activities independent of ²¹³Bi activities:

$$C{F}_{\text{SC,}{221}_{\text{Fr}}}=\frac{CP{M}_{{\text{SC,EW}}_{{221}_{\text{Fr}}}}}{A_{{225}_{\text{Ac}}}}$$ 5

Multiple time-point GC measurements to quantify ²²⁵Ac doped with ²¹³Bi

Immediately after preparation of the two samples with an additional amount of ²¹³Bi activity (compared to ²¹³Bi activity in SEq with ²²⁵Ac), GC measurements were performed sequentially, at intervals of 5 min, for a total duration of 5–6 h after preparation, using the ${\text{EW}}_{{213}_{\text{Bi}}}$ and corresponding $C{F}_{{213}_{\text{Bi}}}$. Given $A_{{225}_{\text{Ac}}}^0$, the initial activity of ²¹³Bi in SEq with ²²⁵Ac, and $A_{{213}_{\text{Bi}}}^0$, the additional amount of ²¹³Bi activity at the start of the measurement (t = 0), the total activity of ²¹³Bi at time t is given by (see Eqs. 1, 2):

$$\frac{CP{M}_{{\text{EW}}_{{213}_{\text{Bi}}}}(t)}{C{F}_{{213}_{\text{Bi}}}}=A_{\text{total},{213}_{\text{Bi}}}\left(t\right)=A_{{225}_{\text{Ac}}}^0\times {\text{e}}^{-{\lambda }_{{225}_{\text{Ac}}}t}+A_{{213}_{\text{Bi}}}^0\times {\text{e}}^{-{\lambda }_{{213}_{\text{Bi}}}t}$$ 6

with $CP{M}_{{\text{EW}}_{{213}_{\text{Bi}}}}\text{(}t\text{)}$ the GC measurement at time t using ${\text{EW}}_{{213}_{\text{Bi}}}$ and with ${\lambda }_{{225}_{\text{Ac}}}$ and ${\lambda }_{{213}_{\text{Bi}}}$ the physical decay constants for ²²⁵Ac and ²¹³Bi respectively. Therefore, GC measurements using ${\text{EW}}_{{213}_{\text{Bi}}}$ were analyzed as a function of time t after start of the measurement and used to determine the initial ²¹³Bi activity in SEq with ²²⁵Ac and the additional amount of ²¹³Bi at the start of the GC measurement. This was done by non-linear least squares fitting (GraphPad Prism version 9.1.0) of a double exponential function to the GC measurements at different time-points with the physical decay constants fixed.

Single time-point GC measurements to quantify ²²⁵Ac doped with ²¹³Bi

In the second approach, a single time-point GC measurement using both ${\text{EW}}_{{221}_{\text{Fr}}}$ and ${\text{EW}}_{{213}_{\text{Bi}}}$ was considered, which theoretically should allow an estimation of both ²²⁵Ac activity in SEq with ²¹³Bi and an additional amount of ²¹³Bi activity. This approach assumes one single GC measurement after SEq is reached between ²²⁵Ac and ²²¹Fr (after ~ 30 min), but as soon as possible thereafter, to ensure that any ²¹³Bi present in the sample has not yet reached SEq with ²²⁵Ac. This way, one can still differentiate between the amount of ²¹³Bi activity in SEq with ²²⁵Ac and the additional amount of ²¹³Bi activity. If we assume the single time-point GC measurement at time t after sample preparation, the additional amount of ²¹³Bi activity at the start of the measurement ($A_{{213}_{\text{Bi}}}^0$) can be estimated using the ${\text{EW}}_{{213}_{\text{Bi}}}$ once the initial activity of ²²⁵Ac ($A_{{225}_{\text{Ac}}}^0$) at the start of the measurement is known:

$$A_{{213}_{\text{Bi}}}^0=\left(\frac{CP{M}_{{\text{EW}}_{{213}_{\text{Bi}}}}\text{(}t\text{)}}{CF{}_{{213}_{\text{Bi}}}}-A_{{225}_{\text{Ac}}}^0\times {\text{e}}^{-{\lambda }_{{225}_{\text{Ac}}}t}\right)\times {\text{e}}^{{\lambda }_{{213}_{\text{Bi}}}t}$$ 7

with $CP{M}_{{\text{EW}}_{{213}_{\text{Bi}}}}\text{(}t\text{)}$ the GC measurement at time t using ${\text{EW}}_{{213}_{\text{Bi}}}$ and with ${\lambda }_{{225}_{\text{Ac}}}$ and ${\lambda }_{{213}_{\text{Bi}}}$ the physical decay constant for ²²⁵Ac and ²¹³Bi respectively. In turn, the initial activity of ²²⁵Ac ($A_{{225}_{\text{Ac}}}^0$) can be estimated using the ${\text{EW}}_{{221}_{\text{Fr}}}$ either from:

$$A_{{225}_{\text{Ac}}}^0=\frac{CP{M}_{{\text{EW}}_{{221}_{\text{Fr}}}}(t)}{C{F}_{{221}_{\text{Fr}}}}\times {\text{e}}^{{\lambda }_{{225}_{\text{Ac}}}t}$$ 8

with $CP{M}_{{\text{EW}}_{{221}_{\text{Fr}}}}\text{(}t\text{)}$ the GC measurement at time t using ${\text{EW}}_{{221}_{\text{Fr}}}$ without scatter correction (see Eq. 3), or from:

$$A_{{225}_{\text{Ac}}}^0=\frac{CPM{}_{{\text{SC,EW}}_{{221}_{\text{Fr}}}}(t)}{C{F}_{{\text{SC,221}}_{\text{Fr}}}}\times {\text{e}}^{{\lambda }_{{\text{225}}_{\text{Ac}}}t}$$ 9

with $CP{M}_{{\text{SC,EW}}_{{221}_{\text{Fr}}}}(t)$ the GC measurement at time t using ${\text{EW}}_{{221}_{\text{Fr}}}$ with scatter correction (see Eq. 5). In both Eq. 8 and Eq. 9, ${\lambda }_{{225}_{\text{Ac}}}$ represents the physical decay constant for ²²⁵Ac.

Both Eqs. 8 and 9 were considered to estimate the initial activity of ²²⁵Ac using ${\text{EW}}_{{221}_{\text{Fr}}}$.

Quantification of the bound fraction of ²²⁵Ac and ²¹³Bi during radiopharmaceutical QC of [²²⁵Ac]Ac-DEPA and [²²⁵Ac]Ac-DOTA complexes

As a direct application, we performed GC measurements at multiple time-points during the stability test of two constructs, [²²⁵Ac]Ac-DEPA and [²²⁵Ac]Ac-DOTA, as part of radiopharmaceutical QC. For this stability test, two ethanolic solutions of 50 μL, each containing one of the constructs, were added immediately after purification to 450 μL of human serum and incubated at 37 °C. Samples were collected at 15 min and 24 h post reaction. The RCY of each reaction mixture was determined by instant thin-layer liquid chromatography (iTLC-SG, Varian, Diegem, Belgium) with an elution chamber using acetonitrile/water (75%/25% v/v) such that bound ²²⁵Ac and bound daughter radionuclides will migrate with the solvent front to the upper part of the iTLC strip, while unbound radionuclides will remain at the lower part where the mixture was originally spotted (Fig. 2) (Cassells et al. 2021). Once the solvent front reached the 1-cm mark of the iTLC strip at time t_i (cfr solvent front Fig. 2), the iTLC strip is removed from the mobile phase and cut in half. Immediately after, the activity of the upper and lower parts of the iTLC strip were measured with GC using both ${\text{EW}}_{{221}_{\text{Fr}}}$ and ${\text{EW}}_{{213}_{\text{Bi}}}$ with the previously described energy window settings.

Fig. 2.

Schematic representation of the migration of radiolabeled compounds in the iTLC strip. Upon exposure of the strip to the mobile phase, unbound radionuclides will remain in the spotting site, whereas bound radionuclides will move with the solvent front to the upper part of the iTLC strip

The ²²⁵Ac activity was estimated for each part of the iTLC strip using a single time-point GC measurement after more than 5 h to ensure SEq between ²²⁵Ac and ²¹³Bi such that the ²²⁵Ac activity could be estimated from the CPM data acquired with ${\text{EW}}_{{213}_{\text{Bi}}}$ and extrapolated to the start of the iTLC elution at t₀.

In addition, a single time-point measurement was performed at 30 min after starting the iTLC elution to ensure SEq between ²²⁵Ac and ²²¹Fr such that the ²²⁵Ac activity could be estimated from the CPM data acquired with ${\text{EW}}_{{221}_{\text{Fr}}}$ with (Eq. 9) and without scatter correction (Eq. 8). Next, the increase (or decrease) in ²¹³Bi activities compared to SEq (dependent on the part of the strip) was estimated from the CPM acquired with ${\text{EW}}_{{213}_{\text{Bi}}}$. In case of an increase of ²¹³Bi, the ²¹³Bi activity at the start of the iTLC elution (t₀) was estimated using Eq. 7.

For the upper part of the iTLC strips obtained after 24 h of incubation in human serum, multiple time-point measurements were performed before SEq between ²²⁵Ac and ²¹³Bi (> 5 h) while only the CPM data acquired with the ${\text{EW}}_{{213}_{\text{Bi}}}$ were used for the analysis. In case of increased or reduced ²¹³Bi activity compared to SEq with ²²⁵Ac, fitting of a double exponential function (i.e. Eq. 6) was performed by non-linear least squares fitting (GraphPad Prism version 9.1.0) to the multiple GC measurements at different time-points. For both ²²⁵Ac and ²¹³Bi, the bound fraction was determined as the ratio of the activity of either radionuclide measured for the upper part of the iTLC over the sum of activities measured for both the upper and the lower part of the iTLC.

Results

²²⁵Ac/²¹³Bi samples and [²²⁵Ac]-labeled constructs

Table 1 gives an overview of the different samples for GC measurements and the activity at the start of the measurements. To evaluate the GC linearity a total of 19 test samples were prepared from sample 1. The samples were prepared with equal volume (0.5 mL), to avoid a volume effect on sensitivity, and with varying activities ranging from 1 Bq up to 500 kBq of ²²⁵Ac in SEq with ²²¹Fr and ²¹³Bi.

Table 1.

Overview of the different samples for GC measurements and the activity at the start of the measurements

Sample	225Ac (in SEq with 213Bi)	Added 213Bi	Experiment
1	1.5 MBq (total)	0 kBq	GC calibration
2	0 kBq	117 kBq	Quantifying down scatter of higher-energy gamma emissions by 213Bi in ${\text{EW}}_{{221}_{\text{Fr}}}$
3	94 kBq	55 kBq	Simulating non-SEq conditions between 225Ac and 213Bi
4	116 kBq	32 kBq
5	1–2 MBq	0 kBq	Radiolabeling of [225Ac]Ac-DOTA and incubation in human serum for 15 min and 24 h
6	1–2 MBq	0 kBq	Radiolabeling of [225Ac]Ac- DEPA and incubation in human serum for 15 min and 24 h

Specifications of the samples used for determining the linear range of GC measurements and evaluating the impact of different sample volumes on GC measurements is given in the Additional file 1

Gamma counter measurements

For both EW setting for ²²¹Fr and ²¹³Bi, the GC response expressed as count rate (CPM) was measured as a function of the different activities obtained from sample 1 which was cross-calibrated with a standard HPGe detector (see Fig. 3). A non-linearity of more than 3% in the GC response was observed for activities above 150 kBq, resulting in a CPM underestimation of up to 17% and 25% for activities around 0.5 MBq when using the ${\text{EW}}_{{221}_{\text{Fr}}}$ and the ${\text{EW}}_{{213}_{\text{Bi}}}$ respectively. Therefore, GC response was considered linear up to 150 kBq ²²¹Fr and ²¹³Bi, in SEq with ²²⁵Ac. For this linear range, CFs were determined by linear regression, resulting in GC CFs for the EWs of ²¹³Bi ($C{F}_{{213}_{\text{Bi}}}$) and ²²¹Fr ($C{F}_{{221}_{\text{Fr}}}$) of 6.1E+06 CPM/MBq and 7.4E+06 CPM/MBq, respectively. The CPMs obtained with GC using the ${\text{EW}}_{{221}_{\text{Fr}}}$ ($CP{M}_{{\text{213}}_{\text{Bi}}\to {\text{EW}}_{{221}_{\text{Fr}}}}$) are shown as a function of different CPM measured with ${\text{EW}}_{{213}_{\text{Bi}}}$ ($CP{M}_{{213}_{\text{Bi}}}$) for different ²¹³Bi activities obtained from a cross-calibration with the HPGe detector (see Fig. 4). Results indicated a clear, linear relationship between $CP{M}_{{213}_{\text{Bi}}\to {\text{EW}}_{{221}_{\text{Fr}}}}$ and $CP{M}_{{213}_{\text{Bi}}}$ (linear regression, slope = 0.205 ± 0.001, R² > 0.99) which can be used to estimate the scatter contribution of ²¹³Bi to GC measurements in the ${\text{EW}}_{{221}_{\text{Fr}}}$. This scatter fraction can be subtracted from ${\text{EW}}_{{221}_{\text{Fr}}}$, and ²²⁵Ac activities can be accurately estimated even when there is no SEq between ²²⁵Ac and ²¹³Bi (Eq. 9). The corresponding GC calibration factor for the ${\text{EW}}_{{221}_{\text{Fr}}}$, when a correction for ²¹³Bi photon down scatter is applied, was determined as 6.1E+06 CPM/MBq.

Fig. 3.

GC response for ²²⁵Ac in SEq with ²²¹Fr and ²¹³Bi, measured with both EWs of ²²¹Fr and ²¹³Bi. Error bars represent the standard deviation provided by the GC software

Fig. 4.

Count rate of the down scatter of gamma emissions by ²¹³Bi in the ${\text{EW}}_{{221}_{\text{Fr}}}$ ($CP{M}_{{213}_{\text{Bi}}\to {\text{EW}}_{{221}_{\text{Fr}}}}$) for different count rates of ²¹³Bi measured with the ${\text{EW}}_{{213}_{\text{Bi}}}$ ($CP{M}_{{\text{213}}_{\text{Bi}}}$)

Multiple time-point GC measurements to quantify ²²⁵Ac doped with ²¹³Bi

For the multiple time-point approach, activities measured by the gamma counter using ${\text{EW}}_{{213}_{\text{Bi}}}$ are plotted as a function of the measurement time for the sample 3 (see Table 1) containing ²¹³Bi activity in SEq with ²²⁵Ac and an additional amount of ²¹³Bi activity (see Fig. 5). Based on a bi-exponential fit with fixed physical decay constants for ²²⁵Ac and ²¹³Bi (cfr Eq. 6), ²²⁵Ac and ²¹³Bi activities were estimated (see Table 2), both with a relative percentage difference lower than 3% compared to the reference activities determined with the HPGe detector.

Fig. 5.

²¹³Bi activities of sample 3 (see Table 1) containing ²¹³Bi in SEq with ²²⁵Ac and an added amount of ²¹³Bi. GC measurements were performed at different time-points before and after SEq between ²¹³Bi and ²²⁵Ac using the ${\text{EW}}_{{213}_{\text{Bi}}}$. Error bars represent the standard deviation provided by the GC software

Table 2.

Multiple and single time-point (at 30 min) estimation of the ²²⁵Ac and ²¹³Bi activity for sample 3 and 4 containing ²¹³Bi in SEq with ²²⁵Ac and an additional amount of ²¹³Bi

	CPM	213Bi (SEq with 225Ac)		Added 213Bi
		kBq	%diff	kBq	%diff
Sample 3
Multiple time-points	$CP{M}_{{\text{EW}}_{{213}_{\text{Bi}}}}$	93.7	< 3	54.9	< 3
Single time-point at 30 min	$CP{M}_{{\text{EW}}_{{213}_{\text{Bi}}}}$, $CP{M}_{{\text{EW}}_{{221}_{\text{Fr}}}}$	101.8	9	47.0	− 15
Single time-point at 30 min (scatter corrected)	$CP{M}_{{\text{EW}}_{{213}_{\text{Bi}}}}$, $CP{M}_{{\text{SC,EW}}_{{221}_{\text{Fr}}}}$	93.4	< 3	55.3	< 3
Sample 4
Multiple time-points	$CP{M}_{{\text{EW}}_{{213}_{\text{Bi}}}}$	116.2	< 3	32.9	< 3
Single time-point at 30 min	$CP{M}_{{\text{EW}}_{{213}_{\text{Bi}}}}$, $CP{M}_{{\text{EW}}_{{221}_{\text{Fr}}}}$	122.9	6	28.4	− 11
Single time-point at 30 min (scatter corrected)	$CP{M}_{{\text{EW}}_{{213}_{\text{Bi}}}}$, $CP{M}_{{\text{SC,EW}}_{{221}_{\text{Fr}}}}$	116.7	< 3	32.8	< 3

Corresponding CPM approaches are indicated and the relative difference (%diff) compared to the reference activities in both samples

Single time-point GC measurements to quantify ²²⁵Ac doped with ²¹³Bi

For the single time-point approach, ²²⁵Ac activities measured with ${\text{EW}}_{{221}_{\text{Fr}}}$ with and without scatter correction are plotted as function of time for the sample 3 containing ²²⁵Ac in SEq with ²¹³Bi and additional ²¹³Bi activity (Fig. 6A). This measurement was started after SEq was reached between ²²¹Fr and ²²⁵Ac (~ 30 min) such that ²²⁵Ac activity could be estimated from the CPMs measured within ${\text{EW}}_{{221}_{\text{Fr}}}$. When no scatter correction was applied, ²²⁵Ac activities showed an overestimation due to the additional down scatter of gamma-emissions by the added ²¹³Bi activity. The overestimation gradually decreased because of the decay of this additional ²¹³Bi till SEq was again reached between ²²⁵Ac and ²¹³Bi (Fig. 6B). Applying a correction for down scatter of ²¹³Bi gamma emissions in the ${\text{EW}}_{{221}_{\text{Fr}}}$ reduces this overestimation of ²²⁵Ac activities. For a single time-point GC measurement at 30 min, omission of the scatter correction resulted in an overestimation of 6 to 9% of the ²²⁵Ac activity while the estimated activity was within 3% of the reference value when scatter correction was applied. When using the estimated ²²⁵Ac activity to determine the additional ²¹³Bi activity, this resulted in an underestimation of 11 to 15% when no scatter correction was applied and while it was within 3% of the reference activity after applying a correction for down scatter (Table 2).

Fig. 6.

A ²²⁵Ac activities measured with ${\text{EW}}_{{221}_{\text{Fr}}}$ with and without scatter correction are plotted as function of measurement time for the sample 3 (see Table 1) containing ²²⁵Ac and additional ²¹³Bi activity. Error bars represent the standard deviation provided by the GC software. B Relative bias (percentage relative difference) of ²²⁵Ac activity estimated using ${\text{EW}}_{{221}_{\text{Fr}}}$ as function of the added ²¹³Bi activity (compared to SEq between ²²⁵Ac and ²¹³Bi) when no correction for the additional down scatter of ²¹³Bi gamma-emissions in the ${\text{EW}}_{{221}_{\text{Fr}}}$ is applied

Quantification of ²²⁵Ac and ²¹³Bi during radiopharmaceutical QC of [²²⁵Ac]Ac-DEPA and [²²⁵Ac]Ac-DOTA complexes

An overview of the bound fraction of [²²⁵Ac]Ac-DEPA/DOTA after a 15 min and 24 h incubation in human serum is given in Table 3. These estimates are based on single time-point GC measurement protocols.

Table 3.

Bound fraction of ²²⁵Ac (activity upper part iTLC/activity iTLC) to [²²⁵Ac]Ac-DEPA/DOTA complexes for samples 5 and 6 (see Table 1) after 15 min and 24 h incubation in human serum

EW	CPM	[225Ac]Ac-DOTA		[225Ac]Ac-DEPA
		15 min	24 h	15 min	24 h
${\text{EW}}_{{213}_{\text{Bi}}}$(at 5 h)	$CP{M}_{{\text{EW}}_{{213}_{\text{Bi}}}}$	88%	91%	96%	96%
${\text{EW}}_{{221}_{\text{Fr}}}$(at 30 min, without scatter correction)	$CP{M}_{{\text{EW}}_{{221}_{\text{Fr}}}}$	84%	78%	88%	83%
${\text{EW}}_{{221}_{\text{Fr}}}$, ${\text{EW}}_{{213}_{\text{Bi}}}$(at 30 min, with scatter correction)	${\text{CPM}}_{{\text{SC,EW}}_{{221}_{\text{Fr}}}}$, $CP{M}_{{\text{EW}}_{{213}_{\text{Bi}}}}$,	89%	90%	95%	93%

²²⁵Ac activities were determined with a single time-point GC measurement using ${\text{EW}}_{{213}_{\text{Bi}}}$ at 5 h, to ensure SEq between ²¹³Bi and ²²⁵Ac, and using ${\text{EW}}_{{221}_{\text{Fr}}}$ with and without scatter correction at 30 min, to ensure SEq between ²²¹Fr and ²²⁵Ac

Multiple time-point GC measurements, performed of the upper part of iTLC strip for the 24 h incubation time in human serum using ${\text{EW}}_{{213}_{\text{Bi}}}$ (see Fig. 7), showed an ingrowth of ²¹³Bi for both [²²⁵Ac]Ac-DOTA and [²²⁵Ac]Ac-DEPA until SEq was again restored between ²²⁵Ac and ²¹³Bi after 5 h (i.e. ²¹³Bi reached ~ 99% of ²²⁵Ac activity). These findings correspond to a lower fraction of bound ²¹³Bi compared to the fraction of bound ²²⁵Ac.

Fig. 7.

Multiple time-point GC measurements were performed of the upper part of iTLC strip using ${\text{EW}}_{{213}_{\text{Bi}}}$ before SEq was reached between ²¹³Bi and ²²⁵Ac (< 5 h), to determine the amount of bound ²¹³Bi after 24 h of incubation in human serum of [²²⁵Ac]Ac-DEPA (A) and [²²⁵Ac]Ac-DOTA (B). The solid line represents the total amount of ²²⁵Ac (from GC of both parts of the iTLC strips) and the dotted line the amount of bound ²²⁵Ac. Error bars represent the standard deviation provided by the GC software

For [²²⁵Ac]Ac-DOTA, fitting of the non-linear least squares fitting of a double exponential (i.e. Eq. 6) function to the multiple GC measurements at different time-points estimated the initial ²¹³Bi activity in the upper part of the iTLC strip as zero, within a 95% confidence interval (0.01 ± 0.02 kBq), meaning that no bound ²¹³Bi was present in these samples after 24 h of incubation in human serum.

Discussion

This study focused on GC measurements to quantify ²²⁵Ac activity when SEq is not guaranteed or not yet reached between ²²⁵Ac and its daughter radionuclide ²¹³Bi. Before performing our experiments, we first determined the linear range and calibration factor of the GC system and ensured that all activities for this study were within this range to guarantee optimal quantitative performance. In addition, samples were prepared to have an equal volume of 0.5 mL to avoid a volume effect on the detection efficiency. As GC measurements of ²²⁵Ac-activity rely on the gamma emissions by daughter radionuclides ²¹³Bi and ²²¹Fr, this indirect approach requires SEq between ²²⁵Ac on the one hand and ²¹³Bi and/or ²²¹Fr on the other hand, especially if only one time-point is measured. When using an EW for ²¹³Bi, one should wait for more than 5 h to ensure that ²¹³Bi and ²²⁵Ac activities are in agreement (~ 99%) and bias on ²²⁵Ac activity measurements is avoided as much as possible. While this long waiting time can prove to be challenging from a practical point of view, it also prevents the quantification of ²¹³Bi activities before SEq with ²²⁵Ac. This information is however needed to monitor the relocation of free ²¹³Bi, released from the molecular vector, from the tumor site or tissues showing target expression to organs involved in excretory pathway of ²¹³Bi. A straightforward approach to avoid the need for SEq between ²²⁵Ac and ²¹³Bi when using the EW of ²¹³Bi for ²²⁵Ac quantification, is a multiple GC measurement protocol where activities are measured at different time points before and/or during SEq between ²²⁵Ac and ²¹³Bi. As the approach does not require SEq, neither between ²²⁵Ac and ²¹³Bi nor between ²²⁵Ac and ²²¹Fr, GC measurements can be initiated as soon as samples are available to ensure that the highest activity of ²¹³Bi can be measured. This can be very useful for biodistribution studies where the ²¹³Bi activity in the different organs is not known in advance and sensitivity to pick up even low levels of ²¹³Bi activities should be maximized. For our experiments, we performed measurements every 5 min to demonstrate feasibility but in practice, the optimal timing for the measurements will depend on the number of samples which need to be counted and the availability of the GC system. However, we would advise to maximize the number of measurements to reduce the impact of noise, since ²¹³Bi activities are expected to be rather low in preclinical biodistribution and radiotoxicity studies on rodents (Kruijff et al. 2019; Miederer et al. 2004a, 2008; Poty et al. 2019; Nedrow et al. 2017; Schwartz et al. 2011). In addition, this approach using multiple GC measurements could also be considered for monitoring whether ²²¹Fr activities are different from the activities expected for SEq with ²²⁵Ac. However, non-SEq between ²²¹Fr and ²²⁵Ac is generally considered irrelevant and challenging to assess, due to its relatively short physical half-life of only a few minutes. Moreover, because ²²¹Fr is the first gamma-emitting daughter in the decay chain of ²²⁵Ac, with this short half-life, it is generally considered as the closest proxy daughter to determine the presence/location and activity of ²²⁵Ac.

Therefore, we suggested a single GC measurement to determine the ²²⁵Ac activity using the EW of ²²¹Fr. This can be done once SEq is established between ²²⁵Ac and ²²¹Fr around 30 min after mixed ²²⁵Ac/²¹³Bi samples have been synthetized as was previously reported (Hooijman et al. 2021; Pretze et al. 2021). However, we noticed that ²²⁵Ac activity estimated with the EW of ²²¹Fr is biased when the activity of ²¹³Bi does not correspond with the expected activity in case of SEq with ²²⁵Ac. This problem can be addressed by using a HPGe detector due to its superior energy resolution which provides a more definite isotopic identification for low-energy emitters than NaI(Tl) detectors (Perez-Andujar and Pibida 2004). However, the purpose of this study was to optimize the GC protocols because these detectors are much more accessible than HPGe detectors. Moreover, commercial GC systems allow automatic measurements of many samples, making it a very suitable technique for the multiple time point protocols that were used for this study. Therefore, we advise to estimate the down scatter of the higher-energy gamma rays by ²¹³Bi into the EW of ²²¹Fr when using GC protocols. This way, the count rate in the EW of ²²¹Fr can be corrected, such that ²²⁵Ac-estimates using the EW of ²²¹Fr are unbiased and independent of the ²¹³Bi activity present in the sample or mixture. Once ²²⁵Ac activity has been determined, the remaining ²¹³Bi activity can be estimated using the EW of ²¹³Bi. However, this single GC measurement approach requires a waiting time of around 30 min which reduces the sensitivity for measuring low amounts of ²¹³Bi compared to a GC measurement protocol using multiple time points. On the other hand, a single GC measurement protocol can be considered when higher levels of ²¹³Bi activities are anticipated, like for example during the synthesis of ²²⁵Ac-labeled radiopharmaceuticals, or when standardized QC procedures need to be balanced between unbiased activity estimates and short measurement times. A single GC measurement at 2 h after radiolabeling was already suggested as ideal time point for GC measurements to balance the need for a fast release and accurate assessment of the radiochemical yield (Kelly et al. 2021; Eryilmaz and Kilbas 2021). However, one could argue that 2 h waiting time will delay administration to patients, while the bound fraction of both ²¹³Bi and ²²⁵Ac will be reduced to the RDE. Therefore, a GC measurement protocol at 30 min to indirectly quantify ²²⁵Ac activity by measuring ²²¹Fr once SEq is reached between ²²⁵Ac and ²²¹Fr, can be a valid alternative, provided that a correction is applied for the down scatter of the higher-energy gamma emissions by ²¹³Bi.

For our study, we used both single and multiple time-point GC measurements to evaluate the stability of [²²⁵Ac]Ac-DEPA and [²²⁵Ac]Ac-DOTA constructs in human serum to simulate an in vivo situation and challenge the radiocomplexes to test their stability (e.g. tranchelation by metalloproteins). After 24 h of incubation in human serum, negligible amount of bound ²¹³Bi were observed for both constructs based on the GC measurements of the upper part of the iTLC strips just after elution (see Fig. 7). Following the GC measurements, ²¹³Bi activity gradually recovered till SEq was reached with ²²⁵Ac, and ²¹³Bi activity was again representative for the fraction of bound ²²⁵Ac. These findings showed that, after 24 h incubation in human serum, ²¹³Bi was not bound to the chelator anymore and was most likely released due to the RDE, while the fraction of bound ²²⁵Ac remained very high (Kratochwil et al. 2016) and very stable for both constructs (see Table 3). To reduce potential radiotoxicity caused by the RDE, diethylenetriamine pentaacetic acid (DTPA, hydrophilic chelate) can be added to the final formulation buffer for complexation of free ²²⁵Ac and recoiled daughters before administration and combined with diuretic drugs to increase renal excretion (Kratochwil et al. 2016). However, once administered, the ²²⁵Ac-labeled compound is being added to a diluted medium, such as blood pool, and ²¹³Bi will still be released and cause additional radiotoxicity because of RDE. This can justify, to some extent, the high uptake of free ²¹³Bi in healthy (i.e. non-targeted) organs (e.g. kidneys Kruijff et al. 2019; Song et al. 2009; Drecoll et al. 2009) early after injection. Ideally, this risk of potential redistribution and additional radiotoxicity should be minimized by using more stable targeting systems with high radiolabeling yields capable of retaining part of the daughter nuclides or strategies to retain radionuclides in the tumor cells/tissues (Kruijff et al. 2019; Robertson et al. 2018).

In terms of clinical translation, one could consider using the proposed GC protocols to quantify activity levels of ²²⁵Ac and ²¹³Bi in blood and urine samples of patients undergoing ²²⁵Ac -TAT. This way, renal, bone marrow, urinary bladder wall, or gastrointestinal toxicity can be estimated and whole-body clearance can be monitored in a more patient-specific manner, contrary to the more empirically dose estimates to OARs based on the retrospective evaluation of radiotoxicity and treatment response in groups of patients (Siegel et al. 1999). Moreover, accurate GC measurements of the ²²⁵Ac and ²¹³Bi activity levels in patient samples could be combined with compartmental models to unravel the biokinetics of ²²⁵Ac-pharmaceuticals and recoiling daughters for a better dosimetry (Hooijman et al. 2021), such to allow better prediction of radiotoxicity and treatment efficacy in patients.

The main limitation of this study is the limited number of experiments because of the limited availability of ²²⁵Ac. Therefore, the proposed GC protocols should be further validated and especially the time schedule of the multiple GC measurements for each specific application.

Conclusions

For this study, we evaluated two GC measurement protocols for quantifying ²²⁵Ac-activity when no SEq is guaranteed between ²²⁵Ac and its daughter radionuclide ²¹³Bi. A first protocol performed multiple measurements using only the ²¹³Bi energy window and requires no secular equilibrium between ²²⁵Ac and its gamma emitting daughter radionuclides. For the second protocol, SEq was required between ²²⁵Ac and ²²¹Fr corresponding to a waiting time of around 30 min but only one measurement was needed using both the ²¹³Bi and ²²¹Fr energy window. Both protocols were able to accurately estimate ²²⁵Ac-activities provided the ²²¹Fr energy window was corrected for the down scatter of the higher-energy gamma-emissions by ²¹³Bi. In addition, these two protocols were able to quantify ²¹³Bi-activities which cannot be attributed to the parent-daughter decay of ²²⁵Ac. From this perspective, a multiple GC measurement protocol could prove more sensitive to pick up low levels of ²¹³Bi since it doesn’t require SEq and allows measurements as soon as samples are available. This could prove beneficial to study the recoil daughter effect and redistribution of free ²¹³Bi by monitoring the accumulation or clearance of ²¹³Bi in different tissues during biodistribution studies or in patient samples during clinical studies. On the other hand, the single GC measurement protocol, although required a 30 min waiting time, is more time and cost efficient and therefore more appropriate for standardized QC procedures of ²²⁵Ac-labeled radiopharmaceuticals.

Abbreviations

CF

Calibration factor

CPM

Counts per minute

DOTA

1,4,7,10-Tetraazacyclododecane-1,4,7,10-tetracetic acid

DEPA

7-[2-(Bis-carboxymethyl-amino)-ethyl]-4,10-bis-carboxymethyl-1,4,7,10-tetraazacyclododec-1-yl-acetic acid

DTPA

Diethylenetriamine pentaacetic acid

EW

Energy window

GC

Gamma counter

iTLC

Instant thin-layer liquid chromatography

LET

Linear energy transfer

QC

Quality control

RCY

Radiochemical yield

RDE

Recoil daughter effect

SEq

Secular equilibrium

SPECT

Single photon emission computed tomography

TAC

Time–activity curves

TAT

Targeted alpha-particle therapy

Author contributions

DCS: experimental design, experimental setup, data analysis, discuss data analytics, draft manuscript. MDSH: methodology, discuss data analytics, draft manuscript. SA: experimental design, experimental setup, radiopharmaceutical radiolabeling, discuss data analytics, writing-review. CSV: experimental design, discuss data analytics, methodology, writing-review. MO: radiopharmaceutical radiolabeling, discuss data analytics, review. LS: methodology, discuss data analytics, writing-review. MK: methodology, discuss data analytics, draft manuscript. All authors read and approved the final manuscript.

Funding

Not applicable.

Availability of data and materials

All data generated or analysed during this study are included in this published article and its supplementary information files.

Declarations

Ethics approval and consent to participate

Not applicable.

Consent for publication

Not applicable.

Competing interests

The authors certify that there is no conflict of interest with any financial organization regarding the material discussed in the manuscript.