The CFs for 212Pb were stable when the total imaged activity exceeded 1 MBq (0.16 kBq/ml) for all four imaging protocols studied with an acquisition time of 30 min. Additionally, it was found that the activity in volumes of 2.6 ml could be quantified with a fractional uncertainty around 20% with 212Pb with all protocols except HE 239 keV. This uncertainty includes contributions from the calibration factors and from small volume effects, but other sources of uncertainty, such as from a dose calibrator, were not included. All the imaging protocols had a large increase in fractional uncertainty for the two smallest volumes, and volumes of 1.15 ml were considered too small for reliable activity quantitation with 212Pb. When evaluating the visual quality of the images, the 79 keV window gave images which converged with fewer reconstruction updates, but the images were noisier than the 239 keV window images. The HE 79 keV stood out as the visually best protocol due to more visible spheres in the images with a lower activity concentration. There were only small differences in the quantitative uncertainties and visual quality of the protocols, which all showed promise for clinical imaging.

The limit of quantitative ability was determined to be 1 MBq (or 0.16 kBq/ml), based on the CFs no longer being stable. This limit might be lower if the acquisition time is increased. While the limit is based on the total activity in the field of view, it is not a hard limit and smaller total activities with much higher activity concentrations can still be quantified. This can be seen from Fig. 4, where the lowest activity concentration is 17.2 kBq/ml, corresponding to a total activity of 0.8 MBq, but the data points still lie close to the mean. Depending on the treatment (amount of activity administered, biodistribution, biological half-life, etc.), this lower limit can be used to estimate the latest feasible imaging time points in upcoming trial protocols. For example, for the PSMA-targeting 212Pb-NG001, if it has a similar biological half-life as PSMA-617, the effective half-life of 212Pb-NG001 should be around 8.7 h. The effective half-life with [lutetium-177 (177Lu)]Lu-PSMA-617 was calculated to be between 35 and 40 h for most patients [30], giving a biological half-life of around 49 h. As clinically relevant administered activity is likely to be 60–80 MBq [25], there will probably be around 1 MBq 212Pb-NG001 left in the patient after 48 h. However, since close to 1 MBq is probably needed in the camera field of view to obtain reliable quantitative results and the activity will be distributed throughout the body, the final imaging time point should be less than 48 h post-injection.

As stable quantitative results can be obtained with around 1 MBq in the field of view, spatial resolution is likely a larger issue than sensitivity, as the primary target for most 212Pb-based therapies will be micrometastases. If the tumours are smaller than 2.6 ml, one cannot expect quantitative tumour dosimetry based on these results. However, as long as the volume is larger than 2.6 ml, it should be possible to calculate the activity in organs at risk and larger tumours with a reasonable uncertainty of around 20% from the CFs and small volume effects. The uncertainty did not decrease with increasing volume, and an uncertainty around 20% should be expected for all volumes larger than 2.6 ml. From Fig. 4, it could, however, be seen that the variation in measured to known activity in the spheres increased at lower activity concentrations. Likely, greater accuracy than 20% can be achieved for VOIs with high activity. Performing dosimetry on these volumes is therefore feasible, but factors such as daughter nuclides released from the carrier molecule, the complex dose dependence of relative biological effectiveness, and non-uniform radiation at the micro- and multicellular levels will also add uncertainty to the dosimetry calculations [31,32,33,34]. The fractional uncertainties on activity quantitation in spheres were very similar between using mean counts (on the left of Fig. 6) and maximum counts (on the right of Fig. 6), but these results were obtained with the same activity concentration in the entire spherical volume. This is rarely the case in patient tumours and the uncertainties associated with a maximum rather than a mean value are expected to increase.

In Fig. 8, 17–19 kBq/ml is referred to as a low activity concentration. In terms of quantitative imaging, this is a low activity concentration, as it corresponds to a total activity of 0.8 MBq in the phantom, which is just below the limit for stable CFs. 17–19 kBq/ml is likely also a low activity concentration in terms of tumour concentration. For example, for [177Lu]Lu-PSMA-617 it has been shown that a typical tumour reaches its maximum activity concentration around 10 h post-injection [35]. Correcting for physical half-lives and assuming similar pharmacokinetic properties of the radiotherapeutics when replacing 177Lu with 212Pb, this would give an activity concentration around 32 kBq/ml with 212Pb after a 100 MBq injection. While there are possibly large variations, low activity images in Fig. 8 might still give an indication of the visibility of a typical tumour at the later imaging time points.

Whether monitoring dose to organs at risk is more important than tumour dosimetry is debatable. Quantitation of tumour absorbed doses are very useful for dose–effect estimates and to avoid undertreating, but doses to organs at risk are important to ensure the safety of the radiopharmaceutical. Kidneys are considered one of the main organs at risk for many radionuclide therapies including 212Pb-NG001 [25] and clinical studies with other PSMA-targeting radiopharmaceuticals have also shown salivary glands, liver, and bone marrow as normal tissues at risk [35,36,37]. Kidney dosimetry should be achievable with 212Pb, but potential non-uniform uptake in the kidneys will be difficult to visualise and quantify. Localisation of the radiopharmaceutical in radiosensitive subregions of the kidneys might give whole organ toxicity that is poorly related to mean absorbed kidney dose [38]. This will be difficult to predict solely on the 212Pb images, and therefore preclinical data or imaging of surrogate diagnostic compounds in combination with pharmacokinetic models should be used for dosimetry calculations on that level [34, 39].

A minimised uncertainty on the activity quantitation was the primary goal when comparing imaging protocols. For instance, the ME 239 keV protocol had the highest activity recovery and was hence the most resilient against intensity spread, but since this can be accounted for with RCs this characteristic was deemed less substantial. The uncertainties of the curve fits are hence a more relevant property for comparison. Importantly, the uncertainties given in Table 1 reflect the appropriateness of the fitted function, not the quantitative ability of the protocol. The fractional errors on the fitting parameters were smaller for the 239 keV window, but the fractional uncertainties on activity quantitation in spheres were smaller for the 79 keV window. After inspecting the RC curves, it is not surprising that the fits for the 79 keV window are poorer, as the fitted curve seems to reach towards 1 while the data points to a larger extent flatten out. Attenuation plays a larger role for 79 keV photons than for 239 keV photons and is likely what causes the lower activity recovery seen for 79 keV. The photons lost to attenuation in the NEMA phantom have not been accounted for with the CFs, since they were calculated from homogeneously distributed 212Pb. When adding b3 as a third fitting parameter to the RC function,

$$RC_}}} = b_ - \frac }}^ }} }},$$

(5)

b3 was less than 1 for all the filtered reconstructions, expect 10 × 1, for all four imaging protocols. For the reconstructions 30 × 2, 30 × 3, and 30 × 4, 1 was more than two SE from b3. Hence, it might be inappropriate to force the RC function to 1. An additional challenge posed by increased attenuation of the lower energy photons is that although the NEMA phantom to some degree simulates a body, it would correspond to a small patient. Thus, it is possible, with the small differences observed, that the 239 keV window would give better quantitative results if the circumference of the NEMA phantom was larger.

Since the quantitative ability was similar between the protocols, visual quality more strongly impacts the choice for clinical imaging. No activity was added to the background when imaging the NEMA phantom, based on the assumption that a high tumour to background contrast will be seen in patients treated with 212Pb-NG001, as has been observed in imaging studies with gallium-68-labelled PSMA [40]. For both energy windows, false positives appeared with increased numbers of updates, which can be regarded more concerning than the noise seen in the images. This may suggest making reconstructions tailored to the patient-specific activity concentration and distribution. A large amount of statistical noise was expected in 212Pb images due to the limited number of photons and the large amount of scatter [41] from the 208Tl emission of 2.6 MeV. Filters compensate for the noise from scatter and low count statistics; the filtered 212Pb images being of higher visual quality were therefore expected. Since the quantitative uncertainties were similar in the filtered and unfiltered images, filtering is recommended. Also, since no large quantitative differences were found, only a 12-mm filter was investigated in this study and the filter strength was not optimised. Likely different reconstructions benefit from different filters. In general, the uncertainties found decreased with increasing number of updates. This, in addition to recovery curves not converging with few iterative updates encourages a higher number of reconstruction updates than what is typical in the clinic. If the same images are used for quantitation and visual interpretation, this might also motivate stronger filters.

The question of whether 212Pb can be quantitatively imaged was investigated in this work. As far as we know, no previously published article has undertaken this problem, but an abstract was published in 2019 which compared imaging of one sphere of 212Pb with an ME collimator to simulations [42]. The authors concluded that imaging of 212Pb could be feasible, but features such as intensity spread in small volumes were not discussed. However, quantitative imaging of α-particle emitter 223Ra has been extensively studied. With planar images a 200 ml volume was quantified with 10% uncertainty and a 0.5 ml volume with 40% uncertainty [4]. A SPECT study with 223Ra used an ME collimator, a 5/8″ crystal, 2 iterations and 10 subsets with a Butterworth filter and added three energy windows (40% centred on 85 keV, 20% on 154 keV, and 20% on 270 keV). Similarly to our findings with 212Pb, they achieved quantitation of 5.6 ml volumes with an error smaller than 19% [43]. The count rate achieved with 212Pb with the 79 keV energy window was much higher than when imaging 223Ra [4, 6, 13, 43]. However, a lot of photons contributing to the 79 keV energy peak are characteristic X-rays from the lead collimator and scattered photons from the 2.6 MeV emission of 208Tl, and hence it would be more relevant to report the number of primary photons detected to compare sensitivity. Still, almost 25 times more activity is expected to be administered with 212Pb compared to 223Ra therapy, and it is therefore expected that images of reasonable quality can be obtained. Count rates with 227Th and 225Ac were lower than with 223Ra and hence also lower than with 212Pb [13]. Other studies have attempted to quantify 227Th and 223Ra in combination with planar imaging and found that 227Th can be separated from 223Ra in the images. Spatial filtering improved the images visually, similarly to 212Pb [5]. Using a spectral analysis technique modelling energy spectra and scattered photons, Murray et al. calculated that the average difference between known and estimated activity was 5.1% for 227Th and 3.4% for 223Ra, but differences of 50% were observed [6]. However, even with measurements differing from the known activity with 50%, they obtained differences smaller than 10% when calculating the time integrated activity. Hence, they found that for dosimetry, “uncertainty in individual data measurements may be mitigated by carrying out multiple measurements over several time points” [6]. This is likely also applicable to 212Pb, but will require more imaging time points than usually acquired for clinical dosimetry.