1 Introduction

Over the last 2 decades, targeted radionuclide cancer therapy with 177Lu (T1/2 = 6.65 d [1]) has become of particular interest in the treatment of patients affected by neuroendocrine tumours (NETs) and/or prostate cancers (PCas) due to its intrinsic characteristics. For PCa treatments the main antigen labelled to 177Lu is the prostate-specific membrane antigen (PSMA), while for NET applications common ligand peptides are the somatostatin analogous DOTATATE/DOTATOC [2]. On one hand, the medium-energy beta-particles emission (Emax = 498.3 keV [1]) with a mean range of 0.7 mm in tissue [3] allows the treatment of small volumes and metastatic lesions with a reduced damage to the healthy tissues. On the other hand, the low-energy gamma emission (the gamma with highest energy emission and highest intensity has about 208 keV [1]) represents a relatively minor concern for radiation protection, while enabling to evaluate the biodistribution in patients with the same radiolabelled preparation used for therapy [4]. The radionuclide can be obtained mainly by nuclear reactors through either a direct method or an indirect process [2, 4]. The direct production path, consisting in neutron irradiation of a 176Lu target exploiting the 176Lu(n,γ)177Lu reaction, represents the cheapest option to obtain 177Lu. However, it leads to the co-production of 177mLu, that can often rise some concerns related to radiation protection and waste management due to the longer half-life (T1/2 = 160.4 d [1]) and the conspicuous gamma emissions compared to 177Lu.

As emphasized by Kurth et al. [5], the success of treatments with DOTATOC/DOTATATE and PSMA ligands may lead to a rise in radionuclide therapies with 177Lu, due to the good outcomes demonstrated in terms of response rates with poor side effects. Having PCa an incidence about 40 times higher than NET in the population and being the second most common cancer in male patients, the interest in 177Lu-PSMA treatments as a clinical practice opportunity is rapidly growing. Hehakaya et al. [6] in 2020 reported that in the Netherlands 4500 patients per year were estimated to be eligible for a 4–6 cycled 177Lu-PSMA treatment.

Patients undergoing treatment with radiopharmaceuticals are carriers of radioactivity, which may be released through sweat, saliva, urine and faeces for a period of time related to the administered radionuclide [7]; this constitutes a radiation protection issue for both hospital personnel and population. Depending on the national legislation, excretions must be collected in an adequate storage system in the hospital facility, following appropriate risk reduction procedures, for a period necessary to comply with the clearance criteria stated by the law for the disposal into the sanitary sewerage system [8, 9]. Following Italian legislation (Decree 101/2020, transposition of the European directive 2013/59/EURATOM), the discharge of radioactive liquid effluents evaluations must be included in the practice authorization procedure with the calculation of specific release formulas for each radionuclide intended to be discharged [10, 11]. This calculation aims to demonstrate the compliance with clearance criteria, ensuring that in all feasible circumstances the cumulative dosimetric impact of all the involved radionuclides on the representative person of the population is less than 10 μSv per year. The same legislation (Art. 67 and Art. 82 of 2013/59/EURATOM, Art. 130 and Art. 151 of Decree 101/2020) imposes the verification of what reported in the authorization prior to each discharge, and stresses the need of regularly calibrate the measuring instruments and check their response stability, with the radiation protection expert being required to verify the instrumentation adequacy (Art. 82, par. 2 in 2013/59/EURATOM and Art. 130, par. 1 in D.Lgs. 101/2020). Therefore, the proper measurement of the radioactivity level and nuclide identification in waste samples are of crucial importance to comply with the clearance criteria, aiming to preserve population and environment from exposures above the limits [12].

To verify liquid waste activity, High Purity Germanium (HPGe) detectors with a Marinelli beaker geometry are commonly used. As semiconductor detectors, they have high efficiency and excellent energy resolution and are widely employed in gamma-spectroscopy and low activity measurements [13]. Even if in Italy there are renowned centres allowing the calibration of these systems, such as the ENEA centre, to the best of our knowledge, this procedure on the whole spectrometric chain using specific geometries related to liquid waste management is rarely available, as well as liquid 177Lu and 177mLu standardize sources. Therefore, it is common practice that medical physicists, in cooperation with the manufacturer, calibrate and verify the instrumentation following good technical standards, such as BS ISO 20042:2019 [14]. A customized computational model of the whole system could be a fruitful support to set up an appropriate quality assurance program and to calculate the correction factors to be applied in the evaluation of the activity from the measured spectra.

In this view, the first purpose of this work is to validate a Monte Carlo model of the specific Marinelli detection system used in our clinical research institute and to obtain a reference response curve of the system in the energy range of interest. In particular, the work focuses on liquid waste derived from radionuclide therapy with 177Lu. Depending on manufacturer, some 177Lu-based radiopharmaceuticals also present an amount of 177mLu as impurity. Current Italian legislation allows to exclude radioactive impurities from disposal evaluations, as long as the radiopharmaceuticals involved comply with the applicable good preparation standards (Art. 50, par. 1 in Decree 203/2022). However, since detectable emission peaks of 177Lu are in common with some from the metastable impurity (112.95 keV and 208.37 keV [1]), a correct quantification of 177Lu in the waste sample requires a correct and accurate quantification of 177mLu. Thus, the secondary aim of this work is to propose a framework to properly quantify the amount of 177mLu in a waste sample. To the best of our knowledge, the framework here proposed includes for the first time the role of the True Coincidence Summing (TCS) effect on the quantification of 177mLu. The detection system for Marinelli beaker counting geometry is modelled using GEANT4 (GEometry ANd Tracking) [15].

2 Materials and methods

2.1 Geometry and computational model

The HPGe used in this study is a p-type ORTEC GEM30P4-70 coaxial detector with a Peltier-based cooling system (CFG-X-COOL-III-230) and a nominal resolution of 1.73 keV full width half maximum (FWHM) at 1.33 MeV (second 60Co peak [1]). Its detection volume is composed by a hyper-pure germanium crystal of cylindrical shape with 6.03 cm in height and a nominal diameter of 5.72 cm. According to the manufacturer, the inner dead layer (DL) is made up of a boron-doped layer (P+ contact) with a thickness of 0.30 μm, while the outer DL is a Li-doped layer 0.70 mm thick. An aluminium holder surrounds the sensitive volume, while an external cylindrical aluminium cap encases the whole system. The external cap is located 6.00 cm inside the hole of a cylindrical shield with an external diameter of 45.80 cm and 42.0 cm in height, protecting the detector from the background radiation (e.g. cosmic rays or 222Rn daughters etc.). Such a detector can be used with different geometries, depending on measurement requirements (e.g. blood samples, solid samples etc.).

The Marinelli beaker geometry is used to monitor the activity of the excretions over time. The beaker available at our institute is 13.70 cm in height, with an external radius of 6.50 cm and a thickness of 3.00 mm in all lateral walls, entirely made of polymethyl methacrylate (PMMA) and filled with 1 l of water (density = 1.00 g/cm3). For the measurements, it is always positioned on the bottom of the shielding well, so that the upper wall of the beaker hole is at a height of 2.70 cm from the upper part of the detector aluminium external cap. Representative schemes with detailed dimensions of the cylindrical shield (together with the detector external cap) and the Marinelli beaker are reported in Fig. 1a, b, respectively. The detector model with its detailed dimensions and schemes are shown in Fig. 2.

Fig. 1
figure 1

a Scheme and dimensions of the shielding well geometry, with its transversal section in the dashed circle and related dimensions. Colours refer to: lead (green), tin (red) and copper (orange), aluminium (grey). The external aluminium detector cup is 6 cm inside the well cavity. Inside the well, the Marinelli beaker was positioned on the bottom. b Transversal section of the one-liter Marinelli beaker model and related dimensions. Blue refers to PMMA

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Fig. 2
figure 2

a Simplified scheme of the detector geometry with b a zoom on the detector volume and nominal dimensions listed on the right. Colours refer to: germanium (orange), aluminium (grey) and dead layers (streaky orange). The lower part of the aluminium cup of the detector (dimensions A and E) contains electronic components which were not modelled in the simulations

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The whole geometry was simulated with GEANT4 code (version 10.07) [15]. To replicate the detector response, both internal and external DLs were implemented with the nominal dimensions listed in Fig. 2. According to other authors [16, 17], DLs were approximated as partial volumes of the germanium crystal in which no energy deposition contributes to the total energy record. The detector active volume was set as the scoring volume, where the total energy deposited per event was scored. To allow appropriate comparison between simulated and measured data, the system resolution was implemented [18] combining the FWHM and energy calibrations as:

$${\text{FWHM}}\left( C \right) = a + b \cdot C + c \cdot C^{2}$$
(1)
$$E = d + e \cdot C + f \cdot C^{2}$$
(2)

where a, b, c, d, e, f are parameters extracted from instrument calibrations (Table 1) and C is the channel of the multichannel analyser, corresponding to a certain energy E. Thus, an expression of the FWHM as a function of energy, FWHM(E), was obtained, representing our specific HPGe system resolution characteristics. Quadratic terms are negligible (Table 1). A gaussian smearing was applied to each simulated deposit of energy E0 in the scoring volume, with mean \({E}_{0}\) and standard deviation \({\sigma }_{{E}_{0}}\) given by [18]:

$$\sigma_{{E_{0} }} = \frac{{{\text{FWHM}}\left( {E_{0} } \right)}}{{\sqrt {8 \cdot \ln \left( 2 \right)} }}$$
(3)
Table 1 Calibration parameters used in Eqs. 1 and 2
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2.2 Sources

Three different radionuclides are considered for this study: 99mTc, pure 177Lu and combined 177Lu–177mLu. The 99mTc decay (T1/2 = 6.01 h) has two possible branches [1]. Since the gamma emissions derived from the 99mTc β− branch and from the 99Tc decay have intensities well below 1%, they can be neglected and the only relevant one is that at 140.51 keV derived from the 99mTc Isomeric Transition (IT) branch, with an absolute intensity of 88.5% (Table 2).

Table 2 Summary of the main 177mLu, 177Lu and 99mTc emissions
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177mLu decay (T1/2 = 160.4 d) has two distinct branches, as schematized in Fig. 3 [1, 19]: in the 78.3% of cases, it decays β− into 177Hf stable, whereas in 21.7% it undergoes IT to 177Lu (T1/2 = 6.65 d), which in turn decays 100% β− into 177Hf stable. The main gamma emissions due to 177mLu and 177Lu decays are listed in Table 2 with corresponding intensities in percentage.

Fig. 3
figure 3

Simplified decay scheme of 177mLu and 177Lu. All energies are expressed in keV. Photon data were compiled from Nucléide Lara database [1], some electron and energy level data were taken from National Nuclear Database Center [19]

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A 177Lu direct-produced liquid source, uniformly distributed in 1 l of water, was exploited as a combined 177Lu–177mLu source, mimicking a radioactive waste sample to be disposed in the sanitary sewerage system, with both activity components certified. The total activity of the sample is a consequence of the emissions from primary 177Lu, 177mLu-derived 177Lu and 177mLu impurities. Despite the limited amount, 177mLu has a half-life about 24 times longer than that of 177Lu, thus transient equilibrium [20] is achieved between 177Lu and 177mLu-derived 177Lu [21]. Thus, long after production, the amount of 177Lu drastically decreases and almost all the activity is attributable to the decay of 177mLu. In Fig. 4 the percentage contribution of primary 177Lu, 177mLu-derived 177Lu and 177mLu to the total activity of a 177Lu direct-produced liquid source is represented. As can be observed, initially the sample activity is all attributable to the primary 177Lu, being the main sample component, while 177mLu component is roughly negligible. Over time, the derived 177Lu contribution increases thanks to 177mLu decay. However, 177Lu activity decreasing in time is drastically faster than the 177mLu one, due to its characteristic half-life. Being the total sample activity given by the sum of all component activities, it follows that after a certain period of time 177mLu contribution will dominate on 177Lu.

Fig. 4
figure 4

Percentage contributions to the total activity of the combined 177Lu–177mLu source sample. The red solid line represents the whole 177Lu activity contribution, as a sum of the primary and derived components

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2.3 Single energy full-energy peak efficiency curve: simulation and validation

To obtain a reference full-energy peak (FEP) efficiency curve of the detection system in the energy range of interest, a source of isotropic and monochromatic photons was implemented inside the model of the Marinelli beaker, uniformly distributed in the water. The efficiency curve obtained this way was labelled as “Single Energy” or SE and represented the ideal efficiency curve of the acquisition system in the chosen geometry and sample type. Runs were performed each time simulating 106 events and selecting one of the main gamma peaks of 177Lu, 177mLu and 99mTc decays listed in Table 2 as source energy. Each point of the curve \(\left( {{\text{FEP}}_{{\text{E}}}^{{{\text{SE}}}} } \right)\) was calculated as the ratio between the net area under the peak at the selected energy (\({\text{NA}}_{{\text{E}}}\)) and the number of photons simulated during the correspondent run:

$${\text{FEP}}_{{\text{E}}}^{{{\text{SE}}}} = { }\frac{{{\text{ NA}}_{{\text{E}}} }}{{{ }10^{6} { }}}$$
(4)

NA calculations were based on the summing method [14, 22] and the energy integration interval was always considered as ± 1.5 FWHM centred in the maximum of the selected peak, whose energy dependence was extrapolated from Eq. 1 and Eq. 2.

To validate the FEPSE curve and the HPGe model, comparisons with measurements in the same conditions were needed [14]. Since 177mLu has a complex decay scheme with many cascade gamma emissions, the 99mTc and the pure 177Lu sources were chosen for the purpose. Known activities were uniformly distributed in the Marinelli beaker described in Sect. 2.1 and the same setup was adopted to acquire spectra with dead time always lower than 2%. Each measured FEP efficiency point, \({\text{FEP}}_{E}^{{{\text{meas}}}}\), was obtained as:

$${\text{FEP}}_{E}^{{{\text{meas}}}} = \frac{{ {\text{NA}}_{E}^{i} }}{{A_{i} \left( {t_{0} } \right) \cdot \Delta t \cdot I_{E}^{i} }}$$
(5)

where \(A_{i} \left( {t_{0} } \right)\) is the nominal activity of the source containing the radionuclide i (i.e. 99mTc or 177Lu) at the measurement time \(t_{0}\) and \(I_{E}^{i}\) is the gamma emission intensity at the energy E of the radionuclide i (Table 2). \(A_{i} \left( {t_{0} } \right)\) was considered constant during the measurements because of the short live time (\(\Delta t\) = 3600 s) with respect to the nuclide half-lives considered. As the 99mTc was the radionuclide with the shortest half-life (6 h),\({\text{ NA}}_{140.51}\) could have been the most affected by the activity decreasing during measurements. Accounting for this effect, a percentage difference of about 5.6% in the FEP value at 140.51 keV was derived, which was comparable with the measure relative error (approximately 6.6%). Hence, the assumption of constant \(A_{i} \left( {t_{0} } \right)\) was maintained during all efficiency calculations.

2.4 True Coincidence Summing effect: simulation and validation

TCS effect is a well-known phenomenon [22,23,24,25,26,27] that alters the photopeak counts at different energies: two or more photons emitted within a shorter time than the detector response time can be detected as a single photon event, with an energy given by the sum of each deposition. As the effect is activity-independent [23], the HPGe model was exploited to obtain TCS correction factors for each gamma emission energy of 177mLu, 177Lu and 99mTc decays [28]. For this purpose, simulations were performed both removing (referred as “Partial Decay”, or PD) and including (referred as “Total Decay”, or TD) the TCS effect. Both simulations included the same number of source nuclei of the selected radionuclides (177mLu, 177Lu or 99mTc), uniformly distributed at rest in the Marinelli beaker water, and the use of the GEANT4 decay simulation package [29]. To perform PD simulations, all the gamma tracks resulting from the source decays were suppressed immediately when generated, except those at a specified energy: This was performed each run varying the energy value until the gamma energies listed in Table 2 were all considered. On the contrary, to perform TD simulations all the decay-derived tracks were included: In this way, all the photons belonging to the same cascade and releasing energy in the detector active volume were treated as a single event with energy given by the sum of the gamma energies released throughout the cascade.

For both PD and TD simulations, spectra were registered and each NA under the photopeak at a certain energy E (\({\text{NA}}^{{{\text{PD}}}}\) and \({\text{NA}}^{{{\text{TD}}}}\), respectively) was calculated. From the ratio between \({\text{NA}}^{{{\text{PD}}}}\) and \({\text{NA}}^{{{\text{TD}}}}\) at the same energy E, simulated TCS correction factors (TCSsim) were calculated for each gamma emission energy of interest:

$${\text{TCS}}^{{{\text{sim}}}} = \frac{{{\text{NA}}^{{{\text{PD}}}} { }}}{{{\text{NA}}^{{{\text{TD}}}} }}$$
(6)

The simulated factors were compared with the experimental ones (\({\text{TCS}}^{{{\text{exp}}}}\)) calculated on independent measures as:

$${\text{TCS}}^{{{\text{exp}}}} = \frac{{{\text{EC}}}}{{{\text{NA}}_{{{\text{meas}}}} }}$$
(7)

where \({\text{NA}}_{{{\text{meas}}}}\) is the net area measured under the photopeak at energy E, and the expected counts (EC) at the same energy were calculated as:

$${\text{EC}} = \Delta t \cdot {\text{FEP}}^{{{\text{SE}}}} \cdot \left( {A_{{{\text{mLu}}}} \left( {t_{0} } \right) \cdot I^{{{\text{mLu}}}} + A_{{{\text{Lu}}}} \left( {t_{0} } \right) \cdot I^{{{\text{Lu}}}} } \right)$$
(8)

where \(I^{{{\text{mLu}}}}\) and \(I^{{{\text{Lu}}}}\) are the gamma emission intensities at energy E of 177mLu and 177Lu, respectively. For non-in-common photopeaks, \(I^{{{\text{Lu}}}}\) was considered equal to 0.

2.5 Lutetium quantification


To test the previously calculated FEPSE curve in the high energy range, a direct-produced 177Lu source was exploited as a combined 177mLu–177Lu source mimicking an ideal radioactive waste sample, with both activity contributions certified. The FEPSE curve was adopted for quantifying the contribution of the 177mLu component to the total activity. The 177mLu–177Lu source spectrum was acquired in the same setup described in Sect. 2.1. To quantify the amount of 177mLu in the source, the NAs at the characteristic 177mLu gamma emission energies not in common with the 177Lu ones were calculated (\({\text{NA}}_{E}^{{{\text{mLu}}}}\)) and corrected by the corresponding TCSsim factors (Eq. 6). Using the FEPSE efficiency curve previously obtained, the activity of 177mLu in the sample was estimated as the weighted mean of the activity calculated on each photopeak of interest:

$$\begin{aligned} & A_{{{\text{mLu}}}} \left( {t_{0} ,E} \right) = \frac{{ {\text{TCS}}_{E}^{{{\text{sim}}}} \cdot {\text{NA}}_{E}^{{{\text{mLu}}}} }}{{{\text{FEP}}_{E}^{{{\text{SE}}}} \cdot \Delta t \cdot I_{E}^{{{\text{mLu}}}} }} \\ & A_{{{\text{mLu}}}} \left( {t_{0} } \right) = \frac{{\mathop \sum \nolimits_{E} A_{{{\text{mLu}}}} \left( {t_{0} , E} \right)/\delta_{E}^{2} }}{{\mathop \sum \nolimits_{E} 1/\delta_{E}^{2} }} \\ \end{aligned}$$
(9)

where \(A_{{{\text{mLu}}}} \left( {t_{0} ,E} \right)\) = 177mLu activity estimated from photopeak at energy E and \(\delta_{E}^{2}\) is the square of the associated uncertainty. \(A_{{{\text{mLu}}}} \left( {t_{0} } \right)\) was used to calculate the number of counts that contribute to the area of the photopeaks at 112.95 keV and 208.37 keV due to the 177mLu decay only (i.e. \(C_{E}^{{{\text{mLu}}}}\) in Eq. 8). Then, by subtraction, it was possible to calculate the counts under the area of the photopeaks at 112.95 keV and 208.37 keV due to the 177Lu decay only (\({\text{NA}}_{E}^{{{\text{Lu}}}}\), Eq. 10), and to calculate the activity of the 177Lu component in the sample (\(A_{{{\text{Lu}}}} \left( {t_{0} } \right)\)) using Eq. 9 adapted to 177Lu quantities and emission energies:

$${\text{NA}}_{E}^{{{\text{Lu}}}} = {\text{NA}}_{E}^{{\text{Lu + mLu}}} - C_{E}^{{{\text{mLu}}}} = {\text{NA}}_{E}^{{\text{Lu + mLu}}} - \left( {A_{{{\text{mLu}}}} \left( {t_{0} } \right) \cdot {\text{FEP}}_{E}^{{{\text{SE}}}} \cdot \Delta t \cdot I_{E}^{{{\text{mLu}}}} } \right)$$
(10)

where \({\text{NA}}_{E}^{{\text{Lu + mLu}}}\) is the net area measured at energy E on the whole source spectrum.

3 Results


The FEPSE efficiency curve was validated in the low energy range by the measurements of the pure 177Lu and 99mTc sources (Fig. 5), with a maximum absolute relative difference of 2% between the simulated SE efficiency value (2.84%) and the measured value (2.9%) deriving from the 177Lu spectrum acquisition (Table 3). This difference was observed at 208.37 keV and turned out to be comparable with the 177Lu-derived maximum relative uncertainty (about 7%).

Fig. 5
figure 5

Efficiency curve versus energy related to single energy (SE) simulations and measurements of 177Lu and 99mTc sources

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Table 3 FEPSE efficiency values and calculated values from measured spectra of pure 177Lu and 99mTc sources
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Figure 6a shows the measured 177mLu–177Lu, pure 177Lu (Fig. 6b) and 99mTc (Fig. 6c) spectra, exhibiting a good agreement with the TD-simulated ones, rescaled by proper scaling factors. TD-simulated spectra were compared with PD-simulated ones (Fig. 7), that were obtained by summing the corresponding mono-peak PD spectra. The 177mLu spectra showed an appreciable disagreement due to the TCS effect, as well as the absence of some photopeaks not considered in this work due to the low associated emission intensities or the presence of multiplet regions (Fig. 7a). Conversely the 177Lu and the 99mTc PD-simulated spectra were comparable with the corresponding TD-simulated ones (Fig. 7b, c).

Fig. 6
figure 6

Comparison between the measured and the simulated TD spectra of the radionuclide sources: a 177Lu–177mLu, b 177Lu, c 99mTc

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Fig. 7
figure 7

Comparison between the partial decay (PD) and the total decay (TD) simulated spectra of the radionuclide sources: a 177mLu, b 177Lu, c 99mTc. Not all the gamma emission energies of the 177mLu decay were considered in the PD simulations

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The TCS correction factors, calculated for each source from PD and TD simulations, are listed in Table 4. While for 177Lu and 99mTc values approached unity for each gamma emission energy, correction factors associated to the 177mLu source were more significant and varied at different emission energies. The simulated TCS factors were comparable with the measured ones in the selected energy range (Table 4). A maximum absolute relative difference of 7% (at 327.68 keV) was observed in the energy range from 105.36 to 378.50 keV. At 413.66 keV and 418.54 keV absolute relative differences of about 18% were observed, however values were comparable with simulated ones.

Table 4 Simulated and measured TCS correction factors at different energies for 177mLu, 177Lu and 99mTc sources
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Eventually, Table 5 shows the estimated activities of the 177Lu and 177mLu components of the composited source. Discrepancies of maximum 16% could be noted, not significantly different from the nominal values.

Table 5 Activities of the 177Lu and 177mLu components of the therapy-derived radioactive liquid waste sample emulator, nominal (second column) and derived from the spectrum analysis (third column)
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4 Discussion and conclusion

In this work, the customized GEANT4 model of the HPGe detection system available at our institute was implemented with a Marinelli beaker geometry. Using this model, the FEP efficiency calibration curve of the system in the working energy range (from about 100 keV to about 420 keV [1]) was calculated by SE simulations, as described in Sect. 2.3. This curve should offer the most accurate evaluation of the system efficiency achievable, being unaffected by the complex mechanisms originating from source decays and depending only on the acquisition geometry (including the sample type) and the detected gamma energies. FEP efficiency values calculated from the acquisition of the pure 177Lu and 99mTc sources spectra validated the FEPSE curve in the low energy range.

To test the higher energy range of the curve, a different approach was adopted, which allowed both to exploit the potential of the computational model and to propose an operational framework for quantifying the 177mLu component in a therapy-derived liquid waste sample. The dosimetric impact of 177mLu is at least an order of magnitude greater than that of 177Lu, as shown by the weight factors given in the NCRP Report No.123 to calculate the release formulas [10]. Therefore, from an ethical and a radiation protection point of view, its careful evaluation contributes to compliance with the ALARA principle and ensures a correct evaluation of the before mentioned release formula. Thus, a therapy-derived liquid waste sample was simulated by a direct-produced 177Lu source containing 177mLu as impurity, with both activity contributions certified. The NAs of the 177mLu characteristic photopeaks were calculated to estimate the 177mLu activity component in the sample, considering the FEPSE curve valid for this measure setup. However, due to the complexity of the 177mLu decay scheme, a strong TCS effect was expected during the spectrum measurement. The HPGe GEANT4 model was adopted to simulate partially (PD) or completely (TD) influenced spectra from whom to estimate the TCS correction factors for 177Lu, 177mLu and 99mTc sources. The positive outcome of the comparison between the measured and the TD-simulated spectra (properly rescaled) ensured an accurate reproduction of the radioactive decay processes of 177Lu, 177mLu and 99mTc sources by the GEANT4 decay simulation package. Minimal variations may have been caused by small inaccuracies in the GEANT4 library of gamma emission intensities. Moreover, the accuracy given by the manufacturer in geometrical specifications could also have been very relevant: Other works show that discrepancies in the real distances, dead layers and material thicknesses compared to the nominal values could lead to even significant variations [16, 17].

Confirming the expectation, significant discrepancies were noted comparing the PD and TD 177mLu simulated spectra, whereas the similar comparisons for 177Lu and 99mTc sources showed good agreements. This was because the simpler, cascade-poorer decay schemes of 177Lu and 99mTc compared to 177mLu, hence showing a negligible TCS effect. Confirmation was found in TCS correction factors obtained for each energy and radionuclide of interest: for both 177Lu and 99mTc spectra they were unitary at all gamma emission energies, whereas for 177mLu spectrum the lowest value of 1.2 was obtained at 309.02 keV. Thus, TCSsim factors were applied to correct the net areas of the photopeaks related to the 177mLu decay only, calculated on the acquired spectra of the combined 177mLu–177Lu source mimicking the radioactive waste sample. The estimation of the 177mLu activity component in the sample was adopted to derive the 177Lu activity contribution.

As TCS effect does not affect 177Lu spectrum acquisition, it worth noting that during 177mLu and 177Lu quantification TCSsim factors related to the common photopeaks should be applied to the portion of counts associated with the 177mLu decay only. Being these TCSsim factors greater than 1 for all emission energies, their application to the whole peaks could lead to an overestimation of the 177Lu activity in the sample. This overestimation is certainly conservative from the perspective of clearance, but it may impact in the clinical flow management and storage system sizing optimization. However, if measurements are performed at a time point ensuring a strong predominance of 177mLu contribution to the total sample activity, 177Lu overestimation pitfalls could be reasonably acceptable in favour of a streamlined and timesaving procedure. Results showed good agreements with the nominal values for both the radionuclide components, thus completing the validation of the HPGe computational model, the FEPSE curve and the TCSsim correction factors.

Once validated, the HPGe model could be exploited for a wide range of applications such as planning a robust quality assurance program, investigating the causes of possible drifts in system stability or extend and verify the system response with other geometries or complex radionuclides of interest adopted in daily clinical routine (e.g. 131I). Moreover, it could be adopted to obtain different crucial correction factors (e.g. density correction, self-absorption correction, etc.) in other context [30,31,32], for example in the field of radiopharmaceutical purity controls.

In conclusion, the potential and the versatility of the Monte Carlo approach make this model a powerful resource for a wide range of applications, not only in a research facility but also in a daily clinical routine. Regarding the discharge of radioactive effluents, it could be a useful tool to ensure an effective application of the optimization of the radiation protection of members of the public, according to the provisions of the directive 2013/59/EURATOM [33].