Half-life measurement of the medical radioisotope 177Lu produced from the 176Yb(n,γ) reaction

177Lu is a medium energy beta-emitter commonly used in Nuclear Medicine for radiotherapeutic applications. In this work, the half-life of 177Lu has been measured using a re-entrant ionisation chamber over a period of 82 days (approximately 12 half-lives). Unlike the majority of previous studies, the material used in this work was produced via the 176Yb(n,γ )177Yb reaction followed by the β-decay to 177Lu, producing insignificant quantities of 177mLu. This has resulted in the most precise half-life measurement of 177Lu to date. A half-life of 6.6430 (11) days has been determined. This value is in statistical agreement with the currently recommended half-life of 6.6463 (15) days (z-score = 1.8).


Introduction
Lutetium-177 is commonly used in the radiotherapeutic treatment of neuroendocrine tumours and relapsed non-Hodgkin Lymphoma [1,2].Lutetium-177 decays by the emission of medium energy β particles with a maximum β energy of 498.3 (8) keV to excited and ground states of the stable 177 Hf nucleus [3].These β particles have a maximum tissue penetration of approximately 1-2 mm [4].The excited states (life-times < 1 ns) of 177 Hf decay via characteristic γ -ray emissions to the ground state, with the most abundant γ rays being from the 9/2 + level (112.9 keV) and 9/2 − level (208.4 keV) (see Fig. 1) [3].These γ -ray emissions provide 177 Lu with the benefits of both radiotherapeutic treatment and imaging capability [4].
There are two methods used for the production of medically suitable 177 Lu; 1) via the 176 Lu(n,γ ) 177 Lu reaction, which results in the production of significant quantity of 177m Lu (T 1/2 ∼ 160 days) as an impurity or 2) produced via the 176 Yb(n,γ ) 177 Yb reaction followed by β − decay to 177 Lu, which produces no carrier added (n.c.a) 177 Lu.This second production mode is claimed to produce significantly smaller activity ratios of the 177m Lu impurity to the desired 177 Lu product [5].
There have been 14 previous publications reporting half-life measurements of 177 Lu [6][7][8][9][10][11][12][13][14][15][16][17][18][19], which are summarised in Table 1.Of these only the measurement reported by Dryak et al. [18] has used 177 Lu from production method 2) and therefore not required corrections for the 177m Lu impurity.In a recent evaluation, Kellett [20] identified that the presence of 177m Lu has had a significant influence on the half-life determinations, while Pommé et al. [14] observed that the omission of the impurity subtraction led to a 0.5% error in their determined halflife after only 7.6 days in their measurement campaign.A recent investigation at IFIN-HH [19] has highlighted the difficulty in determining an accurate activity ratio between the 177 Lu and 177m Lu.Therefore, for an accurate a e-mail: kelley.ferreira@npl.co.uk half-life determination it would be beneficial that insignificant levels of 177m Lu were present to cause interferences in the measured exponential decay of the 177 Lu activity.
The work reported here has used 177 Lu generated from the 176 Yb(n,γ ) 177 Yb reaction to determine a precise halflife value.The associated uncertainty budget is presented.Throughout this article, uncertainties are stated as standard uncertainties or combined standard uncertainties as defined in the Guide to the Expression of Uncertainty in Measurement (GUM) [21].

Source preparation
An aqueous solution of 177 Lu n.c.a was received from Isotope Technologies Garching GmbH (ITG) and diluted at the National Physical Laboratory (NPL) using an aqueous solution of 0.04 M HCl containing stable lutetium at a concentration of 10 µg g −1 .A nominal mass of 10 g of this solution was gravimetrically dispensed to a 10 mL flame sealed glass ampoule [22] with a total activity of 200 MBq at the start of the measurement campaign.A 1 g aliquot was dispensed to a 2 mL ISO ampoule for impurity assay by high purity germanium (HPGe) γ -ray spectrometry.
Additionally, 233 days after the start of the measurement campaign (∼ 35 half-lives of 177 Lu), the solution from the 10 mL ampoule was transferred to a 20 mL plastic vial, for assay by HPGe γ -ray spectrometry for the presence of 177m Lu in the absence of 177 Lu.

HPGe γ -ray spectrometer
The 2 mL ISO ampoule was assayed at the start of the campaign using a 20% relative efficiency coaxial ntype HPGe γ -ray spectrometer to check for the presence of any γ -ray emitting radionuclides in the solution.No γ -ray emitting radionuclide impurities were detected.The 10 mL aliquot used for the half-life measurement was assayed 233 days after the start of the campaign using a  Both γ -ray spectrometers had been previously calibrated for their full-energy peak detection efficiency using radionuclide standard solutions, in matching geometries, traceable to national standards.

Ionisation chamber
The half-life of 177 Lu was measured using the NPL secondary standard re-entrant ionisation chamber (IC) [23].The system is comprised of two identical TPA Mk II ionisation chambers [23], filled with argon gas at a pressure of 2 MPa, connected in a "back-to-back" formation as previously described by Fenwick et al. [24].Each IC is surrounded by an inner 5 cm thick lead shield and an outer 10 cm thick lead shield.The "back-to-back" formation and the dual lead shield reduces the background noise and consequently the effect of the background in low current measurements.The background was measured daily before starting the 177 Lu measurements (see Fig. 2a).
The mean background over the course of the campaign was 1.2 (23) × 10 −6 pA.The ratio of the mean background/ 177 Lu current was 0.0003% at the start of the measurement campaign, 0.02% after 38 days and 1.2% at the end of the measurement campaign (82 days).A 226 Ra check source was measured prior to the 177 Lu measurements to check the stability of the system (see Fig. 2b).The variations of the 226 Ra were attributed to the check source geometrical reproducibility in the well of the IC and statistical variations.For the 177 Lu measurements, the 10 ml ampoule was placed in a dedicated plastic holder for reproducible positioning in the well of the ionisation chamber.

Measurement results
A total of 11370 individual measurements were acquired over a period of 82 days (∼ 12 half-lives), shown in Fig. 3a.The measurements were grouped in sets of ten and the standard uncertainty for each data point was determined from the standard deviation of the mean of the ten measurements.In the course of the measurement campaign the source was repositioned a total of 37 times over the 82 days.The number of measurements made for each repositioning were not equal, therefore to remove possible biases due to any repositioning, the same number of measurements were used for each positioning.The halflife was determined from the least squares fit of: where A t is the IC response at time t, a 0 and b 0 are the respective responses to 177 Lu and 177m Lu at t = 0, C is the background response, λ 1 and λ 2 are the decay constants of 177 Lu and 177m Lu respectively.As the measurement times varied over the campaign period an additional correction factor [k = (1 − e −λ t )/λ t] was incorporated to account for decay during the measurement, where t is the measurement time.
Using fixed values for b 0 , C and λ 2 , the half-life of 177 Lu was derived by the iterative refinement of parameters a 0 and λ 1 , where the sum of squares of the relative deviations between calculated and measured values were

Uncertainty
The uncertainty of each component was calculated using the uncertainty propagation formula proposed by Pommé [25] and combined in quadrature to determine the standard uncertainty of the half-life.The uncertainty budget is presented in Table 2.
The main sources of uncertainty are the systematic errors associated with the detector stability and the background subtraction.As the background value C has a high systematic relative uncertainty (see Sect. 2) the uncertainty contribution of the background subtraction increases significantly as the measured current reached low currents.Due to this effect there was no benefit to the accuracy of the measurement in using the entire dataset.Therefore, the initial 36.8days (∼ 5.5 halflives) of the measurement campaign were found to provide the optimum balance for the assessment of the uncertainty budget.This provided a total of 230 sets of 10 measurements for the half-life determination.
The low frequency components of uncertainty are not visible in the residuals plot, therefore an attentive analysis needs to be performed.In this paper, a conservative approach was considered for the analysis of the low frequency components, therefore n =1 for the stability, linearity, background and impurity components.The standard deviation of the 226 Ra measurements was used to estimate the uncertainty associated with the electrometer stability, all the measurements from day 0 to 82 were included.The standard deviation of the background measurements was also included in the uncertainty associated with the background.The uncertainty associated with the presence of 177m Lu is also reported in table and is shown to be negligible.The system linearity has been tested previously for the DVM range 1 V to 10 V and the uncertainty associated was estimated to be 0.010%.
The first published values (from 1958 and 1990) for the determination of the half-life used 177 Lu from the 176 Lu(n,γ ) 177 Lu reaction, however no correction was applied for the presence of the 177m Lu impurity, resulting in an overestimation of the half-lives values determined [6][7][8]10], with the exception of the value reported by Lagoutine and Legrand (1982) [9].
For this work 177 Lu from the 176 Yb(n,γ ) 177 Yb reaction was used and showed to be advantageous in determining a more accurate half-life, since no additional correction for the 177m Lu response was required.The low activity of 177m Lu present in the solution was found to have no effect in determining the half-life of 177 Lu.Dryak et al. [18], reported a detection limit of 6 × 10 −9 for 177m Lu when using 177 Lu n.c.a., confirming the results presented in this paper regarding the negligible amount of impurity present in solution for this method of production.
Previous published values showed that the presence of 177m Lu and the effect of background when measuring low currents in the ionisation chamber are the components with the highest impact in the uncertainty budged [13,14,19].The improved uncertainty achieved in this work compared to previous published values is due to a combination of: the negligible amount of 177m Lu present, low background (due to the "back-to-back" formation and the dual lead shield) and the high starting 177 Lu activity.These allowed the useful measurement campaign to extend over 36.8 days (over five half-lives), which resulted in an uncertainty propagation factor that allowed the significant reduction of the initial uncertainty component estimates.
The determined value in this work of T 1/2 ( 177 Lu) = 6.6430 (11) days is the most accurate value to date.It was found to be in agreement with the recommended value of 6.6463 (15) days (z-score = 1.8).[20].

Conclusion
This work used a n.c.a. 177Lu solution produced by the 176 Yb(n,γ ) 177 Yb reaction followed by β decay to 177 Lu.This production mode was found to contain negligible 177m Lu activity, with an activity ratio of 177m Lu/ 177 Lu = 1.1 × 10 −7 % determined at the start of the measurement campaign.
The half-life of 177 Lu was measured using a reentrant ionisation chamber over a campaign period of 82 days.A total of 11370 measurements were acquired.To obtain a good balance between the campaign length and the standard uncertainty only the first 36.8days (∼5.5 half-lives) of the measurement campaign were used to determine the half-life.
The value of the 177 Lu half-life was determined by a least squares fit of an exponential decay to the measured data.A half-life of 6.6430 (11) days was determined, with a full uncertainty budget presented.This value is the most accurate and precise value to date due in part to the low background of the IC and the negligible 177m Lu content.This value was found to be in good agreement with the current recommended value (z-score = 1.8).

Figure 2 .
Figure 2. a) Background measurements and b) residuals of the stability checks measurements using a 226 Ra check source.The uncertainties in the graph correspond to the standard error of the mean of 2 measurements of 6 cycles each.

Figure 3 .
Figure 3.The ionisation chamber current response to the 177 Lu source as a function of time (hollow squares) is shown in a).The mean background current, fitted exponential decay curves of 177 Lu and 177 mLu and the sum of these components are shown.The residuals of the least squares fit to the selected measurements the initial 36.8days are shown in b), the uncertainty bars represent the standard deviation of the mean of the ten measurements.

Table 1 .
Summary of published half-lives of 177 Lu.

Table 2 .
Half-life of 177 Lu and respective uncertainty.