Production of Lu-177 Radionuclide using Deuteron Beams: Comparison between (d,n) and (d,p) Nuclear Reactions

Lutetium-177 (177Lu) radioisotope has been suggested for radioimmunotherapy application in nuclear medicine. Presently 177Lu has been mostly produced using neutron activation in nuclear reactors, whereas cyclotron-based production has not been well explored. In this paper, we theoretically propose cyclotron-based deuteron beams for 177Lu production. By Employing the TALYS 2017 codes, we calculated nuclear cross-sections and the End-of-Bombardment (EOB) yields of 176Yb(d,n) 177Lu reaction for direct production of 177Lu as well as 176Yb(d,p)177Yb→177Lu reaction for indirect production of 177Lu. The TALYS calculated cross-sections indicated that the threshold energy of both investigated nuclear reactions is 0 MeV; thus 177Lu could be produced at low deuteron energy bombardment, though significant amount of 177Lu radioactivity could only be generated for deuteron beams with energy greater than 6 MeV. The calculated EOB yields for 176Yb(d,n)177Lu reaction and 176Yb(d,p)177Yb reaction were 0.519 and 181.1 MBq/μAh respectively, which well agreed with previous experimental results published elsewhere. In conclusion, both nuclear reactions are possible for 177Lu production though the indirect method via 176Yb(d,p)177Yb→177Lu reaction would give much better EOB yield than that of direct method.


Introduction
In nuclear medicine, cancer therapy requires alpha, beta or gamma emitting radioisotopes since the particles could destroy cancer cells, though direct proton beam irradiation could also be employed in solid cancer therapy [1][2]. One of the emerging radioisotopes suggested for targeted therapy is lutetium-177 ( 177 Lu), which emits beta particle at a half life of 6.65 days. When 177 Lu is labeled to a certain chemical compound or antibody, it can be employed as a therapeutic agent, which is often coined as radioimmunotherapy. Recent studies suggest that 177 Lu could deliver positive therapeutic effects to a wide range of solid cancers such as prostate cancer [3][4][5][6][7], neuroendocrine tumor [8][9][10], breast cancer [11][12][13][14] and some other tumors.
Lutetium-177 production has been mostly conducted by irradiating enriched 176 Yb target with high flux neutrons in nuclear reactors [15][16][17][18], though 177 Lu separation from the impurities could be very difficult. New methods of 177 Lu production have also been suggested for new reactor-based neutron source [19] as well as for targets other than enriched 176 Yb [20][21][22][23]. Alternative 177 Lu production pathways have also been suggested, particularly using accelerators or cyclotrons where particle such  3 He and 4 He are accelerated to gain high energy applicable for radioisotope production [24][25] as well as for material studies [26][27][28].
There has been very limited number of literatures on production of 177 Lu using deuteron beam which indicates that such a new method needs more studies. Previous investigations by Hermanne et al [29] and Manenti et al [30][31] reported that excitation functions for 176 Yb(d,p) 177 Yb  177 Lu and 176 Yb(d,n) 177 Lu nuclear reactions could be sufficiently high for indirect and direct production of 177 Lu using deuteron beams. Similar experimental investigation on the nuclear cross-section for 177Lu production was also highlighted by Tárkányi et al [32][33]. Another nuclear cross-section research by Siiskonen et al [34] suggested that proton beam could be employed to produce 177 Lu by bombarding nat Hf target through nat Hf(p,x) 177 Lu nuclear reaction. Moreover, a theoretical investigation was conducted to study (d,x) nuclear reactions on natural ytterbium up to 24 MeV relevant for deuteronbased 177 Lu production [35].
To the best of our knowledge, there has been no specific report on 177 Lu production at various deuteron doses; therefore this work will explore the dependence of deuteron dose on the end-ofbombardment (EOB) yield of 177 Lu radionuclide for (d,n) and (d,p) nuclear reactions.

Materials and Methods
In this study, deuteron was the main particle used in the calculations and simulations while the target of interest would be enriched 176 Yb. The range and stopping power (energy loss) of deuteron in 176 Yb target was simulated using the Stopping and Range of Ion in Matter (SRIM) code version 2013 which had been widely used elsewhere [36].
The excitation functions of two nuclear reactions, namely 176 Yb(d,p) 177 Yb  177 Lu and 176 Yb(d,n) 177 Lu were calculated using the TALYS code [37]. The TALYS-calculated nuclear crosssections were then employed to calculate the end-of-bombardment (EOB) yield using available mathematical expression published earlier [38][39]; and in this work, a Matlab code was developed for the EOB yield calculation.
To study the dependence of deuteron beam dose on the EOB yield, the bombardment was simulated with a fixed 50-µA deuteron beam current (referred to the IBA's cyclone 70 specifications [40]) while the deuteron energy was varied from 15 to 35 MeV and the irradiation time was varied from 1 to 6 hours.

SRIM-calculated Range and Stopping Power
When deuteron passes through a target, it is expected to lose some or all of its energy. According to the SRIM calculation, a 10-MeV deuteron is able to penetrate as deep as 314.93 µm in a 176 Yb target, whereas the range of a 40-MeV deuteron in the same target is approximately 2930 µm as shown in Figure 1. In addition, the energy losses (stopping powers) of the deuteron particles are relatively large, i.e. 2.90×10 -2 and 1.16×10 -2 mg/cm 2 for 10-MeV and 40-MeV deuterons respectively. For the purpose of 177 Lu radionuclide production, the recommended thickness of 176 Yb target is listed in Table 1 for deuteron energy ranging from 10 to 40 MeV. The target thickness prepared for the irradiation should be made thicker with increasing deuteron energy. Increasing deuteron energy from 15 MeV to 30 MeV would consequently require increasing the 176 Yb target thickness from nearly 0.6 mm to nearly 2 mm. Note that one could add up to 10% of the recommended thickness to account for the deviation of the deuteron range.  Figure 2, which indicates that the threshold energy for both reactions is 0 MeV. While the shape of the excitation function for both reactions is very similar, there is a notable difference in the cross-sections between the two reactions, particularly the maximum cross-section for the (d,p) reaction, which is nearly 9 times that of the (d,n) reaction. As well, the maximum cross-section for both reactions occurs at deuteron incident energy of 10 MeV.  As can be seen in Figure 3, based on the calculated EOB yields, the radioactivity yield for 176 Yb(d,n) 177 Lu nuclear reaction is relatively negligible compared to the 176 Yb(d,p) 177 Yb  177 Lu nuclear reaction. In the inset of Figure 3, it is clear that the maximum 177 Lu EOB yield is only 0.519 MBq/µAh, which occurs when the incoming deuteron energy is 40 MeV. In contrast, the maximum 177 Lu EOB yield for the 176 Yb(d,p) 177 Yb  177 Lu reaction is 181.1 MBq/µAh at deuteron energy of 22 MeV.
Thus when deuteron beam is used for 177 Lu production, (d,n) nuclear reaction would give insignificant contribution to the radioactivity yield as compared to the (d,p) reaction. Furthermore these calculated results are in good agreement with earlier published work [29][30][31][32][33].

Deuteron Dose Dependence of 177 Lu Radioactivity Yield
The 177 Lu production yield is strongly dependence on the deuteron dose as can be seen in Figure 4 and Figure 5 for 176 Yb(d,n) 177 Lu and 176 Yb(d,p) 177 Yb  177 Lu nuclear reactions respectively. In general, the yield increases with increasing deuteron dose. The yield calculations for different deuteron energies ranging from 10 to 35 MeV and various deuteron doses between 50 and 300 µAh indicate that the 177 Lu yield obtained from 176 Yb(d,n) 177 Lu nuclear reaction remains low (maximum of 151.82 MBq for incident deuteron energy of 35 MeV and deuteron dose of 300 µAh). Such a low yield would not be sufficient for radioimmunotherapy purpose even just for 1 patient (assuming 1 patient requires at least over 300 MBq). Therefore 177 Lu production through 176 Yb(d,n) 177 Lu reaction would not be economically viable.  In contrast to the previous 177 Lu production route, the latter pathway through 176 Yb(d,p) 177 Yb  177 Lu nuclear reaction seems very promising as shown in Figure 5. Even for low deuteron energy (10 MeV, for instance) the 177 Lu radioactivity yield at the end of irradiation would be as high as 25231.8 MBq for deuteron dose of 300 µAh. Such a value would be sufficient for over 80 patients to get radioimmunotherapy procedures. Even one can use 20-MeV deuterons to produce much higher 177 Lu of up to 50139 MBq (enough to support as many as 167 patients). Therefore this typical route of 177 Lu production is highly recommended. Further examples of the produced radioactivity yield corresponding to the number of patients could benefit from is shown in Table 2.

Conclusion
Production of 177 Lu radioisotope using deuteron beams have been discussed in this paper, particularly for two different nuclear reactions, namely through 176 Yb(d,n) 177 Lu and 176 Yb(d,p) 177 Yb  177 Lu. Theoretical calculations show that as thick as 1 mm 176 Yb target should be prepared when bombarding the target with 20-MeV deuterons to produce 177 Lu. The TALYS-calculated excitation functions indicate that the deuteron threshold energy for 177 Lu production is 0 MeV, though significant radioactivity yield would not be generated for deuteron energy lower than 6 MeV. In general, the calculated the nuclear cross-section for 176 Yb(d,p) 177 Yb  177 Lu is much higher than that of 176 Yb(d,n) 177 Lu reaction. In conclusion, 77 Lu radioisotope production is very promising using deuteron beam irradiation through 176 Yb(d,p) 177 Yb  177 Lu nuclear reaction, in which up to 50139 MBq could be produced at a 300-µAh deuteron dose.

Acknowledgements
The author would like to acknowledge funding from The Indonesian National Nuclear Energy Agency (BATAN). Discussion with the staff and technicians of the Center for Radioisotope and Radiopharmaceutical Technology, BATAN is also gratefully acknowledged.