Production route analysis of a therapeutic radionuclide ¹⁷⁷Lu

Radionuclide therapy uses open sources of radiotherapeutic agents. It is rapidly emerging as an essential part of nuclear medicine, primarily due to the development of a diversity of sophisticated molecular carriers.¹ The targeted radiotherapy (TRT) with its ability to deliver the radiation dose preferably to cancer cells is a quickly developing modality of cancer treatment and treatment of other pathological conditions such as rheumatoid arthritis.

In recent years, the interest in Lu-177 in nuclear medicine has grown tremendously.² Its attractive decay characteristics and the emission of both low-energy β-rays and ɣ-rays upon decay allow for simultaneous imaging and radionuclide therapy.^3,4 The nuclear properties of ¹⁷⁷Lu are very advantageous compared to other therapeutic radionuclides, e.g., ⁹⁰Y.⁵ 

The half-life of ¹⁷⁷Lu is T_1/2 = 6.659 days, which may be required for the use of more sophisticated procedures for the radiolabel and purification of ¹⁷⁷Lu-labeled radiopharmaceuticals, as well as for performing quality control and administration. The physical half-life of Lu-177, which is relatively long, minimizes decay losses. The maximum β energy of 498 keV of ¹⁷⁷Lu and average energy of 130 keV provide the short-range 0.2–0.25 mm, which is effective in destroying small malignant tumors with less damage to healthy cells.^1,2,5,6

Therefore, the low exposure to gamma rays is caused by the low energy and emission probability of the main transitions: 112 keV (6.17 ± 0.08)% and 208 keV (10.36 ± 007%). This gamma emission is suitable for direct imaging by gamma scintigraphy cameras, thus eliminating the need for a surrogate such as ¹¹¹ln.^5,7

Symphonic improvement may occur with ¹⁷⁷Lu-labeled somatostatin analogs that have been used for peptide receptor radionuclide therapy (PRPT) on the neuroendocrine tumours (NET).⁸ The gamma lines are suitable for imaging the in vivo localization with a gamma camera, which is much more effective on SPECT single photon emission computed tomography.⁹ 

The chemical characteristics of Lu³⁺ are suitable for peptide and protein radiolabeling by attachment of a bi-functional cleating agent (BFCA) through a metabolically resistant covalent bond, which may be important for positron emission tomography (PET) already used in many clinics.^10–12 

The Food Drug and Authority (FDA) approve ¹⁷⁷Lu for use in gastroenteropancreatic neuroendocrine tumors (GEP-NETs) in Jan-2018.^13,14

Two methods may be used to produce Lu-177:¹⁵ 

1. Neutron irradiation of the target material continuum ¹⁷⁶Lu is called the direct method.

2. Neutron irradiation of the target materials containing ytterbium-176 is called the indirect method.

The direct production route is based on the 1/v (where v is the velocity of the neutron) behavior of the radiative capture cross section of ¹⁷⁶Lu in the thermal neutron region where the resonance is strong at about 0.1413 eV.^5,6,16

Data prediction of neutron radiative capture cross section σ^o = 2090 ± 70b at the V_o = 2200 ms⁻¹ and I_o = 4.7.^1,5,15,16

As an alternative route, ¹⁷⁶Yb(n_th, ɣ) ¹⁷⁷Yb, the product ¹⁷⁷Yb (T_1/2 = 1.9 h) decays by β⁻ to Lu-177. The drawback of this production modality is that it requires the chemical separation of ¹⁷⁷Lu from the ¹⁷⁶Yb target, resulting in an excessive amount of time, complexity, and costs.

This work will help to comprehend the prospects of production routes of the radioisotopes from their element in the target. To realize the reliability of the calculation, evaluations were analyzed with the calculation by EMPIRE 3.2.2 and TENDL-2019 data for some probable reactions.

As the paper deals with the enumeration of integral yield, first, we have to determine the production cross sections. The computer based simulation programs TALYS-1.95 (Linux) and EMPIRE (Windows) have been used for determining the production cross sections. The thick target integration yield can be determined easily by the following formula at the incident energy in a laboratory system E_in (MeV),¹⁷ 

where N_A (mol⁻¹) is Avogadro’s constant, A_p is the mass number of the projectile, A_T (g mol⁻¹) is the mass number of the target, σ(E) is the cross section, and S(E) is the stopping power.

The average energy loss of projectiles by the atomic collisions as a function of their energy in (MeV/cm) is known as stopping power. To determine the stopping power, we can use the Bethe–Bloch theorem,

Here, dE/dx is the stopping power in (MeV/cm), ρ is the mass density in (g/cm³), Z is the target charge number, z_p is the projectile charge number, and β represents a beam particle at the relative velocity.

TALYS is a computer code system for analyzing basic scientific experiments or generating nuclear data for applications. It can provide the simulation of nuclear reactions that involve neutrons, photons, protons, deuterons, tritons, and 3 He- and alpha-particles, in the 1 KeV to 200 MeV energy range accurately.^17–19 TALYS can generate nuclear data for all open reaction channels on user-defined energy and angle grid, beyond the resonance region. TALYS 1.95 has been used with the GNU FORTRAN compiler in the Linux Ubuntu operating system. The FORTRAN compiler is a modular system of reaction codes used for model and data evaluation of nuclear reactions. TALYS-1.95 has been used for calculating the production cross section and irradiation yield of medical isotopes in this paper.

EMPIRE is a modular system of nuclear reaction codes comprising various nuclear models designed for calculations over a broad range of energies and incident particles, says Herman. It can be used for simulation of nuclear reactions while the projectile can be neutrons, photons, protons, deuterons, tritons, and 3 He- and alpha-particles in the energy range ∼keV and goes up to several hundred MeV for heavy-ion induced reactions.^20–22 It can also provide a full ENDF-6 formatted file and comparison plots with automatically retrieved experimental data. We used EMPIRE 3.2.3 for determining the cross section only; thus, we can evaluate our data with the exfor library data and calculated data of TALYS-1.95.

Among the reactions, ¹⁷⁶Yb(t, 2n)¹⁷⁷Lu, ¹⁷⁶Yb(d, p)¹⁷⁷Lu, and ¹⁷⁶Yb(α, p3n)¹⁷⁷Lu show a very notable production cross section. Production cross sections have been determined for the reactions shown in the figure where different light beams including proton, neutron, deuteron, triton, ³He, and alpha-particle were used as a projectile.

The cross section was calculated by using TALYS-1.95 and EMPIRE 3.2.3. The production cross section by the TALYS data is tabulated in Table I. The EMPIRE cross section data have been consigned to the graph to make the evaluation more accurate. Yb and Lu were considered as targets, and the following beam parameters were used: particle beam current 1.0 mA, area of the thick target 10.0 cm, irradiation time 24 h, and target cooling time 24 h. We have used the nuclear data library EXFOR to obtain the experimental data. The comparisons are made between the calculated and experimental excitation functions.

It is not possible to draw all the graphs in a single figure. As (d, p), (d, n), and (t, 2n) reactions were starting above 6 MeV, they decreased after 15 MeV and finished at almost 30 MeV, and thus, these reactions are shown in the same figure; although the (h, t) reaction was starting above 15 MeV, it was added. The existing experimental reactions have a plot in the same figure, as they started with a higher value and finished by almost 10 MeV (Fig. 1).

The integral yield for the ¹⁷⁶Yb (a, p2n) reaction is plotted in different figures. As it started with a higher energy level above 30 MeV, it could not be consigned in the same figure, but for comparison with the other reaction, 28 energy points are taken.

Different isotopes of Yb have the natural abundance: ¹⁶⁸Yb (0.126%), ¹⁷⁰Yb (3.023%), ¹⁷¹Yb (14.216%), ¹⁷²Yb (21.754%), ¹⁷³Yb (16.098%), ¹⁷⁴Yb (31.896%), and ¹⁷⁶Yb (12.887%). Among these, medically important isotope ¹⁷⁷Lu can be produced from ¹⁷⁴Yb and ¹⁷⁶Yb using n, d, p, t, ³He, and α particle beams. Hence, in the current work, cross sections of nimble light particle induced ^174,176Yb and ¹⁷⁶Lu reactions were checked for the production of ¹⁷⁷Lu. The maximum production cross sections with the corresponding incident particle energies are tabulated in Table I.

The existing experimental method for producing ¹⁷⁷Lu is based on the neutron induced reaction (at.). There are two processes, which can produce ¹⁷⁷Lu, one is called the direct process by bombarding ¹⁷⁶Lu and the other is called the indirect process, which first produces ¹⁷⁷Yb and then, by beta decay, produces ¹⁷⁷Lu. ¹⁷⁶Yb(n, γ)¹⁷⁷Yb → ¹⁷⁷Lu and ¹⁷⁶Lu(n, γ) → ¹⁷⁷Lu both reactions occur at zero threshold energy with the highest production cross section value σ_max = 42.7458 MB at 1.2 MeV and σ_max = 118.314 MB at 1 MeV.

The deuteron induced ¹⁷⁶Yb reaction can produce ¹⁷⁷Lu in two paths: the direct process and the indirect process. The direct process and the indirect process of deuteron induced reaction, e.g., ¹⁷⁶Yb(d, n)¹⁷⁷Lu and ¹⁷⁶Yb(d, p)¹⁷⁷Yb → ¹⁷⁷Lu, respectively, have shown non-zero cross section values. Although both reactions take place at zero threshold energy, the peak values of the cross section are different. The direct process has maximum ranges of cross section between 6 and 7 MB; on the other-hand, the indirect process has maximum ranges of a cross section between 40 and 60 MB, which means that the (d, p) reaction has almost nine times better production cross section than the (d, n) reaction for ¹⁷⁷Lu.

The proton induced reaction on the ¹⁷⁶Yb isotope has not shown promising production cross sections. The production cross section has maximum ranges between 0.12 and 0.19 MB.

The triton-induced reaction for the ¹⁷⁶Yb isotope has cross section values for ¹⁷⁷Lu, and it has shown very notable results with respect to the existential experimental reactions. The peak value of the production cross section is σ_max = 203.579 MB at 10 MeV with the 2.34 MeV threshold energy, which is almost two times better than that of the neutron induced reaction.

The lowest value, but consign in this study, was from the ³He induced reaction. It also produces cross sections for ¹⁷⁷Lu at the energy level above 15 MeV whereas the maximum reactions start from 5 MeV. Although the ¹⁷⁶Yb(³He, p2n) → ¹⁷⁷Lu reaction shows non-zero cross section values, it is very low in comparison to others.

Alpha induced reactions for ¹⁷⁴Yb and ¹⁷⁶Yb isotopes have production cross sections for ¹⁷⁷Lu. Among the alpha reactions, ¹⁷⁶Yb has the maximum cross section σ_max. The ¹⁷⁶Yb(α, p3n) → ¹⁷⁷Lu reaction has a threshold energy of 13.939 MeV, and the maximum cross section reaches σ_max = 29.0266 MB at 10 MeV. On the other-hand, ¹⁷⁴Yb(α, p) → ¹⁷⁷Lu has the range of 1.2–1.4 MB at above 30 MeV. As the ¹⁷⁴Yb reaction has a very low cross section value, it has been plotted in a different figure.

The yield for ¹⁷⁷Lu production has also been diagnosed for the same reactions with a decent cross section value. The production yield of ¹⁷⁷Lu from different isotopes Yb and Lu has been enumerated for different projectiles. We cannot determine the yield for the neutron induced reaction by TALYS-1.95 because the isotope production is not yet enabled for incident photons and neutrons in TALYS-1.95. The maximum production yield has been found for the ¹⁷⁶Yb(d, p)¹⁷⁷Yb → ¹⁷⁷Lu reaction and the ¹⁷⁶Yb(α, p3n) → ¹⁷⁷Lu reaction. The ¹⁷⁶Yb(t, 2n) → ¹⁷⁷Lu reaction and the ¹⁷⁶Yb(d, n) → ¹⁷⁷Lu reaction are in the second and third positions, respectively. We have not determined the yield for ¹⁷⁶Yb(p, γ) → ¹⁷⁷Lu, ¹⁷⁶Yb(³He, p2n) → ¹⁷⁷Lu, and ¹⁷⁴Yb(α, p) → ¹⁷⁷Lu because they could not have cross section over 7 MB.

The integral yield vs energy curves is shown in Figs. 2(a) and 2(b). The enumeration of the integral yield for ¹⁷⁷Lu production was measured up to 30 MeV except for the ¹⁷⁶Yb(α, p3n) → ¹⁷⁷Lu reaction. For more accuracy, the cross sections are compared with the EMPIRE and TENDL-2017 data. The comparison is shown in Figs. 3(a) and 3(c). The EMPIRE calculation gives a lower cross section than the TALYS-1.95.

We added different isotopes of ¹⁷⁶Lu to evaluate the existence method through our theoretical calculation. The reactions are shown in Fig. 3(b) for the existance method. It started with the maximum values less than 0–1 MeV, then decreased, and lowered at almost 8 MeV. Although it increases a little, finally, it again falls by 15 MeV. The direct process has shown a more steep figure than the indirect process. ¹⁷⁴Yb(α, pn) → ¹⁷⁷Lu and ¹⁷⁶Yb(p, γ) → ¹⁷⁷Lu reactions show very low production cross section values; on the other hand, the ¹⁷⁶Yb(α, p3n) → ¹⁷⁷Lu reaction shows promising data with the higher energy over 30 MeV. Hence, they are plotted in different figures, as shown in Figs. 3(a)–3(d).

The calculation of the production cross section of the therapeutically imperative isotope ¹⁷⁷Lu from Yb and Lu with the interaction of different light beams has been shown where the targeted isotopes are ^174,176Yb and ¹⁷⁶Lu. The production of cross sections of some Lu isotopes from the interaction of the isotope of Yb and Lu has been compared with various projectiles as presented in the graphs. The production yield has been calculated, and the integral yield against the energy has been plotted and evaluated in such a way that possible routes for the processing of Lu isotopes can be seen. The EXFOR Nuclear Data Library was used to collect the experimental data, and distinctions have been created between measured and practical functions. To make the estimation more accurate, the prediction of certain possible responses was assessed using the data of EMPIRE 3.2.2 and TENDL-2019. ¹⁷⁶Yb(d, p), ¹⁷⁶Yb(α, p3n), ¹⁷⁶Yb(d, n), and ¹⁷⁶Yb(t, 2n) reactions show auspicious data for producing ¹⁷⁷Lu, and the relationship between the integral yields shows that the various possible routes for the Lu isotope can be seen in Figs. 2(a) and 2(b).

This work was supported by Abul Khaer Mohammad Rezaur Rahman’s Lab at the Department of Physics, University of Chittagong, Chattagram, Bangladesh.

The authors have no conflicts to disclose.

A. K. M. Rezaur Rahman: Conceptualization (equal); Investigation (equal); Methodology (equal); Resources (lead); Supervision (equal); Visualization (equal); Writing – review & editing (equal). Rifat Amin: Conceptualization (equal); Formal analysis (equal); Investigation (lead); Methodology (equal); Software (equal); Writing – original draft (lead); Writing – review & editing (equal).

The data that support the findings of this study are available within the article.