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Theoretical study of Sc production for theranostic applications using proton beams on enriched titanium targets

Recently, scandium-47 has attracted attention in the scientific community thanks to its promising features, making it suitable for targeted radiotherapy and theranostic applications, also in combination with the β emitters Sc/Sc. However, in view of possible pre-clinical and clinical studies, finding efficient production routes is still a current research topic. In this work we investigate Sc cyclotron production using proton beams on enriched titanium targets. The analysis of the cross sections and yields of both Sc (T1/2 = 3.35 d) and its main contaminant Sc (T1/2 = 83.79 d) has been performed with the nuclear reaction code Talys (v.1.95). The experimental data (scarce and relatively old) are compared with model calculations and some discrepancies emerge even after the tuning of parameters defining the nuclear level densities, involved in the compound nucleus formation. The Ti case allows a more precise cross sections reproduction, conversely the Ti case requires further theoretical investigations. Preliminary yields analysis has been carried out for both Sc and Sc.

Indeed, chemically identical radiopharmaceuticals with the same pharmacokinetics are optimal tools in advanced nuclear medicine. Currently preclinical studies have revealed tumor growth delay and an increased survival time of mice treated with the novel 47 Sc DOTA-folate conjugate (cm10), demonstrating the therapeutic potential of this radionuclide. For all these reasons 47 Sc is a promising new candidate and a potential competitor of 177 Lu for targeted radionuclide therapy [2]. However an efficient and convenient production route has still to be identified and the research is devoted to find a reliable production route which guarantees a sufficient quantity and purity of the radionuclide. In this work we investigate the cyclotron proton-beam production of 47 Sc using 49 Ti (5.41%) and 50 Ti (5.18%) targets, the only two titanium isotopes that could provide an efficient 47 Sc production. Since no measurements for 49 Ti targets are available and the sole data for 50 Ti are quite old [3], theoretical studies are essential to identify the best irradiation parameters for maximizing 47 Sc production on both targets, while limiting the co-production of the 46

Production cross sections
The simulation of the relevant cross sections and preliminary yields has been carried out mainly with the nuclear reaction code Talys (v.1.95) [4]. Talys describes the nuclear reaction mechanisms with a variety of models, in particular with 4 pre-equilibrium models (PE) and 6 level density models (LD), for a total of 24 possible combinations of models. Commonly in literature Talys default (PE2-LD1) and Talys adjusted (PE3-LD5) are reference options, but they are not always the most representative ones. For this reason, instead of selecting a specific combination of models we describe the results statistically, taking into account the large variety of models that can be selected with this tool. We refer to 18 combinations of models (PE 1-3 and LD 1-6). We excluded the PE4 model because, in this mass region, its results turned out to be not stable and not physical. In the figure shown in this work the maximum and the minimum of the selected Talys models are represented by dashed lines and the interquartile band, defined as the difference between the upper (Q3) and lower (Q1) quartile by a grey band. It exhibits graphically the dispersion introduced by the variety of models. We denote as the most representative value the BTE "Best Theoretical Evaluation", the median of this interquartile band, depicted as a solid black line. For a comprehensive explanation of this statistical approach, we refer to [5]. The large discrepancies between models and experimental data that emerges from the plots, in particular Fig. 1 and Fig. 4, and the practical aim of the project oriented to medical applications compelled us to improve the model description. Indeed, a better reproduction of the relevant cross sections would allow to achieve a higher accuracy in the predicted yields, purities, and in the assessment of the absorbed dose to the patients' organs. The new analysis approach refers to the microscopic theory of the nuclear reactions where the thermalisation processes use the nuclear level density based on the Hartree-Fock (HF) method. The original HF microscopic level densities can be rescaled by tuning two parameters, c and p, responsible for a normalization change and an energy shift of the level density curves, respectively. A detailed description of the method is presented in [6]. Predictions for the cross sections of the reactions 49 Ti(p,x) 47 Sc and 49 Ti(p,x) 46 Sc are presented in Figs 1 and 2. In particular, these figures show the comparison between the statistical approach (BTE curve) and the results of the optimization performed by tuning the c and p parameters trying to reproduce the experimental data available only for the contaminant 46 Sc [7]. The best agreement has been achieved with the values c = 0.11 and p = -0.17 (red line) for the LD4 model and considering the default option for preequilibrium (PE2). The good agreement obtained for the 46 Sc case and the lack of 47 Sc data from 49 Ti targets led us to consider the selected set of parameters for 46 Sc to be reliable also for the 47 Sc cross section. Starting from the cross sections we identified the optimal energy window that maximizes the yield of 47 Sc while minimizing the coproduction of 46 Sc. Comparing both curves it is evident that the energy range 32 -40 MeV could optimize the production with 49 Ti targets.    The same analysis has been performed for the production routes 50 Ti(p,x) 47 Sc and 50 Ti(p,x) 46 Sc, Figs 3 and 4. For both cases a dataset is available to guide the optimization procedure of the theoretical curves. A good reproduction of 46 Sc data is achieved by the combined effects generated by the semi microscopic optical potential JLM (JeukenneLejeune-Mahaux) and by the selected model LD4 without any tuning of the c and p parameters. Conversely for 47 Sc cross section from 50 Ti all Talys models seem not able to reproduce the data peak around 25 MeV. We noticed the persistence of an offset of about 5 MeV between the data by Gadioli et al. [3] and the model results. Further investigations are necessary, and the new experimental data planned at ARRONAX within the REMIX project will be fundamental to validate the theoretical models and to optimize the models free parameters. In the present situation of uncertainty, we consider the theoretical cross sections to set an optimal range of 8-18 MeV, for 50 Ti targets. This range will be employed to evaluate yields, purities, and dosimetric assessments.

Yields
In this paper we considered the results obtained within the statistical approach, denoted as BTE cross sections. The analysis performed with the optimized cross section are presently in development. As first step we calculated the production rate for both radionuclides of interest. Secondly, we solved numerically the generalized Bateman equations for the decay chains, whose solutions give the time evolution of the number of nuclei of a certain species produced. Then we evaluated the activity produced by radionuclides and the integral yields at the End of Bombardment (EoB), defined as [8]  where i indicates the considered radionuclide, Ai(T) is the activity produced by the radionuclide i at the irradiation time T at EoB, and I0 is the beam current.  The integral yields have been calculated for a current I0 = 1 μA and T = 1 h, with an energy range from Emax to 0, namely, assuming full beam energy loss inside the target. Preliminary results of the 47 Sc integral yields for both 49 Ti and 50 Ti cases are plotted in Figs 5 and 6, with the same notation adopted for the other figures (BTE, interquartile band and min/max). We added a green area highlighting the optimal energy window maximizing 47 Sc production. From the integral yields plots we obtained the yield for these two specific irradiation energy windows by selecting the values at the corresponding energies Ein and Eout. The difference y(Ein ) -y(Eout ) provides the yield for a target of given thickness. In Table 1 we summarize the preliminary yield results for 47 Sc and 46 Sc from both production routes. The optimized energy windows correspond to a thickness of 1.6 mm for 49 Ti target and of 0.93 mm for 50 Ti target.

Outlook on dosimetric studies
In view of possible clinical applications of scandium radionuclides, it is important to consider the impact of the radiocompounds to the patients' health. Indeed, to ensure the safety of a radiopharmaceutical and verify the compliance of the European Pharmacopoeia requirements, biodistribution studies and dosimetric calculations are fundamental to assess the impact of the produced radionuclide and main contaminants in terms of dose released to the patient's organs. Contamination is of primary importance, since a radiopharmaceutical must satisfy a minimal purity to be adequate for clinical applications. Nevertheless, it is not sufficient to verify only the percentage of radionuclidic impurities, but it is fundamental to quantify also the dose increase due to the presence of these impurities.
In the near future we plan to develop our study using the CoKiMo (Compartmental Kinetic Model) software [9], that models the human body in compartments connected one to each other and describes the phase of accumulation of the radiopharmaceutical as well as both the fast and slow elimination phases. The approach allows to determine the absorbed dose to a target tissue with the OLINDA (Organ Level Internal Dose Assessment) software, based on the RADAR (RAdiation Dose Assessment Resource) method for internal dose estimation [10]. Finally, combining the OLINDA output with the information of the activity obtained with the irradiation conditions we evaluate the efficacy and quality of the selected radiopharmaceutical.

Conclusions
The therapeutic potential of 47 Sc has been demonstrated in preclinical trials. However, finding reliable production routes (in terms of quantity and purity) for clinical trials is still an issue that needs to be solved. In this work we report on preliminary results concerning the 47 Sc cyclotron production using proton beams on enriched titanium targets, 49 Ti and 50 Ti. Cross section results, for both 47 Sc and its main contaminant 46 Sc, have been obtained with the nuclear reaction code Talys. We have explored the capacity of Talys predefined models to reproduce the data and applied a tuning procedure for the nuclear level densities to improve the cross-section reproduction. We have found that the level density tuning significantly improves the 46 Sc production cross section in the case 49 Ti targets while no data are available for 47 Sc. In the 50 Ti case, the 46 Sc production cross section is well reproduced by all calculations while for 47 Sc the offset of the lowenergy peak could not be resolved. New measurements, in progress within the REMIX experiment, will be useful to better clarify the situation with that cross sections. We calculated preliminarily the BTE yields of both radionuclides for both enriched targets. The results show a higher yield in the case of 49 Ti targets, however with 50 Ti targets the contamination due to 46 Sc is significantly lower. In addition, in this last case, the lower energy range makes the production suitable for typical hospital cyclotrons. These conclusions need to be validated by the planned measurements. It is expected to complete this study with the evaluation of the dose absorbed in the patients' organs. In fact, in the assessment of the production route, particular attention to contaminants must be paid in order to determine their contribution to the final dose, in line with the European Pharmacopeia requirements.