Discussions on liquid bismuth target use as an alternative for astatine-211 production

. Astatine-211 is an alpha emitter that has been identified as a good candidate for targeted alpha therapy. There is an increasing demand on this radionuclide. Very intense beam from linac being put in operation nowadays could be used to meet this demand. This document presents the design exploration of concepts of liquid bismuth targets dedicated to astatine-211 production. Three concepts are presented and analyzed: a capsule, a fluid loop and a windowless fluid loop. Structural and thermal sizing were performed using mechanical Finite Element models (ANSYS Workbench) and Computational Fluid Dynamic models (FLUENT). Production rates were assessed accordingly. Feasibility and expected performances are discussed in conclusion.


Introduction
While the use of radionuclides for diagnostic purposes (Single Photon Emission Computed Tomography, SPECT, and Positron Emission Tomography, PET) and therapeutic use of beta emitting radionuclides (iodine-131 or lutetium-177) are quite mature fields in nuclear medicine, the therapeutic use of alpha emitting radionuclides is still less developed. Targeted Alpha Therapy aims at using locally highly cytotoxic properties of alpha particles by carrying them to specific sites of cancerous cells thanks to vectors such as peptides or antibodies. This would improve the treatment efficiency, while reducing damages done to healthy tissues. Astatine-211 (T1/2 = 7.2 h) is considered a promising candidate for such application thanks to its adequate half-life and its decay modes leading to the emission of one α particle by decay either directly or through its short lived polonium-211 daughter (T1/2 = 0.515 s ).
This work is part of the ANR-REPARE project that aims at improving astatine-211 availability for research and future medical application. This document focuses on target design for the latest accelerators [1,2], like linear accelerators able to deliver alpha beam at very high intensities (order of magnitude of 1 mA).

Astatine 211 production
Astatine-211 is mainly produced using an alpha beam impinging a bismuth target, through the α+ 209 Bi reaction (energy threshold is 20.72 MeV). Among other parameters, beam energy must be carefully controlled to avoid production of astatine-210, which decays to the * Corresponding author: theo.bigourdan@subatech.in2p3.fr polonium-210, a long-lived (T1/2 = 138 d) and highly cytotoxic bone seeker. Therefore, α energy for astatine-211 production must be in the 28.6 MeV to 20.72 MeV range [3].

Concepts
Solid target design for astatine-211 production must consider the low melting point of both bismuth (271°C) and astatine (approximately 302°C) and the high energy deposition rate of α particles [4]. To overcome these points, it was decided to start a concept study about a liquid bismuth target. Governing idea being to increase admissible temperature, beam intensity and production rate. To this end, three different concepts were evaluated: an encapsulated target, a flowing liquid bismuth target and finally a windowless fluid target.

Description
The capsule solution consists of a circular metallic receptacle, filled with bismuth ( Figure 1). This kind of capsule is currently in service for other applications and material at the ARRONAX facility [1]. Before irradiation, the bismuth is in solid state and it will melt under the beam heat generation (in an uncontrolled manner). A cooling by pressurized water is considered on the back plate. An expansion volume will be included to absorb the bismuth's volume variations during melting and solidification.
The following window structural materials were studied: stainless steel 316, havar and niobium. As a mean to improve mechanical resistance, curved windows were implemented in the model with various curvature radius.

Modelling
At this stage of the study, the model used for the beam power sizing was limited to the capsule itself using reasonable hypotheses regarding the cooling system and other interfaces. The window is the limiting factor regarding thermal and structural resistances. This window and its environment are thus modelled in different modules of the ANSYS Workbench software: Mechanical for structural resistance and Fluent for thermal and fluid considerations [5]. The window was modelled separately for the structural part. It is considered to be pinned on its external radius. Based on engineering judgement, pressure differential of 1 bar is considered between the beam line, which is under vacuum and inside the capsule.
As a conservative approximation, the beam heat generation is modelled by a surface heat flux on the external face of the window. The heat generation follows a Gaussian distribution as a function of the radius. The incident energy of the beam is fixed so that it enters the bismuth at 28.6 MeV to optimize astatine-211 production. The back plate cooling is modelled by a boundary condition with a heat transfer coefficient of 20000 W·m -2 ·K -1 and a temperature of 20°C, which is achievable with pressurized water.
The volume of bismuth being fully contained in the metallic structure, all the boundaries of the bismuth domain are considered to be fixed walls.
This configuration, summarized in Figure 1, allows us to perform optimizations for various materials and parameters. Table 1 shows the results of the computation for various configurations.

Results
The havar having better yield strength than niobium, it can withstand the mechanical loads with a lower window thickness, which reduces heat generated for the same production rate. It gives the best result for capsule with a plane window. However, using havar would not have significant benefit with a curved window, since the melting temperature starts to be more limiting than the yield strength. The best-case scenario corresponds to niobium with a curved window and leads to an estimated production of 4.9 GBq in 1 hour. Since the astatine-211 available in the system does not increase linearly with time, the production in 1h was used as an indicator instead of the production rate (Bq·h -1 ).

Description
This concept consists of a liquid lead-bismuth eutectic (LBE) circuit, fed by a pump and maintained in a liquid state by a thermal control system. A window (thinner pipe wall) is located where the beam impinges the flow. The flowing LBE contributes to dissipate the heat and act as a coolant for the window. A purging system and an in-line astatine-211 extraction system are considered as option if deemed necessary.
As the LBE only contains 55.5% of bismuth, the 211 At production is reduced by 44.5% compared to pure bismuth for the same beam characteristics. However, flowing liquid metal in metallic structures carries many complex issues that needs to be mastered for each situation and materials (corrosion, erosion, fragilisation…). The feedback from MEGAPIE [6] provides a good experience on flowing LBE in a stainless-steel structure. Moreover, the melting temperature of LBE (123°C) is lower than bismuth's, which reduces the stress on the structure and the risk of clogging. For the same reasons, it was decided based on engineering judgement to consider a minimal window thickness of 500 µm. According to the isotope inventory that was performed, the lead in the target does not create additional problematic isotopes compared to bismuth alone.

Modelling
At this stage of the study, only the surroundings of the window are modelled, as it is most likely to be the limiting factor for the production.
As per the capsule design, the window is modelled separately, in ANSYS Workbench. However, the pressure applied is the pump head pressure, estimated to 3 bars. This significantly increases the window stress.
Regarding thermal and fluid modelling, a tube portion is modelled, including a plane irradiation area. The structure and in particular, the window are not included. The beam heat is directly applied to the fluid beneath the window. Flow rate is set to get a mean speed of 1.2 m·s -1 . [7]

Results
The maximal computed production rate is extremely low: 0.21 GBq in 1 hour. The thicker window, increased pressure and lower efficiency seem to jeopardize this solution by limiting production rate.

Windowless fluid loop
It has been established in previous concepts that the window is the limiting factor for beam intensity and astatine-211 production. In an attempt to bypass this technical limitation, the possibility of a windowless design was explored. The concept consists in irradiating directly an open flow channel of liquid LBE.
While removing the issue of the window, it rises some other questions that will need to be addressed.

Boiling and production rate
Boiling should be avoided as it may lead to excessive evaporation and projection of LBE in the beam line. In a first approach, this is the limiting factor for astatine-211 production.
Boiling temperature is reached when ambient pressure is equal to vapor pressure of the LBE at a given temperature. Ambient pressure is expected to be around 1 Pa as a preliminary assumption.
The LBE handbook [8] provides the following equation for the saturation vapor pressure: However, this formula may not be accurate since available experimental data are not consistent. Thus, to keep some margins we consider a LBE flow temperature of 885 K as a limit (which corresponds to a vapor pressure of 0.1 Pa).
LBE flow velocity in the beamline was assessed through an open flow channel analytic model and some Computational Fluid Dynamics correlations. It is assessed that the flow velocity could reach 3 m·s -1 , in an optimistic configuration. By a subsequent thermal computation, it appears that an approximate production of 11.5 GBq in 1 hour can be achieved (14 kW of beam power). However, several issues need to be tackled.

LBE evaporation in the beamline
As the pressure around the free surface will be very low, the evaporation rate of the LBE must be considered. This sub-section aims at evaluating the corresponding flow rate and checking that sufficiently pressure can be maintained.
The LBE handbook [8] recommends the use of the Langmuir formulae to extrapolate the evaporation rate from the vapor pressure. Evaporation rate (kg·m -2 ·s -1 ) As described in SLEEVE report [9], this formula is consistent with the rare experimental results available.
Gas flow was then evaluated based on the preliminary geometry described in Figure 2 and based on methods from [10]. Results summarized in the same Figure 2 show that the preservation of the pressure in the beam line is achievable.

Astatine evaporation in the beamline
With this design, some extraction and losses of astatine-211 are foreseen. Our estimate relies on data provided by the LBE handbook [8] on iodine evaporation in LBE. As halogen, they may have similar behaviour. As there are no data available on astatine, it is the best assumption that we can use pending a dedicated astatine experiment. We will consider that main losses occur by evaporation in the beamline. Losses and extraction rate will be assessed by assuming the evaporation rate in the vacuum. Evaporation is quite slow up to 700 K and almost instant at 1000 K. It may impose a criterion on maximal temperature in the irradiation area to avoid massive loss in the beamline.
Thus, based on these formulae and on simple time discretization, we performed a preliminary assessment on astatine-211 distribution between losses and extraction. We assessed that astatine-211 was uniformly distributed in the LBE volume and that the extraction occurs at the same time as the irradiation. The varying factor was the irradiation area temperature. Figure 3 shows the fraction of astatine-211 that can be retrieved (evaporated in the extractor) out of the remaining astatine-211 in the system (not decayed) as a function of said temperature.
Based on these results, we can assess the following: • Evaporation rate increases greatly with temperature, with a major shift between 700 and 900 K. • High temperatures in the irradiation area can lead to significant astatine-211 loss.

Astatine fixation to metallic structure
Halogens are known for binding to metallic compounds. As the LBE loop structure will be most likely made of stainless steel, there is a risk that an important part of the produced astatine-211 stays trapped there and cannot be retrieved. As per evaporation, there are no available data on the particular topic of migration of astatine from a LBE solution to a steel structure. However, we can find some data regarding iodine, the neighbor lighter halogen. Reference [6] provides with measurement of the distribution of iodine-129 in the LBE circuit of the MEGAPIE experiment (a liquid LBE spallation target). The results shows that 93% of the iodine is located at the interface between LBE and steel. If the astatine behaves in a similar way, the concept of fluid loop may be jeopardized. While it is possible to extract astatine from steel, treating the whole LBE loop is unachievable. An experiment is under preparation to investigate this matter.

Discussion
Three metal liquid target concepts were described to produce astatine-211 and try to take advantage of the very high intensity α-beam that can be available in linac machine. Their efficiency and feasibility were assessed.
The interest of a very high-power beam dedicated installation should be questioned. Using reasonable technical means, it seems not feasible to use an intense beam (>1 mA) and a liquid target to produce large amounts of astatine. As shown in proposed concepts, it leads to important complexity, it is limited by physical constraints and it relies on knowledge on astatine behavior unavailable at this point. In addition, due to the half-life of astatine-211 an important proportion of production will be lost during transportation. Thus, a network of smaller regional production facilities (using solid targets or encapsulated liquid ones) should be investigated as it could be a more efficient way to provide the medical field with astatine-211.