Dosimetry model of 213Bi exposure in reaction vials

The degradation of radiopharmaceuticals by radiolysis is dependent on the amount of energy absorbed within the ligand. Most of the α-particle energy emitted by ²¹³Bi and its daughter ²¹³Po will be absorbed within the reaction vial with the ²¹³Bi-labelled compound, as their particle ranges in water are smaller than the vial dimensions. The energy emitted by the α- and β⁻-particles from ²¹³Bi itself and its daughters ²⁰⁹Tl and ²⁰⁹Pb, however, will not be completely absorbed within the small vials. The activity as a function of time for ²¹³Bi, ²¹³Po, ²⁰⁹ Tl and ²⁰⁹Pb was calculated by the Bateman equations, see Additional file 1: Equation 1. The β⁻-emission spectra are summarized in Table 1 together with their ranges in water, from the NIST Star database (http://www.nist.gov/pml/data/star/; assessed 27-11-‘15). The α-particle energies from ²¹³Bi and ²¹³Po are also indicated with their projected ranges as calculated with the Stopping and Range of Ions in Matter (SRIM version 2013.00 software; www.SRIM.org). The recoil energies from the α-particle emissions are 112 keV (²¹³Bi) and 160 keV (²¹³Po) (Eckerman KF MIRD2008 2999).

α- and β-particle emissions by ²¹³Bi and its daughters, emission abundances per decay of ²¹³Bi or daughter nuclide and energies are from the MIRD Radionuclide data and decay schemes book (Eckerman, 2008). Particle ranges (mm) in water were determined from the NIST Star database (electrons) and with the SRIM code (α-particles). Abundance (Ab.) is expressed in % decay and energy (E) in MeV

Radiation transport was calculated for ²¹³Bi containing liquid inside reaction vials to determine the absorbed energy and absorbed dose to the hot liquid. The Monte Carlo codes MCNP5 (MCNP Team The Monte Carlo codes MCNP52005 2999) and MCNPX (Hendricks JS MCNPX Extensions Version 2 5 02005 2999) were used for the calculations. Calculations for the α-particles from ²¹³Bi and ²¹³Po were performed with MCNPX using the α-particle energies listed in Table 1. The β⁻-spectra and low-energy internal conversion and Auger electron spectra for ²¹³Bi, ²⁰⁹Tl and ²⁰⁹Pb from MIRD Radionuclide data and decay schemes book (Eckerman KF MIRD2008 2999) were used in MCNP5. Particulate radiation emissions with the given energy spectra were simulated so as to be uniformly distributed within a conical reaction vial with isotropic direction emission. All physics processes were taken into account by choosing either the α (MODE A) or the photon–electron mode (MODE P E) and the default PHYS cards with the default cut-off energy at 1 keV for electrons and photons and 4 MeV for α-particles. The *F8 tally determined energy absorption within the hot reaction fluid. Sufficient particle histories (NPS) were used to reduce the variation in the data to be less than 5 % for most cases; NPS was set to 1 × 10⁷ particles. A conically shaped 1 mL reaction vial was modelled with various volumes of radioactive fluid inside the vial. The MCNP-model geometry for a vial containing 0.8 mL liquid is shown in Fig. 1. The labelling volumes were modelled: 10, 50, 100, 200, 400 and 800 μL by adjusting the reaction fluid level accordingly. Average dose rates were determined in the vial volume.

MCNP geometry input for 1 mL reaction vial with 0.8 mL radioactive fluid (in blue), water with density 1 g/mL. The vial wall (in grey) had a thickness of 0.65 mm and was polyethylene with density 0.9 g/mL