A re-activation model for ¹⁶⁹Yb intensity modulated brachytherapy sources accounting for spatiotemporal isotopic...

Intensity modulated brachytherapy based on partially shielded intracavitary and interstitial applicators is possible with a cost-effective ¹⁶⁹Yb production method. ¹⁶⁹Yb is a traditionally expensive isotope suitable for this purpose, with an average γ-ray energy of 93 keV. Re-activating a single ¹⁶⁹Yb source multiple times in a nuclear reactor between clinical uses was shown to theoretically reduce cost by approximately 75% relative to conventional single-activation sources. With re-activation, substantial spatiotemporal variation in isotopic source composition is expected between activations via ¹⁶⁸Yb burnup and ¹⁶⁹Yb decay, resulting in time dependent neutron transmission, precursor usage, and reactor time needed per re-activation.

To introduce a generalized model of radioactive source production that accounts for spatiotemporal variation in isotopic source composition to improve the efficiency estimate of the ¹⁶⁹Yb production process, with and without re-activation.

A time-dependent thermal neutron transport, isotope transmutation, and decay model was developed. Thermal neutron flux within partitioned sub-volumes of a cylindrical active source was calculated by raytracing through the spatiotemporal dependent isotopic composition throughout the source, accounting for thermal neutron attenuation along each ray. The model was benchmarked, generalized, and applied to a variety of active source dimensions with radii ranging from 0.4 to 1.0 mm, lengths from 2.5 to 10.5 mm, and volumes from 0.31 to 7.85 mm³, at thermal neutron fluxes from 1 × 10¹⁴ to 1 × 10¹⁵ n cm^-2 s^-1. The ¹⁶⁸Yb-Yb₂O₃ density was 8.5 g cm^-3 with 82% ¹⁶⁸Yb-enrichment. As an example, a reference re-activatable ¹⁶⁹Yb active source (RRS) constructed of 82%-enriched ¹⁶⁸Yb-Yb₂O₃ precursor was modeled, with 0.6 mm diameter, 10.5 mm length, 3 mm³ volume, 8.5 g cm^-3 density, and a thermal neutron activation flux of 4 × 10¹⁴ neutrons cm^-2 s^-1.

The average clinical ¹⁶⁹Yb activity for a 0.99 versus 0.31 mm³ source dropped from 20.1 to 7.5 Ci for a 4 × 10¹⁴ n cm^-2 s^-1 activation flux and from 20.9 to 8.7 Ci for a 1 × 10¹⁵ n cm^-2 s^-1 activation flux. For thermal neutron fluxes ≥2 × 10¹⁴ n cm^-2 s^-1, total precursor and reactor time per clinic-year were maximized at a source volume of 0.99 mm³ and reached a near minimum at 3 mm³. When the spatiotemporal isotopic composition effect was accounted for, average thermal neutron transmission increased over RRS lifetime from 23.6% to 55.9%. A 28% reduction (42.5 days to 30.6 days) in the reactor time needed per clinic-year for the RRS is predicted relative to a model that does not account for spatiotemporal isotopic composition effects.

Accounting for spatiotemporal isotopic composition effects within the RRS results in a 28% reduction in the reactor time per clinic-year relative to the case in which such changes are not accounted for. Smaller volume sources had a disadvantage in that average clinical ¹⁶⁹Yb activity decreased substantially below 20 Ci for source volumes under 1 mm³. Increasing source volume above 3 mm³ adds little value in precursor and reactor time savings and has a geometric disadvantage.