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

Background: Intensity modulated brachytherapy based on partially shielded intracavitary and interstitial applicators is possible with a cost-effective Yb production method. Yb is a traditionally expensive isotope suitable for this purpose, with an average γ-ray energy of 93 keV. Re-activating a single Yb 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 Yb burnup and Yb decay, resulting in time dependent neutron transmission, precursor usage, and reactor time needed per re-activation.

Purpose: 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 Yb production process, with and without re-activation.

Methods And Materials: 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 mm, at thermal neutron fluxes from 1 × 10 to 1 × 10 n cm s. The Yb-YbO density was 8.5 g cm with 82% Yb-enrichment. As an example, a reference re-activatable Yb active source (RRS) constructed of 82%-enriched Yb-YbO precursor was modeled, with 0.6 mm diameter, 10.5 mm length, 3 mm volume, 8.5 g cm density, and a thermal neutron activation flux of 4 × 10 neutrons cm s.

Results: The average clinical Yb activity for a 0.99 versus 0.31 mm source dropped from 20.1 to 7.5 Ci for a 4 × 10 n cm s activation flux and from 20.9 to 8.7 Ci for a 1 × 10 n cm s activation flux. For thermal neutron fluxes ≥2 × 10 n cm s, total precursor and reactor time per clinic-year were maximized at a source volume of 0.99 mm and reached a near minimum at 3 mm. 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.

Conclusions: 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 Yb activity decreased substantially below 20 Ci for source volumes under 1 mm. Increasing source volume above 3 mm adds little value in precursor and reactor time savings and has a geometric disadvantage.