A re‐activation model for 169Yb intensity modulated brachytherapy sources accounting for spatiotemporal isotopic composition
Authors: Flynn Ryan T. , Smith Blake R. , Adams Quentin E. , Patwardhan Kaustubh , Graves Stephen A. , Hopfensperger Karolyn M. 
Published: April 2024

Background

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.

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 169Yb 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 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.

Results

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.

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 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.