{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,23]],"date-time":"2025-08-23T00:07:44Z","timestamp":1755907664777,"version":"3.44.0"},"reference-count":27,"publisher":"Wiley","issue":"5","license":[{"start":{"date-parts":[[2024,4,1]],"date-time":"2024-04-01T00:00:00Z","timestamp":1711929600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"content-domain":{"domain":["aapm.onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Medical Physics"],"published-print":{"date-parts":[[2024,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:sec><jats:title>Background<\/jats:title><jats:p>Intensity modulated brachytherapy based on partially shielded intracavitary and interstitial applicators is possible with a cost\u2010effective <jats:sup>169<\/jats:sup>Yb production method. <jats:sup>169<\/jats:sup>Yb is a traditionally expensive isotope suitable for this purpose, with an average \u03b3\u2010ray energy of 93\u00a0keV. Re\u2010activating a single <jats:sup>169<\/jats:sup>Yb source multiple times in a nuclear reactor between clinical uses was shown to theoretically reduce cost by approximately 75% relative to conventional single\u2010activation sources. With re\u2010activation, substantial spatiotemporal variation in isotopic source composition is expected between activations via <jats:sup>168<\/jats:sup>Yb burnup and <jats:sup>169<\/jats:sup>Yb decay, resulting in time dependent neutron transmission, precursor usage, and reactor time needed per re\u2010activation.<\/jats:p><\/jats:sec><jats:sec><jats:title>Purpose<\/jats:title><jats:p>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 <jats:sup>169<\/jats:sup>Yb production process, with and without re\u2010activation.<\/jats:p><\/jats:sec><jats:sec><jats:title>Methods and Materials<\/jats:title><jats:p>A time\u2010dependent thermal neutron transport, isotope transmutation, and decay model was developed. Thermal neutron flux within partitioned sub\u2010volumes 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\u00a0mm, lengths from 2.5 to 10.5\u00a0mm, and volumes from 0.31 to 7.85 mm<jats:sup>3<\/jats:sup>, at thermal neutron fluxes from 1\u00a0\u00d7\u00a010<jats:sup>14<\/jats:sup>\u00a0to\u00a01\u00a0\u00d7\u00a010<jats:sup>15<\/jats:sup> n cm<jats:sup>\u22122<\/jats:sup> s<jats:sup>\u22121<\/jats:sup>. The <jats:sup>168<\/jats:sup>Yb\u2010Yb<jats:sub>2<\/jats:sub>O<jats:sub>3<\/jats:sub> density was 8.5\u00a0g cm<jats:sup>\u22123<\/jats:sup> with 82% <jats:sup>168<\/jats:sup>Yb\u2010enrichment. As an example, a <jats:styled-content>r<\/jats:styled-content>eference <jats:styled-content>r<\/jats:styled-content>e\u2010activatable <jats:sup>169<\/jats:sup>Yb active <jats:styled-content>s<\/jats:styled-content>ource (RRS) constructed of 82%\u2010enriched <jats:sup>168<\/jats:sup>Yb\u2010Yb<jats:sub>2<\/jats:sub>O<jats:sub>3<\/jats:sub> precursor was modeled, with 0.6\u00a0mm diameter, 10.5\u00a0mm length, 3 mm<jats:sup>3<\/jats:sup> volume, 8.5\u00a0g cm<jats:sup>\u22123<\/jats:sup> density, and a thermal neutron activation flux of 4 \u00d7 10<jats:sup>14<\/jats:sup> neutrons\u00a0cm<jats:sup>\u20102<\/jats:sup>\u00a0s<jats:sup>\u20101<\/jats:sup>.<\/jats:p><\/jats:sec><jats:sec><jats:title>Results<\/jats:title><jats:p>The average clinical <jats:sup>169<\/jats:sup>Yb activity for a 0.99 versus 0.31 mm<jats:sup>3<\/jats:sup> source dropped from 20.1 to 7.5\u00a0Ci for a 4\u00a0\u00d7\u00a010<jats:sup>14<\/jats:sup>\u00a0n\u00a0cm<jats:sup>\u20102<\/jats:sup>\u00a0s<jats:sup>\u20101<\/jats:sup> activation flux and from 20.9 to 8.7\u00a0Ci for a 1\u00a0\u00d7\u00a010<jats:sup>15<\/jats:sup>\u00a0n\u00a0cm<jats:sup>\u20102<\/jats:sup>\u00a0s<jats:sup>\u20101<\/jats:sup> activation flux. For thermal neutron fluxes \u22652\u00a0\u00d7\u00a010<jats:sup>14<\/jats:sup>\u00a0n\u00a0cm<jats:sup>\u20102<\/jats:sup>\u00a0s<jats:sup>\u20101<\/jats:sup>, total precursor and reactor time per clinic\u2010year were maximized at a source volume of 0.99 mm<jats:sup>3<\/jats:sup> and reached a near minimum at 3\u00a0mm<jats:sup>3<\/jats:sup>. 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\u2010year for the RRS is predicted relative to a model that does not account for spatiotemporal isotopic composition effects.<\/jats:p><\/jats:sec><jats:sec><jats:title>Conclusions<\/jats:title><jats:p>Accounting for spatiotemporal isotopic composition effects within the RRS results in a 28% reduction in the reactor time per clinic\u2010year relative to the case in which such changes are not accounted for. Smaller volume sources had a disadvantage in that average clinical <jats:sup>169<\/jats:sup>Yb activity decreased substantially below 20\u00a0Ci for source volumes under 1\u00a0mm<jats:sup>3<\/jats:sup>. Increasing source volume above 3 mm<jats:sup>3<\/jats:sup> adds little value in precursor and reactor time savings and has a geometric disadvantage.<\/jats:p><\/jats:sec>","DOI":"10.1002\/mp.17048","type":"journal-article","created":{"date-parts":[[2024,4,1]],"date-time":"2024-04-01T14:23:36Z","timestamp":1711981416000},"page":"3604-3618","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A re\u2010activation model for <sup>169<\/sup>Yb intensity modulated brachytherapy sources accounting for spatiotemporal isotopic composition"],"prefix":"10.1002","volume":"51","author":[{"given":"Ryan T.","family":"Flynn","sequence":"first","affiliation":[{"name":"Department of Radiation Oncology University of Iowa  Iowa City Iowa USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Blake R.","family":"Smith","sequence":"additional","affiliation":[{"name":"Department of Radiation Oncology University of Iowa  Iowa 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