Abstract

<h3>Purpose</h3> Dosimetry for photon-emitting brachytherapy sources is well established, to the point of commercial software for clinical treatment planning to account for material heterogeneities and patient-specific radiation scatter conditions. However, dosimetry standards for beta sources are simpler and have not been recently investigated. While the AAPM TG-149 and ICRU 72 Reports issue clinical guidance and reference data, a modern evaluation of beta-source dosimetry is missing. This investigation strives to identify the potential role for beta-emitting radionuclides as well as to examine theoretical sources for a deeper understanding of beta dosimetry. <h3>Materials and Methods</h3> Available beta-emitting brachytherapy sources include P-32, Sr/Y-90, and Ru/Rh-106 with Y-90 commonly used for selective internal radiation therapy (SIRT) of cancers in the liver. Energy spectra of these sources were taken from ICRU 72 with dose simulations performed using the MCNP v6.2 Monte Carlo radiation transport code. From ICRU 72, the maximum energies for P-32, Sr/Y-90, Y-90, and Ru/Rh-106 were 1.71, 2.28, 2.28, and 3.54 MeV, respectively. Monoenergetic sources of 0.5, 1, 1.5, 2, 3, and 4 MeV were also simulated to extend the energy range and scrutinize dose-distribution dependence on electron energy. Since 2D dose distribution are highly dependent on the design of a source, point sources were simulated to evaluate the depth-dose distribution as a function of radius, <i>r</i>, as well radial dose functions that removed the inverse-square effect. Dose was sampled in 15 cm diameter spheres comprised of water, tissue (ICRU 44 skeletal muscle), or bone (ICRU 44 cortical bone). To mass density effect was quantified in water for 0.5, 1, and 2 g/cm<sup>3</sup> with 1 and 2 g/cm<sup>3</sup> for tissue and bone, respectively. Observed dose differences were then ascribed to medium differences and not confounded by small differences in mass density. Dose was sampled with radial increments from 0.001 to 0.02 cm for direct comparisons to ICRU 72 results and to evaluate the effect of volume averaging. While only electron sources were considered, dose contributions from bremsstrahlung photons were quantified through comparing results of electron- and electron:photon-transport. Energy deposition was calculated using the MCNP *F8 pulse-height tally, then dividing by the voxel mass to obtain absorbed dose per electron history. With 10<sup>7</sup> source electrons, statistical uncertainties (<i>k</i>=1) were <0.1% for <i>r</i><0.7 CSDA. When studying bremsstrahlung, 10<sup>8</sup> source electrons produced 4% statistical uncertainties for <i>r</i>>1.2 CSDA. <h3>Results</h3> In the high dose-gradient region for radionuclide-based beta emitters, the calculated dose distributions in water were within 20% of those from the ICRU 72 Report, which used binned monoenergetic sources to approximate the continuous beta spectra. The radionuclide-based sources exhibited radial dose functions in water that diminished much more steeply than Pd-103, similar to a <0.01 MeV photon source. Sr/Y-90 had a bimodal distribution. Radial dose functions for radionuclide-based sources were inversely proportional to changes in mass density, differing from the scaling-factor models by Cross (1967) and the ICRU 56 Report over the large range of media and densities examined herein. Further, radial dose functions for monoenergetic sources demonstrated a Bragg peak with dose enhancement at <i>r</i>∼0.7 CSDA for all studied energies and media. A sampling of results for radionuclides and monoenergetic sources in water is given in the figure. <h3>Conclusions</h3> Beta dosimetry is largely governed by the mass density with medium composition being a much lesser effect, unlike for low-energy photons where the photoelectric effect is highly sensitive to <i>Z</i><sub>eff</sub>. Unlike for high-energy photon dosimetry, beta dosimetry is negligibly impacted by radiation scatter conditions due to their short range. While Ru/Rh-106 and Sr/Y-90 are proven for shallow plaque brachytherapy and Y-90 for SIRT, beta-emitting radionuclides do not have adequate range for interstitial implants like prostate brachytherapy since dose uniformity is much worse than with HDR Ir-192 or LDR Pd-103 brachytherapy.

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