<h3>Purpose</h3> Single-fraction (1-fx) <sup>192</sup>Ir prostate high-dose-rate (HDR) brachytherapy prescriptions of 19-20 Gy were derived using the biologically effective dose (BED) calculation in its simplified traditional (BED<sub>T</sub>) form, BED<sub>T</sub>=nd(1+d/α/β). This form of BED, while extremely convenient, was an approximation predicated on instantaneous delivery and may not be an appropriate assumption in certain key scenarios: protracted delivery times (> 15 minutes), high dose/fx (> 5 Gy), late-reacting tissues (low α/β), and/or rapid sublethal damage repair half-time (< 2x delivery time). As these are all characteristic of 1-fx prostate HDR brachytherapy, the aim of this study was to examine the difference between BED<sub>T</sub> and BED by development of a computational framework that can perform patient-specific high-resolution volumetric BED calculations that explicitly consider the effects of dose protraction and the unique temporal sequences arising from the stepping-source delivery. <h3>Materials and Methods</h3> The Lea-Catcheside dose protraction factor, g, was calculated to modify the multi-track term of the linear-quadratic model, such that BED=nd(1+gd/α/β). BED<sub>T</sub> corresponds to the special situation where g=1. For calculations, α/β=3.0 Gy and characteristic sublethal damage repair half-time of 0.27 hours were drawn from AAPM TG-137 radiobiological values, with assumed mono-exponential repair kinetics. For the stepping-source form of dose protraction factor, g<sub>ss</sub>, a script was developed to sequentially calculate the dose rates as a function of time, for each voxel in the calculation grid, from all individual dwell positions based on position and angular orientation extracted from a plan DICOM file using an AAPM TG-43/43U dose-rate calculation methodology. Together with the temporal ordering of dwell positions extracted from DICOM, the script provided a matrix of g<sub>ss</sub> values on a voxel-by-voxel basis with 1.0 × 1.0 × 1.0 mm<sup>3</sup> resolution. A second form of the dose protraction factor g<sub>0</sub>, a commonly-used factor in LDR brachytherapy, was also calculated which approximated the entire delivery as time-averaged uniform dose-rate. BED<sub>T</sub> (g=1) was then compared to BED calculated with actual values of g<sub>0</sub> and g<sub>ss</sub> values. <h3>Results</h3> The DICOM files from a previously-treated patient with representative dose characteristics were imported into our script: a prescription of 19 Gy in 1-fx, 140 active dwell positions in 17 channels, and delivery time of 2076.1 seconds based on 17500 U (4.3 Ci) source strength. An axial slice showing a color wash of the BED (Gy<sub>3</sub>) ranging from 139.3-519.0 Gy<sub>3</sub> (physical dose: 19-38 Gy in 1-fx) is shown for g=1 (BED<sub>T</sub>), g<sub>0</sub>, and g<sub>ss</sub> in Figure 1 which demonstrated significant differences. The nominal BED<sub>T</sub> was 139.3 Gy, which was reduced by 31% using g<sub>0</sub> and, depending on location, reduced between 20-31% using g<sub>ss</sub>. The portion of the PTV covered by 139.3 Gy<sub>3</sub> prescription was 95.9%, 59.6% and 65.7% using g=1 (BED<sub>T</sub>), g<sub>0</sub>, and g<sub>ss</sub>, respectively. Using g=1 (BED<sub>T</sub>), g<sub>0</sub>, and g<sub>ss</sub>, 90% of the PTV was covered by 159.4 Gy<sub>3</sub>, 110.4 Gy<sub>3</sub>, and 112.9 Gy<sub>3</sub>, respectively. <h3>Conclusions</h3> A custom script, capable of recalculating BED on a voxel-by-voxel level with proper accounting of sublethal damage repair arising from protracted dose delivery was developed. Significant differences in BED (∼30%) were shown for 1-fx prostate HDR brachytherapy. Two other general trends emerged in this study: 1) g<sub>0</sub>, while simple, provided a lower bound to volumetric g<sub>ss</sub> values. 2) Voxels closer to an activated dwell position were more resistant to dose protraction effects in an effect we attribute to effective delivery time: the time in which the dose-rate was significantly elevated (>2 orders of magnitude).
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