The evaluation of optimized implants for idealized implant geometries

The purpose of this paper is to investigate the utility of implant quality measures on single stepping‐source brachytherapy treatment plans. Four dwell weight optimization algorithms were applied to four regular geometric implants: single plane, double plane, cuboid, and cylindrical. The dwell weight optimization schemes included equal weighing, two commercial optimization schemes (dose‐point and geometric) and a variation of the Paterson–Parker distribution rules. The implant quality measures were investigated as a function of dose‐per‐integrated reference air kerma (IRAK) to eliminate bias resulting from a prescription choice. A particular dose per IRAK refers to a dose surface that is a function only of the relative dwell weight distribution and is therefore well suited to investigate dwell weight optimization schemes. The implant quality measures included the dose–nonuniformity ratio (DNR) developed by Saw and a coverage index to assess the isodose coverage relative to the implanted volume. These were termed direct quantities due to their clear clinical significance. Additional measures include the ratio of the implant dose–volume histogram (DVH) to that of a point source exhibiting the same IRAK (R p ) and the ratio of the optimized DVH to the equally weighted DVH (EWR). The widths of the R p curves and depths of the EWR curves were used to characterize these indirect implant quality measures. To evaluate the effectiveness of both the direct and indirect measures, they were correlated with the DNR for an isodose surface that covered the implant (D 0). The efficiency of the dwell weight distribution was examined by noting the dose‐per‐IRAK surface D 0. The DNR exhibited a distribution with a minimum value in each implant and optimization method. At this point the high‐dose volume is minimized relative to the prescription volume and choosing this dose as a prescription isodose will provide a relatively homogeneous dose distribution. However, the minimum DNR value did not provide a clinically useful implant coverage with most optimization schemes. The exception was the dose‐point optimization that yielded an adequate coverage at the DNR minimum. The EWR curve exhibited a dip (at doseD n ) for most of the optimization schemes which was deepest for the dose‐point optimization. There was no direct correlation between the EWR(D n ) and homogeneity, but a large value of EWR(D n ) consistently predicted a poor homogeneity. An examination of the coverage versus the DNR showed that in all cases, a tradeoff existed between coverage and dose homogeneity. In all cases the dose‐point optimization provided the best compromise between coverage and homogeneity in addition to the most efficient implant. The application of these implant quality measures allowed an examination of the inherent quality of each dwell weight distribution, a task that would be very difficult without this type of guidance. While the indirect quality measures provided some properties that correlated with the direct quality measures, further study is necessary before their role in dose distribution analysis is completely understood. Use of the dose‐per‐IRAK as the independent variable divorced the analysis from an arbitrary prescription criterion.