An analytical expression for R50% dependent on PTV surface area and volume: A cranial SRS comparison

Abstract

The intermediate dose spill for a stereotactic radiosurgery (SRS) plan can be quantified with the metric R50%, defined as the 50% isodose cloud volume (VIDC50%) divided by the volume of the planning target volume (PTV). By coupling sound physical principles with the basic definition of R50%, we derive an analytical expression for R50% for a spherical PTV. Our analytical expression depends on three quantities: the surface area of PTV (SAPTV), the volume of PTV (VPTV), and the distance of dose drop‐off to 50% (Δr). The value of ∆r was obtained from a simple set of cranial phantom plan calculations. We generate values from our analytical expression for R50% (R50%Analytic) and compare the values to clinical R50% values (R50%Clinical) extracted from a previously published SRS data set that spans the VPTV range from 0.15 to 50.1 cm3. R50%Analytic is smaller than R50%Clinical in all cases by an average of 15% ± 7%, and the general trend of R50%Clinical vs VPTV is reflected in the same trend of R50%Analytic. This comparison suggests that R50%Analytic could represent a theoretical lower limit for the clinical SRS data; further investigation is required to confirm this. R50%Analytic could provide useful guidance for what might be achievable in SRS planning.

How to estimate R50% for cranial SRS/SRT cases with overlapping 50% isodose volumes: A proposed system

“…We used a previously validated surface area script to extract that value 11 . We anticipate that, as the utility of PTV surface area becomes recognized in radiation oncology, surface area will become a standard reported metric by the planning system vendors much like volume is reported currently 10,11 …”

“…Clearly, every PTV has an ICD50% volume that inherently belongs to that PTV. The work of Desai et al 10 . demonstrates that the minimum value for this IDC50% volume for PTV i ($$V_{{\rm{IDC50}}{{\rm{\% }}_{{\rm{R50}}{{\rm{\% }}_{{\rm{Analytic}}}}}}}^{{\rm{PT}}{{\rm{V}}_i}}$$) can be extracted from the R50% Analytic .…”

“…This portion of V IDC50% will be referred to as the fair value estimate (FVE). Previous published work studying the “surface area effect” and the derivation of R50% Analytic implies an accounting system based on PTV surface area (SA PTV ) may prove useful 10–12 . We can assign the $$V_{{\rm{IDC50\% }}}^{{\rm{Remaining}}}$$ according to the surface area ratio.…”

Efficient optimization of R50% when planning multiple cranial metastases simultaneously in single isocenter SRS/SRT

“…As noted in Section 2.A, the AFI strategy can accommodate any stated R50% Goal . Desai et al derive a theoretical value for R50% Goal , which they name R50% Analytic 25 R50% Analytic is explicitly dependent on the volume and surface area of the PTV. Thus, using R50% Goal = R50% Analytic in the AFI strategy would allow one to incorporate the PTV surface area into the optimization criterion.…”

“…The potential for reducing the treatment planning time in these cases may be important in a busy radiation therapy clinic. Additionally, the AFI strategy could be built into a knowledge‐based optimization system, which could be particularly powerful if one used R50% Analytic as R50% Goal 25 . A future comparison of the AFI strategy with current NTO‐driven optimizations (such as HyperArc) or knowledge‐based techniques (such as RapidPlan) could also prove fruitful.…”