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

The intermediate dose spill for a stereotactic radiosurgery (SRS) plan can be quantified with the metric R50%, defined as the 50% isodose cloud volume (V(IDC50%)) 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 (SA(PTV)), the volume of PTV (V(PTV)), 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 V(PTV) range from 0.15 to 50.1 cm(3). R50%(Analytic) is smaller than R50%(Clinical) in all cases by an average of 15% ± 7%, and the general trend of R50%(Clinical) vs V(PTV) 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.