A physically meaningful relationship between R50% and PTV surface area in lung SBRT

Abstract

Purpose We propose a novel understanding of two characteristics of the planning target volume (PTV) that affect the intermediate‐dose spill in lung stereotactic body radiation therapy (SBRT) as measured by R50%. This phantom model research investigates two characteristics of the PTV that have a marked effect on the value of R50%: the mean dose deposited within the PTV (Dav) and the surface area of the PTV (SAPTV). Methods Using a phantom model provided by a CT of the IROC Thorax‐Lung Phantom® (IROC Houston QA Center, Houston, TX) and Eclipse® Treatment Planning System (Varian Medical Systems, Palo Alto, CA), we investigate the two characteristics for spherical and cylindrical PTVs. A total of 135 plans with tightly controlled PTV characteristics are employed. A lower bound for R50% (R50%min∆r) is derived and clearly establishes a relationship between R50% and SAPTV that has not been fully appreciated previously. Results The study of PTV Dav revealed a local minimum for R50% as a function of the PTV Dav at Dav ≈ 110% of Rx dose. As PTV Dav increases above this local minimum, R50% increases; while for PTV Dav less than this local minimum, the R50% value also increases. The study of PTV surface area (SAPTV) demonstrated that as the SAPTV increases, the R50% increases if the PTV volume stays the same. The SAPTV result is predicted by the theoretical investigation that yields the R50% lower bound, R50%min∆r. Conclusions This research has identified two characteristics of the PTV that have a marked influence on R50%: PTV Dav and SAPTV. These characteristics have not been clearly articulated in the vast body of previous research in SBRT. These results could help explain plans that cannot meet the RTOG criteria for R50%. With further development, these concepts could be extended to provide additional guidance for creating acceptable SBRT plans.

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

“…(), and conceptually, this analytic model should be able to account for variations in SA PTV . In fact, the model would predict larger R50% values for targets with increased SA PTV to V PTV ratios, which is consistent with the suppositions in Goldbaum et al In previous work, it was quantitatively shown that an increase in the SA PTV to V PTV ratio leads to an increase in R50% values 9 . For any given volume, the shape that corresponds to the smallest surface area is a sphere, 16 and the assumption of a spherical PTV with an isotropic dose drop‐off is central to the construction of our analytic equation for R50% [Eq.…”

“…() as zeroth order, first order, and second order terms, respectively. This complete expression is an extension of previous work that only used the zeroth order term and, as expected, significantly improves agreement for smaller PTV volumes 9,10 …”

The surface area effect: How the intermediate dose spill depends on the PTV surface area in SRS

“…Utilizing an anthropomorphic head phantom study, we have applied the R50% Analytic approach devised in the lung SBRT study to cranial SRS. We demonstrate that the dependence of the achievable R50% on the SA PTV is consistent with previous lung SBRT results 12 . We test the R50% Analytic methodology on single cranial PTVs of various shapes and sizes.…”

“…We call this observed dependence of R50% on SA PTV the surface area effect. This appears to be a phenomenon not previously elucidated clearly in the literature of SRS, but it has been carefully explored in our previous work in lung SBRT 12,13 …”

“…We believe the SA PTV (i.e., a shape dependency) plays an important role in achievable intermediate dose spill metrics such as R50% in highly conformal approaches such as SRS and we have conducted a study to test this hypothesis. This work explores SA PTV as was done previously in our study of R50% in SBRT, 12 but here we examine R50% in cranial SRS. This work also builds on our previous efforts which derived a semi‐empirical equation for an approximation of R50%, which we refer to as R50% Analytic , based on V PTV and SA PTV in lung SBRT 13 .…”