An analytical expression for R50% dependent on PTV surface area and volume: a lung SBRT comparison.

In stereotactic body radiation therapy (SBRT), R50% is a common metric for intermediate dose spill and is defined in RTOG 0915 as the ratio of 50% isodose cloud volume (IDC50%) to the planning target volume (PTV). By coupling sound physical principles with the basic definition of intermediate dose spill, we derive an exact analytical expression for R50% for the case of a spherical volume. This expression for R50% depends on three quantities: the surface area of PTV (SA ), the volume of PTV (V ), and the dose gradient Δr. Validity of our analytical expression for R50% was confirmed via direct comparison to peer-reviewed, multi-institutional, diverse clinical data. The comparison of our R50% values computed from our analytical expression to the clinical data yielded an average percent difference of 3.8 ± 4.5%.