Population-based asymmetric margins for moving targets in real-time tumor tracking

Both geometric and dosimetric components are commonly considered when determining the margin for planning target volume (PTV). As dose distribution is shaped by controlling beam aperture in peripheral dose prescription and dose-escalated simultaneously integrated boost techniques, adjusting the margin by incorporating the variable dosimetric component into the PTV margin is inappropriate; therefore, geometric components should be accurately estimated for margin calculations.

We introduced an asymmetric margin-calculation theory using the guide to the expression of uncertainty in measurement (GUM) and intra-fractional motion. The margins in fiducial marker-based real-time tumor tracking (RTTT) for lung, liver, and pancreatic cancers were calculated and were then evaluated using Monte Carlo (MC) simulations.

A total of 74 705, 73 235, and 164 968 sets of intra- and inter-fractional positional data were analyzed for 48 lung, 48 liver, and 25 pancreatic cancer patients, respectively, in RTTT clinical trials. The 2.5th and 97.5th percentiles of the positional error were considered representative values of each fraction of the disease site. The population-based statistics of the probability distributions of these representative positional errors (PD-RPEs) were calculated in six directions. A margin covering 95% of the population was calculated using the proposed formula. The content rate in which the clinical target volume (CTV) was included in the PTV was calculated through MC simulations using the PD-RPEs.

The margins required for RTTT were at most 6.2, 4.6, and 3.9 mm for lung, liver, and pancreatic cancer, respectively. MC simulations revealed that the median content rates using the proposed margins satisfied 95% for lung and liver cancers and 93% for pancreatic cancer, closer to the expected rates than the margins according to van Herk's formula.

Our proposed formula based on the GUM and motion probability distributions (MPD) accurately calculated the practical margin size for fiducial marker-based RTTT. This was verified through MC simulations.