Theoretical Calculation of Population-Based Margins in Fiducial Marker-Based Real-time Tumor Tracking

Abstract

We introduced a theoretical margin calculation method based on a combination of the guide to the expression of uncertainty in measurement (GUM) and the probability distribution of the tracking error, and determined the population-based margins in fiducial marker-based real-time tumor tracking (RTTT) radiotherapy.A total of 74,705, 73,235, and 164,968 sets of intrafractional X-ray images were analyzed for 47 lung, 48 liver, and 25 pancreatic cancer patients, respectively, in an RTTT clinical trial using a gimbaled Linac. The 2.5th and 97.5th percentiles of the tracking error, defined as the difference between the predicted and detected target positions, were regarded as representative values in each fraction of the disease site. The population-based statistics of the probability distribution of these representative tracking errors (PD-RTEs) were calculated in six directions. The goodness of fit of the PD-RTEs with the normal distribution were tested. The novel margin theory is expressed as follows: Margin = Υ+k⋅√(υ^2+τ^2), where Υ, υ, and τ are the population-based mean difference, interpatient uncertainty, and intrapatient uncertainty of the population of a representative tracking error in each direction, respectively. k is the factor to expect the margin satisfying 95% of the population. Considering that k depended on the target shape, k = 2.0 for the lung and liver cancer, 2.33 for the pancreatic cancer were applied. To verify the margin formula, the content rate in which the CTV was included in the PTV was calculated through Monte Carlo simulation (MCS) using the PD-RTE. The same calculation was also performed using the van Herk's theory intending to cover 90% of the population.The calculated results are shown in Table. The margins on the left, right, anterior, and posterior were within 4.1 mm for all sites. The superior and inferior margins were up to 6.2, 4.7, and 3.9 mm for lung, liver, and pancreatic cancer, respectively. Although some of the PD-RTEs could not be considered normal distributions, MCS revealed that the median content rates using the proposed margins satisfied 95% for lung and liver cancer, and 93% for pancreatic cancer. By contrast, although the median content rate according to van Herk's equation was 89% for pancreatic cancer, the content rates were more than 96% for lung and liver cancer, which was higher than their expected coverage of the population.In this study, we proposed a theoretically determined margin calculation formula for RTTT based on a combination of the GUM and the probability distribution of the tracking errors. The proposed formula appropriately calculated the practical margin size in fiducial marker-based RTTT for lung, liver, and pancreatic cancer.