Purpose: To determine the PTV margins required to achieve a desired reliability (e.g., 95% of the time) for covering a specified percentage (e.g., at least 95%) of the CTV.
Methods: Monte Carlo simulation was performed to simulate the CTV motion, assuming changes in CTV position follow an independent normal distribution, N (0,µ) in each of the three motion axes. We also limited the CTV to be perfectly spherical. Applying circular symmetry, the three-dimensional random motion was simplified to a one-dimensional random motion in the radius direction following the Chi-square distribution (k=3). For each simulated motion, the percentage of CTV covered by PTV was calculated. The simulation was run for 1 million times for each combination of CTV radius and PTV margin, from which the histogram of percent CTV coverage (by PTV) was obtained.
Results: The reliability function for percent CTV coverage was plotted for CTVs of radius from 1µ to 30µ and PTV margins (M) from 0 to 3µ. We found that the PTV margin required to achieve a desired reliability for covering a specified percentage of the CTV is significantly affected by the CTV dimension. If the clinical goal is at least 95% CTV coverage 95% of the time, a smaller CTV will require a larger PTV margin to achieve this goal, e.g., M=1.97µ for r=5µ, and M=1.19µ for r=15 µ. If M=0, only 59.1% of a CTV with r=5µ can be reliably covered by PTV 95% of the time, while it is 86% for r =15µ. An exponential equation was derived to relate the CTV radius to the required PTV margin, M = 2.72*exp(-r/19.78)-0.11 for achieving this clinical goal.
Conclusion: This study demonstrated a size dependence for coverage-based PTV margin. A useful equation was developed for quick assessment of the required PTV margin for a given CTV radius.