Convolution method and CTV-to-PTV margins for finite fractions and small systematic errors

Area of Science:

• Medical Physics
• Radiation Oncology
• Radiotherapy Planning

Background:

• The van Herk margin formula (VHMF) is commonly used to calculate planning target volume (PTV) margins from clinical target volume (CTV) based on setup error parameters.
• The accuracy of the VHMF relies on the convolution method (CM), which may have limitations under certain clinical conditions.
• Accurate margin calculation is crucial for ensuring adequate dose coverage to the CTV while minimizing dose to organs at risk.

Purpose of the Study:

• To evaluate the accuracy of the convolution method (CM) and the van Herk margin formula (VHMF) across a range of parameters, including the number of fractions (N).
• To propose and validate an alternative margin algorithm designed to ensure consistent CTV dose coverage under diverse clinical scenarios.
• To identify conditions where the VHMF may lead to suboptimal margin calculations and potential underdosage.

Main Methods:

• Dose coverage was evaluated for a spherical target using a simplified dose model and CTV coverage criterion.
• Simulations incorporated systematic (Sigma) and random (sigma) setup errors, assumed to be normally distributed.
• Margins were determined by ensuring 90% of treatment simulations achieved a minimum CTV dose equal to the static PTV minimum dose, with results compared against VHMF and the novel algorithm.

Main Results:

• The CM and VHMF were found accurate when sigma[1 - gammaN/25] < 0.2, with gamma = Sigma/sigma. Inaccuracy arose when sigma[1 - gammaN/25] > 0.2 due to unaddressed dose variability from random setup errors.
• When random setup errors (sigma) were significant compared to the dose penumbra (sigma(P) = 0.32 cm), the VHMF underestimated margins by up to 33% for large sigma, small Sigma, and small N.
• The proposed alternative algorithm demonstrated a maximum margin underestimate of only 7% across examined parameter ranges, offering superior CTV coverage.

Conclusions:

• The VHMF may underestimate margins in hypofractionated treatments and adaptive therapy, potentially leading to inadequate CTV dose in over 10% of treatments.
• The alternative margin algorithm provides more reliable CTV coverage across a wider range of setup error and fractionation parameters.
• Clinicians should exercise caution when applying the VHMF in scenarios with significant random setup errors or hypofractionation, favoring the alternative algorithm for improved treatment accuracy.