A statistical model for analyzing the rotational error of single isocenter for multiple targets technique

Area of Science:

• Radiation Oncology
• Medical Physics
• Statistical Modeling

Background:

• Accurate radiation delivery is crucial for high-precision treatments like SRS and SBRT.
• Rotational errors around the treatment isocenter can compromise target coverage.
• Existing models may not fully account for rotational uncertainties in multi-target techniques.

Purpose of the Study:

• To develop a statistical model for quantifying rotational error in single-isocenter, multi-target radiotherapy.
• To calculate the additional planning target volume (PTV) margin required to compensate for rotational uncertainties.
• To assess the impact of rotational error on clinical target volume (CTV) coverage probability.

Main Methods:

• Modeled setup (S) and rotational (R) errors using 3D normal distributions.
• Derived a Chi distribution for the combined error vector (S+R).
• Determined PTV margin based on the critical value of the Chi distribution for 95% CTV coverage.
• Calculated additional PTV margin as a function of rotational error standard deviation (σR) and isocenter-to-CTV distance (dI⇔T).

Main Results:

• Rotational errors significantly reduce CTV coverage, particularly in SRS/SBRT.
• A rotational error of σR = 0.328 mm decreased coverage from 95% to 90.9% with a 2-mm PTV margin.
• An additional 0.2-mm PTV margin is required to maintain 95% coverage when σR exceeds 0.328 mm.
• Maximal ignorable rotational error (σδ) is 0.45° at dI⇔T = 50 mm and 0.23° at dI⇔T = 100 mm.

Conclusions:

• Rotational errors are a critical factor in high-precision radiotherapy (SRS/SBRT) and cannot be disregarded.
• The developed statistical model provides a method to quantify and compensate for these errors.
• Increased isocenter-to-target distance amplifies the impact of rotational errors, necessitating larger margins.