Analytical probabilistic modeling of RBE-weighted dose for ion therapy.

Area of Science:

• Medical Physics
• Radiation Oncology
• Computational Biology

Background:

• Particle therapy, particularly carbon ion therapy, faces significant uncertainties impacting treatment efficacy.
• Current uncertainty quantification relies on scenario sampling, which can be computationally intensive.
• Analytical probabilistic modeling (APM) offers a promising alternative for proton therapy, demonstrating unique advantages.

Purpose of the Study:

• To apply APM for intensity-modulated carbon ion therapy to quantify setup and range uncertainties.
• To assess the influence of these uncertainties on the biologically effective dose (RBE-weighted dose).
• To develop and evaluate analytical formulas for expectation and variance of the RBE-weighted dose.

Main Methods:

• Derived analytical forms for expectation and variance of RBE-weighted dose using a pencil beam model.
• Propagated linearly correlated Gaussian input uncertainties through the dose calculation algorithm.
• Developed exact and approximation formulas, analyzing accuracy and computational complexity reduction.

Main Results:

• Approximation formulas significantly reduced computational complexity (from O(V^3) to O(V) for expectation, O(V^4) to O(V^2) for variance) with marginal accuracy loss.
• Evaluated approximated calculations on three patient cases, achieving high global γ-pass rates (99.15% for expectation, 94.95% for standard deviation).
• Demonstrated the applicability of the analytical model to carbon ion treatment planning.

Conclusions:

• APM provides an efficient and accurate method for quantifying uncertainties in carbon ion therapy.
• The developed analytical formulas and approximations enhance treatment planning by reducing computational load.
• The approach is adaptable for other ion species and variable RBE models.