Analytical probabilistic modeling of dose-volume histograms.
Niklas Wahl1,2,3, Philipp Hennig4,5, Hans-Peter Wieser1,2,6,7
1German Cancer Research Center - DKFZ, Im Neuenheimer Feld 280, Heidelberg, 69120, Germany.
Medical Physics
|August 3, 2020
Summary
This study introduces Analytical Probabilistic Modeling (APM) to accurately estimate uncertainties in radiotherapy dose-volume histograms (DVHs). The new method provides reliable DVH uncertainty quantification, improving treatment planning accuracy.
Area of Science:
- Medical Physics
- Radiation Oncology
- Computational Biology
Background:
- Radiotherapy, particularly with charged particles, is susceptible to uncertainties in execution and preparation.
- These uncertainties propagate to dose and plan quality indicators like dose-volume histograms (DVHs).
- Current methods for quantifying and mitigating these uncertainties are limited by statistical uncertainty and underlying model assumptions.
Purpose of the Study:
- To present an alternative, analytical method for approximating moments (expectation value and covariance) of DVH-point probability distributions.
- To evaluate the accuracy of this new method on patient data for improved radiotherapy planning.
Main Methods:
- Analytical Probabilistic Modeling (APM) was used to derive moments of DVH-point probability distributions from dose probability distributions.
- Computed moments were used to parameterize normal or beta distributions for DVH-points, enabling calculation of moments and percentiles (α-DVHs).
- The model was evaluated on intracranial, paraspinal, and prostate patient cases across 30- and single-fraction scenarios, comparing results to a discrete random sampling benchmark.
Main Results:
- The APM model demonstrated correctness under ideal conditions and good agreement in realistic scenarios, with ~90% of expected DVH-points and standard deviations within 1% volume of sampling benchmarks.
- For α-DVH computation, the beta distribution assumption showed better agreement with empirical percentiles (up to ±2% volume deviation) compared to the normal distribution (up to ±5% volume deviation).
- The proposed model outperformed a previously published literature model in accuracy.
Conclusions:
- APM provides a mathematically exact method for describing moments of DVH-point probability distributions based on dose probability distributions.
- The model generalizes previous approaches and performs effectively with both normal and beta distributions for DVH-points.
- This analytical method offers a robust and accurate tool for uncertainty quantification in radiotherapy.
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