Application of variance‐based uncertainty and sensitivity analysis to biological modeling in carbon ion treatment plans

Combining inter-observer variability, range and setup uncertainty in a variance-based sensitivity analysis for proton therapy

Margin concepts in proton therapy aim to ensure full dose coverage of the clinical target volume (CTV) in presence of setup and range uncertainty. Due to inter-observer variability (IOV), the CTV itself is uncertain. We present a framework to evaluate the combined impact of IOV, setup and range uncertainty in a variance-based sensitivity analysis (SA). For ten patients with skull base meningioma, the mean calculation time to perform the SA including 1.6 × 10⁴ dose recalculations was 59 min. For two patients in this dataset, IOV had a relevant impact on the estimated CTV D_95% uncertainty.

Uncertainty in tissue equivalent proportional counter assessments of microdosimetry and RBE estimates in carbon radiotherapy

Microdosimetry is an important tool for assessing energy deposition distributions from ionizing radiation at cellular and cellular nucleus scales. It has served as an input parameter for multiple common mathematical models, including evaluation of relative biological effectiveness (RBE) of carbon ion therapy. The most common detector used for microdosimetry is the tissue-equivalent proportional counter (TEPC). Although it is widely applied, TEPC has various inherent uncertainties. Therefore, this work quantified the magnitude of TEPC measurement uncertainties and their impact on RBE estimates for therapeutic carbon beams. Microdosimetric spectra and frequency-, dose-, and saturation-corrected dose-mean lineal energy (****) were calculated using the Monte Carlo toolkit Geant4 for five monoenergetic and three spread-out Bragg peak carbon beams in water at every millimeter along the central beam axis. We simulated the following influences on these spectra from eight sources of uncertainty: wall effects, pulse pile-up, electronics, gas pressure, W-value, gain instability, low energy cut-off, and counting statistics. Statistic uncertainty was quantified as the standard deviation of perturbed values for each source. Bias was quantified as the difference between default lineal energy values and the mean of perturbed values for each systematic source. Uncertainties were propagated to RBE using the modified microdosimetric kinetic model (MKM). Variance introduced by statistic sources iny¯Fandy¯Daveraged 3.8% and 3.4%, respectively, and 1.5% iny*across beam depths and energies. Bias averaged 6.2% and 7.3% iny¯Fandy¯D,and 4.8% iny*.These uncertainties corresponded to 1.2 ± 0.9% on average in RBE_MKM. The largest contributors to variance and bias were pulse pile-up and wall effects. This study established an error budget for microdosimetric carbon measurements by quantifying uncertainty inherent to TEPC measurements. It is necessary to understand how robust the measurement of RBE model input parameters are against this uncertainty in order to verify clinical model implementation.

Variance-based sensitivity analysis for uncertainties in proton therapy: A framework to assess the effect of simultaneous uncertainties in range, positioning, and RBE model predictions on RBE-weighted dose distributions

PURPOSE

Treatment plans in proton therapy are more sensitive to uncertainties than in conventional photon therapy. In addition to setup uncertainties, proton therapy is affected by uncertainties in proton range and relative biological effectiveness (RBE). While to date a constant RBE of 1.1 is commonly assumed, the actual RBE is known to increase toward the distal end of the spread-out Bragg peak. Several models for variable RBE predictions exist. We present a framework to evaluate the combined impact and interactions of setup, range, and RBE uncertainties in a comprehensive, variance-based sensitivity analysis (SA).

MATERIAL AND METHODS

The variance-based SA requires a large number (10⁴ -10⁵ ) of RBE-weighted dose (RWD) calculations. Based on a particle therapy extension of the research treatment planning system CERR we implemented a fast, graphics processing unit (GPU) accelerated pencil beam modeling of patient and range shifts. For RBE predictions, two biological models were included: The mechanistic repair-misrepair-fixation (RMF) model and the phenomenological Wedenberg model. All input parameters (patient position, proton range, RBE model parameters) are sampled simultaneously within their assumed probability distributions. Statistical formalisms rank the input parameters according to their influence on the overall uncertainty of RBE-weighted dose-volume histogram (RW-DVH) quantiles and the RWD in every voxel, resulting in relative, normalized sensitivity indices (S = 0: noninfluential input, S = 1: only influential input). Results are visualized as RW-DVHs with error bars and sensitivity maps.

RESULTS AND CONCLUSIONS

The approach is demonstrated for two representative brain tumor cases and a prostate case. The full SA including ∼ 3 × 10 4 RWD calculations took 39, 11, and 55 min, respectively. Range uncertainty was an important contribution to overall uncertainty at the distal end of the target, while the relatively smaller uncertainty inside the target was governed by biological uncertainties. Consequently, the uncertainty of the RW-DVH quantile D₉₈ for the target was governed by range uncertainty while the uncertainty of the mean target dose was dominated by the biological parameters. The SA framework is a powerful and flexible tool to evaluate uncertainty in RWD distributions and DVH quantiles, taking into account physical and RBE uncertainties and their interactions. The additional information might help to prioritize research efforts to reduce physical and RBE uncertainties and could also have implications for future approaches to biologically robust planning and optimization.