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

Abstract

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 towards 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 (10 4-10 5) 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 repairmisrepair-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: non influential 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 RWD calculations took 39,11 and 55 minutes, respectively. ∼ 3 × 10 4 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 D 98 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.

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

“…phases of a 4D-CT to model breathing motion), at the cost of an increased memory usage and longer calculation times. In the previous publication from our group [10], uncertainties in variable RBE models were evaluated in combination with setup and range uncertainty. In this study, since the focus was on IOV, RBE uncertainty was not taken into account and a constant RBE of 1.1 was assumed.…”

“…Like in a previous study from our group [10], the efficient Monte Carlo method proposed by Saltelli [6] was used for direct calculation of S l and ST l , and sampling from low-discrepancy quasi-random sequences was employed to improve convergence. This method requires N(k +2) model evaluations, where N is typically of the order of 10 3 .…”

“…The sensitivity analysis framework was extended to include IOV. Additionally to the fast, graphics processing unit (GPU) based pencil beam algorithm capable of modeling setup and range variations described in the previous publication from our group [10], the possibility to include multiple treatment plans and to switch randomly between them was added.…”

“…Like in the previous study from our group [10], the variance-based SA was performed assuming the following uncertainty distributions for the input factors mentioned in Section 2.1: For patient shifts in X,Y and Z directions, a normal distribution with standard deviation σ X,Y,Z = 1 mm truncated to 2σ X,Y,Z was assumed. For relative range shifts the probability density was set to a normal distribution with standard deviation σ r,rel = 3 % truncated to 2σ r,rel .…”

“…In the context of patient dose calculation in medical physics, the technique has been previously applied to relative biological effectiveness (RBE) uncertainties in carbon ion therapy [7,8] and to estimate the impact of interpatient variability on organ dose estimates in nuclear medicine [9]. Recently, a framework to evaluate the combined impact of range, setup and RBE uncertainty in a variance-based SA has been presented by our group [10]. In this technical note, an extension of the framework to include IOV is shown.…”