Fast and accurate sensitivity analysis of IMPT treatment plans using Polynomial Chaos Expansion

Abstract

The highly conformal planned dose distribution achievable in intensity modulated proton therapy (IMPT) can severely be compromised by uncertainties in patient setup and proton range. While several robust optimization approaches have been presented to address this issue, appropriate methods to accurately estimate the robustness of treatment plans are still lacking. To fill this gap we present Polynomial Chaos Expansion (PCE) techniques which are easily applicable and create a meta-model of the dose engine by approximating the dose in every voxel with multidimensional polynomials. This Polynomial Chaos (PC) model can be built in an automated fashion relatively cheaply and subsequently it can be used to perform comprehensive robustness analysis. We adapted PC to provide among others the expected dose, the dose variance, accurate probability distribution of dose-volume histogram (DVH) metrics (e.g. minimum tumor or maximum organ dose), exact bandwidths of DVHs, and to separate the effects of random and systematic errors. We present the outcome of our verification experiments based on 6 head-and-neck (HN) patients, and exemplify the usefulness of PCE by comparing a robust and a non-robust treatment plan for a selected HN case. The results suggest that PCE is highly valuable for both research and clinical applications.

Analytical incorporation of fractionation effects in probabilistic treatment planning for intensity‐modulated proton therapy

“…While choosing 5 fractions over 1 fraction significantly decreases plan variability, a less significant decrease can be seen when choosing 30 over 5 fractions, with 30 fractions showing almost no difference in standard deviation compared to an infinite number of fractions. This behavior was also already observed in Perkó et al . (more precisely in the supplementary materials), and suggests that for (non‐hypofracionated) treatment optimized without uncertainty considerations, increasing the fractionation number for the sake of mitigating random uncertainties can be expected to have minimal to negligible benefit.…”

“…The linear relationship for variance computation follows directly from the underlying standard definition of systematic and random errors in the input parameters, namely that systematic errors are perfectly correlated (i.e., they are exactly the same) for all treatment fractions and random errors are completely uncorrelated. 12,[18][19][20][21] In principle, the linear variance computation model can be constructed with any uncertainty propagation method that is able to compute the dose uncertainty for at least two fractionation schemes. However, a sampling-based construction is inevitably sensitive to sampling uncertainties [ Fig.…”

Robustness Analysis for External Beam Radiation Therapy Treatment Plans: Describing Uncertainty Scenarios and Reporting Their Dosimetric Consequences

“…A third option is to describe the simulation of scenarios according to the expectation value or variance of the delivered dose 37,42,43 or according to a model relating dosimetry to the uncertainty values. 44 Techniques to minimize the maximum optimization penalty (ie, minimax problem, or worst-case optimization) and optimize the expected value have been described as specific cases of a general framework. 45 These methods can be used to evaluate dose distributions and radiobiologic parameters or be incorporated into plan generation.…”

“…When describing the set of uncertainty scenarios, a variety of techniques to describe their dosimetric results are valid 44 : probability maps of failure, 29 dose difference and standard deviation distributions, 42 dose uncertainty or error-bar volume histograms, 58,59 volume histograms of the root-mean-square of dose distributions, 60 difference in the area under the DVH curve, 34 and population-based values. 43 Elements for an unambiguous description of uncertainty scenarios and their dosimetric consequences are summarized in Table 1.…”

What will the medical physics of proton therapy look like 10 yr from now? A personal view

“…Probably due to an inherent "knowledge" that the uncertainties related to proton therapy (as compared to photon based techniques) are higher, the concept of robustness analysis and robustness planning has become a hot topic in the proton community. [48][49][50][51][52][53] With these, attempts are being made to represent uncertainty bands on dose distributions and dose-volume histograms, and even include them directly into the optimization process ("robust optimisation"). This is a much welcomed development, and one that should be whole-heartedly supported.…”