The effect of the different uncertainty models in dose expected volume histogram computation

Henríquez, Francisco Cutanda; Castrillón, Silvia

doi:10.1007/bf03179344

Cited by 6 publications

(10 citation statements)

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“…We have not encountered any technique available in the literature that can be as comprehensive as Polynomial Chaos Expansion can. Throughout Section 3.3 we have shown that PCE can practically yield all previously introduced sensitivity and uncertainty metrics, such as expected DVHs and the standard deviation of the DVH [10], DVH bandwidths for arbitrary confidence levels [28,36,29,25], dose standard deviation distribution and Standard Deviation Volume Histograms [5,8], PDFs of point doses and dose interval probabilities [26,10], Dose Population Histograms [27,37], error volume histograms [21], etc. What makes PCE unique is the speed and accuracy with which it can provide all these, and in particular its ability to enable the derivation of the spatial distribution of the probability of under-and overdosage, exact Dose-Population Histograms and Dose-Volume Histogram Distributions, which give a far more comprehensive description of dose uncertainties than previously presented methods.…”

Section: Drawbacks and Limitationsmentioning

confidence: 99%

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

et al. 2016

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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.

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Section: Drawbacks and Limitationsmentioning

confidence: 99%

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

et al. 2016

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“…Nevertheless, assuming a beta distribution (or even a normal distribution), which is parameterized by mean and standard deviation for the DVH-point, could facilitate uncertainty propagation through models that build on DVHs itself, for example, in deriving biologically effective dose, 36 or refining the statistical models for optimization purposes. 19 In comparison to the previous works, [25][26][27] our methodology directly reproduced their model for the expectation value of DVHpoints. 25 Our approach using integration directly generalizes to higher moments like covariance, while their model only yielded upper bounds on the variance because correlations between voxels were not explicitly included.…”

Section: Discussionmentioning

confidence: 84%

“…The result proved to be applicable with different families of assumed probability distributions (i.e., Gaussian, triangular and rectangular/uniform) 25,26 . However, due to the simplified uncertainty model using constant relative standard deviation and no correlation between voxels, an exact computation of higher moments of a DVH‐point's probability distribution was not attempted.…”

Section: Methodsmentioning

confidence: 99%

“…A subsequent work 27 (to Refs. [25,26]) already formulated an analytical calculation of α − DVHs as defined in Eq. .…”

Section: Methodsmentioning

confidence: 99%

“…20,21 For dose-volume histogram (DVH)-points, analytical computation of moments of the probability distribution, given a probability distribution over the dose, has been attempted before. [25][26][27] However, they 25,26 only provide a model for the expected value of DVH-points with an upper bound on the DVH standard deviation. Further, only simplified uncertainty models for the underlying dose distribution were assumed: while different shapes of the distributions were evaluated, correlations between voxels were not modeled, even though correlations having crucial impact on the higher moments of the depending probability distribution.…”

Section: Introductionmentioning

confidence: 99%

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Analytical probabilistic modeling of dose‐volume histograms

et al. 2020

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Purpose: Radiotherapy, especially with charged particles, is sensitive to executional and preparational uncertainties that propagate to uncertainty in dose and plan quality indicators, for example, dose-volume histograms (DVHs). Current approaches to quantify and mitigate such uncertainties rely on explicitly computed error scenarios and are thus subject to statistical uncertainty and limitations regarding the underlying uncertainty model. Here we present an alternative, analytical method to approximate moments, in particular expectation value and (co)variance, of the probability distribution of DVH-points, and evaluate its accuracy on patient data. Methods: We use Analytical Probabilistic Modeling (APM) to derive moments of the probability distribution over individual DVH-points based on the probability distribution over dose. By using the computed moments to parameterize distinct probability distributions over DVH-points (here normal or beta distributions), not only the moments but also percentiles, that is, a À DVHs, are computed. The model is subsequently evaluated on three patient cases (intracranial, paraspinal, prostate) in 30-and single-fraction scenarios by assuming the dose to follow a multivariate normal distribution, whose moments are computed in closed-form with APM. The results are compared to a benchmark based on discrete random sampling. Results: The evaluation of the new probabilistic model on the three patient cases against a sampling benchmark proves its correctness under perfect assumptions as well as good agreement in realistic conditions. More precisely, ca. 90% of all computed expected DVH-points and their standard deviations agree within 1% volume with their empirical counterpart from sampling computations, for both fractionated and single fraction treatments. When computing a À DVH, the assumption of a beta distribution achieved better agreement with empirical percentiles than the assumption of a normal distribution: While in both cases probabilities locally showed large deviations (up to AE0.2), the respective À DVHs for a={0.05,0.5,0.95} only showed small deviations in respective volume (up to AE5% volume for a normal distribution, and up to 2% for a beta distribution). A previously published model from literature, which was included for comparison, exhibited substantially larger deviations. Conclusions: With APM we could derive a mathematically exact description of moments of probability distributions over DVH-points given a probability distribution over dose. The model generalizes previous attempts and performs well for both choices of probability distributions, that is, normal or beta distributions, over DVH-points.

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