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

Wahl, Niklas; Hennig, Philipp; Wieser, Hans-Peter; Bangert, Mark

doi:10.1002/mp.12775

Cited by 12 publications

(27 citation statements)

References 33 publications

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“…[18]). In previous works, we could already show that APM accurately models l and r ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi diagðRÞ p , 33 and that efficient application to patient dataespecially in the context of fractionation 22 is possible. Extension to biological optimization demonstrated applicability of APMs to intensity-modulated carbon ion therapy planning.…”

Section: D2 Computation Of Dose Uncertaintymentioning

confidence: 98%

“…Uncertainty analysis of DVHs is mostly performed on an empirical basis through computation of error dose scenarios (among others Refs. [2,3,6,[13][14][15]17,21,22,24,28,29]). This enables the computation of a DVH for each dose scenario (which can be either a worst-case scenario or a random sample), from which then worst-case estimates, empirical statistical moments as well as quantiles of the probability distribution over DVH-points are derived.…”

Section: A2 Uncertainty Analysis Of Dose-volume Histogramsmentioning

confidence: 99%

“…An explicit derivation of probabilistic models remains the exception. [18][19][20][21][22] Consequently, the analysis of plan uncertainty is based on the derived worst-case dose distributions or "error bar" distributions with their respective histograms, 5,7,11,23 or statistical moments 13,18,21,22,24 as well as percentiles, 14,15,17 according to the very optimization method used in the overall planning workflow. This use of empirical uncertainty estimates, however, exhibits limitations, in particular concerning statistical accuracy and the required recomputations during optimization due to the changing pencil-beam weights.…”

Section: Introductionmentioning

confidence: 99%

“…Since they are able to provide analytical objectives, constraints, and derivatives, they can introduce new mathematical simplifications and improve computational efficiency by exploiting the analytical formulation for both uncertainty quantification and mitigation with probabilistic optimization approaches. 18,22 Because such approaches are not susceptible to statistical errors and the "curse of dimensionality" in scenario-based approaches, they deliver stable and reproducible results also for complex uncertainty models. However, derivation of such models is not trivial: Even if a model for dose probability is available, it still needs to be propagated to the derived plan indicators by hand.…”

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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Section: D2 Computation Of Dose Uncertaintymentioning

confidence: 98%

Section: A2 Uncertainty Analysis Of Dose-volume Histogramsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Analytical probabilistic modeling of dose‐volume histograms

et al. 2020

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“…To a greater or lesser extent, it is possible to use the inverse planning process to compensate for the effects of spatial uncertainty. 8,16 This is the general concept of robust and probabilistic treatment planning, [17][18][19][20][21][22][23] but this is not the primary goal of this study. Instead, the aim is to determine the target dose when prescribing directly to the ITV in the presence of spatial uncertainty.…”

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confidence: 99%

Dose prescription with spatial uncertainty for peripheral lung SBRT

Bedford

Blasiak-Wal

Hansen³

2018

J Applied Clin Med Phys

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Current clinical practice is to prescribe to 95% of the planning target volume (PTV) in 4D stereotactic body radiotherapy (SBRT) for lung. Frequently the PTV margin has a very low physical density so that the internal target volume (ITV) receives an unnecessarily high dose. This study investigates the alternative of prescribing to the ITV while including the effects of positional uncertainties. Five patients were retrospectively studied with volumetric modulated arc therapy treatment plans. Five plans were produced for each patient: a static plan prescribed to PTV D 95%, three probabilistic plans prescribed to ITV D 95% and a static plan re‐prescribed to ITV D 95% after inverse planning. For the three probabilistic plans, the scatter kernel in the dose calculation was convolved with a spatial uncertainty distribution consisting of either a uniform distribution extending ±5 mm in the three orthogonal directions, a distribution consisting of delta functions at ±5 mm, or a Gaussian distribution with standard deviation 5 mm. Median ITV D 50% is 23% higher than the prescribed dose for static planning and only 10% higher than the prescribed dose for prescription to the ITV. The choice of uncertainty distribution has less than 2% effect on the median ITV dose. Re‐prescribing a static plan and evaluating with a probabilistic dose calculation results in a median ITV D 95% which is 1.5% higher than when planning probabilistically. This study shows that a robust probabilistic approach to planning SBRT lung treatments results in the ITV receiving a dose closer to the intended prescription. The exact form of the uncertainty distribution is not found to be critical.

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