F. Fiorini

Using stable distributions to characterize proton pencil beams

Purpose To introduce and evaluate the use of stable distributions as a methodology to quantify the behavior of proton pencil beams in a medium. Methods The proton pencil beams of a clinically commissioned proton treatment facility are replicated in a Monte Carlo simulation system (FLUKA). For each available energy, the beam deposition in water medium is characterized by the dose deposition. Using a stable distribution methodology, each beam with a nominal energy E is characterized by the lateral spread at depth z: S(z; α, γ, E) and a total energy deposition I D(z, E). The parameter α describes the tailedness of the distributions, while γ is used to scale the size of the function. The beams can then be described completely by a function of the variation of the parameters with depth. Results Quantitatively, the fit of the stable distributions, compared to those implemented in some standard treatment planning systems, are equivalent for all but the highest energies (i.e., 230 MeV/u). The decrease in goodness of fit makes this methodology comparable to a double Gaussian approach. The introduction of restricted linear combinations of stable distributions also resolves that particular case. More importantly, the meta‐parameterization (i.e., the description of the dose deposition by only providing the fitted parameters) allows for interpolation of nonmeasured data. In the case of the clinical commissioning data used in this paper, it was possible to only commission one out of five nominal energies to obtain a viable dataset, valid for all energies. An additional parameter β allows to describe asymmetric beam profiles as well. Conclusions Stable distributions are intrinsically suited to describe proton pencil beams in a medium and provide a tool to quantify the propagation of proton beams in a medium.

Technical Note: Defining cyclotron-based clinical scanning proton machines in a FLUKA Monte Carlo system

Purpose Cyclotron‐based pencil beam scanning (PBS) proton machines represent nowadays the majority and most affordable choice for proton therapy facilities, however, their representation in Monte Carlo (MC) codes is more complex than passively scattered proton system‐ or synchrotron‐based PBS machines. This is because degraders are used to decrease the energy from the cyclotron maximum energy to the desired energy, resulting in a unique spot size, divergence, and energy spread depending on the amount of degradation. This manuscript outlines a generalized methodology to characterize a cyclotron‐based PBS machine in a general‐purpose MC code. The code can then be used to generate clinically relevant plans starting from commercial TPS plans. Methods The described beam is produced at the Provision Proton Therapy Center (Knoxville, TN, USA) using a cyclotron‐based IBA Proteus Plus equipment. We characterized the Provision beam in the MC FLUKA using the experimental commissioning data. The code was then validated using experimental data in water phantoms for single pencil beams and larger irregular fields. Comparisons with RayStation TPS plans are also presented. Results Comparisons of experimental, simulated, and planned dose depositions in water plans show that same doses are calculated by both programs inside the target areas, while penumbrae differences are found at the field edges. These differences are lower for the MC, with a γ(3%–3 mm) index never below 95%. Conclusions Extensive explanations on how MC codes can be adapted to simulate cyclotron‐based scanning proton machines are given with the aim of using the MC as a TPS verification tool to check and improve clinical plans. For all the tested cases, we showed that dose differences with experimental data are lower for the MC than TPS, implying that the created FLUKA beam model is better able to describe the experimental beam.

Robustness assessment using probabilistic scenarios of intensity modulated proton therapy and volumetric arc therapy in non-small-cell lung cancer: an in-silico radiotherapy planning study

Abstract Background Radiotherapy is an essential treatment component for patients with stage III non-small-cell lung cancer. Despite advances, survival remains poor. Proton beam therapy holds the promise of improving cure rates without increasing treatment-related toxicity. However, precision in dose delivery is sensitive to setup uncertainties. The conventional method of adding a margin to account for this problem can be inadequate. We aimed to use the probabilistic scenarios methodology to assess the robustness of intensity modulated proton therapy (IMPT) and volumetric arc therapy (VMAT). Methods Plans were optimised by minimax robust optimisation (MM) and margin-based (planning target volume [PTV]) methods (MM–IMPT, PTV–IMPT, and VMAT). Robustness was assessed with probabilistically simulated setup errors. 35 perturbed doses were summed to model a treatment course. The CTV-D98 (dose to 98% of the clinical target volume) of each summed dose distribution was compared with the nominal plan and considered robust if within 5%. The variance of the CTV-D98 in IMPT and VMAT plans were compared using Levenes Test. Findings 700 simulations from 20 plans were analysed. Despite dose variation over a simulated course of treatment, the robustness of each summed plan was within clinical limits. There was significantly less variance in the perturbed CTV-D98 in the MM–IMPT than in PTV–IMPT plans (4·43 cGy 2 vs 16·17, F =50·993, p 2 vs 4·04, F =0·312, p=0·577). Target conformality improved with increasing number of beams and robust optimisation. All summed plans met normal tissue dose constraints. Interpretation Initial results showed that fractionation reduced uncertainties in dose distribution due to setup errors. Robustness of MM–IMPT and VMAT plans were similar. Although the present analysis has not considered range uncertainties and organ motion, the simulations highlight differences in plan qualities with different optimisation strategies. The probabilistic scenarios methodology might be used to estimate robustness of IMPT plans in stage III non-small-cell lung cancer. Funding Cancer Research UK.

SU‐F‐T‐147: An Alternative Parameterization of Scatter Behavior Allows Significant Reduction of Beam Characterization for Pencil Beam Proton Therapy

PURPOSE 1) To describe the characteristics of pencil beam proton dose deposition kernels in a homogenous medium using a novel parameterization. 2) To propose a method utilizing this novel parametrization to reduce the measurements and pre-computation required in commissioning a pencil beam proton therapy system. METHODS Using beam data from a clinical, pencil beam proton therapy center, Monte Carlo simulations were performed to characterize the dose depositions at a range of energies from 100.32 to 226.08 MeV in 3.6MeV steps. At each energy, the beam is defined at the surface of the phantom by a two-dimensional Normal distribution. Using FLUKA, the in-medium dose distribution is calculated in 200×200×350 mm cube with 1 mm3 tally volumes. The calculated dose distribution in each 200×200 slice perpendicular to the beam axis is then characterized using a symmetric alpha-stable distribution centered on the beam axis. This results in two parameters, α and γ, that completely describe shape of the distribution. In addition, the total dose deposited on each slice is calculated. The alpha-stable parameters are plotted as function of the depth in-medium, providing a representation of dose deposition along the pencil beam. We observed that these graphs are isometric through a scaling of both abscissa and ordinate map the curves. RESULTS Using interpolation of the scaling factors of two source curves representative of different beam energies, we predicted the parameters of a third curve at an intermediate energy. The errors are quantified by the maximal difference and provide a fit better than previous methods. The maximal energy difference between the source curves generating identical curves was 21.14MeV. CONCLUSION We have introduced a novel method to parameterize the in-phantom properties of pencil beam proton dose depositions. For the case of the Knoxville IBA system, no more than nine pencil beams have to be fully characterized.

PO-1001: Respiratory gating reduces heart doses for proton radiotherapy of the breast and internal mammary chain

PO-1001 Respiratory gating reduces heart doses for proton radiotherapy of the breast and internal mammary chain S. Hackett, F. Fiorini, S. Petillion, C. Taylor, C. Weltens, K. Vallis, S. Darby, F. Van den Heuvel University of Oxford, Department of Oncology, Oxford, United Kingdom Universitair Ziekenhuis Leuven, Radiotherapie-Oncologie, Leuven, Belgium University of Oxford, Clinical Trial Service Unit, Oxford, United Kingdom

SU-F-BRD-04: Robustness Analysis of Proton Breast Treatments Using An Alpha-Stable Distribution Parameterization

Purpose: Currently, planning systems allow robustness calculations to be performed, but a generalized assessment methodology is not yet available. We introduce and evaluate a methodology to quantify the robustness of a plan on an individual patient basis. Methods: We introduce the notion of characterizing a treatment instance (i.e. one single fraction delivery) by describing the dose distribution within an organ as an alpha-stable distribution. The parameters of the distribution (shape(α), scale(γ), position(δ), and symmetry(β)), will vary continuously (in a mathematical sense) as the distributions change with the different positions. The rate of change of the parameters provides a measure of the robustness of the treatment. The methodology is tested in a planning study of 25 patients with known residual errors at each fraction. Each patient was planned using Eclipse with an IBA-proton beam model. The residual error space for every patient was sampled 30 times, yielding 31 treatment plans for each patient and dose distributions in 5 organs. The parameters’ change rate as a function of Euclidean distance from the original plan was analyzed. Results: More than 1,000 dose distributions were analyzed. For 4 of the 25 patients the change in scale rate (γ) was considerably higher than the lowest change rate, indicating a lack of robustness. The sign of the shape change rate (α) also seemed indicative but the experiment lacked the power to prove significance. Conclusion: There are indications that this robustness measure is a valuable tool to allow a more patient individualized approach to the determination of margins. In a further study we will also evaluate this robustness measure using photon treatments, and evaluate the impact of using breath hold techniques, and the a Monte Carlo based dose deposition calculation. A principle component analysis is also planned.