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FRoG dose computation meets Monte Carlo accuracy for proton therapy dose calculation in lung

  • Giuseppe Magro
    Affiliations
    National Centre for Oncological Hadrontherapy (CNAO), Clinical Department, Pavia, Italy
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  • Stewart Mein
    Affiliations
    Clinical Cooperation Unit Translational Radiation Oncology, National Center for Tumor Diseases (NCT), Heidelberg University Hospital (UKHD) and German Cancer Research Center (DKFZ), Heidelberg, Germany

    Division of Molecular and Translational Radiation Oncology, Department of Radiation Oncology, Heidelberg Faculty of Medicine (MFHD) and Heidelberg University Hospital (UKHD), Heidelberg Ion-Beam Therapy Center (HIT), Heidelberg, Germany

    German Cancer Consortium (DKTK) Core-Center Heidelberg, German Cancer Research Center (DKFZ), Heidelberg, Germany

    Clinical Cooperation Unit Radiation Oncology, Heidelberg Institute of Radiation Oncology (HIRO), National Center for Radiation Oncology (NCRO), Heidelberg University and German Cancer Research Center (DKFZ), Heidelberg, Germany
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  • Benedikt Kopp
    Affiliations
    Clinical Cooperation Unit Translational Radiation Oncology, National Center for Tumor Diseases (NCT), Heidelberg University Hospital (UKHD) and German Cancer Research Center (DKFZ), Heidelberg, Germany

    Division of Molecular and Translational Radiation Oncology, Department of Radiation Oncology, Heidelberg Faculty of Medicine (MFHD) and Heidelberg University Hospital (UKHD), Heidelberg Ion-Beam Therapy Center (HIT), Heidelberg, Germany

    German Cancer Consortium (DKTK) Core-Center Heidelberg, German Cancer Research Center (DKFZ), Heidelberg, Germany

    Clinical Cooperation Unit Radiation Oncology, Heidelberg Institute of Radiation Oncology (HIRO), National Center for Radiation Oncology (NCRO), Heidelberg University and German Cancer Research Center (DKFZ), Heidelberg, Germany

    Faculty of Physics and Astronomy, Heidelberg University, Germany
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  • Edoardo Mastella
    Affiliations
    National Centre for Oncological Hadrontherapy (CNAO), Clinical Department, Pavia, Italy
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  • Andrea Pella
    Affiliations
    National Centre for Oncological Hadrontherapy (CNAO), Clinical Department, Pavia, Italy
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  • Mario Ciocca
    Affiliations
    National Centre for Oncological Hadrontherapy (CNAO), Clinical Department, Pavia, Italy
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  • Andrea Mairani
    Correspondence
    Corresponding author at: National Centre for Oncological Hadrontherapy (CNAO), Clinical Department, Pavia, Italy.
    Affiliations
    National Centre for Oncological Hadrontherapy (CNAO), Clinical Department, Pavia, Italy

    Clinical Cooperation Unit Translational Radiation Oncology, National Center for Tumor Diseases (NCT), Heidelberg University Hospital (UKHD) and German Cancer Research Center (DKFZ), Heidelberg, Germany

    Heidelberg Ion-Beam Therapy Center (HIT), Department of Radiation Oncology, Heidelberg University Hospital, Heidelberg, Germany
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      Highlights

      • GPU-accelerated analytical dose engine (FRoG) established for proton therapy in lung.
      • Dosimetric evaluation of pencil beam algorithm (FRoG) versus RayStation Monte Carlo (RS-MC) using heterogeneous lung phantom.
      • Dose and LETd validated for FRoG against general purpose Monte Carlo (gp-MC) in patients for clinical investigations.
      • FRoG demonstrated prediction power comparable to RS-MC and gp-MC.

      Abstract

      Purpose

      To benchmark and evaluate the clinical viability of novel analytical GPU-accelerated and CPU-based Monte Carlo (MC) dose-engines for spot-scanning intensity-modulated-proton-therapy (IMPT) towards the improvement of lung cancer treatment.

      Methods

      Nine patient cases were collected from the CNAO clinical experience and The Cancer Imaging Archive-4D-Lung-Database for in-silico study. All plans were optimized with 2 orthogonal beams in RayStation (RS) v.8. Forward calculations were performed with FRoG, an independent dose calculation system using a fast robust approach to the pencil beam algorithm (PBA), RS-MC (CPU for v.8) and general-purpose MC (gp-MC). Dosimetric benchmarks were acquired via irradiation of a lung-like phantom and ionization chambers for both a single-field-uniform-dose (SFUD) and IMPT plans. Dose-volume-histograms, dose-difference and γ-analyses were conducted.

      Results

      With respect to reference gp-MC, the average dose to the GTV was 1.8% and 2.3% larger for FRoG and the RS-MC treatment planning system (TPS). FRoG and RS-MC showed a local γ-passing rate of ~96% and ~93%. Phantom measurements confirmed FRoG’s high accuracy with a deviation < 0.1%.

      Conclusions

      Dose calculation performance using the GPU-accelerated analytical PBA, MC-TPS and gp-MC code were well within clinical tolerances. FRoG predictions were in good agreement with both the full gp-MC and experimental data for proton beams optimized for thoracic dose calculations. GPU-accelerated dose-engines like FRoG may alleviate current issues related to deficiencies in current commercial analytical proton beam models. The novel approach to the PBA implemented in FRoG is suitable for either clinical TPS or as an auxiliary dose-engine to support clinical activity for lung patients.

      Keywords

      1. Introduction

      With lung cancer as the leading cause of cancer-related deaths worldwide, innovative and more effective therapies, such as proton therapy (PT), are urgently needed. Improvement in tumor targeting with increased healthy tissue sparing compared to conventional photon beams is especially critical in the treatment of inoperable lung tumors [
      • Han Y.
      Current status of proton therapy techniques for lung cancer.
      ]. Accordingly, interest in PT application is on the rise for lung cancer, one of several disease sites where proton beams show promise in improving clinical efficacy [
      • Bush D.A.
      • Cheek G.
      • Zaheer S.
      • Wallen J.
      • Mirshahidi H.
      • Katerelos A.
      • et al.
      High-dose hypofractionated proton beam radiation therapy is safe and effective for central and peripheral early-stage non-small cell lung cancer: results of a 12-year experience at loma linda university medical center.
      ,
      • Nguyen Q.N.
      • Ly N.B.
      • Komaki R.
      • Levy L.B.
      • Gomez D.R.
      • Chang J.Y.
      • et al.
      Long-term outcomes after proton therapy, with concurrent chemotherapy, for stage II-III inoperable non-small cell lung cancer.
      ], considering the potential for healthy lung sparing and/or the reduction of the dose to the heart [

      James SS, Grassberger C, Lu HM. Considerations when treating lung cancer with passive scatter or active scanning proton therapy. Transl Lung Cancer Res 2018;7:210–5. 10.21037/tlcr.2018.04.01.

      ].
      In practice, several dosimetric limitations and sources of uncertainty arise from treatment planning (TP) to delivery with proton beams for lung cancer. The favorable physical characteristics themselves, e.g. Bragg-peak with reduced lateral penumbra, make PT an ideal candidate for high-precision treatment delivery in heterogeneous anatomical sites such as the lung, but may also make these treatments increasingly prone to uncertainties in range and temporal effects due to breathing/organ motion [
      • Grassberger C.
      • Dowdell S.
      • Lomax A.
      • Sharp G.
      • Shackleford J.
      • Choi N.
      • et al.
      Motion interplay as a function of patient parameters and spot size in spot scanning proton therapy for lung cancer.
      ,
      • Grassberger C.
      • Daartz J.
      • Dowdell S.
      • Ruggieri T.
      • Sharp G.
      • Paganetti H.
      Quantification of proton dose calculation accuracy in the lung.
      ]. Clinical consideration through increased target margins, 4D-robust TP, gating and/or rescanning delivery techniques, has demonstrated promising results to reduce sensitivity to delivery uncertainties and/or interplay effects [
      • Inoue T.
      • Widder J.
      • van Dijk L.V.
      • Takegawa H.
      • Koizumi M.
      • Takashina M.
      • et al.
      Limited impact of setup and range uncertainties, breathing motion, and interplay effects in robustly optimized intensity modulated proton therapy for stage III non-small cell lung cancer.
      ,
      • Teoh S.
      • George B.
      • Fiorini F.
      • Vallis K.A.
      • Van den Heuvel F.
      Assessment of robustness against setup uncertainties using probabilistic scenarios in lung cancer: a comparison of proton with photon therapy.
      ]. Nonetheless, significant discrepancy between planned and delivered dose may occur if dose algorithms are not properly managed by the clinical TP systems (TPSs). For instance recent works highlight relevant dosimetric differences between measured and predicted dose by conventional approaches in most commercial TPSs [
      • Lomax A.J.
      Intensity modulated proton therapy and its sensitivity to treatment uncertainties 1: the potential effects of calculational uncertainties.
      ], in part due to improper modeling of radiation transport in highly heterogeneous tissues such as the lung, consisting of complex bone-air-tissue interfaces, anatomic/geometric complexities and sub-voxel Hounsfield-Units (HU) variations. “Monte Carlo (MC)-versus-analytical algorithm” remains a common debate topic and correspondingly, thoracic subcommittees aim to develop urgently needed consensus and guidelines for quality assurance (QA), TP and delivery of particle therapy for thoracic malignancies [
      • Chang J.Y.
      • Zhang X.
      • Knopf A.
      • Li H.
      • Mori S.
      • Dong L.
      • et al.
      Consensus guidelines for implementing pencil-beam scanning proton therapy for thoracic malignancies on behalf of the PTCOG thoracic and lymphoma subcommittee.
      ].
      Excluding uncertainties attributed to the breathing cycle/dose delivery system, this work specifically focuses on inherent accuracy of an analytical dose algorithm in thoracic regions, which in most other clinical scenarios can provide acceptable plan calculations within well-established tolerances. Despite being subject to scrutiny, the pencil beam algorithm (PBA) in PT provides fast speeds at the potential sacrifice of accuracy in complex tissue inhomogeneities. The gold standard for accuracy is the MC simulation and related codes are only recently introduced to the clinics, fostered by past and on-going efforts to develop clinical dose engines [
      • Jia X.
      • Schümann J.
      • Paganetti H.
      • Jiang S.B.
      GPU-based fast Monte Carlo dose calculation for proton therapy.
      ,
      • Schreuder A.N.
      • Bridges D.S.
      • Rigsby L.
      • Blakey M.
      • Janson M.
      • Hedrick S.G.
      • et al.
      Validation of the RayStation Monte Carlo dose calculation algorithm using a realistic lung phantom.
      ].
      In the case of thoracic treatment sites, several studies demonstrate limitations of clinical TPSs where accuracy is critical [
      • Tommasino F.
      • Fellin F.
      • Lorentini S.
      • Farace P.
      Impact of dose engine algorithm in pencil beam scanning proton therapy for breast cancer.
      ,
      • Langner U.W.
      • Mundis M.
      • Strauss D.
      • Zhu M.
      • Mossahebi S.
      A comparison of two pencil beam scanning treatment planning systems for proton therapy.
      ]. Most notably, investigations with anthropomorphic lung phantoms suggest that application of commercial TPSs using analytical algorithms for the treatment of lung tumors should be deemed unfit for clinical use or used with extreme caution [
      • Taylor P.A.
      • Kry S.F.
      • Followill D.S.
      Pencil beam algorithms are unsuitable for proton dose calculations in lung.
      ]. The lateral dose distribution computed by PBA in the lung and in bone interfaces may reach a level of inaccuracy around 30% [
      • Widesott L.
      • Lorentini S.
      • Fracchiolla F.
      • Farace P.
      • Schwarz M.
      Improvements in pencil beam scanning proton therapy dose calculation accuracy in brain tumor cases with a commercial Monte Carlo algorithm.
      ,

      Saini J, Traneus E, Maes D, Regmi R, Bowen SR, Bloch C, et al. Advanced Proton Beam Dosimetry Part I: Review and performance evaluation of dose calculation algorithms. Transl Lung Cancer Res 2018;7:171–9. 10.21037/tlcr.2018.04.05.

      ], while commercial MC-based TPSs can improve the accuracy of dose calculation in the lung/bone interfaces or through inhomogeneities within ~5% [
      • Schreuder A.N.
      • Bridges D.S.
      • Rigsby L.
      • Blakey M.
      • Janson M.
      • Hedrick S.G.
      • et al.
      Validation of the RayStation Monte Carlo dose calculation algorithm using a realistic lung phantom.
      ,

      Saini J, Traneus E, Maes D, Regmi R, Bowen SR, Bloch C, et al. Advanced Proton Beam Dosimetry Part I: Review and performance evaluation of dose calculation algorithms. Transl Lung Cancer Res 2018;7:171–9. 10.21037/tlcr.2018.04.05.

      ]. Despite being considered clinically tolerable, another source of uncertainty in proton therapy of lung originates from the heterogeneous structure of the lung itself, which leads to a degradation of the Bragg peak and a wider distal fall-off [
      • Baumann K.S.
      • Flatten V.
      • Weber U.
      • Lautenschläger S.
      • Eberle F.
      • Zink K.
      • et al.
      Effects of the Bragg peak degradation due to lung tissue in proton therapy of lung cancer patients.
      ].
      Several other works have investigated the accuracy of analytical algorithms and/or MC codes in clinically-relevant scenarios, especially in head-and-neck phantoms [
      • Widesott L.
      • Lorentini S.
      • Fracchiolla F.
      • Farace P.
      • Schwarz M.
      Improvements in pencil beam scanning proton therapy dose calculation accuracy in brain tumor cases with a commercial Monte Carlo algorithm.
      ,

      Saini J, Traneus E, Maes D, Regmi R, Bowen SR, Bloch C, et al. Advanced Proton Beam Dosimetry Part I: Review and performance evaluation of dose calculation algorithms. Transl Lung Cancer Res 2018;7:171–9. 10.21037/tlcr.2018.04.05.

      ,
      • Winterhalter C.
      • Zepter S.
      • Shim S.
      • Meier G.
      • Bolsi A.
      • Fredh A.
      • et al.
      Evaluation of the ray-casting analytical algorithm for pencil beam scanning proton therapy.
      ,
      • Shirey R.J.
      • Wu H.T.
      Quantifying the effect of air gap, depth, and range shifter thickness on TPS dosimetric accuracy in superficial PBS proton therapy.
      ,
      • Mein S.
      • Kopp B.
      • Tessonnier T.
      • Ackermann B.
      • Ecker S.
      • Bauer J.
      • et al.
      Dosimetric validation of Monte Carlo and analytical dose engines with raster-scanning 1H, 4He, 12C, and 16O ion-beams using an anthropomorphic phantom.
      ], however, few studies perform comprehensive testing for thorax-based treatments beyond commercial approaches.
      In this work, dose calculation for lung cancer patients is investigated using the FRoG system, a GPU-accelerated dose calculation platform for particle therapy with both an enhanced physics-engine and rapid computation speed made possible via task-parallelization for multiple particle species [
      • Choi K.
      • Mein S.B.
      • Kopp B.
      • Magro G.
      • Molinelli S.
      • Ciocca M.
      • et al.
      FRoG—A new calculation engine for clinical investigations with proton and carbon ion beams at CNAO.
      ,
      • Mein S.
      • Choi K.
      • Kopp B.
      • Tessonnier T.
      • Bauer J.
      • Ferrari A.
      • et al.
      Fast robust dose calculation on GPU for high-precision 1H, 4He, 12C and 16O ion therapy: the FRoG platform.
      ]. The capabilities and limits of the FRoG approach are tested via dose calculation for thoracic malignancies. Through extensive benchmarking against in-silico references (clinical TPS and general purpose (gp)-MC simulation), as well as experimental validation through end-to-end QA tests in an in-house built heterogeneous phantom equipped with ionization chambers (ICs), we verify whether analytical methods for PT dose calculation are indeed unsuitable for clinical activity.
      Furthermore, we explore dose-averaged linear energy transfer (LETD) in the context of lung cancer patients, to assess flexibility and feasibility of relating innovative bio-effect quantities with clinical efficacy. This analysis has yet to be presented in the literature. Further efforts are made here to validate FRoG as a secondary dose engine for supporting clinical decision-making at CNAO, the Heidelberg Ion-beam Therapy-center (HIT) and the Aarhus Danish Center for Proton Therapy, where the platform has been installed for rapid physical, LETD, and bio-dose prediction. Here, state-of-the-art GPU-accelerated analytical and CPU-based MC dose engines are rigorously tested in scenarios where conventional approaches to clinical dose calculation often fail.

      2. Material and methods

      2.1 Patients selection

      A total of 9 non-small-cell lung cancer (NSCLC) patients, with tumors differing in stage (I to III) and gross tumor volume (GTV) size (range = 6–160 cc, median = 19 cc), were randomly selected from The Cancer Imaging Archive-4D Lung Database [
      • Clark K.
      • Vendt B.
      • Smith K.
      • Freymann J.
      • Kirby J.
      • Koppel P.
      • et al.
      The cancer imaging archive (TCIA): maintaining and operating a public information repository.
      ] and from the CNAO clinical experience. For the selected cohort, the average minimum and maximum target-to-lung wall distance, expressed as point-to-point surface separation, was 0 cm and 20.5 cm, respectively. On average, GTVs were surrounded by 6.5 cm of lung tissue, with one GTV only (6.12 cc) being completely detached from the lung wall (2 cm and 17 cm were its minimum and maximum distance). All patient calculations performed in this study (FLUKA gp-MC, FRoG and RayStation® v.8-MC (RS-MC) TPS) considered dose-to-water (Dw) as opposed to dose-to-medium following clinical procedure.

      2.2 TPS settings

      Intensity modulated proton therapy (IMPT) was employed during plan optimization of the lung patient data, using 2 orthogonal ports and scanning parameters as established by CNAO clinical protocols [
      • Mirandola A.
      • Molinelli S.
      • Vilches Freixas G.
      • Mairani A.
      • Gallio E.
      • Panizza D.
      • et al.
      Dosimetric commissioning and quality assurance of scanned ion beams at the Italian National Center for Oncological Hadrontherapy.
      ]. The optimization strategy using 4D-computed tomography (CT)-scans is detailed in a previous work [
      • Mastella E.
      • Molinelli S.
      • Pella A.
      • Vai A.
      • Maestri D.
      • Vitolo V.
      • et al.
      4D strategies for lung tumors treated with hypofractionated scanning proton beam therapy: dosimetric impact and robustness to interplay effects.
      ]. Prescription dose was set to 60 Gy(Relative Biological Effectiveness, RBE = 1.1), delivered in 10 equal fractions to the GTV in terms of median dose (D50). The RS v.8-MC clinical v.4.2 was used as dose engine for the optimization problem, as recommended by recent studies [
      • Taylor P.A.
      • Kry S.F.
      • Followill D.S.
      Pencil beam algorithms are unsuitable for proton dose calculations in lung.
      ,

      Maes D, Saini J, Zeng J, Rengan R, Wong T, Bowen SR. Advanced proton beam dosimetry part II: Monte Carlo vs. pencil beam-based planning for lung cancer. Transl Lung Cancer Res 2018;7:114–21. 10.21037/tlcr.2018.04.04.

      ]. A robust optimization strategy, accounting for a set of scenarios which reflect delivery and target motion uncertainties were incorporated in the problem formulation [
      • Mastella E.
      • Molinelli S.
      • Pella A.
      • Vai A.
      • Maestri D.
      • Vitolo V.
      • et al.
      4D strategies for lung tumors treated with hypofractionated scanning proton beam therapy: dosimetric impact and robustness to interplay effects.
      ] and a minimax optimization was performed [
      • Fredriksson A.
      • Forsgren A.
      • Hårdemark B.
      Minimax optimization for handling range and setup uncertainties in proton therapy.
      ]. In this study, all forward calculations were conducted with FRoG and the gp-MC using the end-of-exhale phase as the reference (static) patient anatomy, neglecting the beam distortion effects from the breathing cycle to solely investigate dose engine performance. Ten-thousand ions-per-spot were selected at the optimization stage and an estimated average statistical error per voxel < 0.5% for the final dose distribution was required to the system. The error is estimated over all voxels having a dose above 50% of the maximum dose per beam (RayStation® Reference Manual). The dose grid resolution was fixed to 2 × 2 × 2 mm3, which coincided with the particles transport grid and the CNAO-specific CT calibration curve, used routinely for organ motion-based acquisitions, was assigned to the CT matrix.

      2.3 FRoG settings

      In previous works, FRoG demonstrated excellent performance in terms of both accuracy and speed when compared to gp-MC, clinical TPS predictions and measurements too. Here, those verified settings, i.e. PB splitting multiplicity of ~350 and triple-Gaussian lateral dose parameterization, were implemented for investigating dose calculation in heterogeneous conditions of the lung. FRoG is composed of an analytical PBA algorithm, sampled from a dosimetric database derived from MC simulation and performs rapid computations via GPU-accelerated engines (e.g. raytracing, dose calculation kernels, etc.).

      2.4 gp-MC settings

      The FLUKA gp-MC simulation code [

      Ferrari A, Sala PR, Fasso A, Ranft J. FLUKA: A Multi-Particle Transport Code. Menlo Park, CA: 2005. 10.2172/877507.

      ] was selected as the gold standard reference for accuracy during comparison of patient dose calculation of GPU-based engines adopted by FRoG and by the RS-MC TPS. FLUKA has been supporting clinical and research activities at CNAO since 2011 and it has been extensively validated against clinical data [
      • Mirandola A.
      • Molinelli S.
      • Vilches Freixas G.
      • Mairani A.
      • Gallio E.
      • Panizza D.
      • et al.
      Dosimetric commissioning and quality assurance of scanned ion beams at the Italian National Center for Oncological Hadrontherapy.
      ], therefore providing a valuable reference for the benchmarking of such challenging scenarios. For a straightforward comparison between the performances of the above-mentioned systems and the gp-MC dose calculations in the lung tissue, HU-dependent tuning of the stopping power computation was introduced during runtime, which was specific for the lung, to force the gp-MC to reproduce the same CT calibration curve as used by FRoG and the RS-MC TPS [

      Linz U, editor. Ion Beam Therapy. vol. 320. Berlin, Heidelberg: Springer Berlin Heidelberg; 2012. 10.1007/978-3-642-21414-1.

      ]. The default hadrontherapy setting was selected as the main physics package for lung calculations and the same TPS dose grid resolution was used for plan dose recalculations. Five thousand primary protons per PB on a 2 × 2 × 2 mm3 voxel dose grid were selected to reach a mean statistical uncertainty of ~0.5% for each voxel in the GTV [
      • Mairani A.
      • Böhlen T.T.
      • Schiavi A.
      • Tessonnier T.
      • Molinelli S.
      • Brons S.
      • et al.
      A Monte Carlo-based treatment planning tool for proton therapy.
      ].

      2.5 Phantom study

      For dosimetric validation, a cork box-phantom (15 × 15 × 15 cm3) [
      • Mastella E.
      • Molinelli S.
      • Pella A.
      • Vai A.
      • Maestri D.
      • Vitolo V.
      • et al.
      4D strategies for lung tumors treated with hypofractionated scanning proton beam therapy: dosimetric impact and robustness to interplay effects.
      ,
      • Fuse H.
      • Fujisaki T.
      • Ikeda R.
      • Hakani Z.
      Applicability of lung equivalent phantom using the cork with absorbed water in radiotherapeutic dosimetry.
      ] was assembled in-house to mimic human lung tissue, with a 4 × 4 × 4 cm3 water-filled cavity as the target (Fig. 1). Five calibrated PinPoint ICs (PTW© model 31015) connected to a multi-channel precision electrometer (PTW© Multidos) were placed inside the water cavity to measure absorbed Dw, in accordance with the IAEA TRS 398 code of practice. One IC was placed at isocenter (geometric center of water cavity), while the remaining ICs were displaced within the target and spaced apart (honeycomb scheme) to avoid IC-IC perturbations. For end-to-end testing, a CT scan was acquired following clinical protocol and two plans were optimized on the RS-MC TPS (prescription dose of 6 Gy(RBE) in a single fraction): first, a 2-orthogonal beams IMPT plan (in-field inhomogeneity testing) and second, a single field uniform dose (SFUD) plan, both with a 3 cm-thick range shifter placed at 10 cm distance from the phantom surface. Each IC was contoured on the CT scan and a cross-check was performed on the TPS calculated volume to match the sensitive volume of the detector. Plans were delivered in a fixed-beam room at CNAO, using the horizontal beam port only.
      Figure thumbnail gr1
      Fig. 1Lung phantom experimental setup used for the end-to-end test of FRoG.

      2.6 Dose-averaged LET maps

      Further investigations with the FRoG engine involved selection and testing of the 2 patient cases with the smallest and largest target (GTV: ~6cc and ~160 cc) to evaluate resultant LETD distributions from RS-MC optimized plans. LETD maps were calculated with PB-type (MC-derived) LETD –kernels, as widely described in [
      • Choi K.
      • Mein S.B.
      • Kopp B.
      • Magro G.
      • Molinelli S.
      • Ciocca M.
      • et al.
      FRoG—A new calculation engine for clinical investigations with proton and carbon ion beams at CNAO.
      ].

      2.7 Data analysis

      Dose ratios for FRoG and RS-MC TPS to gp-MC were recorded for the following plan metrics: GTV D50, near-to-maximum dose (D2), near-to-minimum dose (D98) and the average dose to the ipsilateral lung (Dlung). The dose indices D2 and D98 on the target volume were selected as recommended by the ICRU Report 93 for quantification and assessment of coverage, while the median dose was used to evaluate to what degree the prescribed dose level was reached by the calculation engine. Dlung was chosen to give an estimate of the average dose level in the surrounding of the target. To quantify homogeneity of the dose distribution within the GTV at dose-volume histogram (DVH) level, the Homogeneity Index (HI) difference (ΔHI) (where HI[%] = (D2D98)/D50) was computed. The choice of the MC histories (both for the gp-MC and for the RS-MC) allowed us to safely use the above mentioned thresholds to evaluate the steepness of the DVH, which, in general, is highly dependent on the number of simulated primary particles. For avoidance of software-related biases on the computation of the DVHs, all dose matrices were loaded on the TPS to extract the dose statistics used for the data analysis.
      In addition, using the PTW© plan verification software Verisoft® v.6.0, differences in the dose distributions were assessed via 3D-γ-analysis [
      • Low D.A.
      • Harms W.B.
      • Mutic S.
      • Purdy J.A.
      A technique for the quantitative evaluation of dose distributions.
      ], reported as local γ passing rate (Lγ-PR), defined as the percentage of points with γ ≤ 1. For both FRoG and RS-MC, evaluation was conducted under a 1 mm/3% distance-to-agreement/local dose-difference (DTA/LDD) criterion with a 5% low dose-threshold (DT), with gp-MC as the reference. All datasets were normalized to the prescription dose-per-fraction, i.e. 6 Gy(RBE) = 100%. The DTA value of 1 mm reflects the CT axial resolution (0.88 mm), while DT = 5% allowed suppression of doses below clinical relevance for these specific cases. Finally, the LDD = 3% met the recommendation of the AAPM TG 218 [

      Miften M, Olch A, Mihailidis D, Moran J, Pawlicki T, Molineu A, et al. Tolerance limits and methodologies for IMRT measurement-based verification QA: Recommendations of AAPM Task Group No. 218. Med Phys 2018;45:e53–83. 10.1002/mp.12810.

      ]. The strict γ-criteria selected were necessary to appropriately assess dosimetric requirements for thoracic-based treatment sites. The tolerance level for the Lγ-PR was fixed to 90% (action level), corresponding to non-optimal but acceptable plans. A global γ passing rate (Gγ-PR) (with global dose-difference, GDD = 3% of 6 Gy(RBE)) was considered to evaluate how possible local dose discrepancies, detectable via a poor Lγ-PR, might prevent FRoG and RS-MC dose distributions from meeting the tolerance level of 95%.
      For the phantom study, measured IC dose was compared against the average dose () as computed by FRoG and the TPS for each region of interest (IC active volume) via an average dose ratio over the 5 ICs. Additionally, to explore the worst case scenario for potentially non-uniform beams, more in-depth evaluation was conducted for the IMPT plan by determining the global absolute percent dose deviation |%Δ| between each system’s prediction and the corresponding measured dose.
      Lastly, LETD-volume histograms (LVHs) were computed for FRoG and for the gp-MC LETD matrices, to provide further benchmarks of the analytical LETD distributions for the thoracic sites. Average and near-to-maximum LETD from LVH (LETavg and LET2) were computed for the ipsilateral lung, GTV and a ring expansion of the GTV (margins increased by 0.5 cm to 2.5 cm), with the latter to evaluate LETD within the vicinity of the target.

      3. Results

      3.1 Recalculations of patient plans

      3.1.1 DVH analysis

      Table 1 summarizes the DVH statistics as listed in Data analysis for the GPU-based dose engine FRoG and the CPU-based RS-MC, reported in terms of dose ratios against the gp-MC code. In Fig. 2, two representative patient cases are displayed with a FRoG dose map, alongside DVH and dose profiles comparing gp-MC, FRoG and the RS-MC TPS.
      Table 1FRoG-to-gp MC and RS-MC TPS-to-gp MC ratios for D50, D98, and D2. HI-differences and Dlung have been also reported.
      FRoG/gp-MC

      Average ± 1σ

      (min.;max.)
      RS-MC TPS/gp-MC

      Average ± 1σ

      (min.;max.)
      GTVD501.016 ± 0.009

      (1.003;1.029)
      1.022 ± 0.006

      (1.013;1.032)
      D21.024 ± 0.010

      (1.011;1.042)
      1.030 ± 0.008

      (1.019;1.043)
      D981.026 ± 0.010

      (1.016;1.040)
      1.026 ± 0.012

      (1.009;1.044)
      ΔHI(0.1 ± 0.9)%

      (-0.8;1.7)%

      (FRoG – gp-MC)
      0.7 ± 0.8%

      (-0.6;2.2)%

      (RS-MC – gp-MC)
      Ipsilateral lungDlung0.994 ± 0.019

      (0.956;1.016)
      0.998 ± 0.017

      (0.970;1.017)
      Figure thumbnail gr2
      Fig. 2(A, top and bottom) Two examples of dose distribution with the GTV contour on top; (B, top and bottom) GTV and lung DVHs; lateral (C, top and bottom) and posterior (D, top and bottom) beam longitudinal profiles along their central axis.
      In general, DVH metrics indicate that both dose engines slightly overestimate the gp-MC prediction by ~2% (see D50), with the largest discrepancies observed for the near-to-minimum and near-to-maximum doses. Notably, the results in Table 1 demonstrate that D2 and D98 differ from the reference by approximately the same %-value and, correspondingly, the almost zero value observed for ΔHIFRoG–gp-MC is consistent. ΔHIRS-MC–gp-MC has also effectively negligible deviations. Moreover, absorbed dose to the surrounding lung tissue is well reproduced by both FRoG and the RS-MC TPS compared with the gp-MC, further demonstrated by DVH and line profiles.

      3.1.2 Gamma analysis

      Results of 3D-γ-analyses are presented in Fig. 3, in terms of Gγ-PR and Lγ-PR, respectively. The bar-chart presents the patient cohort by increasing GTV, although there is no clear evidence of volume dependency on the passing rate: visualization of both FRoG and RS-MC TPS depicts a nearly random fluctuation of bar height regardless of the target size. Final γ-PRs averaged over the entire cohort follow with the standard deviation and range of variation:
      • Gγ-PR
        • o
          FRoG vs. gp-MC: (97.0 ± 1.4)% ∈ [95.1;99.1]%;
        • o
          RS-MC TPS vs. gp-MC: (97.8 ± 1.2)% ∈ [95.0;98.8]%;
      • Lγ-PR
        • o
          FRoG vs. gp-MC: (95.8 ± 1.8)% ∈ [93.3;98.2]%;
        • o
          RS-MC TPS vs. gp-MC: (92.7 ± 2.0)% ∈ [88.6;95.5]%;
      Figure thumbnail gr3
      Fig. 3Gγ-PR (A) and Lγ-PR (B) for the evaluation doses FRoG (green bars) and RS-MC TPS (blue bars), when compared against the gp-MC. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

      3.2 Experimental validation

      SFUD and IMPT plans were delivered within an end-to-end workflow for the experimental validation of FRoG, RS-MC TPS and gp-MC in thoracic-like settings. Table 2 reports the dose engine-to-data ratios averaged over the 5 ICs placed in the in-house built cork box-phantom.
      Table 2Dose ratios of FRoG, RS-MC TPS and gp-MC against measurements, reported as average value over 5 calibrated ICs for SFUD and IMPT plans.
      gp-MC/Data

      Average ± 1σ

      (min.;max.)
      FRoG/Data

      Average ± 1σ

      (min.;max.)
      RS-MC TPS/Data

      Average ± 1σ

      (min.;max.)
      SFUD1.002 ± 0.017

      (0.974;1.019)
      1.007 ± 0.018

      (0.975;1.021)
      1.001 ± 0.016

      (0.977;1.019)
      IMPT0.988 ± 0.041

      (0.940;1.051)
      1.000 ± 0.046

      (0.977;1.073)
      0.987 ± 0.043

      (0.941;1.053)

      3.3 LETD distributions

      As reported in Table 3, irrespective of target volume and thickness of traversed lung tissue, FRoG and FLUKA LETD predictions are in agreement within 0.1 keV/µm for the GTV (~3% of GTV LETavg) and within 0.5 keV/µm (~7% of lung LET2) for the other analyzed non-target structures.
      Table 3LETavg and LET2 LVH parameters extracted from FRoG and FLUKA LETD maps. Data in keV/µm.
      GTVLETGTVWall 0.5–2.5Ipsilateral lung
      volumeFRoGgp-MCFRoGgp-MCFRoGgp-MC
      6.10 ccLETavg3.43.33.53.30.50.5
      LET24.14.28.48.46.76.8
      160.56 ccLETavg2.82.73.02.81.11.0
      LET23.73.77.06.96.96.4
      In Fig. 4, LETD maps and LVHs plots (GTV, wall and ipsilateral lung) for two representative lung patient cases are presented for the gp-MC and FRoG system.
      Figure thumbnail gr4
      Fig. 4LETD distribution for two patient cases (A, top and bottom), with the GTV and target-wall contour on top; (B, top and bottom) GTV, lung and GTV wall expansion LVHs.

      3.4 Calculation time

      RS-MC, the gp-MC and FRoG are installed on separate platforms and run on different hardware. Hence a fair comparison among the three systems is not justified in terms of calculation speed. Moreover, each code manages radiation transport and dose scoring parameters differently, as addressed in the Material and Methods section: the gp-MC and FRoG perform the particle transport on the native CT voxels and calculate the dose on the 2 mm resolution dose grid; the RS-MC on the other hand works on a transport grid identical to the dose calculation grid (RayStation® Reference Manual). Despite these technical differences, a brief analysis on the computation time was performed.
      For the studied patient cohort, the average computation time per primary was about 8 ms for the gp-MC, resulting in an overall computation time on a cluster with 24 CPUs (Intel Xeon CPU E5-2660 v3 at 2.60 GHz) of about 1.5 to 12 h per beam, for the 6 and 160 cc GTV, respectively.
      For maximum performance with TPS v.8, computations were performed using hardware specifically recommended by RaySearch Laboratories© and available at our clinic for its CPU-based proton MC dose engine, i.e. Intel Xeon CPU E5-2630 v4 at 2.20 GHz (2 processors, 10 cores each). Computation times for the final dose calculation were 20 s per beam, on average. Computation time was recorded when calling the ComputeDose built-in function, i.e. the so-called “dose finalization”, which includes the output of both a physical and a fixed-RBE(=1.1) dose matrix.
      In the context of FRoG runtimes, Choi et al. [
      • Choi K.
      • Mein S.B.
      • Kopp B.
      • Magro G.
      • Molinelli S.
      • Ciocca M.
      • et al.
      FRoG—A new calculation engine for clinical investigations with proton and carbon ion beams at CNAO.
      ] previously demonstrated a time reduction of about 3.5-fold when moving, for example, from a consumer grade GPU card NVIDIA GeForce GTX 1080 Ti to a high-end graphics card NVIDIA Tesla V100, which is the best available configuration where the FRoG code is running so far. Calculation times ranged from 3.5 to 11.5 s per beam, when using NVIDIA Tesla V100 GPU and monitoring the time required for the handling of the dose kernel only, to be fairly comparable against the TPS. Within the overall calculation time, FRoG produces the output for physical dose, biological dose assuming a fixed-RBE, biological dose using a variable-RBE model and a LETD matrix (i.e. two more than the TPS output).

      4. Discussion

      Through systematic evaluations of PT dose calculation in thoracic treatment sites, we provide benchmarks for an innovative approach of the PBA as well as both clinical and research-based MC systems. In the context of results available in recent literature on dosimetric investigations using lung phantoms, this study demonstrated substantially higher PRs and lower dose deviations for an analytical system in spite of the relatively strict γ-criteria. We believe several points regarding lung dose calculation need formal clarification and here we will shed light on potential causes for deviations commonly observed with commercial systems, as well as suggested next steps for collaboration with industry towards improved TP for thoracic cancers.
      First, a brief technical aside: higher deviations in D98 and D2 were observed for both FRoG and RS-MC in the DVH analysis against reference gp-MC. Apart from possible explanations like statistical fluctuation exhibited by MC engines [
      • Bauer J.
      • Sommerer F.
      • Mairani A.
      • Unholtz D.
      • Farook R.
      • Handrack J.
      • et al.
      Integration and evaluation of automated Monte Carlo simulations in the clinical practice of scanned proton and carbon ion beam therapy.
      ,
      • Paganetti H.
      • Jiang H.
      • Parodi K.
      • Slopsema R.
      • Engelsman M.
      Clinical implementation of full Monte Carlo dose calculation in proton beam therapy.
      ], the discrepancy on the coverage of the 98% (D98) of the GTV affected the smallest geometry available for the selected database. This patient case, in particular, exhibited also higher GTV D50 ratios (FRoG = 1.029, RS-MC = 1.032), with overestimations by both dose engines ~3% (see Fig. 2, bottom panels): this may confirm that deviations can be attributed to challenges arising from small target volumes (~6cc), which may amplify possible initial discrepancies on the parameterization of the beam lateral spread in air throughout the beamline. In fact, thoracic treatment sites often host small targets with densities higher than the surroundings normal tissues and the low-density thoracic tissues may prevent the beam from spreading enough to smear out potential differences inherited from the patient entrance surface.
      Overall, FRoG matches well with the gp-MC predictions. Considering all resultant values extracted from the DVHs (Table 1), FRoG reproduces gp-MC within 2.2%, on average. Limiting analysis on the GTV, ΔHI was consistent between both the dose engines, with respect to gp-MC baseline: to the GTV was 1.8% and 2.3% greater for FRoG and the RS-MC TPS, respectively.
      For both the dose engines, the average dose to the Dlung agreed within 0.4%, with a relative standard deviation of the Dlung-ratio < 2% for both the dose engines.
      Considering the challenging nature of thoracic treatments, a Gγ-analysis with distance-to-agreement DTA = 1 mm, global dose-difference GDD = 3% and dose-threshold DT = 5% may be considered sufficiently strict for validation purposes, considering the 5 mm/7% criteria applied in recent works [
      • Taylor P.A.
      • Kry S.F.
      • Followill D.S.
      Pencil beam algorithms are unsuitable for proton dose calculations in lung.
      ]. In this regard, Fig. 3(A) visibly demonstrates that all patient plans in the investigated cohort recalculated by FRoG satisfy the clinically optimal 95%-tolerance level. No failures were detected for the RS-MC TPS as well, with the totality of cases above the 95%-tolerance level. In turn, FRoG and RS-MC TPS exhibited comparable dose calculation performance.
      Investigations were additionally conducted by adopting local dose normalization for the γ-analysis (Fig. 3(B)), a stringent method to validate dosimetric performances of FRoG specifically in lower dose areas. While maintaining the same evaluation criteria, RS-MC TPS exhibited slightly poorer performances when compared to local outcomes for the reference gp-MC. The observed Lγ-PR, in fact, lowers to a mean value of (92.7 ± 2.0)%, with only a single patient case with results above the 95%-tolerance level. FRoG performs better against the gp-MC, even locally, with a mean Lγ-PR of (95.8 ± 1.8)%. Interestingly, for FRoG, 100% of patients exceed the Lγ-PR > 90%, with 2 patients (among the larger GTVs in the cohort and reduced beam path of traversed heterogeneous lung tissue in entrance) above 98% γ-PR.
      As far for the SFUD plan, the 3 systems under study were highly comparable, with a similar average deviation to experimental data (<0.1%) and nearly identical minimum/maximum discrepancies of ~2.5%/~2%. For the IMPT plan, FRoG exhibited predictions closest to measurements, on average, out of the 3 engines, while both the gp-MC and RS-MC TPS underestimated by ~1%. With respect to |%Δ|, gp-MC, FRoG and RS-MC TPS performance were in agreement with values of (3.2 ± 2.3)%, (3.3 ± 2.7)% and (3.4 ± 2.4)%, respectively. Referencing routine patient-specific QA protocol at our facility, these results are clinically acceptable within the 5%-tolerance level of the mean |%Δ| and standard deviation.
      In regard to LETD prediction, FRoG was within a few tenths of keV/µm, compared to reference gp-MC, for both the average and the near-to-maximum LETD. Moreover, results verified that for the selected beam configuration (2 orthogonal ports), the LETD was, on average, ~3keV/µm in the target and in the tissue nearby, reducing to ~1 keV/µm in the remaining portions of the lung. Maximum LETD values within and outside the target volume were ~4 keV/µm and < 8 keV/µm, respectively.
      In this work, FRoG was rigorously benchmarked against dosimetric measurements and gp-MC prediction, as well as in the context of state-of-the-art MC clinical TPSs via end-to-end tests within a thoracic treatment scenario. Recent studies strongly suggest IMPT in the thoracic regions, by means of MC-based calculations, may be necessary to maintain a consistent and acceptable clinical practice for treating lung lesions. Here, we demonstrate that a well-designed analytical PB proton dose engine can effectively predict dose in lung tumors, comparable with gp-MC algorithms, consistent with MC-based clinical TPSs and in good agreement with experimental measurements. This has been verified despite approximations during calculation, e.g. Dw, and neglecting PB degradation in lung, with the latter recently deemed clinically tolerable in most circumstances [
      • Baumann K.S.
      • Flatten V.
      • Weber U.
      • Lautenschläger S.
      • Eberle F.
      • Zink K.
      • et al.
      Effects of the Bragg peak degradation due to lung tissue in proton therapy of lung cancer patients.
      ]. FRoG is an analytical PB-class dose engine with clinically acceptable performance in dose calculation for lung lesions. FRoG predictions are in line with the conclusions reported by [
      • Nenoff L.
      • Matter M.
      • Jarhall A.G.
      • Winterhalter C.
      • Gorgisyan J.
      • Josipovic M.
      • et al.
      Daily adaptive proton therapy: is it appropriate to use analytical dose calculations for plan adaption?.
      ], promoting the use of analytical calculation methods for rapid plan adaptation with NSCLC treatments.
      Furthermore, FRoG uniquely offers MC-validated predictions of patient-specific LETD distributions. Recently, FRoG is supporting the clinical activity at select Varian© PT facilities as an auxiliary dose engine and investigations in which aim to establish novel beams and multi-ion treatment strategies [
      • Kopp B.
      • Mein S.
      • Dokic I.
      • Harrabi S.
      • Böhlen T.T.
      • Haberer T.
      • et al.
      Development and validation of single field multi-ion particle therapy treatments.
      ,
      • Mein S.
      • Dokic I.
      • Klein C.
      • Tessonnier T.
      • Böhlen T.T.
      • Magro G.
      • et al.
      Biophysical modeling and experimental validation of relative biological effectiveness (RBE) for 4He ion beam therapy.
      ]. Future efforts involve multi-institutional collaborations to investigate treatment delivery with lung phantoms using heavier ions.
      A root cause for the relatively poor performance of PT dose engines in lung phantom studies is the TPS beam model design and execution. Lung treatments can be considered a pinnacle of complexity in PT and therefore, proper dose calculation using analytical methods in heterogeneous anatomy requires sophisticated PB deformation procedures, e.g. high order PB subdivision, and in turn, propagation and handling of lateral dose penumbra. More specifically, to model PB distortion in lateral heterogeneities, RS v.8, for example, decomposes each spot by 19 beamlets, while FRoG, on the other hand, reconstructs the PB with ~350 unique beamlets. The issue at hand is simply a computational feat that can most efficiently be performed via GPU-accelerations and similarly, other recently developed systems further demonstrate the potential of accelerated codes, performing both optimization and calculation procedures well under a minute [
      • Matter M.
      • Nenoff L.
      • Meier G.
      • Weber D.C.
      • Lomax A.J.
      • Albertini F.
      Intensity modulated proton therapy plan generation in under ten seconds.
      ].
      Results from the (15)’s study draw attention to important issues regarding mainstream commercial systems which, for thoracic sites, insufficiently describe lateral dose evolution and substantially under-sample the necessary PB decomposition. Not all approaches to dose calculation (analytical or simulation) will be suitable for treating anatomically complex and sensitive cases. Other non-commercial systems, however, using analytical or MC approaches have demonstrated similar accuracy, as FRoG, with significant reductions in calculation time for various anatomic treatment sites [
      • da Silva J.
      • Ansorge R.
      • Jena R.
      Fast pencil beam dose calculation for proton therapy using a double-Gaussian beam model.
      ,

      Beltran C, Tseung HWC, Augustine KE, Bues M, Mundy DW, Walsh TJ, et al. Clinical Implementation of a Proton Dose Verification System Utilizing a GPU Accelerated Monte Carlo Engine. Int J Part Ther 2016;3:312–9. 10.14338/ijpt-16-00011.1.

      ] and may consider following end-to-end tests for TP lung lesions as performed here.
      The employment in the clinical routine of benchmarked fast analytical dose engines, such as FRoG, using also log files reporting the actual delivered spots, could be a valid alternative to QA-program relying solely on dose measurements in a homogeneous water-like phantom [

      Johnson JE, Beltran C, Wan Chan Tseung H, Mundy DW, Kruse JJ, Whitaker TJ, et al. Highly efficient and sensitive patient-specific quality assurance for spot-scanned proton therapy. PLoS One 2019;14. 10.1371/journal.pone.0212412.

      ] or to time-consuming measurements with thermoluminescent dosimeters and radiochromic film in anthropomorphic phantoms.
      The findings of this work, along with key results from the literature, suggest that to improve confidence in TP for lung cancer, prompt redesign of current commercial analytical approaches is warranted. The authors suggest adoption of FRoG or similar approaches may be necessary to balance speed and accuracy for clinical viability, most feasible through GPU-accelerated architecture.

      5. Conclusions

      For thoracic treatment sites, we provide benchmarks for novel analytical methods to PT dose calculation alongside MC methods, both research and clinical. We provide evidence that it is feasible to reach MC accuracy with a fast analytical approach. Our recently developed analytical PBA demonstrated excellent performance in rigorous testing using a heterogeneous lung phantom, further exemplifying the value of PB model reformation. To improve TP quality, commercial vendors should consider state-of-the-art GPU-accelerated analytical PB models and/or fast MC methods.
      Data sharing: Research data are stored in a public repository (The Cancer Imaging Archive-4D Lung Database) [
      • Clark K.
      • Vendt B.
      • Smith K.
      • Freymann J.
      • Kirby J.
      • Koppel P.
      • et al.
      The cancer imaging archive (TCIA): maintaining and operating a public information repository.
      ] and will be shared upon request to the corresponding author.
      Funding: This work was supported by German Research Council [DFG-KFO214], Deutsche Krebshilfe [Max-Eder 108876] and intramural funds from National Center for Tumor diseases [NCT3.0_2015.21/22 NCT-PRO and Biodose programs]. The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript.

      Declaration of Competing Interest

      The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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