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Forward treatment planning for modulated electron radiotherapy (MERT) employing Monte Carlo methods

Purpose: This paper describes the development of a forward planning process for modulated electron radiotherapy (MERT). The approach is based on a previously developed electron beam model used to calculate dose distributions of electron beams shaped by a photon multi leaf collimator (pMLC). Methods: As the electron beam model has already been implemented into the Swiss Monte Carlo Plan environment, the Eclipse treatment planning system (Varian Medical Systems, Palo Alto, CA) can be included in the planning process for MERT. In a first step, CT data are imported into Eclipse and a pMLC shaped electron beam is set up. This initial electron beam is then divided into segments, with the electron energy in each segment chosen according to the distal depth of the planning target volume (PTV) in beam direction. In order to improve the homogeneity of the dose distribution in the PTV, a feathering process (Gaussian edge feathering) is launched, which results in a number of feathered segments. For each of these segments a dose calculation is performed employing the in-house developed electron beam model along with the macro Monte Carlo dose calculation algorithm. Finally, an automated weight optimization of all segments is carried out and the total dose distribution is read back into Eclipse for display and evaluation. One academic and two clinical situations are investigated for possible benefits of MERT treatment compared to standard treatments performed in our clinics and treatment with a bolus electron conformal (BolusECT) method. Results: The MERT treatment plan of the academic case was superior to the standard single segment electron treatment plan in terms of organs at risk (OAR) sparing. Further, a comparison between an unfeathered and a feathered MERT plan showed better PTV coverage and homogeneity for the feathered plan, with V{sub 95%} increased from 90% to 96% and V{sub 107%} decreased from 8% to nearly 0%. For a clinical breast boost irradiation, the MERT plan led to a similar homogeneity in the PTV compared to the standard treatment plan while the mean body dose was lower for the MERT plan. Regarding the second clinical case, a whole breast treatment, MERT resulted in a reduction of the lung volume receiving more than 45% of the prescribed dose when compared to the standard plan. On the other hand, the MERT plan leads to a larger low-dose lung volume and a degraded dose homogeneity in the PTV. For the clinical cases evaluated in this work, treatment plans using the BolusECT technique resulted in a more homogenous PTV and CTV coverage but higher doses to the OARs than the MERT plans. Conclusions: MERT treatments were successfully planned for phantom and clinical cases, applying a newly developed intuitive and efficient forward planning strategy that employs a MC based electron beam model for pMLC shaped electron beams. It is shown that MERT can lead to a dose reduction in OARs compared to other methods. The process of feathering MERT segments results in an improvement of the dose homogeneity in the PTV.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

A lumped particle direct simulation Monte-Carlo method combined with the collisional-radiative model for simulations of non-equilibrium laser-induced plasma plumes

Collisional plasma plumes induced by laser irradiation of material targets exhibit large variations in local density as well as ionization and excitation states, making purely hydrodynamic or kinetic simulations inaccurate or infeasible. To address this challenge and capture non-equilibrium effects in laser-induced plasma plumes at arbitrary degrees of ionization, we develop a hybrid computational approach that combines the kinetic direct simulation Monte Carlo (DSMC) method with a collisional-radiative model (CRM). This ℓDSMC-CRM approach utilizes a lumped particle method to represent minor fractions of excited ions in particle-based simulations and a special coarse-graining technique for atomic spectra and photoionization rates, ensuring numerical convergence at reduced computational cost. The hybrid approach is applied to simulate spatially homogeneous relaxation as well as one- and two-dimensional expansions of plasma plumes induced by irradiation of a copper target by a nanosecond laser pulse in a vacuum or background gas. The comparison with an equilibrium model, where local Saha-Boltzmann equilibrium is enforced, shows that the non-equilibrium effects play a dominant role. The equilibrium model can fail to predict the flow structure and strongly underestimate the degree of absorption of laser radiation by the plume. The ℓDSMC-CRM approach is validated against experimental data demonstrating reasonable agreement with the experimental electron density and temperature, while the equilibrium model is found to dramatically underestimate electron density and temperature. The flexibility of the ℓDSMC-CRM approach allows for its seamless integration into existing DSMC frameworks, making it a valuable tool for high-fidelity plasma modeling in laser-material interactions, laser-based manufacturing, and beyond.

97 MATHEMATICS AND COMPUTING↗

Toward improved property prediction of 2D materials using many-body quantum Monte Carlo methods

The field of 2D materials has grown dramatically in the past two decades. 2D materials can be utilized for a variety of next-generation optoelectronic, spintronic, clean energy, and quantum computing applications. These 2D structures, which are often exfoliated from layered van der Waals materials, possess highly inhomogeneous electron densities and can possess short- and long-range electron correlations. The complexities of 2D materials make them challenging to study with standard mean-field electronic structure methods such as density functional theory (DFT), which relies on approximations for the unknown exchange-correlation functional. To overcome the limitations of DFT, highly accurate many-body electronic structure approaches such as diffusion Monte Carlo (DMC) can be utilized. In the past decade, DMC has been used to calculate accurate magnetic, electronic, excitonic, and topological properties in addition to accurately capturing interlayer interactions and cohesion and adsorption energetics of 2D materials. Here, this approach has been applied to 2D systems of wide interest, including graphene, phosphorene, MoS 2 , CrI 3 , VSe 2 , GaSe, GeSe, borophene, and several others. In this review article, we highlight some successful recent applications of DMC to 2D systems for improved property predictions beyond standard DFT.

2D materials↗

Nanothermodynamics of large iron clusters by means of a flat histogram Monte Carlo method

The thermodynamics of iron clusters of various sizes, from 76 to 2452 atoms, typical of the catalyst particles used for carbon nanotubes growth, has been explored by a flat histogram Monte Carlo (MC) algorithm (called the σ-mapping), developed by Soudan et al. [J. Chem. Phys. 135, 144109 (2011), Paper I]. This method provides the classical density of states, g{sub p}(E{sub p}) in the configurational space, in terms of the potential energy of the system, with good and well controlled convergence properties, particularly in the melting phase transition zone which is of interest in this work. To describe the system, an iron potential has been implemented, called “corrected EAM” (cEAM), which approximates the MEAM potential of Lee et al. [Phys. Rev. B 64, 184102 (2001)] with an accuracy better than 3 meV/at, and a five times larger computational speed. The main simplification concerns the angular dependence of the potential, with a small impact on accuracy, while the screening coefficients S{sub ij} are exactly computed with a fast algorithm. With this potential, ergodic explorations of the clusters can be performed efficiently in a reasonable computing time, at least in the upper half of the solid zone and above. Problems of ergodicity exist in the lower half of the solid zone but routes to overcome them are discussed. The solid-liquid (melting) phase transition temperature T{sub m} is plotted in terms of the cluster atom number N{sub at}. The standard N{sub at}{sup −1/3} linear dependence (Pawlow law) is observed for N{sub at} >300, allowing an extrapolation up to the bulk metal at 1940 ±50 K. For N{sub at} <150, a strong divergence is observed compared to the Pawlow law. The melting transition, which begins at the surface, is stated by a Lindemann-Berry index and an atomic density analysis. Several new features are obtained for the thermodynamics of cEAM clusters, compared to the Rydberg pair potential clusters studied in Paper I.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Neutrino Transport with Monte Carlo Method. I. Toward Fully Consistent Implementation of Nucleon Recoils in Core-collapse Supernova Simulations

The small energy exchange via nucleon recoils in neutrino–nucleon scattering is now supposed to be one of the important factors for successful explosions of core-collapse supernovae (CCSNe), as they can change neutrino spectra through accumulation of a large number of scatterings. In deterministic methods employed for neutrino transport in CCSN simulations, we normally cannot afford to deploy a large enough number of energy bins needed to resolve this small energy exchange, and subgrid techniques are employed one way or another. In this paper, we study quantitatively with the Monte Carlo (MC) method how well such a treatment performs. We first investigate the effects of nucleon recoils on the neutrino spectra and confirm that the average energy is reduced by ~15% for heavy-lepton neutrinos and much smaller amounts for other types of neutrinos in a typical postbounce situation. It is also observed that the nucleon scattering dominates the electron scattering in the thermalization of neutrino spectra in all flavors. We then study possible artifacts that the coarse energy grid may produce in the deterministic methods. In order to mimic the latter calculation, we redistribute MC particles in each energy bin after a certain interval in a couple of ways and study how the results are affected, depending on the energy resolution. We also discuss the possible implications of our results for the deterministic methods.

79 ASTRONOMY AND ASTROPHYSICS↗

Elucid—exploring the local universe with the reconstructed initial density field. I. Hamiltonian Markov chain Monte Carlo method with particle mesh dynamics

Simulating the evolution of the local universe is important for studying galaxies and the intergalactic medium in a way free of cosmic variance. Here we present a method to reconstruct the initial linear density field from an input nonlinear density field, employing the Hamiltonian Markov Chain Monte Carlo (HMC) algorithm combined with Particle-mesh (PM) dynamics. The HMC+PM method is applied to cosmological simulations, and the reconstructed linear density fields are then evolved to the present day with N-body simulations. These constrained simulations accurately reproduce both the amplitudes and phases of the input simulations at various z. Using a PM model with a grid cell size of 0.75 h {sup –1} Mpc and 40 time steps in the HMC can recover more than half of the phase information down to a scale k ∼ 0.85 h Mpc{sup –1} at high z and to k ∼ 3.4 h Mpc{sup –1} at z = 0, which represents a significant improvement over similar reconstruction models in the literature, and indicates that our model can reconstruct the formation histories of cosmic structures over a large dynamical range. Adopting PM models with higher spatial and temporal resolutions yields even better reconstructions, suggesting that our method is limited more by the availability of computer resource than by principle. Dynamic models of structure evolution adopted in many earlier investigations can induce non-Gaussianity in the reconstructed linear density field, which in turn can cause large systematic deviations in the predicted halo mass function. Such deviations are greatly reduced or absent in our reconstruction.

79 ASTRONOMY AND ASTROPHYSICS↗

The Metropolis Monte Carlo method with CUDA enabled Graphic Processing Units

We present a CPU–GPU system for runtime acceleration of large molecular simulations using GPU computation and memory swaps. The memory architecture of the GPU can be used both as container for simulation data stored on the graphics card and as floating-point code target, providing an effective means for the manipulation of atomistic or molecular data on the GPU. To fully take advantage of this mechanism, efficient GPU realizations of algorithms used to perform atomistic and molecular simulations are essential. Our system implements a versatile molecular engine, including inter-molecule interactions and orientational variables for performing the Metropolis Monte Carlo (MMC) algorithm, which is one type of Markov chain Monte Carlo. By combining memory objects with floating-point code fragments we have implemented an MMC parallel engine that entirely avoids the communication time of molecular data at runtime. Our runtime acceleration system is a forerunner of a new class of CPU–GPU algorithms exploiting memory concepts combined with threading for avoiding bus bandwidth and communication. The testbed molecular system used here is a condensed phase system of oligopyrrole chains. A benchmark shows a size scaling speedup of 60 for systems with 210,000 pyrrole monomers. Our implementation can easily be combined with MPI to connect in parallel several CPU–GPU duets. -- Highlights: •We parallelize the Metropolis Monte Carlo (MMC) algorithm on one CPU—GPU duet. •The Adaptive Tempering Monte Carlo employs MMC and profits from this CPU—GPU implementation. •Our benchmark shows a size scaling-up speedup of 62 for systems with 225,000 particles. •The testbed involves a polymeric system of oligopyrroles in the condensed phase. •The CPU—GPU parallelization includes dipole—dipole and Mie—Jones classic potentials.

97 MATHEMATICS AND COMPUTING↗

Electronic band gaps from quantum Monte Carlo methods

We develop a method for calculating the fundamental electronic gap of semiconductors and insulators using grand canonical quantum Monte Carlo simulations. Further, we discuss the origin of the bias introduced by supercell calculations of finite size and show how to correct the leading and subleading finite size errors either based on observables accessible in the finite-sized simulations or from density-functional theory calculations. Our procedure is applied to carbon, silicon, and molecular hydrogen crystals, and compared to experiment for carbon and silicon.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Synergies from using higher order symplectic decompositions both for ordinary differential equations and quantum Monte Carlo methods

Decomposition methods of the Suzuki-Trotter type of various orders have been derived in different fields. Applying them both to classical ordinary differential equations (ODEs) and quantum systems allows to judge their effectiveness and gives new insights for many body quantum mechanics where reference data are scarce. Further, based on data for 6 × 6 system we conclude that sampling with sign (minus-sign problem) is probably detrimental to the accuracy of fermionic simulations with determinant algorithms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Experiments and Theoretical Data for Studying the Impact of Fission Yield Uncertainties on the Nuclear Fuel Cycle with TALYS/GEF and the Total Monte Carlo Method

We describe the research program of the nuclear reactions research group at Uppsala University concerning experimental and theoretical efforts to quantify and reduce nuclear data uncertainties relevant for the nuclear fuel cycle. We briefly describe the Total Monte Carlo (TMC) methodology and how it can be used to study fuel cycle and accident scenarios, and summarize our relevant experimental activities. Input from the latter is to be used to guide the nuclear models and constrain parameter space for TMC. The TMC method relies on the availability of good nuclear models. For this we use the TALYS code which is currently being extended to include the GEF model for the fission channel. We present results from TALYS-1.6 using different versions of GEF with both default and randomized input parameters and compare calculations with experimental data for {sup 234}U(n,f) in the fast energy range. These preliminary studies reveal some systematic differences between experimental data and calculations but give overall good and promising results.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Modelling of radiative transfer by the Monte Carlo method and solving the inverse problem based on a genetic algorithm according to experimental results of aerosol sensing on short paths using a femtosecond laser source

We consider the algorithms that implement a broadband ('multiwave') radiative transfer with allowance for multiple (aerosol) scattering and absorption by main atmospheric gases. In the spectral range of 0.6 – 1 μm, a closed numerical simulation of modifications of the supercontinuum component of a probing femtosecond pulse is performed. In the framework of the algorithms for solving the inverse atmospheric-optics problems with the help of a genetic algorithm, we give an interpretation of the experimental backscattered spectrum of the supercontinuum. An adequate reconstruction of the distribution mode for the particles of artificial aerosol with the narrow-modal distributions in a size range of 0.5 – 2 mm and a step of 0.5 mm is obtained. (light scattering)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

TU-F-BRE-06: Flattening-Filter-Free Beam Quality Correction Factor Determination Using Experimental and Monte Carlo Methods

Purpose: To investigate beam quality correction factors for the flattening-filter-free (FFF) energies of the TrueBeam™ accelerator based on a dosimetry formalism for small and nonstandard fields. Methods: Three detectors - an Exradin W1 scintillator, Sun Nuclear EDGE diode, and LiF(Mg,Tl) TLD-100 chips - were investigated to determine their applicability as tools to measure quality correction factors for ionization chambers in the small and nonstandard fields of the TrueBeam™. Volume-averaging effects and energy dependence were observed in fields ranging from 1×1 to 40×40 cm{sup 2} for 6 MV and 10 MV beam energies using both FFF and flattened beam modes. Correction factors were determined for three ionization chambers: an Exradin A12 Farmer-type chamber, an Exradin A1SL scanning chamber, and an Exradin A26 reference-class microchamber. Beam quality corrections were also obtained using a benchmarked model of the TrueBeam™ created with the BEAMnrc user code of EGSnrc. Results: All three detectors demonstrated measureable energy dependence in the megavoltage range. The EDGE diode was deemed the most appropriate tool for beam quality correction factor measurements due to its low energy dependence and small size; however, alanine will be used in the future to reduce energy dependent effects even further. Measured k{sub Qmsr,Q} corrections of up to 4% were found for the 6MV FFF and 10 MV FFF beams, corresponding to a discrepancy of up to 3% compared to TG-51-determined dose. Up to a 10% k{sub Qclin,Qmsr} correction was measured for small fields referenced to a 10×10 cm{sup 2} field of the same energy. Much larger corrections were determined using the Monte Carlo model, and these discrepancies require further investigation. Conclusion: Progress has been made toward determining beam quality correction factors for the small and nonstandard fields of the TrueBeam™ accelerator. Further work must be done to ensure greater accuracy in patient treatments with this new modality.

07 ISOTOPE AND RADIATION SOURCES↗

SU-C-201-06: Small Field Correction Factors for the MicroDiamond Detector in the Gamma Knife-Model C Derived Using Monte Carlo Methods

Purpose: To determine small field correction factors for PTW’s microDiamond detector in Elekta’s Gamma Knife Model-C unit. These factors allow the microDiamond to be used in QA measurements of output factors in the Gamma Knife Model-C; additionally, the results also contribute to the discussion on the water equivalence of the relatively-new microDiamond detector and its overall effectiveness in small field applications. Methods: The small field correction factors were calculated as k correction factors according to the Alfonso formalism. An MC model of the Gamma Knife and microDiamond was built with the EGSnrc code system, using BEAMnrc and DOSRZnrc user codes. Validation of the model was accomplished by simulating field output factors and measurement ratios for an available ABS plastic phantom and then comparing simulated results to film measurements, detector measurements, and treatment planning system (TPS) data. Once validated, the final k factors were determined by applying the model to a more waterlike solid water phantom. Results: During validation, all MC methods agreed with experiment within the stated uncertainties: MC determined field output factors agreed within 0.6% of the TPS and 1.4% of film; and MC simulated measurement ratios matched physically measured ratios within 1%. The final k correction factors for the PTW microDiamond in the solid water phantom approached unity to within 0.4%±1.7% for all the helmet sizes except the 4 mm; the 4 mm helmet size over-responded by 3.2%±1.7%, resulting in a k factor of 0.969. Conclusion: Similar to what has been found in the Gamma Knife Perfexion, the PTW microDiamond requires little to no corrections except for the smallest 4 mm field. The over-response can be corrected via the Alfonso formalism using the correction factors determined in this work. Using the MC calculated correction factors, the PTW microDiamond detector is an effective dosimeter in all available helmet sizes. The authors would like to thank PTW (Friedberg, Germany) for providing the PTW microDiamond detector for this research.

07 ISOTOPE AND RADIATION SOURCES↗

TH-AB-207A-07: Radiation Dose Simulation for a Newly Proposed Dynamic Bowtie Filters for CT Using Fast Monte Carlo Methods

Purpose: Dynamic bowtie filter is an innovative design capable of modulating the X-ray and balancing the flux in the detectors, and it introduces a new way of patient-specific CT scan optimizations. This study demonstrates the feasibility of performing fast Monte Carlo dose calculation for a type of dynamic bowtie filter for cone-beam CT (Liu et al. 2014 9(7) PloS one) using MIC coprocessors. Methods: The dynamic bowtie filter in question consists of a highly attenuating bowtie component (HB) and a weakly attenuating bowtie (WB). The HB is filled with CeCl3 solution and its surface is defined by a transcendental equation. The WB is an elliptical cylinder filled with air and immersed in the HB. As the scanner rotates, the orientation of WB remains the same with the static patient. In our Monte Carlo simulation, the HB was approximated by 576 boxes. The phantom was a voxelized elliptical cylinder composed of PMMA and surrounded by air (44cm×44cm×40cm, 1000×1000×1 voxels). The dose to the PMMA phantom was tallied with 0.15% statistical uncertainty under 100 kVp source. Two Monte Carlo codes ARCHER and MCNP-6.1 were compared. Both used double-precision. Compiler flags that may trade accuracy for speed were avoided. Results: The wall time of the simulation was 25.4 seconds by ARCHER on a 5110P MIC, 40 seconds on a X5650 CPU, and 523 seconds by the multithreaded MCNP on the same CPU. The high performance of ARCHER is attributed to the parameterized geometry and vectorization of the program hotspots. Conclusion: The dynamic bowtie filter modeled in this study is able to effectively reduce the dynamic range of the detected signals for the photon-counting detectors. With appropriate software optimization methods, the accelerator-based (MIC and GPU) Monte Carlo dose engines have shown good performance and can contribute to patient-specific CT scan optimizations.

60 APPLIED LIFE SCIENCES↗

SU-F-T-376: The Efficiency of Calculating Photonuclear Reaction On High-Energy Photon Therapy by Monte Carlo Method

Purpose: Secondary-neutrons having harmful influences to a human body are generated by photonuclear reaction on high-energy photon therapy. Their characteristics are not known in detail since the calculation to evaluate them takes very long time. PHITS(Particle and Heavy Ion Transport code System) Monte Carlo code since versions 2.80 has the new parameter “pnimul” raising the probability of occurring photonuclear reaction forcibly to make the efficiency of calculation. We investigated the optimum value of “pnimul” on high-energy photon therapy. Methods: The geometry of accelerator head based on the specification of a Varian Clinac 21EX was used for PHITS ver. 2.80. The phantom (30 cm * 30 cm * 30 cm) filled the composition defined by ICRU(International Commission on Radiation Units) was placed at source-surface distance 100 cm. We calculated the neutron energy spectra in the surface of ICRU phantom with “pnimal” setting 1, 10, 100, 1000, 10000 and compared the total calculation time and the behavior of photon using PDD(Percentage Depth Dose) and OCR(Off-Center Ratio). Next, the cutoff energy of photon, electron and positron were investigated for the calculation efficiency with 4, 5, 6 and 7 MeV. Results: The calculation total time until the errors of neutron fluence become within 1% decreased as increasing “pnimul”. PDD and OCR showed no differences by the parameter. The calculation time setting the cutoff energy like 4, 5, 6 and 7 MeV decreased as increasing the cutoff energy. However, the errors of photon become within 1% did not decrease by the cutoff energy. Conclusion: The optimum values of “pnimul” and the cutoff energy were investigated on high-energy photon therapy. It is suggest that using the optimum “pnimul” makes the calculation efficiency. The study of the cutoff energy need more investigation.

60 APPLIED LIFE SCIENCES↗

A backward Monte-Carlo method for time-dependent runaway electron simulations

Kinetic descriptions of runaway electrons (REs) are usually based on Fokker-Planck models that determine the probability distribution function of REs in 2-dimensional momentum space. Despite the simplification involved, the Fokker-Planck equation can rarely be solved analytically and direct numerical approaches [e.g., continuum and particle-based Monte Carlo (MC)] can be time consuming, especially in the computation of asymptotic-type observables including the runaway probability, the slowing-down and runaway mean times, and the energy limit probability. In this study, we present a novel backward MC approach to these problems based on backward stochastic differential equations that describe the dynamics of the runaway probability by means of the Feynman-Kac theory. The key ingredient of the backward MC algorithm is to place all the particles in a runaway state and simulate them backward from the terminal time to the initial time. As such, our approach can provide much faster convergence than direct MC methods (by significantly reducing the number of particles required to achieve a prescribed accuracy) while at the same time maintaining the advantages of particle-based methods (compared to continuum approaches). The proposed algorithm is unconditionally stable and can be parallelized as easy as the direct MC method, and its extension to dimensions higher than two is straightforward, thus paving the way for conducting large-scale RE simulation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Neutral band gap of carbon by quantum Monte Carlo methods

We present a method of calculating the energy gap of a charge-neutral excitation using only ground-state calculations. We report Quantum Monte Carlo calculations of Γ→ Γ and Γ → X particle-hole excitation energies in diamond carbon. We analyze the finite-size effect and find the same 1/L decay rate as that in a charged excitation, where L is the linear extension of the supercell. This slow decay is attributed to the delocalized nature of the excitation in supercells too small to accommodate excitonic binding effects. At larger system sizes, the apparent 1/L decay crosses over to a 1/L 3 behavior. Estimation of the scale of exciton binding can be used to correct finite-size effects of neutral gaps.

36 MATERIALS SCIENCE↗