Monte Carlo simulation of a dynamic MLC based on a multiple source model

Detailed knowledge of the characteristics of the radiation field shaped by a multileaf collimator (MLC) is essential in intensity modulated radiotherapy (IMRT). A previously developed multiple source model (MSM) for a 6 MV beam was extended to a 15 MV beam and supplemented with an accurate model of an 80-leaf dynamic MLC. Using the supplemented MSM and the MC code GEANT, lateral dose distributions were calculated in a water phantom and a portal water phantom. A field which is normally used for the validation of the step and shoot technique and a field from a realistic IMRT treatment plan delivered with dynamic MLC are investigated. To assess possible spectral changes caused by the modulation of beam intensity by an MLC, the energy spectra in five portal planes were calculated for moving slits of different widths. The extension of the MSM to 15 MV was validated by analysing energy fluences, depth doses and dose profiles. In addition, the MC-calculated primary energy spectrum was verified with an energy spectrum which was reconstructed from transmission measurements. MC-calculated dose profiles using the MSM for the step and shoot case and for the dynamic MLC case are in very good agreement with the measured data from film dosimetry. The investigation of a 13 cm wide field shows an increase in mean photon energy of up to 16% for the 0.25 cm slit compared to the open beam for 6 MV and of up to 6% for 15 MV, respectively. In conclusion, the MSM supplemented with the dynamic MLC has proven to be a powerful tool for investigational and benchmarking purposes or even for dose calculations in IMRT.

Monte Carlo simulation of a dynamic MLC: implementation and applications

PURPOSE: Study of behavior and influence of a multileaf collimator (MLC) on dose calculation, verification, and portal energy spectra in the case of intensity-modulated fields obtained with a step-and-shoot or a dynamic technique. METHODS: The 80-leaf MLC for the Varian Clinac 2300 C/D was implemented in a previously developed Monte Carlo (MC) based multiple source model (MSM) for a 6 MV photon beam. Using this model and the MC program GEANT, dose distributions, energy fluence maps and energy spectra at different portal planes were calculated for three different MLC applications. RESULTS: The comparison of MC-calculated dose distributions in the phantom and portal plane, with those measured with films showed an agreement within 3% and 1.5 mm for all cases studied. The deviations mainly occur in the extremes of the intensity modulation. The MC method allows to investigate, among other aspects, dose components, energy fluence maps, tongue-and-groove effects and energy spectra at portal planes. CONCLUSION: The MSM together with the implementation of the MLC is appropriate for a number of investigations in intensity-modulated radiation therapy (IMRT).

Monte-Carlo simulation of Callisto's exosphere

We model Callisto's exosphere based on its ice as well as non-ice surface via the use of a Monte-Carlo exosphere model. For the ice component we implement two putative compositions that have been computed from two possible extreme formation scenarios of the satellite. One composition represents the oxidizing state and is based on the assumption that the building blocks of Callisto were formed in the protosolar nebula and the other represents the reducing state of the gas, based on the assumption that the satellite accreted from solids condensed in the jovian sub-nebula. For the non-ice component we implemented the compositions of typical CI as well as L type chondrites. Both chondrite types have been suggested to represent Callisto's non-ice composition best. As release processes we consider surface sublimation, ion sputtering and photon-stimulated desorption. Particles are followed on their individual trajectories until they either escape Callisto's gravitational attraction, return to the surface, are ionized, or are fragmented. Our density profiles show that whereas the sublimated species dominate close to the surface on the sun-lit side, their density profiles (with the exception of H and H-2) decrease much more rapidly than the sputtered particles. The Neutral gas and Ion Mass (NIM) spectrometer, which is part of the Particle Environment Package (PEP), will investigate Callisto's exosphere during the JUICE mission. Our simulations show that NIM will be able to detect sublimated and sputtered particles from both the ice and non-ice surface. NIM's measured chemical composition will allow us to distinguish between different formation scenarios. (C) 2015 Elsevier Inc. All rights reserved.

More than just Good Luck. How to Explain the Success of Monte Carlo Simulations

Monte Carlo simulation is a powerful method in many natural and social sciences. But what sort of method is it? And where does its power come from? Are Monte Carlo simulations experiments, theories or something else? The aim of this talk is to answer these questions and to explain the power of Monte Carlo simulations. I provide a classification of Monte Carlo techniques and defend the claim that Monte Carlo simulation is a sort of inference.

A ~ 32-70 K formation temperature range for the ice grains agglomerated by Comet 67P/Churyumov-Gerasimenko

Grand Canonical Monte Carlo simulations are used to reproduce the N₂/CO ratio ranging between 1.7 x 10⁻³ and 1.6 x 10⁻² observed in situ in the Jupiter-family comet 67 P/Churyumov-Gerasimenko (67 P) by the ROSINA mass spectrometer on board the Rosetta spacecraft. By assuming that this body has been agglomerated from clathrates in the protosolar nebula (PSN), simulations are developed using elaborated interatomic potentials for investigating the temperature dependence of the trapping within a multiple-guest clathrate formed from a gas mixture of CO and N₂ in proportions corresponding to those expected for the PSN. By assuming that 67 P agglomerated from clathrates, our calculations suggest the cometary grains must have been formed at temperatures ranging between ~ 31.8 and 69.9 K in the PSN to match the N₂/CO ratio measured by the ROSINA mass spectrometer. The presence of clathrates in Jupiter-family comets could then explain the potential N₂ depletion (factor of up to ~ 87 compared to the protosolar value) measured in 67 P/Churyumov-Gerasimenko.

Combining Monte Carlo methods with coherent wave optics for the simulation of phase-sensitive X-ray imaging

Phase-sensitive X-ray imaging shows a high sensitivity towards electron density variations, making it well suited for imaging of soft tissue matter. However, there are still open questions about the details of the image formation process. Here, a framework for numerical simulations of phase-sensitive X-ray imaging is presented, which takes both particle- and wave-like properties of X-rays into consideration. A split approach is presented where we combine a Monte Carlo method (MC) based sample part with a wave optics simulation based propagation part, leading to a framework that takes both particle- and wave-like properties into account. The framework can be adapted to different phase-sensitive imaging methods and has been validated through comparisons with experiments for grating interferometry and propagation-based imaging. The validation of the framework shows that the combination of wave optics and MC has been successfully implemented and yields good agreement between measurements and simulations. This demonstrates that the physical processes relevant for developing a deeper understanding of scattering in the context of phase-sensitive imaging are modelled in a sufficiently accurate manner. The framework can be used for the simulation of phase-sensitive X-ray imaging, for instance for the simulation of grating interferometry or propagation-based imaging.

3D Direct Simulation Monte Carlo Modelling of the Inner Gas Coma of Comet 67P/Churyumov-Gerasimenko: A Parameter Study

Direct Simulation Monte Carlo (DSMC) is a powerful numerical method to study rarefied gas flows such as cometary comae and has been used by several authors over the past decade to study cometary outflow. However, the investigation of the parameter space in simulations can be time consuming since 3D DSMC is computationally highly intensive. For the target of ESA's Rosetta mission, comet 67P/Churyumov-Gerasimenko, we have identified to what extent modification of several parameters influence the 3D flow and gas temperature fields and have attempted to establish the reliability of inferences about the initial conditions from in situ and remote sensing measurements. A large number of DSMC runs have been completed with varying input parameters. In this work, we present the simulation results and conclude on the sensitivity of solutions to certain inputs. It is found that among cases of water outgassing, the surface production rate distribution is the most influential variable to the flow field.

Macro Monte Carlo for dose calculation of proton beams

Although the Monte Carlo (MC) method allows accurate dose calculation for proton radiotherapy, its usage is limited due to long computing time. In order to gain efficiency, a new macro MC (MMC) technique for proton dose calculations has been developed. The basic principle of the MMC transport is a local to global MC approach. The local simulations using GEANT4 consist of mono-energetic proton pencil beams impinging perpendicularly on slabs of different thicknesses and different materials (water, air, lung, adipose, muscle, spongiosa, cortical bone). During the local simulation multiple scattering, ionization as well as elastic and inelastic interactions have been taken into account and the physical characteristics such as lateral displacement, direction distributions and energy loss have been scored for primary and secondary particles. The scored data from appropriate slabs is then used for the stepwise transport of the protons in the MMC simulation while calculating the energy loss along the path between entrance and exit position. Additionally, based on local simulations the radiation transport of neutrons and the generated ions are included into the MMC simulations for the dose calculations. In order to validate the MMC transport, calculated dose distributions using the MMC transport and GEANT4 have been compared for different mono-energetic proton pencil beams impinging on different phantoms including homogeneous and inhomogeneous situations as well as on a patient CT scan. The agreement of calculated integral depth dose curves is better than 1% or 1 mm for all pencil beams and phantoms considered. For the dose profiles the agreement is within 1% or 1 mm in all phantoms for all energies and depths. The comparison of the dose distribution calculated using either GEANT4 or MMC in the patient also shows an agreement of within 1% or 1 mm. The efficiency of MMC is up to 200 times higher than for GEANT4. The very good level of agreement in the dose comparisons demonstrate that the newly developed MMC transport results in very accurate and efficient dose calculations for proton beams.

An efficient framework for photon Monte Carlo treatment planning

Currently photon Monte Carlo treatment planning (MCTP) for a patient stored in the patient database of a treatment planning system (TPS) can usually only be performed using a cumbersome multi-step procedure where many user interactions are needed. This means automation is needed for usage in clinical routine. In addition, because of the long computing time in MCTP, optimization of the MC calculations is essential. For these purposes a new graphical user interface (GUI)-based photon MC environment has been developed resulting in a very flexible framework. By this means appropriate MC transport methods are assigned to different geometric regions by still benefiting from the features included in the TPS. In order to provide a flexible MC environment, the MC particle transport has been divided into different parts: the source, beam modifiers and the patient. The source part includes the phase-space source, source models and full MC transport through the treatment head. The beam modifier part consists of one module for each beam modifier. To simulate the radiation transport through each individual beam modifier, one out of three full MC transport codes can be selected independently. Additionally, for each beam modifier a simple or an exact geometry can be chosen. Thereby, different complexity levels of radiation transport are applied during the simulation. For the patient dose calculation, two different MC codes are available. A special plug-in in Eclipse providing all necessary information by means of Dicom streams was used to start the developed MC GUI. The implementation of this framework separates the MC transport from the geometry and the modules pass the particles in memory; hence, no files are used as the interface. The implementation is realized for 6 and 15 MV beams of a Varian Clinac 2300 C/D. Several applications demonstrate the usefulness of the framework. Apart from applications dealing with the beam modifiers, two patient cases are shown. Thereby, comparisons are performed between MC calculated dose distributions and those calculated by a pencil beam or the AAA algorithm. Interfacing this flexible and efficient MC environment with Eclipse allows a widespread use for all kinds of investigations from timing and benchmarking studies to clinical patient studies. Additionally, it is possible to add modules keeping the system highly flexible and efficient.

Saddlepoint approximations to sensitivities of tail probabilities of random sums and comparisons with Monte Carlo estimators

This article proposes computing sensitivities of upper tail probabilities of random sums by the saddlepoint approximation. The considered sensitivity is the derivative of the upper tail probability with respect to the parameter of the summation index distribution. Random sums with Poisson or Geometric distributed summation indices and Gamma or Weibull distributed summands are considered. The score method with importance sampling is considered as an alternative approximation. Numerical studies show that the saddlepoint approximation and the method of score with importance sampling are very accurate. But the saddlepoint approximation is substantially faster than the score method with importance sampling. Thus, the suggested saddlepoint approximation can be conveniently used in various scientific problems.

Monte Carlo modeling of polarized light propagation: Stokes vs Jones - Part II

In this second part of our comparative study inspecting the (dis)similarities between “Stokes” and “Jones,” we present simulation results yielded by two independent Monte Carlo programs: (i) one developed in Bern with the Jones formalism and (ii) the other implemented in Ulm with the Stokes notation. The simulated polarimetric experiments involve suspensions of polystyrene spheres with varying size. Reflection and refraction at the sample/air interfaces are also considered. Both programs yield identical results when propagating pure polarization states, yet, with unpolarized illumination, second order statistical differences appear, thereby highlighting the pre-averaged nature of the Stokes parameters. This study serves as a validation for both programs and clarifies the misleading belief according to which “Jones cannot treat depolarizing effects.”

Monte Carlo dose calculation improvements for low energy electron beams using eMC

The electron Monte Carlo (eMC) dose calculation algorithm in Eclipse (Varian Medical Systems) is based on the macro MC method and is able to predict dose distributions for high energy electron beams with high accuracy. However, there are limitations for low energy electron beams. This work aims to improve the accuracy of the dose calculation using eMC for 4 and 6 MeV electron beams of Varian linear accelerators. Improvements implemented into the eMC include (1) improved determination of the initial electron energy spectrum by increased resolution of mono-energetic depth dose curves used during beam configuration; (2) inclusion of all the scrapers of the applicator in the beam model; (3) reduction of the maximum size of the sphere to be selected within the macro MC transport when the energy of the incident electron is below certain thresholds. The impact of these changes in eMC is investigated by comparing calculated dose distributions for 4 and 6 MeV electron beams at source to surface distance (SSD) of 100 and 110 cm with applicators ranging from 6 x 6 to 25 x 25 cm(2) of a Varian Clinac 2300C/D with the corresponding measurements. Dose differences between calculated and measured absolute depth dose curves are reduced from 6% to less than 1.5% for both energies and all applicators considered at SSD of 100 cm. Using the original eMC implementation, absolute dose profiles at depths of 1 cm, d(max) and R50 in water lead to dose differences of up to 8% for applicators larger than 15 x 15 cm(2) at SSD 100 cm. Those differences are now reduced to less than 2% for all dose profiles investigated when the improved version of eMC is used. At SSD of 110 cm the dose difference for the original eMC version is even more pronounced and can be larger than 10%. Those differences are reduced to within 2% or 2 mm with the improved version of eMC. In this work several enhancements were made in the eMC algorithm leading to significant improvements in the accuracy of the dose calculation for 4 and 6 MeV electron beams of Varian linear accelerators.

Comparison of monte carlo collimator transport methods for photon treatment planning in radiotherapy

The aim of this work was a Monte Carlo (MC) based investigation of the impact of different radiation transport methods in collimators of a linear accelerator on photon beam characteristics, dose distributions, and efficiency. Thereby it is investigated if it is possible to use different simplifications in the radiation transport for some clinical situations in order to save calculation time.

Monte Carlo Dose Calculation on Deforming Anatomy

This article presents the implementation and validation of a dose calculation approach for deforming anatomical objects. Deformation is represented by deformation vector fields leading to deformed voxel grids representing the different deformation scenarios. Particle transport in the resulting deformed voxels is handled through the approximation of voxel surfaces by triangles in the geometry implementation of the Swiss Monte Carlo Plan framework. The focus lies on the validation methodology which uses computational phantoms representing the same physical object through regular and irregular voxel grids. These phantoms are chosen such that the new implementation for a deformed voxel grid can be compared directly with an established dose calculation algorithm for regular grids. Furthermore, separate validation of the aspects voxel geometry and the density changes resulting from deformation is achieved through suitable design of the validation phantom. We show that equivalent results are obtained with the proposed method and that no statistically significant errors are introduced through the implementation for irregular voxel geometries. This enables the use of the presented and validated implementation for further investigations of dose calculation on deforming anatomy.