Application of Monte Carlo calculations for validation of a treatment planning system in high dose rate brachytherapy

AimThe accuracy of treatment planning systems is of vital importance in treatment outcomes in brachytherapy. In the current study the accuracy of dose calculations of a high dose rate (HDR) brachytherapy treatment planning system (TPS) was validated using the Monte Carlo method.Materials and methodsThree ⁶⁰Co sources of the GZP6 afterloading brachytherapy system were modelled using MCNP4C Monte Carlo (MC) code. The dose distribution around all the sources was calculated by MC and a dedicated treatment planning system. The results of both methods were compared.ResultsThere was good agreement (<2%) between TPS and MC calculated dose distributions except at a point near the sources (<1 cm) and beyond the tip of the sources.ConclusionsOur study confirmed the accuracy of TPS calculated dose distributions for clinical use in HDR brachytherapy.     

Biogas upgrading using single-walled carbon nanotubes by molecular simulation

Abstract

Biogas from anaerobic digestion of biological wastes is a renewable energy resource that mainly contains CH₄, CO₂, trace amounts of H₂S and a fraction of H₂O vapour. In order to transfer biogas into biomethane to meet the standards for use as vehicle fuel or for injection in the natural gas grid, removing H₂S from biogas in advance is necessary. In addition, biogas is usually saturated with water vapour. It is significant to study the effect of the presence of H₂O on the biogas separation performance. Adsorption of H₂S/CO₂/CH₄ and H₂O/CO₂/CH₄ ternary mixtures using single-walled carbon nanotubes (SWCNT) were investigated via the Grand Canonical Monte Carlo (GCMC) method. We studied the effects of carbon nanotube diameter, –COOH modification, temperature and pressure on H₂S adsorption. The results indicate that the presence of hydrophilic –COOH groups does affect the separation of H₂S/CO₂/CH₄ mixtures. Temperature swing adsorption is more suitable than pressure swing adsorption for the separation of H₂S/CO₂/CH₄ mixtures. The effect of water vapour on the separation of CO₂/CH₄ was also investigated. The result shows that the presence of H₂O has little effect on the selectivity of CO₂/CH₄ in pristine CNT, but the selectivity of CO₂/CH₄ with the presence of H₂O is markedly enhanced after modification in –COOH modified SWCNT with specific modification degree. It is expected that this work could provide some useful information for biogas upgrading.     

Modeling the adsorption of aromatic compounds on the TiO2/SiO2 catalyst

The Grand Canonical Monte Carlo method was used to analyse the phenomenon of adsorption of aromatic compounds (i.e. phenol, toluene, benzoic acid and salicylic acid) on the surface of the titania-silica (TiO₂/SiO₂) catalyst. We found that different types of interactions play important roles in the adsorption of molecules having polar and non-polar groups. Moreover, we found that the interactions between sorbate molecules are strong, and are the cause of multilayer adsorption occurring in the investigated temperature and pressure range. Presented at: Modeling and Design of Molecular Materials, 10–15 September 2006, Wrocław, Poland.     

Clinical verification of treatment planning dose calculation in lung SBRT with GATE Monte Carlo simulation code

PurposeThis study aims to use GATE/Geant4 simulation code to evaluate the performance of dose calculations with Anisotropic Analytical Algorithm (AAA) in the context of lung SBRT for complex treatments considering images of patients.MethodsFour cases of non-small cell lung cancer treated with SBRT were selected for this study. Irradiation plans were created with AAA and recalculated end to end using Monte Carlo (MC) method maintaining field configurations identical to the original plans. Each treatment plan was evaluated in terms of PTV and organs at risk (OARs) using dose-volume histograms (DVH). Dosimetric parameters obtained from DVHs were used to compare AAA and MC.ResultsThe comparison between the AAA and MC DVH using gamma analysis with the passing criteria of 3%/3% showed an average passing rate of more than 90% for the PTV structure and 97% for the OARs. Tightening the criteria to 2%/2% showed a reduction in the average passing rate of the PTV to 86%. The agreement between the AAA and MC dose calculations for PTV dosimetric parameters (V₁₀₀; V₉₀; Homogeneity index; maximum, minimum and mean dose; CI_Paddick and D_2cm) was within 18.4%. For OARs, the biggest differences were observed in the spinal cord and the great vessels.ConclusionsIn general, we did not find significant differences between AAA and MC. The results indicate that AAA could be used in complex SBRT cases that involve a larger number of small treatment fields in the presence of tissue heterogeneities.     

Molecular insight into the micro-behaviors of CH4 and CO2 in montmorillonite slit-nanopores

Abstract

The Grand Canonical Monte Carlo (GCMC) and molecular dynamics (MD) simulation methods were used to investigate the adsorption and diffusion properties of CH₄ and CO₂ in montmorillonite slit-nanopores. It is found that, both CH₄ and CO₂ could adsorb closely onto the pore surface, while different adsorption states occur for CH₄ and CO₂, respectively, in montmorillonite slit-nanopores. Competitive adsorption of CO₂ over CH₄ exists in montmorillonite slit-nanopores, especially at the lower pressures, which is attributed to the different interaction intensity between the CH₄–CO₂ molecules and the pore surface. The diffusion coefficients of CH₄ and CO₂ both decrease with the enhanced pressures, while the CO₂ has a relative weak diffusion coefficient comparing with CH₄. A well displacement of the residual CH₄ by CO₂ in montmorillonite slit-nanopores was investigated, which is found that the displacement efficiency increases with the enhanced bulk pressures. It was determined that, the CO₂ can be captured and reserved in the montmorillonite slit-nanopores during the displacement, and the sequestration amount of CO₂ gets enhanced with the bulk pressure increasing. This study provides micro-behaviours of CH₄ and CO₂ in montmorillonite slit-nanopores, for the purpose to give out useful guidance for enhancing shale gas extraction by injecting CO₂.     

Hydrophilicity effect on CO2/CH4 separation using carbon nanotube membranes: insights from molecular simulation

Abstract

Molecular simulation methods were applied to study the effect of hydrophilicity on CO₂/CH₄ separation using carbon nanotube (CNT) membranes. CNTs with a diameter of ~1 nm were functionalised by varying amounts of carbonyl groups, in order to achieve various hydrophilicity. The presence of –CO groups inside the CNT allow a significant gain in the diffusion selectivity of CO₂, while in contrast the adsorption selectivity is hardly changed. The corresponding permeation selectivity increases as the hydrophilicity of the CNT-based membrane increases. However, the permeability of CO₂ decreases due to a combination of the intermolecular interactions between the gas and functional groups and the steric effects of the added functional groups. Considering both the permeation selectivity and permeability, it was found that the maximum separation performance is achieved in a certain hydrophilic CNT membrane. Moreover, the separation performance of hydrophilic CNTs for CO₂/CH₄ mixtures breaks the Robeson upper bound.     

Molecular Simulation of Adsorption of Guest Molecules in Zeolitic Materials: A Comparative Study of Intermolecular Potentials

Abstract

Grand Canonical Monte Carlo simulation, together with an appropriate guest-host forcefield is shown to provide reasonably accurate predictions of adsorption properties of guest molecules in a variety of zeolitic materials. The use of a simple guest-host Kiselev-type potential permits the calculations to capture the essence of the behavior of simple guest-host systems such as rare gases or methane molecules in neutral AlPO₄-5. However, a full scale potential is needed in the more complex cases of large anisotropic molecules adsorbed in cationic zeolites (such as xylene isomers in faujasite). The guest-host potential model developed by Nicholson and coworkers is shown to allow an excellent transferability of the potential parameters from one guest/host system to another.     

Grand Canonical Monte Carlo Simulation for Solubility Calculation in Supercritical Extraction

Abstract

The Grand Canonical Ensemble Monte Carlo (GCEMC) technique is used to simulate highly nonideal dilute mixtures in the near vapor-liquid critical region. These systems are commonly found in supercritical fluid extraction processes. Mixtures composed of model CO₂/naphthalene/water molecules are studied. Very large and highly correlated concentration fluctuations were observed. It was found that when the total number of molecules in the system exceeded about 150, system size dependence was not significant. The GCEMC method breaks down when the system density exceeds about 1.5 times the solvent critical density due primarily to the low probability of successful addition and removal of the large naphthalene molecules. In some systems, the presence of a small amount of water caused a dramatic increase in the system density and in naphthalene solubility. By examining the radial distribution functions in these mixtures, the origin of this effect can be attributed to the preferential aggragation of the solute naphthalene molecules around the highly polar water molecules.     

Multiple-source models for electron beams of a medical linear accelerator using BEAMDP computer code

AimThe aim of this work was to develop multiple-source models for electron beams of the NEPTUN 10PC medical linear accelerator using the BEAMDP computer code.BackgroundOne of the most accurate techniques of radiotherapy dose calculation is the Monte Carlo (MC) simulation of radiation transport, which requires detailed information of the beam in the form of a phase-space file. The computing time required to simulate the beam data and obtain phase-space files from a clinical accelerator is significant. Calculation of dose distributions using multiple-source models is an alternative method to phase-space data as direct input to the dose calculation system.Materials and methodsMonte Carlo simulation of accelerator head was done in which a record was kept of the particle phase-space regarding the details of the particle history. Multiple-source models were built from the phase-space files of Monte Carlo simulations. These simplified beam models were used to generate Monte Carlo dose calculations and to compare those calculations with phase-space data for electron beams.ResultsComparison of the measured and calculated dose distributions using the phase-space files and multiple-source models for three electron beam energies showed that the measured and calculated values match well each other throughout the curves.ConclusionIt was found that dose distributions calculated using both the multiple-source models and the phase-space data agree within 1.3%, demonstrating that the models can be used for dosimetry research purposes and dose calculations in radiotherapy.     

An automated Monte Carlo QC system for volumetric modulated arc therapy: Possibilities and challenges

PurposeTo develop and implement an automated Monte Carlo (MC) system for patient specific VMAT quality control in a patient geometry that generates treatment planning system (TPS) compliant DICOM objects and includes a module for 3D analysis of dose deviations. Also, the aims were to recommend diagnose specific tolerance criteria and an evaluation procedure.MethodsThe EGSnrc code package formed the basis for development of the MC system. The workflow consists of a number of modules connected to a TPS by means of manual DICOM exports and imports which were executed sequentially without user interaction. DVH comparison was performed in the TPS. In addition, MC- and TPS dose distributions were analysed by applying the normalized dose difference (NDD) formalism. NDD failure maps and a pass rate for a certain threshold were obtained. 170 clinical plans (prostate, thorax, head-and-neck and gynecological) were selected for analysis.ResultsAgreement within 1.5% was found between clinical- and MC data for the mean dose to the target volumes and within 3% for parameters more sensitive to the shape of the DVH e.g. D_98% PTV. Regarding the NDD analysis, tolerance criteria 2%/3 mm were established for prostate plans and 3%/3 mm for the rest of the cases.ConclusionsAn automated MC system was developed and implemented. Evaluation procedure is recommended with NDD-analysis as a first step. For pass rate < 95%, the evaluation continues with comparison of DVH parameters. For deviations larger than 2%, a visual inspection of the clinical- and MC dose distributions is performed.     

Simulation of separation of C2H6 from CH4 using zeolitic imidazolate frameworks

Separation of important chemical feedstocks, such as C₂H₆ from natural gas, can greatly benefit the petrochemical industry. In this paper, the grand canonical Monte Carlo method has been used to study the adsorption and separation of CH₄ and C₂H₆ in zeolites, isoreticular metal-organic framework-1 (IRMOF-1) and zeolitic imidazolate frameworks (ZIFs) with different topology, including soadlite, gmelinite and RHO topologies. Compared with mordenite zeolite and IRMOF-1, ZIFs and mordenite framework inverted (MFI) zeolite have better separation performance for C₂H₆/CH₄ mixtures at different mole fractions of C₂H₆. From the study of equilibrium snapshots and density distribution profiles, adsorption sites could be grouped as (1) sites with strong interactions with adsorbent and (2) sites with strong interactions with surrounding adsorbates. The gas molecules occupied the first site and then went on to occupy the second site. In CH₄/C₂H₆ mixture adsorption/separation, the adsorption of CH₄ was confined by the existence of C₂H₆. Due to energetic effect, C₂H₆ selectivity was affected by temperature at a low-pressure range, but did not change as much in a high-pressure range because of packing effect in micropore. In binary adsorption, large C₂H₆ molecules favour sites with strong adsorbent interactions. At high pressures, packing effects played an important role and it became easy for small CH₄ molecules to access the sites with strong adsorbate interactions.     

Polypeptide folding with off-lattice Monte Carlo dynamics: the method

The MC dynamics of an off-lattice all-atom protein backbone model with rigid amide planes are studied. The only degrees of freedom are the dihedral angle pairs of the C-atoms. Conformational changes are generated by Monte Carlo (MC) moves. The MC moves considered are single rotations (simple moves, SM's) giving rise to global conformational changes or, alternatively, cooperative rotations in a window of amide planes (window moves, WM's) generating local conformational changes in the window. Outside the window the protein conformation is kept invariant by constraints. These constraints produce a bias in the distribution of dihedral angles. The WM's are corrected for this bias by suitable Jacobians. The energy function used is derived from the CHARMM force field. In a first application to polyalanine it is demonstrated that WM's sample the conformational space more efficiently than SM's.Abbreviations CPU Central Processing Unit - MC Monte Carlo - MCD Monte Carlo Dynamics - MD Molecular Dynamics - RMS Root-Mean-Square - RMSD Root-Mean-Square-Deviation - SM Simple Move - WM Window Move     

Monte Carlo kilovoltage X-ray tube simulation: A statistical analysis and compact simulation method

IntroductionMonte Carlo (MC) simulations are a powerful tool for improving image quality in X-ray based imaging modalities. An accurate X-ray source model is essential to MC modeling for CBCT but can be difficult to implement on a GPU while maintaining efficiency and memory limitations. A statistical analysis of the photon distribution from a MC X-ray tube simulation is conducted in hopes of building a compact source model.Materials & methodsMC simulations of an X-ray tube were carried out using BEAMnrc. The resulting photons were sorted into four categories: primary, scatter, off-focal radiation (OFR), and both (scatter and OFR). A statistical analysis of the photon components (energy, position, direction) was completed. A novel method for a compact (memory efficient) representation of the PHSP data was implemented and tested using different statistical based linear transformations (PCA, ZCA, ICA), as well as a geometrical transformation.ResultsThe statistical analysis showed all photon groupings had strong correlations between position and direction, with the largest correlation in the primary data. The novel method was successful in compactly representing the primary (error < 2%) and scatter (error < 6%) photon groupings by reducing the component correlations.Discussion & conclusionStatistical linear transforms provide a method of reducing the memory required to accurately simulate an X-ray source in a GPU MC system. If all photon types are required, the proposed method reduces the memory requirements by 3.8 times. When only primary and scatter data is needed, the memory requirement is reduced from gigabytes to kilobytes.     

Solvation Force and Confinement-Induced Phase Transitions of Model Ultra Thin Films

Abstract

The static (equilibrium) properties of atomically thin films confined between two surfaces are studied as a function of surface separation by Grand Canonical Monte Carlo and Molecular Dynamics simulations. A model was used, in which the fluid and wall species consist of two different Lennard-Jones rare gas atoms. This was designed to mimic the static SFA experiments in which it is known that epitaxy is not necessary for inducing an oscillatory solvation force in simple non polar liquids. We have been able to simulate, using this simple system, many aspects of the equilibrium properties observed in the experiments. The solvation force is an exponentially damped, periodic curve. All peaks of maximum amplitude in the solvation force correspond to solid-like structures. These structures melt in increasing the surface separation. A further increase in separation leads to the addition of a whole layer and the recrystallisation of the film. In addition this model displays an interesting phenomenon of confinement induced solid-solid phase transition. Two different stable packing (bcc and triclinic) can be observed in the bilayer film and a transition from one to the other occurs when the surface separation is changed. This phase change has been studied as a function of pressure and temperature. As compared to the simulations using a ‘commensurate’ model, in which the fluid and wall species are made of like atoms, the results obtained here are in much better agreement with experimental findings.     

The FLUKA Monte Carlo code coupled with an OER model for biologically weighted dose calculations in proton therapy of hypoxic tumors

IntroductionThe increased radioresistance of hypoxic cells compared to well-oxygenated cells is quantified by the oxygen enhancement ratio (OER). In this study we created a FLUKA Monte Carlo based tool for inclusion of both OER and relative biological effectiveness (RBE) in biologically weighted dose (ROWD) calculations in proton therapy and applied this to explore the impact of hypoxia.MethodsThe RBE-weighted dose was adapted for hypoxia by making RBE model parameters dependent on the OER, in addition to the linear energy transfer (LET). The OER depends on the partial oxygen pressure (pO₂) and LET. To demonstrate model performance, calculations were done with spread-out Bragg peaks (SOBP) in water phantoms with pO₂ ranging from strongly hypoxic to normoxic (0.01–30 mmHg) and with a head and neck cancer proton plan optimized with an RBE of 1.1 and pO₂ estimated voxel-by-voxel using [¹⁸F]-EF5 PET. An RBE of 1.1 and the Rørvik RBE model were used for the ROWD calculations.ResultsThe SOBP in water had decreasing ROWD with decreasing pO₂. In the plans accounting for oxygenation, the median target doses were approximately a factor 1.1 lower than the corresponding plans which did not consider the OER. Hypoxia adapted target ROWDs were considerably more heterogeneous than the RBE_1.1-weighted doses.ConclusionWe realized a Monte Carlo based tool for calculating the ROWD. Read-in of patient pO₂ and estimation of ROWD with flexibility in choice of RBE model was achieved, giving a tool that may be useful in future clinical applications of hypoxia-guided particle therapy.     

Adsorption and diffusion of CO2 and CH4 in covalent organic frameworks: an MC/MD simulation study

Covalent organic frameworks (COFs) are a promising gas separation material which have been developed recently. In this work, we have used grand canonical Monte Carlo (GCMC) and molecular dynamics (MD) simulations to investigate the adsorption and diffusion properties of CO₂ and CH₄ in five recent synthesised COF materials. We have also considered the properties of amino-modified COFs by adding –NH₂ group to the five COFs. The adsorption isotherm, adsorption/diffusion selectivity, self/transport diffusion coefficients have been examined and discussed. All of the five COFs exhibit promising adsorption selectivity which is higher than common nanoporous materials. An S-shaped adsorption isotherm can be found for CO₂ instead of CH₄ adsorption. The introduction of –NH₂ group is effective at low pressure region (<200?kPa). The diffusion coefficients are similar for TS-COFs but increase with the pore size for PI-COFs, and the diffusion coefficients seem less dependent on the –NH₂ groups.     

Gas adsorption and diffusion in a highly CO2 selective metal–organic framework: molecular simulations

Grand canonical Monte Carlo and equilibrium molecular dynamics simulations were used to assess the performance of an rht-type metal–organic framework (MOF), Cu-TDPAT, in adsorption-based and membrane-based separation of CH₄/H₂, CO₂/CH₄ and CO₂/H₂ mixtures. Adsorption isotherms and self-diffusivities of pure gases and binary gas mixtures in Cu-TDPAT were computed using detailed molecular simulations. Several properties of Cu-TDPAT such as adsorption selectivity, working capacity, diffusion selectivity, gas permeability and permeation selectivity were computed and compared with well-known zeolites and MOFs. Results showed that Cu-TDPAT is a very promising adsorbent and membrane material especially for separation of CO₂ and it can outperform traditional zeolites and MOFs such as DDR, MFI, CuBTC, IRMOF-1 in adsorption-based CO₂/CH₄ and CO₂/H₂ separations.     

Molecular simulations of porous coordination network-based mixed matrix membranes for CO2/N2 separations

In this study, the challenge of selecting porous coordination networks (PCNs) as filler particles in mixed matrix membranes (MMMs) was examined using molecular simulations. PCNs are promising nanoporous materials in gas separations because of their tunable pore sizes, high porosities, good thermal and mechanical stabilities. Gas permeability and selectivity of 200 new MMMs composed of 20 different PCNs and 10 different polymers were calculated for CO₂/N₂ separation. We showed that selecting the appropriate PCN as filler particles in polymers results in MMMs that have high CO₂/N₂ selectivities and high CO₂ permeabilities compared with pure polymer membranes. Several PCN/polymer MMMs were identified to exceed the upper bound established for CO₂/N₂ separation. Effect of framework flexibility of PCNs on the performance of MMMs was also examined. Results showed that considering the flexibility of PCNs is important for predicting gas permeability of pure PCNs but has less significance for predicting gas permeability of PCN-filled MMMs whenever the PCN volume fraction is low. For rapid screening of PCN/polymer MMMs, flexibility of the fillers can be neglected as a reasonable approximation if the filler volume fraction is < 0.3. The methods introduced in this study will create many opportunities for selecting PCN/polymer combinations for MMMs with useful properties in CO₂ separation applications.     

Application of kinetic Monte Carlo method to the vapour–liquid equilibria of associating fluids and their mixtures

Canonical kinetic Monte Carlo (C-kMC) simulations have been carried out to assess their feasibility and potential for calculating the vapour–liquid equilibria of various pure components with increasingly strong electrostatic interactions (carbon dioxide, methanol, ammonia and water) over a wide range of temperatures and for methanol/water mixtures at 298 K. The simulation results show that C-kMC is successful as a method for studying phase equilibria and thermodynamic properties. For all the examples investigated, the performance of the C-kMC method is at least as good as that of the conventional Monte Carlo (MC) methods and is efficient at low temperature where these fail. It also provides a route that is superior to the Widom method for the calculation of chemical potential. We recommend this method for this purpose and as an alternative to conventional MC for simulations of strongly associating fluids and at low temperatures.     

Simulation Study of Sorption of CO2 and N2 with Application to the Characterization of Carbon Adsorbents

Abstract

The Monte Carlo method was used in its grand ensemble variant (GCMC) in combination with CO₂ and N₂ experimental isotherm data at low (77 and 195.5 K) and ambient temperatures (298 and 308 K), in order to characterize microporous carbons and obtain the corresponding pore size distribution (PSD). In particular, the CO₂ and N₂ densities and the isosteric heats of adsorption inside single, slit shaped, graphitic pores of given width were found on the basis of GCMC for pre-defined temperatures and different relative pressures. In a further step, we determined the optimal PSD for which the best match is obtained between computed and measured isotherms. Comparisons were made between the PSDs found for the same carbon sample at low and ambient temperatures for different gases, and conclusions concerning the applicability of the method and the reliability of the resulting micropore size distributions were drawn.