Determination of initial electron parameters by means of Monte Carlo simulations for the Siemens Artiste Linac 6 MV photon beam

AimIn this study, we investigated initial electron parameters of Siemens Artiste Linac with 6 MV photon beam using the Monte Carlo method.BackgroundIt is essential to define all the characteristics of initial electrons hitting the target, i.e. mean energy and full width of half maximum (FWHM) of the spatial distribution intensity, which is needed to run Monte Carlo simulations. The Monte Carlo is the most accurate method for simulation of radiotherapy treatments.Materials and methodsLinac head geometry was modeled using the BEAMnrc code. The phase space files were used as input file to DOSXYZnrc simulation to determine the dose distribution in a water phantom. We obtained percent depth dose curves and the lateral dose profile. All the results were obtained at 100 cm of SSD and for a 10 × 10 cm² field.ResultsWe concluded that there existed a good conformity between Monte Carlo simulation and measurement data when we used electron mean energy of 6.3 MeV and 0.30 cm FWHM value as initial parameters. We observed that FWHM values had very little effect on PDD and we found that the electron mean energy and FWHM values affected the lateral dose profile. However, these effects are between tolerance values.ConclusionsThe initial parameters especially depend on components of a linac head. The phase space file which was obtained from Monte Carlo Simulation for a linac can be used as calculation of scattering, MLC leakage, to compare dose distribution on patients and in various studies.     

Test of the Inverse Monte Carlo Method for the Calculation of Interatomic Potential Energies in Atomic Liquids

Abstract

The principle purpose of this paper is to demonstrate the use of the Inverse Monte Carlo technique for calculating pair interaction energies in monoatomic liquids from a given equilibrium property. This method is based on the mathematical relation between transition probability and pair potential given by the fundamental equation of the “importance sampling” Monte Carlo method. In order to have well defined conditions for the test of the Inverse Monte Carlo method a Metropolis Monte Carlo simulation of a Lennard Jones liquid is carried out to give the equilibrium pair correlation function determined by the assumed potential. Because an equilibrium configuration is prerequisite for an Inverse Monte Carlo simulation a model system is generated reproducing the pair correlation function, which has been calculated by the Metropolis Monte Carlo simulation and therefore representing the system in thermal equilibrium. This configuration is used to simulate virtual atom displacements. The resulting changes in atom distribution for each single simulation step are inserted in a set of non-linear equations defining the transition probability for the virtual change of configuration. The solution of the set of equations for pair interaction energies yields the Lennard Jones potential by which the equilibrium configuration has been determined.     

Experimental and theoretical study of the near IR emission of xenon excited by a fast electron beam

Emission of xenon excited by a 120-keV electron beam at gas pressures of 100, 200, 500, and 760 Torr nm was studied experimentally and theoretically. More than 30 spectral lines were identified in the wavelength range of 750–1000 nm. A self-consistent kinetic model is developed to calculate the emission intensity of xenon atoms in the near IR range. The model includes balance equations for the number densities of electrons, ions and excimer molecules; equations for the populations of electron levels; and the Boltzmann equation for the low-energy part of the electron energy distribution function with a source of slow electrons. Excitation and ionization rates of xenon by the beam electrons and the energy spectrum of slow electrons are calculated by the Monte Carlo method. It is shown that, under these conditions, the main mechanism of xenon atom excitation is dissociative recombination of Xe₃ ⁺ ions.     

Diffusion of low-energy electrons in tissue-like liquids.

The spatial-energetic distribution of low-energy electrons was studied for a source located in a liquid medium simulating biological tissue. A time-independent Boltzmann equation was used to model this distribution microscopically. Ionization was treated as a perturbation to a quasi-elastic collision process between the electron and the medium. A diffusion limit was obtained by using a scale parameter, leading to a sequence of recursive partial differential equations whose solutions, associated with a macroscopic scale, were obtained by numerical approximations. As an application, electron ranges were estimated based on these solutions and then compared with values reported in the open literature based on experimental results and on Monte Carlo calculation. Local dosimetry, i.e., the energy imparted to a volume of a sphere with radius equal to the range of low-energy electrons, of low-energy electrons from internal emitters can benefit by the knowledge of the ranges estimated for biological tissue. Auger electron emitters, for example, have been the object of a number of investigations because of their radiobiological significance.     

Fundamental parameters of a relativistic runaway electron avalanche in air

A relativistic runaway electron avalanche in air is simulated numerically by the Monte Carlo method with allowance for a large number of elementary processes involving electrons, positrons, and photons. The characteristic time scale of the avalanche amplification is calculated as a function of the overvoltage δ relative to the minimum value of the drag force between the electrons and the atomic particles of the medium. The dynamics of the formation of the electron energy distribution is investigated. The steady-state mean electron energy depends weakly on δ. Over a wide range of δ values, there exists a universal electron energy distribution, which is essentially independent of δ. The angular distributions of electrons integrated over energies, as well as the angular distributions for different energy groups, are calculated. Analytic approximations for the energy and angular distributions are obtained.     

Radial secondary electron dose profiles and biological effects in light-ion beams based on analytical and Monte Carlo calculations using distorted wave cross sections

To speed up dose calculation, an analytical pencil-beam method has been developed to calculate the mean radial dose distributions due to secondary electrons that are set in motion by light ions in water. For comparison, radial dose profiles calculated using a Monte Carlo technique have also been determined. An accurate comparison of the resulting radial dose profiles of the Bragg peak for (1)H(+), (4)He(2+) and (6)Li(3+) ions has been performed. The double differential cross sections for secondary electron production were calculated using the continuous distorted wave-eikonal initial state method (CDW-EIS). For the secondary electrons that are generated, the radial dose distribution for the analytical case is based on the generalized Gaussian pencil-beam method and the central axis depth-dose distributions are calculated using the Monte Carlo code PENELOPE. In the Monte Carlo case, the PENELOPE code was used to calculate the whole radial dose profile based on CDW data. The present pencil-beam and Monte Carlo calculations agree well at all radii. A radial dose profile that is shallower at small radii and steeper at large radii than the conventional 1/r(2) is clearly seen with both the Monte Carlo and pencil-beam methods. As expected, since the projectile velocities are the same, the dose profiles of Bragg-peak ions of 0.5 MeV (1)H(+), 2 MeV (4)He(2+) and 3 MeV (6)Li(3+) are almost the same, with about 30% more delta electrons in the sub keV range from (4)He(2+)and (6)Li(3+) compared to (1)H(+). A similar behavior is also seen for 1 MeV (1)H(+), 4 MeV (4)He(2+) and 6 MeV (6)Li(3+), all classically expected to have the same secondary electron cross sections. The results are promising and indicate a fast and accurate way of calculating the mean radial dose profile.     

Clinical implementation of a Monte Carlo based treatment plan QA platform for validation of Cyberknife and Tomotherapy treatments

PurposeThe main focus of the current paper is the clinical implementation of a Monte Carlo based platform for treatment plan validation for Tomotherapy and Cyberknife, without adding additional tasks to the dosimetry department.MethodsThe Monte Carlo platform consists of C++ classes for the actual functionality and a web based GUI that allows accessing the system using a web browser. Calculations are based on BEAMnrc/DOSXYZnrc and/or GATE and are performed automatically after exporting the dicom data from the treatment planning system. For Cyberknife treatments of moving targets, the log files saved during the treatment (position of robot, internal fiducials and external markers) can be used in combination with the 4D planning CT to reconstruct the actually delivered dose. The Monte Carlo platform is also used for calculation on MRI images, using pseudo-CT conversion.ResultsFor Tomotherapy treatments we obtain an excellent agreement (within 2%) for almost all cases. However, we have been able to detect a problem regarding the CT Hounsfield units definition of the Toshiba Large Bore CT when using a large reconstruction diameter. For Cyberknife treatments we obtain an excellent agreement with the Monte Carlo algorithm of the treatment planning system. For some extreme cases, when treating small lung lesions in low density lung tissue, small differences are obtained due to the different cut-off energy of the secondary electrons.ConclusionsA Monte Carlo based treatment plan validation tool has successfully been implemented in clinical routine and is used to systematically validate all Cyberknife and Tomotherapy plans.     

Lower confidence bounds for prediction accuracy in high dimensions via AROHIL Monte Carlo

MOTIVATION: Implementation and development of statistical methods for high-dimensional data often require high-dimensional Monte Carlo simulations. Simulations are used to assess performance, evaluate robustness, and in some cases for implementation of algorithms. But simulation in high dimensions is often very complex, cumbersome and slow. As a result, performance evaluations are often limited, robustness minimally investigated and dissemination impeded by implementation challenges. This article presents a method for converting complex, slow high-dimensional Monte Carlo simulations into simpler, faster lower dimensional simulations. RESULTS: We implement the method by converting a previous Monte Carlo algorithm into this novel Monte Carlo, which we call AROHIL Monte Carlo. AROHIL Monte Carlo is shown to exactly or closely match pure Monte Carlo results in a number of examples. It is shown that computing time can be reduced by several orders of magnitude. The confidence bound method implemented using AROHIL outperforms the pure Monte Carlo method. Finally, the utility of the method is shown by application to a number of real microarray datasets.     

A Partition Function Approximation Using Elementary Symmetric Functions

In statistical mechanics, the canonical partition function can be used to compute equilibrium properties of a physical system. Calculating however, is in general computationally intractable, since the computation scales exponentially with the number of particles in the system. A commonly used method for approximating equilibrium properties, is the Monte Carlo (MC) method. For some problems the MC method converges slowly, requiring a very large number of MC steps. For such problems the computational cost of the Monte Carlo method can be prohibitive. Presented here is a deterministic algorithm – the direct interaction algorithm (DIA) – for approximating the canonical partition function in operations. The DIA approximates the partition function as a combinatorial sum of products known as elementary symmetric functions (ESFs), which can be computed in operations. The DIA was used to compute equilibrium properties for the isotropic 2D Ising model, and the accuracy of the DIA was compared to that of the basic Metropolis Monte Carlo method. Our results show that the DIA may be a practical alternative for some problems where the Monte Carlo method converge slowly, and computational speed is a critical constraint, such as for very large systems or web-based applications.     

Determination of order parameters and correlation times in proteins: A comparison between Bayesian, Monte Carlo and simple graphical methods

We describe a novel approach to deducing order parameters and correlation times in proteins using a Bayesian statistical method, and show how likelihood contours, P(,S), and confidence levels can be obtained. These results are then compared with those obtained from a simple graphical method, as well as those from Monte Carlo simulations. The Bayes approach has the advantage that it is simple and accurate. Unlike Monte Carlo methods, it gives useful contour plots of probability (also not provided by the simple graphical method), and provides likelihood/confidence information. In addition, the Bayesian approach gives results in very good agreement with those obtained from Monte Carlo simulations, and as such use of Bayesian statistical methods appears to have a promising future for studies of order and dynamics in macromolecules.     

Microdosimetry of electron microbeams

Track structures of 25, 50 and 80 keV primary electrons, simulated by the detailed-history Monte Carlo method, were analyzed for the frequency distributions of energy deposited in spheres with a diameter of 1 microm, placed in a cylindrically symmetrical array around the projected initial direction of the primary electron. The frequency mean of specific energy, the dose mean of lineal energy, and the parameters of lognormal functions fit to the dose distributions were calculated as a function of beam penetration and radial distance from the projected beam axis. Given these data, the stochastics of dose and radiation quality for micrometer-scale sites targeted by a medium-energy electron microbeam can be predicted as a function of the site's location relative to the beam entry point.     

反卷积在生物组织光传输特性研究中的应用

生物组织中的光传输特性可以以点扩散函数表征,即在线状光束入射条件下,生物组织中某一深度层面上的光强度场分布。为获得点扩散函数的具体形式,已发展了多种理论分析方法,其中以Monte Carlo模拟方法最具代表性。但现有理论计算方法都要以生物组织的光学参数已知为前提,而光学参数的准确度直接影响着计算的精度。从线性平移不变系统理论出发,生物组织内一定深度层面上的光强分布被看成是光源强度分布与点扩散函数的卷积,从而提出通过测量在轴对称的准直扩展光源照射条件下,组织中特定层面上的光强度分布,利用反卷积重建生物组织的点扩散函数的方法,并将这种方法应用于典型生物组织透射面上点扩散函数的重建,得到了相应的点扩散函数。实验结果与Monte Carlo模拟的结果吻合较好,表明该方法从实验上获得生物组织点扩散函数的正确性和有效性。     

Modeling of Coulomb collisions in a kinetic description of the electron cyclotron resonance plasma heating

The electron distribution function is modeled numerically with allowance for Coulomb collisions and quasilinear effects under cyclotron resonance conditions by solving a two-dimensional kinetic equation containing the quasilinear diffusion operator and the Coulomb collision operator in the Landau form. Two simplified model collision integrals that make it possible to describe electron heating by microwave radiation are considered. The first model collision operator is obtained by introducing the parametric time dependence of the temperature of the background Maxwellian electrons into the linear collision integral. It is shown that the heating of the bulk electrons can be described in a noncontradictory way if the temperature dynamics of the background electrons is calculated from the equation of energy balance, which is governed by the amount of the microwave power absorbed by the resonant electrons with the distribution function modified due to quasilinear effects. This conclusion is confirmed in a more rigorous fashion by comparing the solutions obtained using the first model Coulomb collision integral with those obtained using the second model integral, namely, the nonlinear operator derived by averaging the distribution function of the scattering electrons over pitch angles. The time-dependent linear collision integral is used to obtain analytic solutions describing quasi-steady electron heating with allowance for the quasilinear degradation of microwave power absorption.     

Monte Carlo simulation of the spatial distribution of energy deposition for an electron microbeam

Dosimetry calculations characterizing the spatial variation of the energy deposited by the slowing and stopping of energetic electrons are reported and compared with experimental measurements from an electron microbeam facility. The computations involve event-by-event, detailed-histories Monte Carlo simulations of low-energy electrons interacting in water vapor. Simulations of electron tracks with starting energies from 30 to 80 keV are used to determine energy deposition distributions in thin cylindrical rings as a function of penetration and radial distance from a beam source. Experimental measurements of the spatial distribution of an electron microbeam in air show general agreement with the density-scaled simulation results for water vapor at these energies, yielding increased confidence in the predictions of Monte Carlo track-structure simulations for applications of the microbeam as a single-cell irradiator.     

Extinction risk of a density-dependent population estimated from a time series of population size

Environmental threats, such as habitat size reduction or environmental pollution, may not cause immediate extinction of a population but shorten the expected time to extinction. We develop a method to estimate the mean time to extinction for a density-dependent population with environmental fluctuation. We first derive a formula for a stochastic differential equation model (canonical model) of a population with logistic growth with environmental and demographic stochasticities. We then study an approximate maximum likelihood (AML) estimate of three parameters (intrinsic growth rate r, carrying capacity K, and environmental stochasticity sigma(2)(e)) from a time series of population size. The AML estimate of r has a significant bias, but by adopting the Monte Carlo method, we can remove the bias very effectively (bias-corrected estimate). We can also determine the confidence interval of the parameter based on the Monte Carlo method. If the length of the time series is moderately long (with 40-50 data points), parameter estimation with the Monte Carlo sampling bias correction has a relatively small variance. However, if the time series is short (less than or equal to 10 data points), the estimate has a large variance and is not reliable. If we know the intrinsic growth rate r, however, the estimate of K and sigma(2)(e)and the mean extinction time T are reliable even if only a short time series is available. We illustrate the method using data for a freshwater fish, Japanese crucian carp (Carassius auratus subsp.) in Lake Biwa, in which the growth rate and environmental noise of crucian carp are estimated using fishery records.     

Electron and photon spectra for three gadolinium-based cancer therapy approaches

Some recent neutron capture therapy research has focused on using compounds containing the element gadolinium, which produces internal conversion and Auger cascade electrons. The low-energy, short-range Auger electrons are absorbed locally and increase cell killing dramatically as the gadolinium compounds are introduced into the cell nucleus and bind to the DNA. Detailed electron and photon spectra are needed for biophysical modeling and Monte Carlo calculations of damage to DNA. This paper presents calculated electron and photon spectra for three cases: thermal neutron absorption by (157)Gd, the beta-particle decay of (159)Gd, and the K-shell photoelectric event in gadolinium. The Monte Carlo sampling of atomic and nuclear transitions for each of the three cases was used to calculate a large number of representative decays. The sampled decays were used to determine average emissions and energy deposited in small spheres of tissue. The kinetic energy nuclear recoil from gamma-ray and electron emissions was calculated and found to be more than 10 eV for 26% of all (157)Gd neutron capture reactions.     

Gibbs Ensemble Calculations with an Equation of State: An Application to Vapor-Liquid Equilibria

Abstract

A new modification of the Gibbs ensemble Monte Carlo computer simulation method for fluid phase equilibria is described. The modification is based on a thermodynamic model for the vapor phase, and uses an equation of state to account for the weak interactions between the vapor phase molecules. Reductions in the computational time by 30–40% as compared to the original Gibbs ensemble method are obtained. The algorithm is applied to Lennard-Jones - (12,6) fluids and their mixtures and the results are in good agreement with results obtained from simulations using the full Gibbs ensemble method.     

Model for radial dependence of frequency distributions for energy imparted in nanometer volumes from HZE particles

This paper develops a deterministic model of frequency distributions for energy imparted (total energy deposition) in small volumes similar to DNA molecules from high-energy ions of interest for space radiation protection and cancer therapy. Frequency distributions for energy imparted are useful for considering radiation quality and for modeling biological damage produced by ionizing radiation. For high-energy ions, secondary electron (delta-ray) tracks originating from a primary ion track make dominant contributions to energy deposition events in small volumes. Our method uses the distribution of electrons produced about an ion's path and incorporates results from Monte Carlo simulation of electron tracks to predict frequency distributions for ions, including their dependence on radial distance. The contribution from primary ion events is treated using an impact parameter formalism of spatially restricted linear energy transfer (LET) and energy-transfer straggling. We validate our model by comparing it directly to results from Monte Carlo simulations for proton and alpha-particle tracks. We show for the first time frequency distributions of energy imparted in DNA structures by several high-energy ions such as cosmic-ray iron ions. Our comparison with results from Monte Carlo simulations at low energies indicates the accuracy of the method.     

A Monte Carlo sampling method of amino acid sequences adaptable to given main-chain atoms in the proteins

We have developed a computational method of protein design to detect amino acid sequences that are adaptable to given main-chain coordinates of a protein. In this method, the selection of amino acid types employs a Metropolis Monte Carlo method with a scoring function in conjunction with the approximation of free energies computed from 3D structures. To compute the scoring function, a side-chain prediction using another Metropolis Monte Carlo method was performed to select structurally suitable side-chain conformations from a side-chain library. In total, two layers of Monte Carlo procedures were performed, first to select amino acid types (1st layer Monte Carlo) and then to predict side-chain conformations (2nd layers Monte Carlo). We applied this method to sequence design for the entire sequence on the SH3 domain, Protein G, and BPTI. The predicted sequences were similar to those of the wild-type proteins. We compared the results of the predictions with and without the 2nd layer Monte Carlo method. The results revealed that the two-layer Monte Carlo method produced better sequence similarity to the wild-type proteins than the one-layer method. Finally, we applied this method to neuraminidase of influenza virus. The results were consistent with the sequences identified from the isolated viruses.     

Conformation study on heparin by intermediate-angle X-ray scattering

The conformation of heparin in water was investigated by intermediate-angle x-ray scattering (IAXS). The theoretical scattering function for the coil conformation was calculated by the Monte Carlo method using the approximation of separable conformation energies and the conformation energies computed for two disaccharide pairs in heparin. From x-ray scattering in a relatively small-angle region, the conformation of heparin is not the ordered 2₁ helix conformation but the coil conformation obtained by the Monte Carlo calculation. It is expected, from x-ray scattering in a relatively wide-angel region, that the sulfate groups of heparin maintain about 7 Å between them.