Depth dose dependence of the mouse bone using kilovoltage photon beams: A Monte Carlo study for small-animal irradiation

This study investigated the dose enhancement due to the presence of mouse bone irradiated by the kilovoltage (kV) photon beams. Dosimetry of the bone associated with soft and lung tissue was determined by Monte Carlo simulations using the EGSnrc-based code in millimeter scale. Two inhomogeneous phantoms with 2 mm of bone layer sandwiched by: (1) water and lung (bone–lung phantom); and (2) water (bone–water phantom), were used. Relative depth doses along the central beam axes in the phantoms and dose enhancement ratios (bone dose in the above inhomogeneous phantoms to the dose at the same point in the water phantom) were determined using the 100 and 225 kVp photon beams. For the 100 kVp photon beams, the depth dose gradient in the bone was significantly larger compared to that in a water phantom without the bone. This is due to the beam hardening effect that some low-energy photons were filtered out in the deeper depth, resulting in less photoelectric interactions and hence energy depositions in the bone. Moreover, dose differences between the top and downstream (bottom) bone edges at depths of 1–5 mm were 168–192% and 149–166% for the bone–lung and bone–water phantom, respectively. These differences were larger than 21–27% (bone–lung) and 12–23% (bone–water) for the 225 kVp photon beams. The maximum dose enhancement ratio in the bone for the bone–lung and bone–water phantoms in various depths was about 5.7 using the 100 kVp photon beams. This ratio was larger than two times of that (2.4) for the 225 kVp photon beams. It is concluded that, apart from the basic beam characteristics such as attenuation and penumbra, which are related to the photon beam energy in the mouse irradiation, the bone dose is another important factor to consider when selecting the beam energy in the small-animal treatment planning, provided that the bone dose enhancement is a concern in the preclinical model.     

Monte Carlo study of electron correlation functions for small molecules

A study is made of electron-electron correlation functions for use in trial wave functions for small molecules. New forms are proposed that have only a few variational parameters, and these parameters have physical meanings that are easily discerned. Total energies for H₂, LiH and Li₂ computed using these correlation functions are presented, and comparison is made with previous forms, including the Jastrow-Pade form often used in Monte Carlo studies. We further treat the possibility that correlation depends not only on the separation of a pair of electrons but also on the location of the electron pair relative to the nuclei — indicative of a density-dependent or many body correlation effect. Our results indicate that such a many-body correlation effect is weakly present.This work was supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Chemical Sciences Division of the U.S. Department of Energy under Contract No. DE-AC03-76SF00098     

Deterministic and Monte Carlo codes for multiple scattering photon transport with arbitrary polarization states

The Boltzmann–Chandrasekhar vector equation is the best model known for describing the diffusion of incoherent photon beams with arbitrary polarization state. A brief comparison of the transport equations (scalar and vector) is presented. Then, the state-of-the-art of the transport codes developed at Bologna based on these models is described. Finally, the application of these codes is illustrated with examples.     

Monte Carlo simulations of heterogeneous electron transfer: New challenges

We report results of MC simulations of electron transfer across a metal electrode/electrolyte solution interface. The model presumes the Landau–Zener theory and a random walk on a two-dimensional lattice formed by crossing parabolic reaction free energy surfaces along the solvent coordinate. Emphasis is put on investigating the activationless discharge regime; the bridge-assisted electron transfer is also partially addressed. We have calculated effective electronic transmission coefficient as a function of the electrode overpotential and temperature in a wide range of orbital overlap. The dependence of the transmission coefficient on the electronic density of states is analyzed as well.     

Zero-variance zero-bias quantum Monte Carlo estimators for the electron density at a nucleus

We derive new quantum Monte Carlo (QMC) estimators for the electronic density at the position of a point nucleus using the zero-variance and zero-bias principles. The resulting estimators are highly efficient, and are significantly simpler to implement and use than alternative methods, as they contain no adjustable parameters. In addition, they can be used in both variational and diffusion QMC calculations. Our best estimator is used to calculate the most accurate available estimates of the total electron density at the nucleus for the first-row atoms Li-Ne, the Ar atom, and the diatomic molecules B(2), N(2), and F(2).     

Correlated electron dynamics with time-dependent quantum Monte Carlo: three-dimensional helium

Here the recently proposed time-dependent quantum Monte Carlo method is applied to three dimensional para- and ortho-helium atoms subjected to an external electromagnetic field with amplitude sufficient to cause significant ionization. By solving concurrently sets of up to 20,000 coupled 3D time-dependent Schro?dinger equations for the guide waves and corresponding sets of first order equations of motion for the Monte Carlo walkers we obtain ground state energies in close agreement with the exact values. The combined use of spherical coordinates and B-splines along the radial coordinate proves to be especially accurate and efficient for such calculations. Our results for the dipole response and the ionization of an atom with un-correlated electrons are in good agreement with the predictions of the conventional time-dependent Hartree-Fock method while the calculations with correlated electrons show enhanced ionization that is due to the electron-electron repulsion.     

Spatial resolution optimization of backscattered electron images using Monte Carlo simulation

The relation between probe size and spatial resolution of backscattered electron (BSE) images was studied. In addition, the effect of the accelerating voltage, the current intensity and the sample geometry and composition were analyzed. An image synthesis method was developed to generate the images from backscattered electron coefficients obtained from Monte Carlo simulations. Spatial resolutions of simulated images were determined with the SMART-J method, which is based on the Fourier transform of the image. The resolution can be improved by either increasing the signal or decreasing the noise of the backscattered electron image. The analyses demonstrate that using a probe size smaller than the size of the observed object (sample features) does not improve the spatial resolution. For a probe size larger than the feature size, the spatial resolution is proportional to the probe size.     

Characterization of computer simulated radiotherapy beams for Monte-Carlo treatment planning

Beam characterization consists of two parts: Beam simulation and beam modeling. The EGS4/BEAM Monte-Carlo code system has been used for the simulation of the beams from different clinical linear accelerators and a multiple-source model has been proposed to represent and reconstruct the simulated beam phase–space data. Benefits of well-designed beam models over phase–space data include shorter beam simulation time, a smaller disk space requirement, and improved understanding of the clinical beams used for radiotherapy.     

Prospects for release-node quantum Monte Carlo

We perform release-node quantum Monte Carlo simulations on the first row diatomic molecules in order to assess how accurately their ground-state energies can be obtained. An analysis of the fermion-boson energy difference is shown to be strongly dependent on the nuclear charge, Z, which in turn determines the growth of variance of the release-node energy. It is possible to use maximum entropy analysis to extrapolate to ground-state energies only for the low Z elements. For the higher Z dimers beyond boron, the error growth is too large to allow accurate data for long enough imaginary times. Within the limit of our statistics we were able to estimate, in atomic units, the ground-state energy of Li(2) (-14.9947(1)), Be(2) (-29.3367(7)), and B(2)(-49.410(2)).     

Monte Carlo correction programme for PC

A Monte Carlo correction program for quantitative microanalysis on PC computer is introduced in this paper. The elastic scattering is described by the screened Rutherford cross section. Instead of computing the energy loss according to the actual path between two scatterings we have defined the Bethe inelastic cross section determined by the Bethe-slowing-down approximation. It is assumed that it causes no angular departure of the scattered electron. In the second model we took into account the angular dependence of inelastic scattering assuming that the primary electron interacts with quasi-free atom electrons. On the basis of these two models analytical Monte Carlo programmes were developed and experimentally tested on some oxide glass. Our results are fully comparable to those obtained by ten world microprobe laboratories using classical ZAF correction or Bence-Albee methods. We have found that introducing angular part of the inelastic cross section analytical results did not significantly change. All of our results were carried out for bulk specimens but extending it to layers is under the development.     

Monte Carlo global sensitivity analysis of Boltzmann equation for electron kinetics in H2 discharges

Global sensitivity analysis with the Monte Carlo method is applied to the Boltzmann equation for the electron energy distribution function (eedf). The results show the sensitivity of eedf and related quantities on the global variation of cross sections set. A new indicator of global sensitivity is used, which appears to be of easy applicability.     

A Monte Carlo treatment of the decay of80mBr,a novel Auger electron emitting isotope with potential for therapy

Monte Carlo calculations were done to simulate the decay of^80mBr in order to estimate the energies and distribution of Auger and Coster-Kronig electrons emitted in this de-excitation process. Results show that for an isolated atom, the average number of electrons emitted per decay is 6.926 and 8.016 for an atom in the condensed state. These values agree well with experimental results of Wexler and Anderson. The average calculated electron energies were 1122 eV and 991 eV with ranges of 8.02 A° and 6.71 A° in unit density matter for the isolated an condensed states, respectively. These results will be used to estimate localized energy deposition which will be correlated to the radiotoxic effects of^80mBr-bromo-deoxyuridine as measured in experiments currently underway in our laboratory using cell cultures. Our aim is to assess the radiotoxicity of low energy, short range electrons for its eventual use in cancer therapy.Deceased, to whose memory this paper is dedicated.     

Reactive Monte Carlo and grand-canonical Monte Carlo simulations of the propene metathesis reaction system

The influence of silicalite-1 pores on the reaction equilibria and the selectivity of the propene metathesis reaction system in the temperature range between 300 and 600 K and the pressure range from 0.5 to 7 bars has been investigated with molecular simulations. The reactive Monte Carlo (RxMC) technique was applied for bulk-phase simulations in the isobaric-isothermal ensemble and for two phase systems in the Gibbs ensemble. Additionally, Monte Carlo simulations in the grand-canonical ensemble (GCMC) have been carried out with and without using the RxMC technique. The various simulation procedures were combined with the configurational-bias Monte Carlo approach. It was found that the GCMC simulations are superior to the Gibbs ensemble simulations for reactions where the bulk-phase equilibrium can be calculated in advance and does not have to be simulated simultaneously with the molecules inside the pore. The confined environment can increase the conversion significantly. A large change in selectivity between the bulk phase and the pore phase is observed. Pressure and temperature have strong influences on both conversion and selectivity. At low pressure and temperature both conversion and selectivity have the highest values. The effect of confinement decreases as the temperature increases.     

Rejection-free Monte Carlo scheme for anisotropic particles

We extend the geometric cluster algorithm [J. Liu and E. Luijten, Phys. Rev. Lett. 92, 035504 (2004)], a highly efficient, rejection-free Monte Carlo scheme for fluids and colloidal suspensions, to the case of anisotropic particles. This is made possible by adopting hyperspherical boundary conditions. A detailed derivation of the algorithm is presented, along with extensive implementation details as well as benchmark results. We describe how the quaternion notation is particularly suitable for the four-dimensional geometric operations employed in the algorithm. We present results for asymmetric Lennard-Jones dimers and for the Yukawa one-component plasma in hyperspherical geometry. The efficiency gain that can be achieved compared to conventional, Metropolis-type Monte Carlo simulations is investigated for rod-sphere mixtures as a function of rod aspect ratio, rod-sphere diameter ratio, and rod concentration. The effect of curved geometry on physical properties is addressed.     

Auxiliary field Monte Carlo for charged particles

This article describes Monte Carlo algorithms for charged systems using constrained updates for the electric field. The method is generalized to treat inhomogeneous dielectric media, electrolytes via the Poisson-Boltzmann equation and considers the problem of charge and current interpolation for off lattice models. We emphasize the differences between this algorithm and methods based on the electrostatic potential, calculated from the Poisson equation.     

Energy-consistent pseudopotentials for quantum Monte Carlo calculations

The authors present scalar-relativistic energy-consistent Hartree-Fock pseudopotentials for the main-group elements. The pseudopotentials do not exhibit a singularity at the nucleus and are therefore suitable for quantum Monte Carlo (QMC) calculations. They demonstrate their transferability through extensive benchmark calculations of atomic excitation spectra as well as molecular properties. In particular, they compute the vibrational frequencies and binding energies of 26 first- and second-row diatomic molecules using post-Hartree-Fock methods, finding excellent agreement with the corresponding all-electron values. They also show their pseudopotentials give superior accuracy than other existing pseudopotentials constructed specifically for QMC. Finally, valence basis sets of different sizes (VnZ with n=D,T,Q,5 for first and second rows, and n=D,T for third to fifth rows) optimized for our pseudopotentials are also presented.     

Optimum and efficient sampling for variational quantum Monte Carlo

Quantum mechanics for many-body systems may be reduced to the evaluation of integrals in 3N dimensions using Monte Carlo, providing the Quantum Monte Carlo ab initio methods. Here we limit ourselves to expectation values for trial wave functions, that is to variational quantum Monte Carlo. Almost all previous implementations employ samples distributed as the physical probability density of the trial wave function, and assume the central limit theorem to be valid. In this paper we provide an analysis of random error in estimation and optimization that leads naturally to new sampling strategies with improved computational and statistical properties. A rigorous lower limit to the random error is derived, and an efficient sampling strategy presented that significantly increases computational efficiency. In addition the infinite variance heavy tailed random errors of optimum parameters in conventional methods are replaced with a Normal random error, strengthening the theoretical basis of optimization. The method is applied to a number of first row systems and compared with previously published results.     

Monte Carlo computer simulations and electron microscopy of colloidal cluster formation via emulsion droplet evaporation

We consider a theoretical model for a binary mixture of colloidal particles and spherical emulsion droplets. The hard sphere colloids interact via additional short-ranged attraction and long-ranged repulsion. The droplet-colloid interaction is an attractive well at the droplet surface, which induces the Pickering effect. The droplet-droplet interaction is a hard-core interaction. The droplets shrink in time, which models the evaporation of the dispersed (oil) phase, and we use Monte Carlo simulations for the dynamics. In the experiments, polystyrene particles were assembled using toluene droplets as templates. The arrangement of the particles on the surface of the droplets was analyzed with cryogenic field emission scanning electron microscopy. Before evaporation of the oil, the particle distribution on the droplet surface was found to be disordered in experiments, and the simulations reproduce this effect. After complete evaporation, ordered colloidal clusters are formed that are stable against thermal fluctuations. Both in the simulations and with field emission scanning electron microscopy, we find stable packings that range from doublets, triplets, and tetrahedra to complex polyhedra of colloids. The simulated cluster structures and size distribution agree well with the experimental results. We also simulate hierarchical assembly in a mixture of tetrahedral clusters and droplets, and find supercluster structures with morphologies that are more complex than those of clusters of single particles.     

An efficient sampling algorithm for variational Monte Carlo

We propose a new algorithm for sampling the N-body density mid R:Psi(R)mid R:(2)R(3N)mid R:Psimid R:(2) in the variational Monte Carlo framework. This algorithm is based upon a modified Ricci-Ciccotti discretization of the Langevin dynamics in the phase space (R,P) improved by a Metropolis-Hastings accept/reject step. We show through some representative numerical examples (lithium, fluorine, and copper atoms and phenol molecule) that this algorithm is superior to the standard sampling algorithm based on the biased random walk (importance sampling).