Monte Carlo treatment planning for photon and electron beams

During the last few decades, accuracy in photon and electron radiotherapy has increased substantially. This is partly due to enhanced linear accelerator technology, providing more flexibility in field definition (e.g. the usage of computer-controlled dynamic multileaf collimators), which led to intensity modulated radiotherapy (IMRT). Important improvements have also been made in the treatment planning process, more specifically in the dose calculations. Originally, dose calculations relied heavily on analytic, semi-analytic and empirical algorithms. The more accurate convolution/superposition codes use pre-calculated Monte Carlo dose “kernels” partly accounting for tissue density heterogeneities. It is generally recognized that the Monte Carlo method is able to increase accuracy even further. Since the second half of the 1990s, several Monte Carlo dose engines for radiotherapy treatment planning have been introduced. To enable the use of a Monte Carlo treatment planning (MCTP) dose engine in clinical circumstances, approximations have been introduced to limit the calculation time. In this paper, the literature on MCTP is reviewed, focussing on patient modeling, approximations in linear accelerator modeling and variance reduction techniques. An overview of published comparisons between MC dose engines and conventional dose calculations is provided for phantom studies and clinical examples, evaluating the added value of MCTP in the clinic. An overview of existing Monte Carlo dose engines and commercial MCTP systems is presented and some specific issues concerning the commissioning of a MCTP system are discussed.     

A new procedure for dose measurements in mixed high-energy electron and photon fields

A new procedure for the measurement of H_p(10) and H′(10) in mixed high-energy electron and photon radiation fields was developed. By variation of the electron fluence with respect to an unchanged photon fluence in the mixture, the values of the two quantities varied by a factor of up to 1.9.     

The features of electron dose distributions in circular objects: Comparison of Monte Carlo calculation predictions with dosimetry

The features of electron dose field formation in the multi-layer circular objects are related with its surface irregularity such as convexity, concavity and roundness of inner and outer layers. The simulation of dose distributions in multi-layer tubes irradiated with a scanned electron beam (EB) was carried out by Monte Carlo (MC) method with utilization of the software ModeCEB. The effects of mutual influence on dose field formation in contacting multi-layers tubes irradiated with EB were MC simulated and measured with a film dosimetry. An experimental validation of the obtained simulation predictions for dose distributions in multi-layer tubes irradiated with 10 MeV electrons was performed on radiation facility with linear electron accelerator LAE 13/9, INCT, Warsaw. Comparison of MC simulation results with a film dosimetry is discussed in the report.     

Clinical considerations of Monte Carlo for electron radiotherapy treatment planning

Technical requirements for Monte Carlo based electron radiotherapy treatment planning are outlined. The targeted overall accuracy for estimate of the delivered dose is the least restrictive of 5% in dose, 5 mm in isodose position. A system based on EGS4 and capable of achieving this accuracy is described. Experience gained in system design and commissioning is summarized. The key obstacle to widespread clinical use of Monte Carlo is lack of clinically acceptable measurement based methodology for accurate commissioning.     

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.     

DMC: A multifunctional hybrid dynamics/Monte Carlo simulation algorithm for the evaluation of conformational space

A hybrid conformational search algorithm (DMC) is described that combines a modified form of molecular dynamics with Metropolis Monte Carlo sampling, using the COSMIC(90) force field. Trial configurations are generated by short bursts of high-temperature dynamics in which the initial kinetic energy is focused into single bond rotations or alternatively into “corner-flapping” motions in ring systems. Constant temperature and simulated annealing search protocols have been applied to the conformational analysis of several model hydrocarbons (cyclopentane, cyclohexane, cycloheptane, cyclooctane, cycloheptadecane, decane, and tetradecane), and the performance compared with conventional molecular dynamics and Monte Carlo sampling methods. Optimum Metropolis sampling temperatures have been determined and range from 1000–2000 K for acyclic molecules to 3000 K for cyclic systems. Simulated annealing runs are most successful at locating the global minimum when cooling slowing from these optimum temperatures.     

Surface excitations in electron spectroscopy. Part I: dielectric formalism and Monte Carlo algorithm

The theory describing energy losses of charged non‐relativistic projectiles crossing a planar interface is derived on the basis of the Maxwell equations, outlining the physical assumptions of the model in great detail. The employed approach is very general in that various common models for surface excitations (such as the specular reflection model) can be obtained by an appropriate choice of parameter values. The dynamics of charged projectiles near surfaces is examined by calculations of the induced surface charge and the depth‐ and direction‐dependent differential inelastic inverse mean free path (DIIMFP) and stopping power. The effect of several simplifications frequently encountered in the literature is investigated: differences of up to 100% are found in heights, widths, and positions of peaks in the DIIMFP. The presented model is implemented in a Monte Carlo algorithm for the simulation of the electron transport relevant for surface electron spectroscopy. Simulated reflection electron energy loss spectra are in good agreement with experiment on an absolute scale. Copyright © 2012 John Wiley & Sons, Ltd.     

Effects of physics change in Monte Carlo code on electron pencil beam dose distributions

Pencil beam algorithms used in computerized electron beam dose planning are usually described using the small angle multiple scattering theory. Alternatively, the pencil beams can be generated by Monte Carlo simulation of electron transport. In a previous work, the 4th version of the Electron Gamma Shower (EGS) Monte Carlo code was used to obtain dose distributions from monoenergetic electron pencil beam, with incident energy between 1 MeV and 50 MeV, interacting at the surface of a large cylindrical homogeneous water phantom. In 2000, a new version of this Monte Carlo code has been made available by the National Research Council of Canada (NRC), which includes various improvements in its electron-transport algorithms. In the present work, we were interested to see if the new physics in this version produces pencil beam dose distributions very different from those calculated with oldest one. The purpose of this study is to quantify as well as to understand these differences. We have compared a series of pencil beam dose distributions scored in cylindrical geometry, for electron energies between 1 MeV and 50 MeV calculated with two versions of the Electron Gamma Shower Monte Carlo Code. Data calculated and compared include isodose distributions, radial dose distributions and fractions of energy deposition. Our results for radial dose distributions show agreement within 10% between doses calculated by the two codes for voxels closer to the pencil beam central axis, while the differences are up to 30% for longer distances. For fractions of energy deposition, the results of the EGS4 are in good agreement (within 2%) with those calculated by EGSnrc at shallow depths for all energies, whereas a slightly worse agreement (15%) is observed at deeper distances. These differences may be mainly attributed to the different multiple scattering for electron transport adopted in these two codes and the inclusion of spin effect, which produces an increase of the effective range of electrons.     

A benchmark calculation for the fuzzy c-means clustering algorithm: initial memberships

We report a benchmark calculation for the fuzzy c-means clustering algorithm that can be used as a reference in theoretical and practical studies related to classification methodologies. A full exploration of the hard-initialization space is done for all possible different groupings on a simple fifteen-pattern system to describe their stationary points. Numerical problems associated with the stopping criteria are discussed in relation with the calculation of some validity indexes. All necessary information to assure an easy reproduction of the obtained results is clearly reported.     

A new algorithm for the fixed-node quantum Monte Carlo method

A novel algorithm is proposed for the fixed-node quantum Monte Carlo (FNQMC) method.In contrast to previous procedures,its "guiding function" is not optimized prior to diffusion quantum Monte Carlo (DMC) computation but synchronistically in the diffusion process The new algorithm can not only save CPU time,but also make both of the optimization and diffusion carried out according to the same sampling fashion,reaching the goal to improve each other This new optimizing procedure converges super-linearly,and thus can accelerate the particle diffusion During the diffusion process,the node of the "guiding function" changes incessantly,which is conducible to reducing the "fixed-node error" The new algorithm has been used to calculate the total energies of states X3B1 and a1A1 of CH2 as well as π-X2B1 and λ-2A1 of NH2 The singlet-triplet energy splitting (λEsT) in CH2 and π energy splitting in NH2 obtained with this present method are (45 542±1.840) and (141.644±1.589) kJ/mol,respectively The calculated     

Stochastic approximation Monte Carlo algorithm for calculation of diagram of states of a single flexible-semiflexible copolymer chain

We report in this paper on details and special aspects of using the stochastic approximation Monte Carlo (SAMC) algorithm for the calculation of the diagram of states of a single flexible-semiflexible copolymer chain. The SAMC algorithm is a quite recently suggested mathematical generalization of Wang-Landautype algorithms for very precise Monte Carlo estimates of the density of states function g(E) in computer simulations. It has been mathematically proven that the SAMC algorithm converges to the true g(E) function in the limit of infinite sampling, i.e. systematic errors are smaller than statistical errors. However, in practice one faces the reality that statistical errors become small enough only in the limit of the prohibitively large computation time, if one applies this algorithm in a straightforward way, as it is described. Therefore, one usually needs to apply additional technical tricks to accelerate the convergence to a reasonably good function g(E) sampling all most important conformations. In this paper we discuss all details of these inner workings to make the reader aware of real computational efforts, available accuracy, reachable limits, etc. We do this for the first realization of this algorithm for calculation of the two-dimensional density of states function g(E_contact, E_stiffness) which depends on two contributions to the total energy—intermonomer contact energy and the intramolecular stiffness energy due to chain bending.     

Communication: Monte Carlo calculation of the exchange energy

In recent generalized Kohn-Sham (GKS) schemes for density functional theory (DFT) Hartree-Fock type exchange is important. In plane waves and grid approaches the high cost of exchange energy calculations makes these GKS considerably more expensive than Kohn-Sham DFT calculations. We develop a stochastic approach for speeding up the calculation of exchange for large systems. We show that stochastic error per particle does not grow and can even decrease with system size (at a given number of iterations). We discuss several alternative approaches and explain how these ideas can be included in the GKS framework.     

A new technique for metropolis Monte Carlo simulation to capture aggregate structures of fine particles: Cluster-moving Monte Carlo algorithm

We present a new Monte Carlo simulation procedure which is capable of capturing aggregate structures in a suspension where fine particles are dispersed. The algorithm we call the “cluster-moving” Monte Carlo algorithm involves moving aggregates (clusters) as unitary particles at every certain Monte Carlo step. We discuss here the theoretical background of the cluster-moving Monte Carlo algorithm and the availability of the algorithm for simulations of systems where fine particles aggregate. The results of simulations for two model systems, magnetic fluids and colloidal dispersions, have shown that the new algorithm produces much more rapid convergence than the conventional one for unstable dispersion systems and reproduces physically reasonable aggregate structures of fine particles.     

Signal-to-background in EPMA: Measurement and Monte Carlo calculation

By the method of Monte Carlo calculation, the dependence of the signal-to-background ratio of detected X-rays on the energy of electrons as well as on the thickness of the sample was calculated. The range of energy was 40 ÷ 120 keV, the range of thickness was approximately 8 ÷ 80 g/cm² (40 ÷ 400 nm at density = 2 g/cm³). The results were compared with measurements in electron microscope on thin resin standard for biological microanalysis. The measured dependence of signal-to-background ratio on the energy of electrons has the maximum at 80 keV, the calculated one changes at increased thickness from a monotonic form to one with a maximum at a particular thickness. The absolute values (Hall correction procedure was used for measured values) differs mainly at the highest energy used (120 keV); the difference is probably caused by unproper correction of measured value of background at this energy. Simultaneously, the source distribution of emitted X-ray photons is calculated. Its knowledge gives the possibility to estimate simply the interaction volume diameter and, by this way, to determine the spatial resolution of electron probe X-ray microanalysis.     

Path integral Monte Carlo method for ab initio calculation

The Feynman path integral method is applied to the many-electron problem. We first give new closure relations in terms of ordinary complex and real numbers, which could be derived from an arbitrary complete set of state vectors. Then, in the path integral form, the partition function of the system and the ensemble average of energy are explicitly expressed in terms of these closure relations. It is impossible to evaluate the path integral by direct numerical integrations because of its huge amount of integration variables. Therefore, we develop an algorithm by the Monte Carlo method with constraints corresponding to the normalization condition of states to calculate the required integral. Finally, the ensemble average of energy for the hydrogen molecule is explicitly evaluated by the quantum Monte Carlo method and results are compared with the result obtained by the ordinary full configuration interaction (CI) method. © 1996 John Wiley & Sons, Inc.     

Hybrid Monte Carlo: An efficient algorithm for condensed matter simulation

A detailed comparison has been made of the performance of molecular dynamics and hybrid Monte Carlo simulation algorithms for calculating thermodynamic properties of 2D Lennard-Jonesium. The hybrid Monte Carlo simulation required an order of magnitude fewer steps than the molecular dynamics simulation to calculate reproducible values of the specific heat. The ergodicity of the two algorithms was compared via the use of intermediate scattering functions. For classical systems the intermediate scattering functions should be real; however, a simple analysis demonstrates that this function will have a significant imaginary component when ergodicity breaks down. For q vectors near the zone boundary, the scattering functions are real for both algorithms. However, for q vectors near the zone center (i.e., harmonic, weakly coupled modes), the scattering function calculated via molecular dynamics had a significantly larger imaginary component than that calculated using hybrid Monte Carlo. Therefore, the hybrid Monte Carlo algorithm is more ergodic and samples phase space more efficiently than molecular dynamics for simulations of 2D Lennard-Jonesium. © 1994 by John Wiley & Sons, Inc.     

Radial dose profiles for pencil electron beams

The relationship between the Boltzmann and Fermi-Eyges-Yang equations governing electron transport is examined. Radial dose profiles for a pencil beam obtained by numerical solution of the Boltzmann equation in the small angle approximation are compared with both the Gaussian approximation and with Monte Carlo simulations for a carbon medium. For energies ranging from 5 to 20 MeV and penetration depths up to 75% of the range the numerical results are within 10% of the Monte Carlo results for the radial distance encompassing 63% of the energy deposition.     

Vector processing algorithm for electron repulsion integrals in Ab Initio HF calculation based upon the PK supermatrix

An efficient vector processing algorithm generating PK supermatrices has been developed, in particular aiming at calculations on large molecules. The algorithm utilizes the recurrence relations for electron repulsion integrals. The PK supermatrices are listed in a nearly canonical order so that the Fock matrix generation is efficiently vectorized, no temporary ERI and PK files being used. This is effected by partition of the basis set (atomic orbitals) into subsets of certain appropriate sizes, and the partition approach is named as the three-dimensional partial space method. A high-speed Hartree–Fock calculation including integrals and SCF procedures is achieved. © 1992 by John Wiley & Sons, Inc.     

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).