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.     

Super-Monte Carlo: A photon/electron dose calculation algorithm for radiotherapy

Super-Monte Carlo (SMC) is a method of dose calculation for radiotherapy which combines both analytical calculations and Monte Carlo electron transport. Analytical calculations are used where possible, such as the determination of photon interaction density, to decrease computation time. A Monte Carlo method is used for the electron transport in order to obtain high accuracy of results. To further speed computation, Monte Carlo is used once only, to form an electron track kernel (etk). The etk is a dataset containing the lengths and energy deposition of each step of a number of electron tracks. The etk is transported from each incident particle interaction site, from which the dose is calculated. Dose distributions calculated in heterogeneous media show SMC results similar to those of Monte Carlo. For the same statistical uncertainty, SMC takes an order of magnitude less computation time than a full Monte Carlo simulation. SMC has only been implemented for photons and electrons, however the same basic method could be used for the transport of other particles. Current development includes the optimisation of the etks and the code in order to decrease computation time, and also the inclusion of SMC onto a clinical planning system.     

Advantages of mesh tallying in MCNPX for 3D dose calculations in radiotherapy

The energy deposition mesh tally option of MCNPX Monte Carlo code is very useful for 3-Dimentional (3D) dose calculations. In this study, the 3D dose calculation was done for CT-based Monte Carlo treatment planning in which the energy deposition mesh tally were superimposed on merged voxel model. The results were compared with those of obtained from the common energy deposition (*F8) tally method for all cells of non-merged voxel model. The results of these two tallies and their respective computational times are compared, and the advantages of the proposed method are discussed. For this purpose, a graphical user interface (GUI) application was developed for reading CT slice data of patient, creating voxelized model of patient, optionally merging adjacent cells with the same material to reduce the total number of cells, reading beam configuration from commercial treatment planning system transferred in DICOM-RT format, and showing the isodose distribution on the CT images. To compare the results of Monte Carlo calculated and TiGRT planning system (LinaTech LLC, USA), treatment head of the Siemens ONCOR Impression accelerator was also simulated and the phase-space data on the scoring plane just above the Y-jaws was created and used. The results for a real prostate intensity-modulated radiation therapy (IMRT) plan showed that the proposed method was fivefold faster while the precision was almost the same.     

On gauging and control of grainy materials by gamma-ray absorptiometry in hydraulic transport of solids in pipes

Grain-size effects on γ-ray absorptiometry in non-destructive assay of rainy solid materials with uniform grain radii are widely investigated. In many applications the grain radii are not uniform, but follow more or less a distribution function. The present work offers a Monte Carlo model for γ-ray attenuation in materials with grain-size distributions. Suitable correction functions for grain-size effects have been derived. A comparison between the Monte Carlo results and those from analytical calculations shows a good agreement when the grain sizes are uniform, but a disagreement appears when grain sizes are statistically distributed. This disagreement between the two results may be due to the several approximations introduced in the analytical calculations.     

Two-Term and multi-term approximation of the nonstationary electron velocity distribution in an electric field in a gas

A very efficient, strict nonstationary multi-term approach has been developed as a generalization of the conventional and the strict nonstationary two-term approximations used for solving the nonstationary , electron Boltzmann equation. As a first application the temporal relaxation of electrons in a model plasma acted upon by a de electric field has been investigated. The results are compared with corresponding ones obtained by the conventional and the strict nonstationary two-term approach as well as with very accurate Monte Carlo simulations. Perfect agreement between nonstationary eight-term Boltzmann and Monte Carlo calculations is found.     

Moderator for neutron activation with the photoneutrons produced by a LINAC

Using Monte Carlo methods a polyethylene moderator has been designed to induce activation using the photoneutrons field of a 15 MV linear accelerator for radiotherapy. In the calculations the photoneutron spectrum at 1 m from the isocenter was used as a source term and the neutron spectra were calculated in the center of different size cylindrical moderators. The best size was selected defining the thermal-to-fast-neutron ratios as a figure of merit. The moderator was built and its performance was evaluated by inducing the activation of Mn dissolved in water, silver coins and souvenir coin. The thermal neutron fluence rate was determined with the Mn samples being 9.96 × 10⁵ cm^?2 Gy _x ^?1 .     

Valence energy in variational Monte Carlo: CuH dissociation energy

We show how to estimate the dissociation energy of CuH using the variational Monte Carlo method. The techniques involved are (i) an all-electron approach, (ii) a diffusion-only Metroplis algorithm which is well-suited for sampling the nodal regions properly, and (iii) a core-valence partitioning scheme such that the dissociation energy is estimated from the valence energies of CuH and Cu only. This approach avoids several of the approximations inherent in pseudopotential methods. Using relatively crude wave functions, we obtain an estimate of the dissociation energy and dipole moment with an accuracy on par with much more elaborate calculations in the literature. © 1996 John Wiley & Sons, Inc.     

A general theory of DNA-mediated and other valence-limited colloidal interactions

We present a general theory for predicting the interaction potentials between DNA-coated colloids, and more broadly, any particles that interact via valence-limited ligand-receptor binding. Our theory correctly incorporates the configurational and combinatorial entropic factors that play a key role in valence-limited interactions. By rigorously enforcing self-consistency, it achieves near-quantitative accuracy with respect to detailed Monte Carlo calculations. With suitable approximations and in particular geometries, our theory reduces to previous successful treatments, which are now united in a common and extensible framework. We expect our tools to be useful to other researchers investigating ligand-mediated interactions. A complete and well-documented Python implementation is freely available at http://github.com/patvarilly/DNACC.     

New insights into zeolite formation from molecular modeling

We review recent molecular modeling efforts to shed light on the mechanisms of zeolite formation. We focus on studies that model the early stages of silica polymerization and zeolite nucleation. Electronic structure calculations, classical molecular dynamics, atomistic Monte Carlo simulations and Monte Carlo simulations of lattice models have been used to probe the formation of zeolites and mesoporous materials. Results from these modeling studies predict that in early stages of formation, the silicate material is amorphous. Cluster growth is predicted to occur primarily through Ostwald ripening, and by aggregation of small fragments.     

Full optimization of Jastrow-Slater wave functions with application to the first-row atoms and homonuclear diatomic molecules

We pursue the development and application of the recently introduced linear optimization method for determining the optimal linear and nonlinear parameters of Jastrow-Slater wave functions in a variational Monte Carlo framework. In this approach, the optimal parameters are found iteratively by diagonalizing the Hamiltonian matrix in the space spanned by the wave function and its first-order derivatives, making use of a strong zero-variance principle. We extend the method to optimize the exponents of the basis functions, simultaneously with all the other parameters, namely, the Jastrow, configuration state function, and orbital parameters. We show that the linear optimization method can be thought of as a so-called augmented Hessian approach, which helps explain the robustness of the method and permits us to extend it to minimize a linear combination of the energy and the energy variance. We apply the linear optimization method to obtain the complete ground-state potential energy curve of the C(2) molecule up to the dissociation limit and discuss size consistency and broken spin-symmetry issues in quantum Monte Carlo calculations. We perform calculations for the first-row atoms and homonuclear diatomic molecules with fully optimized Jastrow-Slater wave functions, and we demonstrate that molecular well depths can be obtained with near chemical accuracy quite systematically at the diffusion Monte Carlo level for these systems.     

Quantum Monte Carlo study of the first-row atoms and ions

Quantum Monte Carlo calculations of the first-row atoms Li-Ne and their singly positively charged ions are reported. Multideterminant-Jastrow-backflow trial wave functions are used which recover more than 98% of the correlation energy at the variational Monte Carlo level and more than 99% of the correlation energy at the diffusion Monte Carlo level for both the atoms and ions. We obtain the first ionization potentials to chemical accuracy. We also report scalar relativistic corrections to the energies, mass-polarization terms, and one- and two-electron expectation values.     

X-ray treatment at 5 MeV and above

There is agreement in the scientific community that X-ray treatment of food at 7.5 MeV can be safe. Possible process improvements for treating at higher than 5 MeV X-rays have been re-visited. Monte Carlo methods have been applied to simulate the X-ray conversion process and to calculate dose distributions in homogeneous phantoms. Experimental data obtained using X-rays produced with a Rhodotron TT200 at 5 and 10 MeV verifies a representative set of data which is calculated with the presented method.

With this qualified Monte Carlo tool, calculations at 7.5 MeV incident electron energy were performed. The analysis gives special attention to higher photon yield, improved product penetration, as well as surface and edge effects.     

Electron beam process validation for sterilization of complex geometries

The application of low-energy electrons for the disinfection of containers of complex geometries has been limited due to their inability to efficiently penetrate the rigid walls. Most three-dimensional applications have been evaluated using higher energy processors with bulk or through-the-wall treatment. This work has been directed to the validation of electron disinfection of interior surfaces by injecting electrons through the open-mouth of the container. Both direct thin-film dosimetric mapping of the interior and exterior dose distributions for in-line treatment have been conducted and compared with the results of Monte Carlo modeling utilizing 10⁶ or more source electron histories. Sterilizer characterization and model assumptions are described and the advantages of the modeling technique for process parameter optimization discussed.     

Theoretical advances in the dissolution studies of mineral–water interfaces

This article presents theoretical advances in computational modeling of dissolution at mineral–water interfaces with specific emphasis on silicates. Two different Monte Carlo methods have been developed that target equilibrium properties and kinetics in silicate–water dissolution. The equilibrium properties are explored using the combined reactive Monte Carlo and configurational bias Monte Carlo (RxMC-CBMC) method. The new RxMC-CBMC method is designed to affordably simulate the three-dimensional structure of the mineral with explicit water molecules. The kinetics of the overall dissolution process is studied using a stochastic kinetic Monte Carlo method that utilizes rate constants obtained from accurate ab initio calculations. Both these methods provide important complementary perspective of the complex dynamics involving chemical and physical interactions at the mineral–water interface. The results are compared to experimental and previous computational data available in the literature.     

Numerical study of the accuracy and efficiency of various approaches for Monte Carlo surface hopping calculations

A one-dimensional, two-state model problem with two well-separated avoided crossing points is employed to test the efficiency and accuracy of a semiclassical surface hopping technique. The use of a one-dimensional model allows for the accurate numerical evaluation of both fully quantum-mechanical and semiclassical transition probabilities. The calculations demonstrate that the surface hopping procedure employed accounts for the interference between different hopping trajectories very well and provides highly accurate transition probabilities. It is, in general, not computationally feasible to completely sum over all hopping trajectories in the semiclassical calculations for multidimensional problems. In this case, a Monte Carlo procedure for selecting important trajectories can be employed. However, the cancellation due to the different phases associated with different trajectories limits the accuracy and efficiency of the Monte Carlo procedure. Various approaches for improving the accuracy and efficiency of Monte Carlo surface hopping procedures are investigated. These methods are found to significantly reduce the statistical sampling errors in the calculations, thereby increasing the accuracy of the transition probabilities obtained with a fixed number of trajectories sampled.     

Blueshift and intramolecular tunneling of NH3 umbrella mode in 4He n clusters

We present diffusion Monte Carlo calculations of the ground and first excited vibrational states of NH(3) (4)He(n) for n< or =40. We use the potential energy surface developed by one of us [M. P. Hodges and R. J. Wheatley, J. Chem. Phys. 114, 8836 (2001)], which includes the umbrella mode coordinate of NH(3). Using quantum Monte Carlo calculations of excited states, we show that this potential is able to reproduce qualitatively the experimentally observed effects of the helium environment, namely, a blueshift of the umbrella mode frequency and a reduction of the tunneling splittings in ground and first excited vibrational states of the molecule. These basic features are found to result regardless of whether dynamical approximations or exact calculations are employed.     

Approaching chemical accuracy with quantum Monte Carlo

A quantum Monte Carlo study of the atomization energies for the G2 set of molecules is presented. Basis size dependence of diffusion Monte Carlo atomization energies is studied with a single determinant Slater-Jastrow trial wavefunction formed from Hartree-Fock orbitals. With the largest basis set, the mean absolute deviation from experimental atomization energies for the G2 set is 3.0 kcal/mol. Optimizing the orbitals within variational Monte Carlo improves the agreement between diffusion Monte Carlo and experiment, reducing the mean absolute deviation to 2.1 kcal/mol. Moving beyond a single determinant Slater-Jastrow trial wavefunction, diffusion Monte Carlo with a small complete active space Slater-Jastrow trial wavefunction results in near chemical accuracy. In this case, the mean absolute deviation from experimental atomization energies is 1.2 kcal/mol. It is shown from calculations on systems containing phosphorus that the accuracy can be further improved by employing a larger active space.     

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.     

Monte Carlo Simulation of Electron Transport and X-Ray Generation. I. Electron Elastic and Inelastic Scattering

We present different theoretical approaches to determine differential cross sections for elastic and inelastic interactions of electrons. These cross sections are the basic ingredients for accurate Monte Carlo simulation of electron transport in matter. The considered models range from simple analytical approximations employed in early calculations to purely numerical differential cross sections described by large databases calculated with state-of-the-art theory.     

Recognition of amino acids in solution

The basic solvation shells of all the amino acids, of use in the study of their recognition in aqueous solutions, are determined by means of a method based on the use of 1/R expansions parameterized on the basis of the results from accurate SCF calculations. The accuracy of the calculations is tested in a more extensive study of the solvation of glycine, for which the results of Monte Carlo calculations are reproduced.