Examination of pencil beam predictions of small-field dose using dosimetry film and Monte Carlo simulations

The iPlan treatment planning sys-tem uses a pencil beam algorithm, with density cor-rections, to predict the doses delivered by very small (stereotactic) radiotherapy fields. This study tests the accuracy of dose predictions made by iPlan, for small-field treatments delivered to a planar solid wa-ter phantom and to heterogeneous human tissue using the BrainLAB m3 micro-multileaf collimator.

Investigation of stereotactic radiotherapy dose using dosimetry film and Monte Carlo simulations

This study uses dosimetry film measurements and Monte Carlo simulations to investigate the accuracy of type-a (pencil-beam) dose calculations for predicting the radiation doses delivered during stereotactic radiotherapy treatments of the brain. It is shown that when evaluating doses in a water phantom, the type-a algorithm provides dose predictions which are accurate to within clinically relevant criteria, gamma(3%,3mm), but these predictions are nonetheless subtly different from the results of evaluating doses from the same fields using radiochromic film and Monte Carlo simulations. An analysis of a clinical meningioma treatment suggests that when predicting stereotactic radiotherapy doses to the brain, the inaccuracies of the type-a algorithm can be exacerbated by inadequate evaluation of the effects of nearby bone or air, resulting in dose differences of up to 10% for individual fields. The results of this study indicate the possible advantage of using Monte Carlo calculations, as well as measurements with high-spatial resolution media, to verify type-a predictions of dose delivered in cranial treatments.

Monte Carlo simulations of dynamic radiotherapy treatments

The effects of tumour motion during radiation therapy delivery have been widely investigated. Motion effects have become increasingly important with the introduction of dynamic radiotherapy delivery modalities such as enhanced dynamic wedges (EDWs) and intensity modulated radiation therapy (IMRT) where a dynamically collimated radiation beam is delivered to the moving target, resulting in dose blurring and interplay effects which are a consequence of the combined tumor and beam motion. Prior to this work, reported studies on the EDW based interplay effects have been restricted to the use of experimental methods for assessing single-field non-fractionated treatments. In this work, the interplay effects have been investigated for EDW treatments. Single and multiple field treatments have been studied using experimental and Monte Carlo (MC) methods. Initially this work experimentally studies interplay effects for single-field non-fractionated EDW treatments, using radiation dosimetry systems placed on a sinusoidaly moving platform. A number of wedge angles (60º, 45º and 15º), field sizes (20 × 20, 10 × 10 and 5 × 5 cm2), amplitudes (10-40 mm in step of 10 mm) and periods (2 s, 3 s, 4.5 s and 6 s) of tumor motion are analysed (using gamma analysis) for parallel and perpendicular motions (where the tumor and jaw motions are either parallel or perpendicular to each other). For parallel motion it was found that both the amplitude and period of tumor motion affect the interplay, this becomes more prominent where the collimator tumor speeds become identical. For perpendicular motion the amplitude of tumor motion is the dominant factor where as varying the period of tumor motion has no observable effect on the dose distribution. The wedge angle results suggest that the use of a large wedge angle generates greater dose variation for both parallel and perpendicular motions. The use of small field size with a large tumor motion results in the loss of wedged dose distribution for both parallel and perpendicular motion. From these single field measurements a motion amplitude and period have been identified which show the poorest agreement between the target motion and dynamic delivery and these are used as the „worst case motion parameters.. The experimental work is then extended to multiple-field fractionated treatments. Here a number of pre-existing, multiple–field, wedged lung plans are delivered to the radiation dosimetry systems, employing the worst case motion parameters. Moreover a four field EDW lung plan (using a 4D CT data set) is delivered to the IMRT quality control phantom with dummy tumor insert over four fractions using the worst case parameters i.e. 40 mm amplitude and 6 s period values. The analysis of the film doses using gamma analysis at 3%-3mm indicate the non averaging of the interplay effects for this particular study with a gamma pass rate of 49%. To enable Monte Carlo modelling of the problem, the DYNJAWS component module (CM) of the BEAMnrc user code is validated and automated. DYNJAWS has been recently introduced to model the dynamic wedges. DYNJAWS is therefore commissioned for 6 MV and 10 MV photon energies. It is shown that this CM can accurately model the EDWs for a number of wedge angles and field sizes. The dynamic and step and shoot modes of the CM are compared for their accuracy in modelling the EDW. It is shown that dynamic mode is more accurate. An automation of the DYNJAWS specific input file has been carried out. This file specifies the probability of selection of a subfield and the respective jaw coordinates. This automation simplifies the generation of the BEAMnrc input files for DYNJAWS. The DYNJAWS commissioned model is then used to study multiple field EDW treatments using MC methods. The 4D CT data of an IMRT phantom with the dummy tumor is used to produce a set of Monte Carlo simulation phantoms, onto which the delivery of single field and multiple field EDW treatments is simulated. A number of static and motion multiple field EDW plans have been simulated. The comparison of dose volume histograms (DVHs) and gamma volume histograms (GVHs) for four field EDW treatments (where the collimator and patient motion is in the same direction) using small (15º) and large wedge angles (60º) indicates a greater mismatch between the static and motion cases for the large wedge angle. Finally, to use gel dosimetry as a validation tool, a new technique called the „zero-scan method. is developed for reading the gel dosimeters with x-ray computed tomography (CT). It has been shown that multiple scans of a gel dosimeter (in this case 360 scans) can be used to reconstruct a zero scan image. This zero scan image has a similar precision to an image obtained by averaging the CT images, without the additional dose delivered by the CT scans. In this investigation the interplay effects have been studied for single and multiple field fractionated EDW treatments using experimental and Monte Carlo methods. For using the Monte Carlo methods the DYNJAWS component module of the BEAMnrc code has been validated and automated and further used to study the interplay for multiple field EDW treatments. Zero-scan method, a new gel dosimetry readout technique has been developed for reading the gel images using x-ray CT without losing the precision and accuracy.

Multiple scattering in deep inelastic neutron scattering : Monte Carlo simulations and experiments at the ISIS eVS inverse geometry spectrometer

A procedure for the evaluation of multiple scattering contributions is described, for deep inelastic neutron scattering (DINS) studies using an inverse geometry time-of-flight spectrometer. The accuracy of a Monte Carlo code DINSMS, used to calculate the multiple scattering, is tested by comparison with analytic expressions and with experimental data collected from polythene, polycrystalline graphite and tin samples. It is shown that the Monte Carlo code gives an accurate representation of the measured data and can therefore be used to reliably correct DINS data.

Effect of CT electron density identification on Monte Carlo simulations of radiotherapeutic treatments

Introduction: The accurate identification of tissue electron densities is of great importance for Monte Carlo (MC) dose calculations. When converting patient CT data into a voxelised format suitable for MC simulations, however, it is common to simplify the assignment of electron densities so that the complex tissues existing in the human body are categorized into a few basic types. This study examines the effects that the assignment of tissue types and the calculation of densities can have on the results of MC simulations, for the particular case of a Siemen’s Sensation 4 CT scanner located in a radiotherapy centre where QA measurements are routinely made using 11 tissue types (plus air). Methods: DOSXYZnrc phantoms are generated from CT data, using the CTCREATE user code, with the relationship between Hounsfield units (HU) and density determined via linear interpolation between a series of specified points on the ‘CT-density ramp’ (see Figure 1(a)). Tissue types are assigned according to HU ranges. Each voxel in the DOSXYZnrc phantom therefore has an electron density (electrons/cm3) defined by the product of the mass density (from the HU conversion) and the intrinsic electron density (electrons /gram) (from the material assignment), in that voxel. In this study, we consider the problems of density conversion and material identification separately: the CT-density ramp is simplified by decreasing the number of points which define it from 12 down to 8, 3 and 2; and the material-type-assignment is varied by defining the materials which comprise our test phantom (a Supertech head) as two tissues and bone, two plastics and bone, water only and (as an extreme case) lead only. The effect of these parameters on radiological thickness maps derived from simulated portal images is investigated. Results & Discussion: Increasing the degree of simplification of the CT-density ramp results in an increasing effect on the resulting radiological thickness calculated for the Supertech head phantom. For instance, defining the CT-density ramp using 8 points, instead of 12, results in a maximum radiological thickness change of 0.2 cm, whereas defining the CT-density ramp using only 2 points results in a maximum radiological thickness change of 11.2 cm. Changing the definition of the materials comprising the phantom between water and plastic and tissue results in millimetre-scale changes to the resulting radiological thickness. When the entire phantom is defined as lead, this alteration changes the calculated radiological thickness by a maximum of 9.7 cm. Evidently, the simplification of the CT-density ramp has a greater effect on the resulting radiological thickness map than does the alteration of the assignment of tissue types. Conclusions: It is possible to alter the definitions of the tissue types comprising the phantom (or patient) without substantially altering the results of simulated portal images. However, these images are very sensitive to the accurate identification of the HU-density relationship. When converting data from a patient’s CT into a MC simulation phantom, therefore, all possible care should be taken to accurately reproduce the conversion between HU and mass density, for the specific CT scanner used. Acknowledgements: This work is funded by the NHMRC, through a project grant, and supported by the Queensland University of Technology (QUT) and the Royal Brisbane and Women's Hospital (RBWH), Brisbane, Australia. The authors are grateful to the staff of the RBWH, especially Darren Cassidy, for assistance in obtaining the phantom CT data used in this study. The authors also wish to thank Cathy Hargrave, of QUT, for assistance in formatting the CT data, using the Pinnacle TPS. Computational resources and services used in this work were provided by the HPC and Research Support Group, QUT, Brisbane, Australia.

Using narrow beam profiles to quantify focal spot size, for accurate Monte Carlo simulations of SRS/SRT systems

This study investigates the variation of photon field penumbra shape with initial electron beam diameter, for very narrow beams. A Varian Millenium MLC (Varian Medical Systems, Palo Alto, USA) and a Brainlab m3 microMLC (Brainlab AB. Feldkirchen, Germany) were used, with one Varian iX linear accelerator, to produce fields that were (nominally) 0.20 cm across. Dose profiles for these fields were measured using radiochromic film and compared with the results of simulations completed using BEAMnrc and DOSXYZnrc, where the initial electron beam was set to FWHM = 0.02, 0.10, 0.12, 0.15, 0.20 and 0.50 cm. Increasing the electron-beam FWHM produced increasing occlusion of the photon source by the closely spaced collimator leaves and resulted in blurring of the simulated profile widths from 0.26 to 0.64 cm, for the MLC, from 0.12 to 0.43 cm, for the microMLC. Comparison with measurement data suggested that the electron spot size in the clinical linear accelerator was between FWHM = 0.10 and 0.15 cm, encompassing the result of our previous output-factor based work, which identified a FWHM of 0.12. Investigation of narrow-beam penumbra variation has been found to be a useful procedure, with results varying noticeably with linear accelerator spot size and allowing FWHM estimates obtained using other methods to be verified.

Monte Carlo simulations of small field output factors in solid phantoms

Introduction Total scatter factor (or output factor) in megavoltage photon dosimetry is a measure of relative dose relating a certain field size to a reference field size. The use of solid phantoms has been well established for output factor measurements, however to date these phantoms have not been tested with small fields. In this work, we evaluate the water equivalency of a number of solid phantoms for small field output factor measurements using the EGSnrc Monte Carlo code. Methods The following small square field sizes were simulated using BEAMnrc: 5, 6, 7, 8, 10 and 30 mm. Each simulated phantom geometry was created in DOSXYZnrc and consisted of a silicon diode (of length and width 1.5 mm and depth 0.5 mm) submersed in the phantom at a depth of 5 g/cm2. The source-to-detector distance was 100 cm for all simulations. The dose was scored in a single voxel at the location of the diode. Interaction probabilities and radiation transport parameters for each material were created using custom PEGS4 files. Results A comparison of the resultant output factors in the solid phantoms, compared to the same factors in a water phantom are shown in Fig. 1. The statistical uncertainty in each point was less than or equal to 0.4 %. The results in Fig. 1 show that the density of the phantoms affected the output factor results, with higher density materials (such as PMMA) resulting in higher output factors. Additionally, it was also calculated that scaling the depth for equivalent path length had negligible effect on the output factor results at these field sizes. Discussion and conclusions Electron stopping power and photon mass energy absorption change minimally with small field size [1]. Also, it can be seen from Fig. 1 that the difference from water decreases with increasing field size. Therefore, the most likely cause for the observed discrepancies in output factors is differing electron disequilibrium as a function of phantom density. When measuring small field output factors in a solid phantom, it is important that the density is very close to that of water.

Monte Carlo Simulations of Molecular Clusters in Nucleation

A better understanding of the limiting step in a first order phase transition, the nucleation process, is of major importance to a variety of scientific fields ranging from atmospheric sciences to nanotechnology and even to cosmology. This is due to the fact that in most phase transitions the new phase is separated from the mother phase by a free energy barrier. This barrier is crossed in a process called nucleation. Nowadays it is considered that a significant fraction of all atmospheric particles is produced by vapor-to liquid nucleation. In atmospheric sciences, as well as in other scientific fields, the theoretical treatment of nucleation is mostly based on a theory known as the Classical Nucleation Theory. However, the Classical Nucleation Theory is known to have only a limited success in predicting the rate at which vapor-to-liquid nucleation takes place at given conditions. This thesis studies the unary homogeneous vapor-to-liquid nucleation from a statistical mechanics viewpoint. We apply Monte Carlo simulations of molecular clusters to calculate the free energy barrier separating the vapor and liquid phases and compare our results against the laboratory measurements and Classical Nucleation Theory predictions. According to our results, the work of adding a monomer to a cluster in equilibrium vapour is accurately described by the liquid drop model applied by the Classical Nucleation Theory, once the clusters are larger than some threshold size. The threshold cluster sizes contain only a few or some tens of molecules depending on the interaction potential and temperature. However, the error made in modeling the smallest of clusters as liquid drops results in an erroneous absolute value for the cluster work of formation throughout the size range, as predicted by the McGraw-Laaksonen scaling law. By calculating correction factors to Classical Nucleation Theory predictions for the nucleation barriers of argon and water, we show that the corrected predictions produce nucleation rates that are in good comparison with experiments. For the smallest clusters, the deviation between the simulation results and the liquid drop values are accurately modelled by the low order virial coefficients at modest temperatures and vapour densities, or in other words, in the validity range of the non-interacting cluster theory by Frenkel, Band and Bilj. Our results do not indicate a need for a size dependent replacement free energy correction. The results also indicate that Classical Nucleation Theory predicts the size of the critical cluster correctly. We also presents a new method for the calculation of the equilibrium vapour density, surface tension size dependence and planar surface tension directly from cluster simulations. We also show how the size dependence of the cluster surface tension in equimolar surface is a function of virial coefficients, a result confirmed by our cluster simulations.

Monte Carlo simulations of molecular clusters in nucleation

A better understanding of the limiting step in a first order phase transition, the nucleation process, is of major importance to a variety of scientific fields ranging from atmospheric sciences to nanotechnology and even to cosmology. This is due to the fact that in most phase transitions the new phase is separated from the mother phase by a free energy barrier. This barrier is crossed in a process called nucleation. Nowadays it is considered that a significant fraction of all atmospheric particles is produced by vapor-to liquid nucleation. In atmospheric sciences, as well as in other scientific fields, the theoretical treatment of nucleation is mostly based on a theory known as the Classical Nucleation Theory. However, the Classical Nucleation Theory is known to have only a limited success in predicting the rate at which vapor-to-liquid nucleation takes place at given conditions. This thesis studies the unary homogeneous vapor-to-liquid nucleation from a statistical mechanics viewpoint. We apply Monte Carlo simulations of molecular clusters to calculate the free energy barrier separating the vapor and liquid phases and compare our results against the laboratory measurements and Classical Nucleation Theory predictions. According to our results, the work of adding a monomer to a cluster in equilibrium vapour is accurately described by the liquid drop model applied by the Classical Nucleation Theory, once the clusters are larger than some threshold size. The threshold cluster sizes contain only a few or some tens of molecules depending on the interaction potential and temperature. However, the error made in modeling the smallest of clusters as liquid drops results in an erroneous absolute value for the cluster work of formation throughout the size range, as predicted by the McGraw-Laaksonen scaling law. By calculating correction factors to Classical Nucleation Theory predictions for the nucleation barriers of argon and water, we show that the corrected predictions produce nucleation rates that are in good comparison with experiments. For the smallest clusters, the deviation between the simulation results and the liquid drop values are accurately modelled by the low order virial coefficients at modest temperatures and vapour densities, or in other words, in the validity range of the non-interacting cluster theory by Frenkel, Band and Bilj. Our results do not indicate a need for a size dependent replacement free energy correction. The results also indicate that Classical Nucleation Theory predicts the size of the critical cluster correctly. We also presents a new method for the calculation of the equilibrium vapour density, surface tension size dependence and planar surface tension directly from cluster simulations. We also show how the size dependence of the cluster surface tension in equimolar surface is a function of virial coefficients, a result confirmed by our cluster simulations.

Hydrogen Storage Capacity of Carbon-Foams: Grand Canonical Monte Carlo Simulations

Hydrogen storage in the three-dimensional carbon foams is analyzed using classical grand canonical Monte Carlo simulations. The calculated storage capacities of the foams meet the material-based DOE targets and are comparable to the capacities of a bundle of well-separated similar diameter open nanotubes. The pore sizes in the foams are optimized for the best hydrogen uptake. The capacity depends sensitively on the C-H-2 interaction potential, and therefore, the results are presented for its ``weak'' and ``strong'' choices, to offer the lower and upper bounds for the expected capacities. Furthermore, quantum effects on the effective C-H-2 as well as H-2-H-2 interaction potentials are considered. We find that the quantum effects noticeably change the adsorption properties of foams and must be accounted for even at room temperature.

Uncertainty Quantification in Helicopter Performance Using Monte Carlo Simulations

The effect of structural and aerodynamic uncertainties on the performance predictions of a helicopter is investigated. An aerodynamic model based on blade element and momentum theory is used to predict the helicopter performance. The aeroelastic parameters, such as blade chord, rotor radius, two-dimensional lift-curve slope, blade profile drag coefficient, rotor angular velocity, blade pitch angle, and blade twist rate per radius of the rotor, are considered as random variables. The propagation of these uncertainties to the performance parameters, such as thrust coefficient and power coefficient, are studied using Monte Carlo Simulations. The simulations are performed with 100,000 samples of structural and aerodynamic uncertain variables with a coefficient of variation ranging from 1 to 5%. The scatter in power predictions in hover, axial climb, and forward flight for the untwisted and linearly twisted blades is studied. It is found that about 20-25% excess power can be required by the helicopter relative to the determination predictions due to uncertainties.

Permeability of Fractal Porous Media by Monte Carlo Simulations

The permeability of the fractal porous media is simulated by Monte Carlo technique in this work. Based oil the fractal character of pore size distribution in porous media, the probability models for pore diameter and for permeability are derived. Taking the bi-dispersed fractal porous media as examples, the permeability calculations are performed by the present Monte Carlo method. The results show that the present simulations present a good agreement compared with the existing fractal analytical solution in the general interested porosity range. The proposed simulation method may have the potential in prediction of other transport properties (such as thermal conductivity, dispersion conductivity and electrical conductivity) in fractal porous media, both saturated and unsaturated.